Level I Math
Black Line Masters
(Part 2)
NSSAL
(Draft)
C. David Pilmer
2012
(Last Updated: July, 2014)
This resource is the intellectual property of the Adult Education Division of the Nova Scotia
Department of Labour and Advanced Education.
The following are permitted to use and reproduce this resource for classroom purposes.
• Nova Scotia instructors delivering the Nova Scotia Adult Learning Program
• Canadian public school teachers delivering public school curriculum
• Canadian non-profit tuition-free adult basic education programs
The following are not permitted to use or reproduce this resource without the written
authorization of the Adult Education Division of the Nova Scotia Department of Labour and
Advanced Education.
• Upgrading programs at post-secondary institutions (exception: NSCC's ACC program)
• Core programs at post-secondary institutions (exception: NSCC)
• Public or private schools outside of Canada
• Basic adult education programs outside of Canada
Individuals, not including teachers or instructors, are permitted to use this resource for their own
learning. They are not permitted to make multiple copies of the resource for distribution. Nor
are they permitted to use this resource under the direction of a teacher or instructor at a learning
institution.
Acknowledgments
The Adult Education Division would like to thank the following ALP instructors for piloting this
resource and offering suggestions during its development.
Andre Davey (Metroworks)
Shannon Davis (YCLA)
Andrea Fitzgerald (CLANS)
Elizabeth Grzesik (EHALA)
Cheryl Mycroft (GALA)
Joyce Power (Metroworks)
David Sweeny (YCLA)
Kirsteen Thomson (Can-U)
Table of Contents
Difficulty
Introduction …………………………………………………………
iii
Consumer Math ………………………………………………………
How Much Do They Have? (A to E) …………………………….
Emptying the Junk Drawer ……………………………………….
Connect Four Money Game ……………………………………..
Find the Price …………………………………………………….
Name a Product near that Price ………………………………….
Least to Most Expensive …………………………………………
What Are the Three Items Worth? ………………………………..
What Is It Worth? (A and B) …………………………………….
Paying With Cash ………………………………………………..
Cash Purchases …………………………………………………..
Purchasing Groceries …………………………………………….
Unit Price ……………………………………………………….
Examining Unit Prices ………………………………………….
ATMs and Debit Cards …………………………………………
Bank Account Options ………………………………………….
Credit Cards …………………………………………………….
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Measurement …………………………………………………………
Which Measurement Is Reasonable? ……………………………
What is the Appropriate Temperature? …………………………
Measurement; Insert the Appropriate Number ………………….
Metric Measures for Length …………………………………….
Converting Metric Measures for Length ………………………..
Metric Measures for Liquid Capacity and Weight ………………
Area and Perimeter ………………………………………………
Approximately How Much Time Will It Take? …………………
Telling Time (A to F) ……………………………………………
Connect Four Time Ahead Game (A and B) ……………………
How Much Time Has Passed? (A to C) …………………………
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Statistics and Probability ……………………………………………
Likelihood; Part 1 ……………………………………………….
Likelihood; Part 2 ……………………………………………….
Likelihood; Part 3 ……………………………………………….
Is It What You Expect? …………………………………………..
Data and Survey Questions ………………………………………
Gathering Data and Creating Bar Graphs ………………………….
Interpreting Bar Graphs ……………………………………………
Double Bar Graphs ………………………………………………...
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85
90
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Game
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Puzzle
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Introduction to Line Graphs ………………………………………
Interpreting Line Graphs …………………………………………
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101
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Geometry (From 3D to 2D) …………………………………………
Isoball ……………………………………………………………
Other Cool Math Games ………………………………………...
Orthographic Projections (A) ……………………………………
Orthographic Projections (B) …………………………………….
Transfer Image to Dot Paper …………………………………….
Isometric Projections ……………………………………………
Orthographic Isometric Challenge ………………………………
Edges, Faces, and Vertices (A and B) ……………………...…..
Construct the Geometric Figure …………………………………
Nets ………………………………………………………………
Describe the Faces ……………………………………………….
Geometry Terminology Crossword ………………………………
Reflections (A to C) ……………………………………………...
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Base Ten Blocks ……………………………………………………..
What's the Number? ……………………………………………..
Express the Number Different Ways ……………………………
Express with the Fewest Number of Manipulatives …………….
Adding ……………………………………………………………
Adding with Regrouping …………………………………………
Subtracting ……………………………………………………….
Subtracting with Regrouping …………………………………….
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Answers ………………………………………………………………
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Introduction
The concepts covered in Level I Math fit into one of the following five categories.
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Number and Operations
Patterns and Relations
Statistics and Probability
Shape, Space, and Measurement
Consumer Math
The specific outcomes aligned with each of these categories can be found in the ALP Level I
Math Curriculum Guide.
Over the years, Community-Learning Organizations have collected, and the Adult Education
Division has supplied, a variety of print resources used in the delivery of Level I Math. Many of
those resources can still be used with this new curriculum but we emphasize that there is a much
greater emphasis on mathematical understanding and multiple representations of concepts in this
new program. Although we want our learners to develop a level of automaticity as it pertains to
operations with whole numbers, we do not want this math course, or any other ALP math course,
to focus primarily on the mastery of skills. Unfortunately many of the "traditional" textbooks
used in adult basic education programs do have this as their primary focus. For this reason, the
Adult Education division would like all instructors to use the following ALP resources in the
delivery of Level I Math, and to supplement that material with the more traditional resources
they have collected over the years.
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•
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Level I Math Black Line Masters Part 1 and Part 2
Mental Math
Customized Practice
Number Sense
These resources include activities, exercises, investigations, and games that encourage
understanding and thinking, rather than solely focussing on the mastery of algorithms. Learners
are ultimately better served when mathematical concepts are examined and taught in this matter.
We do not expect all Level I learners to complete all the worksheets or activities in the resources
above, rather instructors will use their professional judgement to choose the items that are most
appropriate for their individual learners. By supplying these materials, the LAE is providing a
greater variety of education tools for ALP instructors; the instructors have to decide what tools
are best suited for their learners, at what times, and in what sequence. For example, let's
consider multiplication of two multi-digit numbers. Most instructors are familiar with the
traditional algorithm for such multiplication, but some instructors are unfamiliar with
multiplication of multi-digit numbers using the expanded forms of the numbers and/or lattice
multiplication. These latter two techniques are found in this resource. Does that mean that all
learners need to know all three methods? Definitely not; chose the technique that works best for
your learner.
Please do not view these specific resources as textbooks. Although within sections, the activity
sheets are generally arranged from easiest to hardest, a seamless flow from one activity to the
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next was not created. These booklets are merely a collection of black line masters to be used as
the instructor sees fit.
All of these materials are available at the
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NSSAL site (http://gonssal.ca/documents/NSSALdevelopedresources.pdf)
NSSAL Practitioners Website (http://instructors.gonssal.ca/login)
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Consumer Math
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How Much Do They Have? (A)
Determine the amount of money each person has.
Kate’s Money:
Paula’s Money:
Meera’s Money:
Ryan’s Money:
Yoshi’s Money:
Your Answers:
Kate’s Money: _______
Paula’s Money: _______
Ryan’s Money: _______
Yoshi’s Money: _______
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Meera’s Money: _______
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How Much Do They Have? (B)
Determine the amount of money each person has.
Dave’s Money:
Shelly’s Money:
Maurita’s Money:
Jun’s Money:
Lei’s Money:
Your Answers:
Dave’s Money: _______
Shelly’s Money: _______
Jun’s Money:
Lei’s Money:
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Maurita’s Money: _______
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How Much Do They Have? (C)
Determine the amount of money each person has.
Andrew’s Cash:
Mary’s Cash:
Kara’s Cash:
Montez’s Cash:
Shima’s Cash:
Your Answers:
Andrew’s Cash: _______
Mary’s Cash:
Montez’s Cash: _______
Shima’s Cash: _______
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Kara’s Cash:
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How Much Do They Have? (D)
Determine the amount of money each person has.
Hamid’s Cash:
Tanya’s Cash:
Samir’s Cash:
Mark’s Cash:
Hatsu’s Cash:
Your Answers:
Hamid’s Cash: _______
Tanya’s Cash: _______
Mark’s Cash:
Hatsu’s Cash: _______
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Samir’s Cash: _______
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How Much Do They Have? (E)
Determine the amount of money each person has. We apologize that the bills are not the
appropriate size compared to the coins.
Sasha’s Money:
Hinto’s Money:
Lisa’s Money:
Tiva’s Money:
Meera’s Money:
Your Answers:
Sasha’s Money: _______
Hinto’s Money: _______
Tiva’s Money: _______
Meera’s Money: _______
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Lisa’s Money:
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Emptying the Junk Drawer
You were emptying your junk drawer and scattered the money across the top of your table (See
below.). You have few bills and lots of change. How much money do you have from that
drawer? Use the chart on the next to organize the information and complete your calculations.
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Bills or Change
Number of Each
Value in Dollars
$20 bills
$10 Bills
$5 Bills
Toonies ($2 coins)
Loonies ($1 coins)
Quarters (25¢ coins)
Dimes (10¢ coins)
Nickels (5¢ coins)
Total:
If you found three more nickels, five more quarters, and four more loonies, how much would you
have in total?
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Connect Four Money Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place a paper clip on each of the strips below (i.e. Nickel and Dime Strip, and Quarter and
Loonie Strip). Once they have chosen the coinage, they can capture one square with the
appropriate total (e.g. 3 nickels plus 1 loonie is equal to $1.15). They either mark the square
with an X or place a colored counter on the square. There may be other squares with that
same total but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that total using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
$0.35 $1.05 $1.10 $0.45 $0.35 $0.95
$0.45 $0.85 $0.60 $1.15 $0.65 $1.10
$1.10 $0.95 $1.20 $0.30 $0.90 $0.85
$0.65 $0.55 $0.70 $1.10 $1.20 $0.35
$0.30 $0.90 $0.35 $0.60 $0.80 $0.40
$0.60 $1.05 $0.70 $0.85 $1.15 $0.55
Nickel and Dime Strip:
1
nickel
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nickels
3
nickels
Quarter and Loonie Strip:
1
dime
2
dimes
9
1
quarter
2
quarters
3
quarters
1
loonie
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Find the Price
Using the internet, flyers, and/or catalogues, find the price of each of the items. Assume that we
are purchasing new items. If the price is a sale price, check off the appropriate box. Also
identify the name of the business in which you can purchase the item at that price. Answers are
going to vary because learners are likely to be using different websites, flyers, and catalogues.
Milk (2 litres)
Price:
Tube of Toothpaste
Sale 
Sale 
Price:
Hamburger Meat (1 kg)
Price:
Sale 
Business:
Business:
Business:
Cooked Chicken
Head of Lettuce
20 inch Delivery Pizza
Price:
Sale 
Sale 
Price:
Price:
Business:
Business:
Business:
Woman's Winter Boots
Pair of Men's Jeans
Leather Gloves
Price:
Sale 
Sale 
Price:
Price:
Business:
Business:
Business:
Mountain Bike (Adult)
Table Lamp
Toaster Oven
Price:
Sale 
Sale 
Price:
Price:
Sale 
Sale 
Sale 
Business:
Business:
Business:
Queen Size Mattress
Gas Barbeque
Portable Music Player
Price:
Sale 
Sale 
Price:
Price:
Sale 
Business:
Business:
Business:
40 inch Flatscreen TV
Leather Sofa
Compact Car (e.g. Corolla)
Price:
Business:
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Sale 
Sale 
Price:
Business:
Price:
Sale 
Business:
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Name a Product near that Price
In this activity you are to name a product near the indicated price. Naturally every learner will
have different answers. You can use flyers or catalogues to assist with this activity.
e.g. Name a product that is worth approximately $2.
Some Possible Answers: Can of Soup, Pen, Comb, Small Package of Screws
Price
1.
Your Product
8.
Your Product
Your Product
Your Product
Your Product
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Your Product
$2000
Price
$4000
Your Product
$1000
Price
14.
Your Product
$400
Price
12.
Your Product
$150
Price
10.
Your Product
$70
Price
$1500
Price
15.
6.
Your Product
$20
Price
$700
Price
13.
Your Product
$250
Price
11.
4.
Your Product
$5
Price
$100
Price
9.
Your Product
$40
Price
7.
2.
$10
Price
5.
Price
$1
Price
3.
Your Product
Your Product
$8000
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Least to Most Expensive
In each case you are supplied with four common items that one might purchase. Your mission is
to number the items 1 through 4 in the space below, where 1 is the least expensive, and 4 is the
most expensive.
1.
Two Slice Toaster
Litre of Milk
Refrigerator
Electric Fry Pan
2.
Silver Earrings
Leather Jacket
Pair of Socks
Pencil
3.
Power Drill
Winter Gloves
Fingernail Clippers
Mattress (Queen)
4.
Hardcover Book
Birthday Card
Prescription Glasses
Pair of Winter Boots
5.
Coffee Table
Kitchen Stove
Can Opener
Electric Kettle
6.
Four Winter Tires
20 inch Television
DVD Player
Four Litres of Oil
7.
Small Flashlight
Delivery Pizza
Reclining Chair
Table Lamp
8.
Hair Dryer
Coffee Mug
Chocolate Bar
Toaster Oven
9.
Paperback Novel
Big Concert Ticket
Spring Jacket
Bus Toll
10.
Love Seat
Dish Soap
10 kg Turkey
Four Litres of Milk
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What Are the Three Items Worth?
In each case, you are given three items and four prices. Match the best price to the item.
1.
3.
5.
Item:
Hammer
Price
2.
Item:
Box of
Cereal
Price
Florescent
Light Bulb
A Pair of
Jeans
Can of Pop
T-shirt
Price Choices: $1, $3, $10, $50
Price Choices: $2, $6, $12, $50
Item:
Sofa
Item:
Fast-food
Hamburger
Price
4.
Price
A Pair of
Sunglasses
A Pair of
Work Boots
Microwave
Oven
Knapsack
for School
Price Choices: $2, $20, $150, $600
Price Choices: $3, $40, $90, $400
Item:
A Man's
Haircut
Price
6.
Item:
Tube of
Toothpaste
Price
Loaf of
Bread
Small
Waste Paper
Basket
An Adult
Bicycle
Winter Coat
Price Choices: $2, $25, $80, $250
Price Choices: $3, $15, $35, $120
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What Is It Worth? (A)
You have been given a list of items and been asked to select a price that best matches that item.
The prices have been supplied below. Only use each price once. You will also be asked to write
out the value using words (e.g. $1249 is one thousand two hundred forty-nine dollars).
Item
Approximate
Price (Number)
(a)
Ride-on Lawn Mower
(b)
DVD/Blu-ray Player
(c)
Toaster
(d)
HD Video Camera
(e)
Compact Car
(f)
42 inch Flat Screen TV
(g)
Tank of Gas (Compact
Car)
Prices to Choose From:
$17
$14 900
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$50
$2149
Approximate Price
(Words)
$549
14
$329
$38 900
$99
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What Is It Worth? (B)
You have been given a list of items and been asked to select a price that best matches that item.
The prices have been supplied below. Only use each price once. You will also be asked to write
out the value using words (e.g. $1249 is one thousand two hundred forty-nine dollars).
Item
Approximate
Price (Number)
(a)
Washing Machine
(b)
Hair Dryer
(c)
Minivan
(d)
Fast Food Meal for One
(e)
Gasoline Push Mower
(f)
Child's Bicycle
(g)
Four Person Hot Tub
Prices to Choose From:
$239
$8
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$3599
$21
Approximate Price
(Words)
$12 900
15
$469
$22 900
$69
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Paying with Cash
When you pay with cash, it is important to know how to pay using the fewest number of bills and
coins. For example, if an item costs $7.35, then you would pay with one $5 bill, one $2 coin,
one quarter, and one dime.
Example
Your bill comes to $17.15. You want to pay using the fewest number of bills and coins. If you
are going to pay with the exact change, what bills and coins should you use?
Answer:
Always start with the bills and coins of the largest values.
- you need one $10 bills
- you need one $5 bill
- you need one $2 coin (toonie)
- no $1 coins (loonies) are needed
- no 25¢ coins (quarters) are needed
- you need one 10¢ coin (dime)
- you need one 5¢ coin (nickel)
$10.00
$5.00
$2.00
$0.10
$0.05
$17.15
Final Answer: one $10 bills, one $5 bill, one $2 coin, one 10¢ coin, and one 5¢ coin
Questions
1. A partially completed answer has been provided for each of these questions. Finish the
answer by filling the blanks with the word zero, one, two, or three.
(a) Using the fewest number of bills and coins, make $3.65.
Answer:
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
(b) Using the fewest number of bills and coins, make $7.95.
Answer:
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
$2.00
$1.00
$0.50
$0.10
$0.05
$3.65
$5.00
$2.00
$0.75
$0.20
$7.95
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(c) Using the fewest number of bills and coins, make $13.30.
Answer:
- you need ___________ $10 bill(s)
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
(d) Using the fewest number of bills and coins, make $16.40.
Answer:
- you need ___________ $10 bill(s)
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
$10.00
$2.00
$1.00
$0.25
$0.05
$13.30
$10.00
$5.00
$1.00
$0.25
$0.10
$0.05
$16.40
2. A partially completed answer has been provided for each of these questions. Finish the
answer by filling in the column on the right hand side of the page.
(a) Using the fewest number of bills and coins, make $4.85.
Answer:
- you need zero $10 bills
- you need zero $5 bills
- you need two $2 coins
- you need zero $1 coins
- you need three 25¢ coins
- you need one 10¢ coin
- you need zero 5¢ coins
$4.85
(b) Using the fewest number of bills and coins, make $11.70.
Answer:
- you need one $10 bill
- you need zero $5 bills
- you need zero $2 coins
- you need one $1 coin
- you need two 25¢ coins
- you need two 10¢ coins
- you need zero 5¢ coins
$11.70
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(c) Using the fewest number of bills and coins, make $19.80.
Answer:
- you need one $10 bill
- you need one $5 bill
- you need two $2 coins
- you need zero $1 coins
- you need three 25¢ coins
- you need zero 10¢ coins
- you need one 5¢ coin
$19.80
3. Complete the following questions by filling in the blanks and the column on the right side of
the page.
(a) Using the fewest number of bills and coins, make $8.20.
Answer:
- you need ___________ $10 bill(s)
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
$8.20
(b) Using the fewest number of bills and coins, make $12.45.
Answer:
- you need ___________ $10 bill(s)
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
$12.45
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(c) Using the fewest number of bills and coins, make $13.95.
Answer:
- you need ___________ $10 bill(s)
- you need ___________ $5 bill(s)
- you need ___________ $2 coin(s)
- you need ___________ $1 coin(s)
- you need ___________ 25¢ coin(s)
- you need ___________ 10¢ coin(s)
- you need ___________ 5¢ coin(s)
$13.95
4. Using the fewest number of bills and coins, make each of the following amounts of money.
(a) $3.15 _________________________________________________________________
_________________________________________________________________
(b) $6.75 _________________________________________________________________
_________________________________________________________________
(c) $12.55 _________________________________________________________________
_________________________________________________________________
(d) $18.85 _________________________________________________________________
_________________________________________________________________
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Cash Purchases
In each case, you have a specific amount of cash (limited to bills, $2 coins, and $1 coins). You
need to:
• Determine how much cash you have,
• Determine whether it is enough to purchase the indicated item, and
• If so, how much change will you receive?
Cash
1.
2.
3.
4.
5.
NSSAL
©2012
Item
Questions
Toaster
$15.49 (before tax)
$17.81 (after tax)
How much cash do you
have?
________
Is it enough?
________
If so, how much change
will you receive?
________
How much cash do you
have?
________
Is it enough?
________
If so, how much change
will you receive?
________
How much cash do you
have?
________
Is it enough?
________
If so, how much change
will you receive?
________
How much cash do you
have?
________
Is it enough?
________
If so, how much change
will you receive?
________
How much cash do you
have?
________
Is it enough?
________
If so, how much change
will you receive?
________
Blu-Ray Movie
$22.99 (before tax)
$26.44 (after tax)
Alarm Clock
$27.99 (before tax)
$32.18 (after tax)
Blouse
$47.95 (before tax)
$55.14 (after tax)
Video Game
$61.99 (before tax)
$71.29 (after tax)
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C. D. Pilmer
Purchasing Groceries
On this page and the next, you have been provided with a list of common items
that can be found at a grocery store. Your job is to indicate which products you
would purchase for each of the four scenarios.
Scenario #1: You are single and have a limited budget of $150.
Scenario #2: You are single and have a limited budget of $230.
Scenario #3: You are a parent with two children (ages 7 and 10), and have
a limited budget of $250.
Scenario #4: You are a parent with two children (ages 7 and 10), and have a limited budget
of $350.
Be prepared to discuss your selections with your instructor and/or classmates.
Please note that items whose weight is marked with an asterisk (*), do not have to purchase at
that weight. For example, one pound (lb.) of tomatoes can be purchased for $2, but half a pound
of tomatoes can be purchased for $1. You decide how much you need. In these cases just
indicate the amount to be purchased using the appropriate dollar value.
Item
Potatoes (10 lb. bag)
Potato Salad (454 g)
Green Peppers (four pack)
Tomatoes (1 lb.*)
Baby Carrots (340 g)
Cucumber
Cauliflower (1 lb.*)
Apples (5 lbs.)
Oranges (4 lbs.)
Pears (1 lb.*)
Peaches (1 lb.*)
Seedless Red Grapes (1 lb.*)
Bananas (1 lb.*)
Strawberries (1 lb.)
Kiwi (4)
Whole Pineapple
Loaf of Bread (675 g)
Crackers (450 g)
Cereal (445 g)
Milk (2 l)
Cheese (500 g block)
Cheese Slices (500 g)
Parmesan Cheese (250 g)
Margarine (454 g)
NSSAL
©2012
Price
Scenario #1
Single,
$150 budget
Scenario #2
Single,
$220 budget
Scenario #3
Family of 3,
$250 budget
Scenario #4
Family of 3,
$350 budget
$4
$3
$6
$2
$2
$2
$4
$5
$4
$2
$3
$4
$2
$3
$2
$5
$2
$2
$4
$4
$6
$6
$6
$3
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C. D. Pilmer
Item
Price
Dozen Small Eggs
Stew Beef (1 lb.)
Ground Beef (1 lb.*)
Port Tenderloin (1 lb.*)
Bacon (500 g)
Roasting Chicken (5 lb.)
Trout Fillets (1 lb.*)
Haddock Fillets (1 lb.*)
Salmon Portion (140 g)
Canned Tuna (170 g)
Canned Cooked Ham (454 g)
Chicken Noodle Soup (540 mL)
Canned Chili (425 g)
Frozen Pizza (400 g)
Frozen Lasagna (1 kg)
Frozen Meatballs (680 g)
Frozen French Fries (454 g)
Frozen Corn (750 g)
Frozen Mixed Vegetables (1 kg)
Frozen Lemonade (295 mL)
Peanut Butter (500 g)
Roasted Cashews (100 g)
Macaroni and Cheese (200 g)
Ketchup (1 L)
Sunflower Oil (1 L)
Tea (240 bags)
Coffee (300 g)
Cranberry Cocktail (1.89 L)
Pop (2 L)
Potato Chips (235 g)
Chocolate Bars (four pack)
Ice Cream (1.5 L)
Deodorant (150 g)
Toothpaste (130 mL)
Bathroom Tissue (8 rolls)
Paper Towels (2 rolls)
Dishwashing Liquid (950 mL)
Bathroom Cleaner (500 mL)
$2
$6
$6
$5
$6
$14
$8
$6
$5
$2
$7
$2
$3
$6
$9
$10
$4
$3
$3
$1
$4
$2
$1
$3
$6
$11
$8
$3
$2
$4
$4
$4
$4
$3
$5
$3
$2
$2
Scenario #1
Single,
$150 budget
Scenario #2
Single,
$220 budget
Scenario #3
Family of 3,
$250 budget
Scenario #4
Family of 3,
$350 budget
Total:
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Unit Price
The unit price tells us the cost per liter, per kilogram, per pound, etc, of an item we want to buy.
It is used when we are comparing prices of items in an effort to get the best buy. The unit price
of an item is found by dividing the cost of the item by its quantity. It is most often done using a
calculator.
Example 1
A two litre (2000 millitre) bottle of pop sells for $2.89. A 750 millitre bottle of the
same pop sells for $1.29.
(a) Determine the unit price for each of these items.
(b) If you are purchasing pop for a party involving six adults, which of these
two options is your best buy? Justify your answer.
(c) If you are purchasing the pop for yourself and you would describe
yourself as someone who drinks pop occasionally, which of these is your
best option? Justify your answer.
Answers:
(a) Unit Price of 2000 ml bottle:
289
= = 0.1445 ¢ per ml
2000
Unit Price of 750 ml bottle:
129
= = 0.172 ¢ per ml
750
(b) Since you are purchasing pop for a party of six, then you will need a large quantity of
pop. Therefore, the lowest unit price will determine which option you will purchase.
That means you will purchase one or more 2 litre (2000 ml) bottles.
(c) In this case, you are purchasing the pop for yourself, and the question states that you only
occasionally drink pop. Although the larger bottle has a better unit price, you are
unlikely going to drink the whole bottle before it goes flat. The smaller bottle (750 ml)
seems like a more appropriate purchase even though the unit price is higher.
Example 2
An 18 pack of Brand A single-ply toilet paper costs $6.75. A 12 pack of Brand
B double-ply toilet paper costs $5.39.
(a) Determine the unit price for each of these items.
(b) Which is a better buy?
Answer:
(a) Unit Price of 18 Pack:
675
= = 37.5 ¢ per roll
18
Unit Price of 12 Pack:
539
= = 44.9 ¢ per roll
12
(b) There is not a clear answer to this question. If you just look at unit price, Brand A is the
better buy. However, many people would still prefer Brand B because it is double-ply, as
opposed to single-ply.
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C. D. Pilmer
Questions
You are permitted to use a calculator for all of these questions.
1. Determine the unit price for each of these items. Include the appropriate units of measure.
(a) 680 gram box of macaroni for $2.64
(b) 411 gram can of diced tomatoes for $1.29
(c) $4.59 for a 3 litre container of cranberry juice
(d) $3.89 for a 510 gram box of cereal
(e) Eight small containers of yogurt for $4.29
(f) $17.99 for 1.4 kilograms of grass seed
(g) 20 metres of rope for $6.89
(h) $310.50 for 4.5 cubic metres of topsoil
(i) Twelve color pencils for $2.69
2. Which one of these products is the best buy based solely on the unit price?
• $5.29 for 475 millilitres of Brand A salad dressing
• $6.49 for 700 millilitres of Brand B salad dressing
• $3.77 for 350 millilitres of Brand C salad dressing
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C. D. Pilmer
3. Which one of these products is the best buy based solely on the unit price?
• 250 grams of Brand A margarine for $2.29
• 500 grams of Brand B margarine for $4.49
• 1 kilogram (1000 grams) of Brand A margarine for $7.59
• 2 kilograms (2000 grams) of Brand B margarine for $13.99
4. A popular brand name of potato chips is selling 180 gram bag for $2.29. A 245 gram bag of
the same brand is selling for $2.79. A 245 gram bag of the grocery store's no-name brand of
potato chips sells for $2.49.
(a) Determine the unit price for each of these items.
(b) Based solely on the unit price, which one of the options is the best buy?
(c) If you are purchasing the chips for your family and they refuse to eat no-name products,
which of the remaining options is the best buy?
5. Most meat, fish and poultry products are sold using a unit price. For example, salmon might
be advertised as $19.90 per kilogram. If you purchases a 0.8 kg fillet of salmon, you would
end up paying $15.99. This price was found by taking the unit price and multiplying it by the
quantity purchased (i.e. 19.90 × 0.8 =
15.99 ) using a calculator. Calculate the cost of each of
these items.
(a) 1.2 kilograms of lean ground meat which sells for $7.69 per kilogram
(b) 1.4 kilograms of chicken drumsticks which sell for $6.81 per kilogram.
(c) 2.3 kilograms of beef sirloin roast that sells for $16.45 per kilogram.
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C. D. Pilmer
6. A local building supply website lists the following grass seed items.
Product
EcoTurf Grass Seed
For a low maintenance lawn with low environmental
impact. Grows in shade and sun. 2 kg.
(7611110)
CIL Golfgreen® Grass Seed Shady
1.5 kg. Covers 100 sq. m. for new lawns. Over seeds up to
300 sq. m. Contains SureStart®.
(7677123)
Pickseed Town & Country Grass Seed
All-purpose grass seed for both sunny and shady areas.
Contains luxurious cultivars for a thick, green lawn. 4kg.
(7611102)
Scotts Turf Builder Dense Shade Mix
1.4 kg.
(7611026)
Pickseed Shade Grass Seed
Grows in mostly shady areas. 1kg.
(7611106)
Pickseed Town & Country Grass Seed
All-purpose grass seed for both sunny and shady areas.
Contains luxurious cultivars for a thick, green lawn. 10kg.
(7611011)
Price
$28.49
$16.99
$37.49
$16.99
$9.99
$86.99
(a) If you need regular grass seed for a large area of lawn, which of these is your best buy?
Justify your answer.
(b) If you need grass seed for a large shaded portion of your lawn, which of these is your best
buy? Justify your answer.
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Examining Unit Prices
To complete this activity sheet, you will have to visit your local grocery store and record the
prices and quantities of specific food items. In the first case, you will be asked to look up three
different quantities and/or types of cereal. You might find that a 525 gram box of cornflakes is
selling for $2.99. That gives a unit price of 0.57¢ per gram. These three pieces of information
would then have to be recorded in the chart below.
Cereal
Cheese
Ketchup
Canned
Peas
Dish Soap
Item A
Item B
Item C
Name:
Name:
Name:
Quantity:
Quantity:
Quantity:
Unit Price:
Unit Price:
Unit Price:
Name:
Name:
Name:
Quantity:
Quantity:
Quantity:
Unit Price:
Unit Price:
Unit Price:
Name:
Name:
Name:
Quantity:
Quantity:
Quantity:
Unit Price:
Unit Price:
Unit Price:
Name:
Name:
Name:
Quantity:
Quantity:
Quantity:
Unit Price:
Unit Price:
Unit Price:
Name:
Name:
Name:
Quantity:
Quantity:
Quantity:
Unit Price:
Unit Price:
Unit Price:
After completing the table, sit down with your instructor and/or classmates to discuss which of
these products are best buys. Remember that the unit price might not be the deciding factor.
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ATMs and Debit Cards
For the first three questions you will find links to a variety of online ATM (Automated Teller
Machine) and debit card simulators. We have chosen sites that ask you to complete a variety of
different tasks on slightly different machines.
1. Go to http://oclf.org/atm/debit.html (or Google Search: OCLF Debit Card
Simulation) and complete a debit card transaction. The PIN (Personal
Identification Number) in this case is 1234. You have two accounts to
choose from (Chequing or Savings); at times one of the accounts may not
have adequate funds. Run through the simulation until you have
successfully completed three transactions.
2. Go to http://www.gamvak.com/Kids_Games/Atm--Bank-Cash-Machine (or Google Search: GamVak
ATM Cash Machine). Complete the five activities
associated with the virtual ATM machine. You will
have to:
• Change the PIN on your new card
• Check your balance
• Withdraw $50 with a receipt
• Withdraw $50 without a receipt
• Print a mini statement
With this simulation, you will have to start by
reading the mail regarding your new ATM card.
3. Go to http://www.gcflearnfree.org/edlall/atm (or Google Search: GCF Learn ATM) and
complete the ATM simulation where you check how much money is in your two accounts
and then withdraw $40 from the appropriate account.
4. What are the advantages and disadvantages to using a debit card and an automated teller
machine?
Advantages
Disadvantages
Debit Card
ATM
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C. D. Pilmer
Bank Account Options
Chequing accounts are primarily designed to allow people to pay bills
and make purchases. For this reason, their main features often include
the following.
• Allow you to write numerous or unlimited number of cheques.
• Allow you to make numerous or unlimited number of debit card
and ATM transactions.
• Charges a monthly fee.
• Returns little or no interest.
Savings accounts, by their very description, are designed to encourage people to save money.
For this reason, their main features often include the following.
• Limits the number of monthly withdrawals (often 6 or less; otherwise, fees are charged).
• No monthly fee (Often if a minimum balance is required.)
• Returns interest (at a rate higher than a chequing account).
If you visit a bank's website, they will provide all the necessary information regarding their
chequing and savings account options. For example, below we have provided the important
information regarding Scotiabank's Money Master savings account (date: May 2014)
Scotia Money Master Savings Account:
1. Rewards you with more interest when your balance grows
2. No minimum balance to earn interest or open the account
3. No monthly fee
4. 24/7 account access with ATM, Telescotia (i.e. telephone banking), online & mobile
banking)
5. Unlimited free fund transfers
6. Monthly record keeping (paperless is free, paper statement is $2.00 per month)
Go to a Canadian bank's website and examine the various bank account options. Decide which
option is best for you. List the information regarding that option and be prepared to discuss your
selection with your instructor.
Your Selection:
Information:
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Credit Cards
There are three questions people ask regarding credit cards.
1. Should I have a credit card?
2. If so, when should I use it?
3. What credit card should I select?
Answers:
1. Credit cards are not for everyone; people, who lack self-control in regards to money and
purchases, can get themselves into a long-term financial mess by using credit cards.
However, most people do use credit cards recognizing that they are necessary in some
circumstances; for example, reserving a hotel room or making online purchases. Credit
cards are also one of the first ways people establish a credit rating; hopefully a good one.
2. Only use a credit card when you know that you have the cash to cover the purchases.
The rates of interest you are charged are extremely high that you should be prepared to
pay off the balance before the typical 21 day interest-free grace period is over. To give
you an idea of how high the rates are, consider that a mortgage charged around 4%
interest and a car loan charges around 7% interest, while a bank credit card charges
around 20% and a department store credit card charges around 30%.
3. The number of credit card options available to people are numerous. There are several
factors you need to consider. We have arranged these factors from most important to
least important.
• What is the annual rate of interest charged?
• Is there an introductory annual rate of interest that jumps up drastically after a
certain period of time (e.g. increases after the first six months)?
• Is there an annual fee? (This typically varies from none to $400.)
• How long is the interest-free grace period? (Typically, it is 21 days.)
• What awards are available through the card (e.g. cash-back, travel awards,
savings on gasoline purchases, savings on grocery purchases, etc.)
• What is the minimum monthly payment? (Typically 1% to 2% of balance or $10
to $15)
• What credit rating is needed to obtain the card? (Typically, people with poor
credit ratings can only use cards with higher annual fees, higher interest rates, and
fewer rewards.)
Questions
1. Do you feel you need a credit card? Why or why not?
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C. D. Pilmer
2. Go to http://itools-ioutils.fcac-acfc.gc.ca/STCV-OSVC/ccst-oscc-eng.aspx (or Google
Search: FCAC Credit Card Selector Tool). This government website provides you with a list
of credit cards that best suit your personal needs. You first have to indicate what type of
features you are looking for in the card by completing some, by not all, of the checklist found
on the left hand side of the page.
Record at least three of the credit cards the site recommends and the important features of
those cards (e.g. interest rate, annual fees, rewards, service fees, etc.). All of these important
features can be accessed by clicking on the tabs at the top of the chart.
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C. D. Pilmer
Measurement
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C. D. Pilmer
Which Measurement Is Reasonable?
In each case, you have been given a situation or object in which you must consider which
supplied measurement is most appropriate.
1. The length of an adult's arm
(a) 65 centimetres
(c) 45 kilometres
(b) 30 metres
(d) 110 centimetres
2. The length of three city blocks
(a) 9 metres
(c) 3 centimetres
(b) 20 kilometres
(d) 1 kilometre
3. The amount of lemonade that could be held in a pitcher
(a) 30 millilitres
(b) 8 litres
(c) 2 litres
(d) 50 millilitres
4. The weight of a ten year old boy
(a) 75 grams
(c) 100 kilograms
(b) 34 kilograms
(d) 450 grams
5. The amount of water in a drinking glass
(a) 3 litres
(c) 350 millilitres
(b) 300 litres
(d) 40 millilitres
6. The height of a three-story apartment building
(a) 12 metres
(b) 100 cm
(c) 1 kilometre
(d) 30 metres
7. The weight of a compact car
(a) 900 grams
(c) 300 kilograms
(b) 1800 kilograms
(d) 7000 grams
8. The length of a man's fingernail on his pinkie finger
(a) 4 centimetres
(b) 7 metres
(c) 2 metres
(d) 1 centimetre
9. The distance from Halifax, Nova Scotia to Truro, Nova Scotia
(a) 15 kilometres
(b) 4000 metres
(c) 125 centimetres
(d) 100 kilometres
10. The amount of gasoline that can be held in a compact car's gas tank
(a) 50 millilitres
(b) 8 litres
(c) 40 litres
(d) 130 millilitres
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C. D. Pilmer
What's the Appropriate Temperature?
Match the temperature to the given situation. We have provided the temperatures in both
degrees Fahrenheit and degrees Celsius; use the one you prefer.
Situation
Body Temperature of a Human
Temperature
1
2.
Boiling Temperature of Water
1200oC
or
2192oF
3.
A Hot Summer's Day in Nova Scotia
-20oC
or
-4oF
4.
Temperature at the North Pole in the
Middle of Winter
70oC
or
158oF
5.
Freezing Temperature of Water
100oC
or
212oF
6.
Temperature of Molten Iron
-40oC
or
-40oF
7.
A Comfortable Room Temperature
0oC
or
32oF
8.
A Cold Winter's Day in Nova Scotia
20oC
or
68oF
9.
The Serving Temperature of a Cup of
Coffee
37oC
or
98oC
NSSAL
©2012
28oC
or
84oC
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C. D. Pilmer
Measurement; Insert the Appropriate Number
Statements involving units of measure are supplied. For each statement three numbers are
supplied. Insert the numbers into their appropriate positions in each statement.
1.
The distance between Halifax and Sydney is _______ km.
It takes approximately ______ hours to travel this distance
and you would likely use ______ L of gasoline to complete
this trip by car.
5
30
425
2.
The ______ L container weighs ______ g when it is full of
orange juice. John, who is thirty years old and weighs
______ kg, usually drinks a container of OJ each week.
85
2
2300
3.
The cupcake recipe requires ______ mL of flour. It also
states that the oven must be at a temperature of ______ oC,
and that the cupcakes must be baked for ______ minutes.
750
15
180
4.
A ______ kg stuffed turkey takes ______
minutes to cook in the oven, assuming that
the oven is set at ______ oC.
165
420
5
5.
Nashi is running a ______ km road race. She
expects that it will take her ______ minutes and
that she will drink ______ mL of fluid during the
race.
50
500
10
6.
The college basketball player is approximately ______
metres tall and weighs ______ kg. He usually plays much
of the ______ minute game.
2
40
93
7.
The baseball bat that Jun uses is ______
centimeter(s) long and weighs ______
kilogram(s). The nine inning baseball games
that Jun plays typically lasts for ______ hour(s).
1
95
3
8.
Cathy's dishwasher heats the water up to ______ oC; hot
enough to kill any bacteria. The dishwasher is ______
centimetres tall and weighs ______ kilograms.
38
55
88
9.
Kadeer likes to use ______ grams of ground
coffee to make ______ millilitres of coffee. He
also likes the coffee to be served at ______ oC.
150
70
10
10.
The average adult giraffe is ______ metres tall
and weighs ______ kilograms. The body
temperature should be approximately ______ oC.
1100
5
41
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Metric Measures for Length
Most countries in the world (with the exception of the United States, Burma, and Liberia)
presently use the metric system. The reason for its wide acceptance is that it is a base 10 system
which allows one to easily convert from one unit of measure to another.
The basic metric measure for length is metres. We combine this basic metric unit for length (m)
with the prefixes (k, h, da, d, c, and m) to obtain the desired unit of measure for length.
Prefix
kilometre
hectometre
dekametre
metre
decimetre
centimetre
millimetre
Symbol
km
hm
dam
m
dm
cm
mm
Multiple or Submultiple
1000 metres
100 metres
10 metres
---0.1 of a metre
0.01 of a metre
0.001 of a metre
For this course, we are only concerned with kilometres, metres, centimetres, and millimetres.
•
•
Kilometres are used to measure large distances (e.g. distance between two towns)
Metres are used to measure lengths associated with large objects (e.g. the dimensions of
building)
Centimetres and millimetres are used to measure lengths associated with small objects
(e.g. the dimensions of a piece of paper, thickness of a piece of steel)
•
Measuring Length with a Ruler
When you pick up a ruler, the scale is either in millimetres or centimeters.
If the ruler is in centimetres (cm), then every tick mark represents one tenth of a centimetre.
1
2
3
4
5
6
7
cm
If the ruler is in millimetres (mm), then every tick mark represents one millimetre.
10
20
30
40
50
60
70
mm
It should be noted that 10 millimetres (i.e. 10 mm) is equivalent to 1 centimetre (i.e. 1 cm).
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Example 1
What is the length of the line segment?
1
2
3
4
5
6
7
cm
Answer:
5.3 cm (which is equal to 53 mm)
Example 2
What is the length of the line segment?
10
20
30
40
50
60
70
mm
Answer:
48 mm (which is equal to 4.8 cm)
Questions
1. Using the ruler drawn on the page, determine the length of each line segment in centimetres.
(a)
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
cm
(b)
cm
(c)
cm
(d)
cm
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C. D. Pilmer
(e)
1
2
3
4
5
6
7
1
2
3
4
5
6
7
cm
(f)
cm
2. Using the ruler drawn on the page, determine the length of each line segment in millimetres.
(a)
10
20
30
40
50
60
70
10
20
30
40
50
60
70
10
20
30
40
50
60
70
10
20
30
40
50
60
70
10
20
30
40
50
60
70
10
20
30
40
50
60
70
mm
(b)
mm
(c)
mm
(d)
mm
(e)
mm
(f)
mm
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3. Determine the length and width of each of these rectangles in metric measure.
(a)
(b)
4. Measure the length of these two objects in both millimetres and centimetres.
(a)
(b)
5. Using a ruler, measure the following in centimetres.
(a) the width of your thumb.
_______________
(b) the length of your foot
_______________
(c) the length of your little finger
_______________
6. Name the best unit of metric measurement (millimetre, centimetre, metre, or kilometre) for
each of the following.
(a) the length of a swimming pool
_______________
(b) the length of a hockey stick
_______________
(c) the thickness of a coin
_______________
(d) the length of a river
_______________
(e) the depth of a well
_______________
(f) the distance one cycles in three hours
_______________
(g) the length of a wrench
_______________
(h) the length of an insect
_______________
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C. D. Pilmer
7. Fill in the blanks.
(a) 9.8 cm = ________ mm
(b) 145 mm = ________ cm
(c) 210 cm = ________ mm
(d) ________ cm = 13 mm
(e) ________ mm = 0.9 cm
(f) ________ cm = 122.9 mm
(g) 4500 mm = ________ cm
(h) 63 cm = _________ mm
8. Which is larger? Circle the correct answer.
(a) 4 km or 4 m
(b) 60 mm or 60 cm
(c) 7 cm or 7 km
(d) 12 m or 12 mm
(e) 500 m or 500 cm
(f) 49 mm or 49 km
9. Using a tape measurer measure each in metric.
(a) the length and width of the classroom desk or table that you are working at.
(b) the length and width of the classroom door
(c) the length and width of your classroom.
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C. D. Pilmer
Converting Metric Measures for Length
The easiest way to visual the metric system, which is a base 10 system of measurement, is to
consider a set of stairs. Every time you go down a stair, you multiply by 10. Every time you go
up a stair, you divide by ten. We have constructed a set of stairs to illustrate this relationship for
measures of length (metres).
Length Measurements
km
hm
Multiply by 10
dam
m
dm
Divide by 10
cm
mm
Example
Convert the following measures.
(a) Convert 7 centimetres to metres.
(b) Convert 2.5 metres to millimetres.
(c) Convert 0.8 kilometres to centimetres.
(d) Convert 96 000 metres to kilometres.
Answers:
(a) If you wanted to convert 7 centimetres (cm) to metres (m), you would move up two
steps. You would divide by 10 twice (or divide by 100 once). This can be done by
moving the decimal point two places to the left.
• Therefore 7 centimetres is equal to 0.07 metres.
(b) If you wanted to convert 2.5 metres (m) to millimetres (mm), you would move down
three steps. You would multiple by 10 three times (or multiply by 1000 once). This can
be done by moving the decimal point three places to the right.
• Therefore 2.5 metre is equal to 2500 millimetres.
(c) If you wanted to convert 0.8 kilometres (km) to centimetres (cm), you would move down
five steps. You would multiple by 10 five times (or multiply by 100 000 once). This can
be done by moving the decimal point five places to the right.
• Therefore 0.8 kilometres is equal to 80 000 centimetres.
(d) If you wanted to convert 96 000 metres (cm) to kilometres (km), you would move up
three steps. You would divide by 10 three time (or divide by 1000 once). This can be
done by moving the decimal point three places to the left.
• Therefore 96 000 metres is equal to 96 kilometres.
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Questions
1. Complete the conversions and explanations by inserting the appropriate words and numbers
into the five blanks. Two examples have been completed for you; the underlined words and
numbers were those that had to be added to complete the conversion and explanation. You
are allowed to use a calculator.
e.g. To convert 45 decimetres (dm) to millimetres (mm), we move down two step(s) on the
diagram. That means we need to multiple the 45 by 10 two time(s). Therefore, 45
decimetres is equal to 4500 millimetres.
e.g. To convert 9700 decimetres (dm) to hectometers (hm), we move up three step(s) on the
diagram. That means we need to divide the 9700 by 10 three time(s). Therefore, 9700
decimetres is equal to 9.7 hectometres.
(a) To convert 80 metres (m) to centimetres (cm), we move _________ _________ step(s)
on the diagram. That means we need to ____________ the 80 by 10 _________ time(s).
Therefore, 80 metres is equal to __________ centimetres.
(b) To convert 5600 millimetres (mm) to metres (m), we move _________ _________
step(s) on the diagram. That means we need to ____________ the 5600 by 10 _________
time(s). Therefore, 5600 millmetres is equal to __________ metres.
(c) To convert 70 kilometres (km) to metres (m), we move _________ _________ step(s) on
the diagram. That means we need to ____________ the 70 by 10 _________ time(s).
Therefore, 70 kilometres is equal to __________ metres.
(d) To convert 320 centimetres (cm) to decimetres (dm), we move _________ _________
step(s) on the diagram. That means we need to ____________ the 320 by 10 _________
time(s). Therefore, 320 centimetres is equal to __________ decimetres.
(e) To convert 93 kilometres (km) to hectometres (hm), we move _________ _________
step(s) on the diagram. That means we need to ____________ the 93 by 10 _________
time(s). Therefore, 93 kilometres is equal to __________ hectometres.
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C. D. Pilmer
2. Convert the following measures. You are allowed to use a calculator.
Suggestion: You might want to write yourself a quick note to remind yourself how you did
the conversion. For example, you might write something like "two steps down, multiply by
10 two times."
(a) 320 cm = __________ mm
(b) 800 mm = __________ cm
(c) 72 000 m = __________ km
(d) 83 m = __________ cm
(e) 4 km = __________ m
(f) 320 cm = __________ m
(g) 140 cm = __________ dm
(h) 29 dm = __________ mm
(i) 70 hm = __________ m
(j) 60 000 dm = __________ hm
3. Which is larger? Circle the correct answer.
(a) 395 mm or 2 m
(b) 4 km or 5000 m
(c) 7 m or 60 cm
(d) 19 mm or 150 cm
(e) 2000 m or 6 km
(f) 3 m or 800 cm
(g) 1 km or 6000 cm
(h) 23 cm or 500 mm
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Metric Measures for Liquid Capacity and Weight
Liquid Capacity
The basic metric measure for liquid capacity is litres. We combine this basic metric unit for
liquid capacity (L) with the prefixes (k, h, da, d, c, and m) to obtain the desired unit of measure
for liquid capacity.
Prefix
kilolitre
hectolitre
dekalitre
litre
decilitre
centilitre
millilitre
Symbol
kL
hL
daL
L
dL
cL
mL
Multiple or Submultiple
1000 litres
100 litres
10 litres
---0.1 of a litre
0.01 of a litre
0.001 of a litre
In the real world, you are likely only going to encounter litres (L) and millilitres (mL).
•
Litres are used to describe the capacity of large containers or objects. Consider these
examples.
- The largest container of milk you can purchase is a 4 litre container.
- The gasoline tank in a typical compact car holds between 50 and 58 litres.
- A circular above swimming pool might hold 50 000 litres of water.
•
Millilitres are used to describe the capacity of small containers. Consider these
examples.
- The typical pop can holds 355 mL of pop.
- A single dose of liquid cough medicine might be 10 mL.
- A large bottle of shampoo might hold 1183 mL of shampoo.
Based on this, the only important conversion you should know is that 1 L equals 1000 mL.
Weight (Actually Mass)
The basic metric measure for weight (actually mass) is grams. We combine this basic metric
unit for weight (g) with the prefixes (k, h, da, d, c, and m) to obtain the desired unit of measure
for weight.
Prefix
kilogram
hectogram
dekagram
gram
decigram
centigram
milligram
NSSAL
©2012
Symbol
kg
hg
dag
g
dg
cg
mg
Multiple or Submultiple
1000 grams
100 grams
10 grams
---0.1 of a gram
0.01 of a gram
0.001 of a gram
44
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C. D. Pilmer
In the real world, you are likely only going to encounter kilogram (kg) and grams (g).
•
Kilograms are used to describe the heavy objects. Consider these examples.
- An adult male (50 years of age) may weigh 78 kg.
- A large bag of dry dog food weighs approximately 9 kg.
- A mid-size car weighs around 1500 kg.
•
Grams are used to describe light objects. Consider these examples.
- A blue berry muffin recipe may ask you to add 9 g of baking soda.
- A small paper clip weighs approximately 1 g.
- A family size of potato chips weighs 270 g.
Based on this, the only important conversion you should know is that 1 kg equals 1000 g.
Conversions
• To convert litres to millilitres, multiply by 1000.
• To convert millilitres to litres, divide by 1000.
• To convert kilograms to grams, multiply by 1000.
• To convert grams to kilograms, divide by 1000.
Example
Convert the following units of measure. You are permitted to use a calculator.
(a) 42 litres to millilitres
(b) 50 000 millilitres to litres
(c) 620 000 grams to kilograms
(d) 4.2 kilograms to grams
Answers
(a) 42 litres to millilitres (multiply by 1000)
Therefore 42 litres equals 42 000 mL
(b) 50 000 millilitres to litres (divide by 1000)
Therefore 50 000 millilitres equals 50 litres
(c) 620 000 grams to kilograms (divide by 1000)
Therefore 620 000 grams equals 620 kilograms
(d) 4.2 kilograms to grams (multiply by 1000)
Therefore 4.2 kilograms equals 4200 grams
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C. D. Pilmer
Questions
On a previous activity sheet, you worked with the more common metric measures for length.
These were kilometres (km), metres (m), centimetres (cm) and millimetres (mm). These units of
measure plus the two measures for liquid capacity (i.e. L and mL) and the two measures for
weight (i.e. kg and g) will be addressed in the questions that follow.
1. In each case, choose the most appropriate unit of measure. You can choose from km, m, cm,
mm, L, mL, kg and g.
Situation
Unit
(a)
the length of a coil of rope
(b)
the weight of a gorilla
(c)
the amount of milk that can be poured into a coffee cup
(d)
the distance between Halifax and Amherst
(e)
the amount of salt in a serving of potato chips
(f)
the width of a small river
(g)
the amount of oil that can be pumped into a home heating oil tank
(h)
the thickness of a pane of glass
(i)
the weight of a chocolate bar
(j)
the dimensions of a building
(k)
the weight of a small boulder
(l)
the amount of water in a bathtub
(m) the distance covered on a two day bike trip
(n)
the length of your foot
(o)
the amount of cooking oil added to a recipe
(p)
the amount of fat in a cookie
(q)
the dimensions of a postage stamp
(r)
the amount of weight a pair of snowshoes can support
(s)
the amount of fuel a jet airplane burns in an hour
(t)
the height of a flagpole
(u)
the amount of water needed to fill a bottle cap
(v)
the length of a hockey stick
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C. D. Pilmer
2. Use a variety of devices to measure the height, weight, and liquid capacity of a regular can of
pop or fruit juice, and a large bottle of pop or water. Record the information in the chart
below. Include the appropriate units of measure.
Height
Weight
Liquid Capacity
Can of Pop
Large Bottle of Pop
3. Convert the following units of measure. You are permitted to use a calculator.
(a) 8200 grams to kilograms
(b) 86 000 millilitres to litres
(c) 7.8 litres to millilitres
(d) 123 kilograms to grams
(e) 27 litres to millilitres
(f) 980 grams to kilograms
(g) 12.9 kilograms to grams
(h) 1200 millilitres to litres
(i) 64.9 litres to millilitres
(j) 0.3 kilograms to grams
(k) 750 millilitres to litres
(l) 18 500 grams to kilograms
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C. D. Pilmer
Area and Perimeter
The square, shown on the right, measures 1 centimetre by 1 centimetre.
Therefore, it has an area of 1 square centimetre (cm2). Use this information to
figure out the area and perimeter of the figures below. Two worked examples
have been provided to assist you.
e.g.
Perimeter = 8 cm
Area = 3 cm2
e.g.
Perimeter = 12 cm
Area = 5 cm2
1.
Perimeter =
Area =
2.
Perimeter =
Area =
3.
Perimeter =
Area =
4.
Perimeter =
Area =
5.
Perimeter =
Area =
6.
Perimeter =
Area =
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C. D. Pilmer
7.
Perimeter =
Area =
8.
Perimeter =
Area =
9.
Perimeter =
Area =
10.
Perimeter =
Area =
11.
Perimeter =
Area =
12.
Perimeter =
Area =
True or False:
(a) If two figures have the same perimeter, then they must have the same area.
True False
(b) If two figures have the same area, then they must have the same perimeter.
True False
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C. D. Pilmer
Approximately How Much Time Will It Take?
In each case, you are given a task or situation. You are then asked to estimate the amount of
time it will take to complete the task or situation. Make sure you include the appropriate units of
measure (i.e. seconds, minutes, hours, days, weeks, months). Obviously, everyone is going to
come up with slightly different answers; that's OK. However, be prepared to justify your answer
to your instructor.
1.
Situation or Task
Approximately how much time will it take for a contractor to
build an average size home?
2.
Approximately how much time will it take for a person to
prepare and eat a breakfast for themselves?
3.
Approximately how much time will it take for a person to walk
five kilometres?
4.
When a working person goes down south for a vacation,
approximately how much time do they spend down south?
5.
During a one hour television show, how much time is given to
television commercials?
6.
Approximately how long does it take to sing "Happy Birthday to
You?"
7.
Approximately how much time will it take for a person to drive
from Halifax, N.S. to Truro, N.S.?
8.
Approximately how long is the average movie?
9.
How much time passes between pay periods for a full-time
employee?
10.
Approximately how long is each of the four seasons of the year?
11.
Approximately how long does the average full-time employee
work each week?
12.
Approximately how long is the average song?
13.
Approximately how long does it take for an athletic person to
run 100 metres (slightly less than the length of a football field)?
14.
Approximately how much time is needed to wash a full load of
clothes in a washing machine?
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Your Estimated Time
Draft
C. D. Pilmer
Telling Time (A)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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C. D. Pilmer
Telling Time (B)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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Telling Time (C)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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C. D. Pilmer
Telling Time (D)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
NSSAL
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Telling Time (E)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
NSSAL
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C. D. Pilmer
Telling Time (F)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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Connect Four Time Ahead Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place paper clips on the strips below; one on the Start Time Strip and one on the Minutes
Ahead Strip. If the player chose 3:30 (start time) and 45 (minutes ahead), then they could
capture a square labelled 4:15. They either mark the square with an X or place a colored
counter on the square. There may be other squares with this same time but only one square
can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that time using a O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
5:00
4:30
6:00
4:15
3:30
5:45
3:45
5:15
4:00
4:45
3:45
4:30
4:45
5:45
3:15
5:00
4:00
5:15
3:15
4:00
5:30
4:15
6:00
3:45
4:15
5:00
4:45
5:15
3:15
5:30
5:30
3:30
4:30
3:45
5:00
4:15
Start Time Strip
Minutes Ahead Strip
3:00 3:30 4:00 4:30 5:00
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15
30
45
60
Draft
C. D. Pilmer
Connect Four Time Ahead Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place paper clips on the strips below; one on the Start Time Strip and one on the Minutes
Ahead Strip. If the player chose 2:45 (start time) and 30 (minutes ahead), then they could
capture a square labelled 3:15. They either mark the square with an X or place a colored
counter on the square. There may be other squares with this same time but only one square
can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that time using a O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
3:45
3:00
4:15
3:15
4:00
3:30
3:15
4:30
2:30
3:30
2:45
3:45
2:45
4:00
3:15
3:45
3:30
4:15
3:45
3:30
4:15
3:00
4:00
3:15
4:30
3:00
3:45
3:15
2:30
3:30
3:15
2:45
3:30
4:00
3:45
3:00
Start Time Strip
Minutes Ahead Strip
2:15 2:30 2:45 3:00 3:15 3:30
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15 30 45 60
Draft
C. D. Pilmer
How Much Time Has Passed? (A)
With each question you have been given a start time and a finish time. Your job is to determine
how much time has passed between those two times.
Start Time
Finish Time
Your Answers:
(a)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(b)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(c)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(d)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
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C. D. Pilmer
Start Time
Finish Time
Your Answers:
(e)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(f)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(g)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(h)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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How Much Time Has Passed? (B)
With each question you have been given a start time and a finish time. Your job is to determine
how much time has passed between those two times.
Start Time
Finish Time
Your Answers:
(a)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(b)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(c)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(d)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
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Draft
C. D. Pilmer
Start Time
Finish Time
Your Answers:
(e)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(f)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(g)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(h)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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Draft
C. D. Pilmer
How Much Time Has Passed? (C)
With each question you have been given a start time and a finish time. Your job is to determine
how much time has passed between those two times.
Start Time
Finish Time
Your Answers:
(a)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(b)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(c)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(d)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
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Draft
C. D. Pilmer
Start Time
Finish Time
Your Answers:
(e)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(f)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(g)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
(h)
Start Time: _________
Finish Time: _________
Time Passed:
____ hour(s), _____ minutes
All images generated using the online applet found at:
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf
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C. D. Pilmer
Statistics and Probability
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Likelihood; Part 1
The likelihood of events varies greatly.
• Some events are impossible. For example, the likelihood of finding a spider that talks is
impossible.
• Some events are possible but unlikely. For example, the likelihood of having a snow
storm in Nova Scotia in mid-April is possible but unlikely.
• Some events are possible and likely. For example, the likelihood of having four
consecutive days of sunshine during a Nova Scotia summer is possible and likely.
• Some events are certain. For example, if six randomly chosen students are selected from
an all-girls private school, then we are certain that all of those students will be girls.
Certain
Possible and
Likely
Possible but
Unlikely
Impossible
Look at each of these situations and check off the box that best represents the likelihood of that
event occurring.
What is the likelihood that the outdoor temperature in Nova Scotia will
be cold enough to freeze water on March 15?
What is the likelihood that a metal bolt will sink when
dropped into water?
What is the likelihood that one of the learners in an adult education
class will be 15 years old?
What is the likelihood that you or a family member will
get in an accident today?
What is the likelihood that an office administrator at a major
landscaping company would receive at least twenty calls a day?
What is the likelihood that you will be struck by lightning
within your lifetime?
What is the likelihood that you will experience at least one high tide in
the Bay of Fundy within a 24 hour period?
What is the likelihood that at least a three children will be absent from
the local elementary school on Monday?
What is the likelihood that a Nova Scotia campground will
be fully occupied in December?
What is the likelihood that the sun will rise tomorrow?
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Certain
Possible and
Likely
Possible but
Unlikely
Impossible
With the last set of questions, everyone should be reporting the same likelihoods. However, with
the next set of questions, we expect different answers from different people. Answer the
following questions and be prepared to discuss your answers with your instructor and/or
classmates.
What is the likelihood that you will complete at least one marathon in
the next year?
What is the likelihood that you will go swimming
tomorrow?
What is the likelihood of you drinking at least one cup of coffee within
the next 24 hours?
What is the likelihood you will be spending at least 15 minutes today
commuting in your own vehicle (e.g. bike, car, truck)?
What is the likelihood of you spending at least 10 minutes today on a
social media website (e.g. Facebook, Twitter)?
What is the likelihood of you walking a dog today?
What is the likelihood of you eating red meat, fish, or
poultry within the next week?
What is the likelihood of you attending work or school tomorrow?
What is the likelihood of you caring for a family member (e.g. younger
sibling, aging parents or grandparents) within the next week?
What is the likelihood that you will watch at least one hour
of television today?
What is the likelihood of you fixing a broken device in your home
within the next month?
What is the likelihood that you will go on an out-of-province vacation
within the next year?
Did You Know?
Did you know that your likelihood of winning the Lotto 649 is worse than you likelihood of
being struck by lightning or your likelihood of dying in a plane crash.
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Likelihood; Part 2
You are given three situations.
First Situation
A six-sided die, numbered 1
through 6
Second Situation
A bag of marbles that
contains:
• 6 orange marbles
• 10 green marbles
• 2 blue marbles
Third Situation
A spinner divided into three
sections, not of equal size.
A
B
C
Certain
Possible and
Likely
Possible but
Unlikely
Impossible
Look at each of these situations and check off the box that best represents the likelihood of that
event occurring.
What is the likelihood of obtaining a 2 with a single roll of the die?
What is the likelihood of randomly selecting a green marble on a
single draw from the marble bag?
What is the likelihood of obtaining the letter "D" on a single spin of
the spinner?
What is the likelihood of obtaining a number less than 5 with a single
roll of the die?
What is the likelihood of randomly selecting a blue marble on a single
draw from the marble bag?
What is the likelihood of obtaining the letter "A" on a single spin of
the spinner?
What is the likelihood of randomly selecting an orange, green or blue
marble on a single draw from the marble bag?
What is the likelihood of obtaining a 7 with a single roll of the die?
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Certain
Possible and
Likely
Possible but
Unlikely
Impossible
What is the likelihood of obtaining the letter "A" or letter "C" on a
single spin of the spinner?
What is the likelihood of obtaining a 6 with a single roll of the die?
What is the likelihood of randomly selecting a purple marble on a
single draw from the marble bag?
What is the likelihood of obtaining the letter "A", "B" or "C" on a
single spin of the spinner?
What is the likelihood of obtaining an even number with a single roll
of the die?
What is the likelihood of obtaining a 1 and a 2 with a single roll of the
die?
What is the likelihood of randomly selecting an orange or green
marble on a single draw from the marble bag?
What is the likelihood of obtaining the number 1 or greater with a
single roll of the die?
Did You Know?
The chance of winning the Lotto 649 grand prize by purchasing one ticket is 1 in approximately
14 million.
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Likelihood; Part 3
On this worksheet, we will give you partial description of a situation and the likelihood of certain
events associated with that situation. Your mission is to complete the description of the situation
by labeling, coloring, or drawing objects. In each case, there are a range of acceptable answers.
Therefore it is important to review your answers with your instructor and/or classmates.
1. You have a marble bag that contains 20 marbles. You
do know that the marbles may be red, green, purple or
yellow. Color the twenty marbles on the right such that
they would produce the following likelihoods.
• Possible and likely to randomly select a blue marble
on a single draw from the bag.
• Impossible to randomly select a red marble on a
single draw from the bag.
• Possible but unlikely to randomly select a green
marble on a single draw from the bag.
• Certain to randomly select a blue, green, or yellow
marble on a single draw from the bag.
• Possible but unlikely to randomly select a green or
yellow marble on a single draw from the bag.
• Slightly better likelihood of drawing a yellow
marble over a green marble on a single draw from
the bag.
2. You have a spinner that can possibly be divided into
five sections; not necessarily of equal size. Complete
the spinner on the right (i.e. divide it into sections and
label those sections) such that it would produce the
following likelihoods.
• The likelihood of obtaining the letter "A" or letter
"C" on a single spin is exactly the same.
• Possible but unlikely to obtain the letter "A" on a
single spin.
• Impossible to obtain the letter "B" on a single spin.
• Possible and likely to obtain the letter "E" on a
single spin.
• Slightly better likelihood of obtaining the letter "E"
over the letter "D" on a single spin.
• Certain to obtain the letter "A", "C", "D", or "E" on
a single spin.
• Possible but unlikely to obtain the letter "A" or
letter "C" on a single spin.
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Is It What You Expect?
To complete this activity sheet, you will need:
• a six-sided die, numbered 1 through 6
• 8 playing cards of the diamond suit numbered 2 through 9.
In this activity, you will predict whether an event is impossible, possible but unlikely, possible
and likely, and certain. Then you will run 15 trials (e.g. roll the die 15 times) and see if the
results of your experiment (i.e. trails) match your prediction.
Predictions:
Possible and
Likely
Certain
Certain
Possible but
Unlikely
Possible but
Unlikely
Possible and
Likely
Impossible
Impossible
Part 1: Six-sided Die
Likelihood of obtaining a 4 with a single roll of the die
Likelihood of obtaining a 3 or more with a single roll of the die.
Likelihood of obtaining an odd number with a single roll of the die
Likelihood of obtaining a 9 with a single roll of the die.
Likelihood of obtaining a 6 or less with a single roll of the die.
Part 2: Eight Playing Cards
Likelihood of obtaining a diamond with one draw from the deck.
Likelihood of obtaining an even number with one draw from the deck.
Likelihood of obtaining a king with one draw from the deck.
Likelihood of obtaining a 6 or less with one draw from the deck.
Likelihood of obtaining a 5 with one draw from the deck
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Trials
Part 1: Six-sided Die
Trial 15
Trial 14
Trial 13
Trial 12
Trial 11
Trial 10
Trial 9
Trial 8
Trial 7
Trial 6
Trial 5
Trial 4
Trial 3
Trial 2
Trial 1
You will be rolling the die fifteen times. After each roll, record whether each event was
successful or unsuccessful. Use a check mark for successful and an "X" for unsuccessful. For
example, if on the first trial you rolled a 3, then you would put an "X" for "obtaining a 4", put a
"" for "obtaining a 3 or more", put a "" for "obtaining an odd number, and so on.
obtaining a 4
obtaining a 3 or more
obtaining an odd number
obtaining a 9
obtaining a 6 or less
Part 2: Eight Playing Cards
Trial 15
Trial 14
Trial 13
Trial 12
Trial 11
Trial 10
Trial 9
Trial 8
Trial 7
Trial 6
Trial 5
Trial 4
Trial 3
Trial 2
Trial 1
You will complete fifteen trials where each time you randomly draw one card from your eight
card deck. After each trial, record whether each event was successful or unsuccessful. Again,
use a "" for successful and an "X" for unsuccessful. Before drawing on each trial, made sure
you have returned the card that was removed on the previous trial and remember to shuffle the
eight card deck.
obtaining a diamond
obtaining an even number
obtaining a king
obtaining a 6 or less
obtaining a 5
Did the results of your experiments match up with what you predicted or expected? Explain.
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Data and Survey Questions
Statistics is the discipline concerned with the collection, organization, and analysis of data to
draw conclusions or make predictions. Statistics is widely employed in government, business,
and the natural and social sciences.
The key word in this definition is "data." Data is merely a collection of measurements or
observations. There are two types of data; numerical and categorical.
•
Numerical data is data comprised of numbers.
e.g. Ten randomly selected adults were asked the question, "What was your cell phone
bill for the previous month?"
Here are the responses.
{$47.80, $33.50, $65.70, $82.00, $54.90, $72.00, $43.65, $67.40, $95.89, $49.67}
This data is classified as numerical because it is comprised of numbers.
e.g. Twelve randomly selected employees of a government agency
were asked the question, "How many days of vacation did you
take during the months of July and August of this year?"
Here are the responses.
{7, 10, 5, 8, 3, 6, 15, 10, 9, 4, 5, 12}
This data is classified as numerical because it is comprised of
numbers.
•
Categorical data is data that can be assigned to distinct non-overlapping categories.
e.g. Sixteen randomly selected car owners we asked, "What is the color of your primary
car.?" They could choose from the following options: red, white, black, silver-grey,
dark green, blue or other.
Here are the responses.
{White, Black, Black, Red, Red, Other, Black, Dark Green, White, Blue, Black,
Dark Green, Other, Black, Red, Blue}
This data is classified as categorical data because it is broken down into distinct
color categories.
e.g. Fourteen randomly selected cell phone users were asked, "What
cell phone provider do you use?" They could choose from the
options: Telus, Bell Aliant, Rogers, Koodo, or other.
Here are the responses.
{Telus, Bell Aliant, Other, Telus, Bell Aliant, Rogers, Rogers,
Koodo, Rogers, Telus, Rogers, Rogers, Other, Koodo}
This data is classified as categorical data because it is broken down to distinct cell
phone provider categories.
The next matter to consider is who collected the data. Is it first-hand data (i.e. data you
collected yourself)? Or is it second-hand data (i.e. data collected by another individual or
organization)?
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e.g. Marcus was helping his daughter with a school project on rainfall in their
community. Over the next 30 days, the two of them measured and recorded
the daily rainfall using a rain gauge in their backyard. For both Marcus and
his daughter, this is first-hand data because they collected it themselves.
e.g. Maurita was helping her son with a school project on the annual precipitation in fifteen
major Canadian cities. There were able to obtain these annual precipitation data from a
government website. For both Maurita and her son, this is second-hand data because
they did not collect it themselves.
The last thing we have to consider is the nature of the questions an individual should ask when
conducting a survey and collecting data. Consider the following pairs of questions. In each
case, one question is flawed and the other question is an appropriate. Indicate which is which by
circling the appropriate word found on the right.
Do you watch a lot of television?
 Yes
 No
Flawed Appropriate
How many hours of television do you typically watch in one week? ___
Flawed Appropriate
What is your favorite team sport to play?
 Hockey Soccer  Football  Basketball  Other
Flawed Appropriate
What is your favorite team sport to play?
 Hockey Soccer  Football  Baseball
Flawed Appropriate
Doctors recommend that school-age children should get approximately
ten hours of sleep each night. How many hours of sleep do your schoolage children typically get each night? ___
Flawed Appropriate
How many hours of sleep do your school-age children typically get each
night? ___
Flawed Appropriate
Sit down with your instructor and/or classmate(s) and discuss your choices regarding the above
survey questions. In the space below, briefly explain what was wrong with the flawed survey
questions.
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Questions
(a)
Second-hand
First-hand
Categorical
Numerical
1. In each case, determine whether we are dealing with numerical or categorical data, and
whether we are dealing with first-hand or second hand data. That means you must check off
two of the four categories in each case.
Six hundred randomly selected adults were
asked, "How many hours of sleep do you
typically get on a weeknight?" This data was
collected by a polling company and the data
was given to you for analysis.
   
You randomly selected forty adults and asked them,
"From which retailer (e.g. Sobeys, Superstore,
Costco, etc.) do you buy most of your groceries?"
   
You went to the Statistics Canada website and downloaded the
data regarding the average household income of Canadians for
2014.
   
You got to the ESPN website and record the goals
saved by Josh Harding (NHL goalie) in each of
his first eight years in the league.
   
You ask the fifty-eight members of your local legion hall,
"What percentage of your income do you send on
entertainment (e.g. movies, concerts, restaurants, etc.)?"
   
Prior to the federal election, a polling company
asked 1500 randomly selected adults the
following. "Which federal party will you be
voting for in the upcoming election? You decided
to use this data in a paper you were doing for school.
   
You need to pick up coffee for a large staff
meeting. You can choose from Tim Hortons,
Starbucks, Second Cup and Jim's Specialty
Coffee. You ask each of the staff members
which one of the four they would prefer.
   
(h)
You roll two dice forty times. Each time you record the sum of
the two numbers rolled on the two dice.
   
(i)
The local children's hospital records the weight of all
newborns. They supply you with this data.
   
(b)
(c)
(d)
(e)
(f)
(g)
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2. Each of the following survey questions is flawed. Write a better question for each.
(a) Do you usually drive or walk to school?
(b) The Public Health Agency of Canada recommends that adults (18 to 64 years) get at 2.5
hours of moderate to vigorous aerobic exercise each week. Typically how many hours of
moderate to vigorous aerobic exercise do you get each week?
(c) Do you and your direct family members spend enough quality family time together?
(d) Do you prefer watching trashy reality television shows or clever comedies?
3. Design a question to help you determine the favorite type of music of students in your class.
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Gathering Data and Creating Bar Graphs
In this section, we are going to conduct experiments, gather data from that experiment, and
create a bar graph using that data.
Data is usually recorded in a table (or chart). In this section we will focus on tally and
frequency charts. We often use a tally system to record results because it is faster than writing
down words or numbers. Once the experiment is completed we can then look at the tallies to
determine the frequency of each outcome (i.e. the number of times each outcome occurs). For
example, if you are recording the brands of cars that passes through a particular point on a road
over a specific 10 minute period, you want to place a tally mark for each car in the appropriate
row of the chart. Once the 10 minutes is up, you would count the tallies in each row and write
down the appropriate frequency.
Brand of Car
Toyota
Tally
Frequency
11
Ford
7
Chevrolet
8
Hyundai
7
Honda
9
Chrysler
6
Volkswagen
5
Mercedes
4
Mazda
10
Other
5
Bar graphs are used to display categorical data or discrete numerical data. Numerical data is
discrete if the possible values are isolated points on a number line. For example, if survey
participants were asked how many phone calls they made today, their responses would be whole
numbers like 0, 4 or 12. They would not respond with something like 7.8 phone calls. Since
they can only report isolated points, then we end up with discrete numerical data.
Whether we are dealing with a horizontal bar graph or a vertical bar graph, all bar graphs have
the following features.
• A title is describes what the graph is about in a few words
• Labels on both the vertical and horizontal axes explaining what is being measured.
• A scale showing the numerical values that we are working with.
• Bars which act much like a ruler to show the frequency in each category or for each
discrete number.
Let's look at a bar graph in the context of "brand of car" data shown above.
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Title: Brands of Cars Observed
Labels: Brand of Car and Frequency
Scale: Every tick mark on the vertical axis represents "1."
Bars: There are 10 bars ranging from a high to 11 to a low of 4.
Example 1
Roll a six-sided die 50 times; recording each outcome in a table. Construct a bar graph using this
data. Are these the results you expected?
Answer:
We completed the experiment and recorded the data in the tally and frequency chart below.
If you were to conduct the same experiment, you would get similar, but not identical, results
to these.
Outcome
(i.e. Number
Rolled)
1
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Frequency
7
2
10
3
9
4
7
5
8
6
9
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This is maybe a little different than what
you expected. You might think that all six
outcomes would occur the same number of
times (8 or 9 times) since we are rolling a
"fair" die. However, with only 50 rolls,
there is a fairly good chance that some
outcomes would occur more frequently
than others. Things would even out more if
the die was rolled 500 times.
Example 2
Francine gave pedometers to five of her classmates. A pedometer is an electronic device that
tracks the number of steps the user takes. She had them wear the device for two days and then
recorded the readings from the pedometers into the table below. She also constructed a bar
graph using this data.
Classmate
Kadeer
Candice
Jacob
Nashi
Rana
(a)
(b)
(c)
(d)
(e)
(f)
Number of Steps
11 294
12 901
9242
14 496
8565
Is Francine dealing with first-hand or second-hand data?
Francine made a mistake when constructing the bar graph. What mistake was made?
What scale is used on the vertical axis?
What is the title of the bar graph?
What label is used for the horizontal axis?
What label is used for the vertical axis?
Answers:
(a) First-hand data (She collected it herself.)
(b) She made the mistake of mixing up Jacob and Nashi's data.
(c) Scale: Each tick mark represents 1000 steps
(d) Title: Pedometer Results of Five Classmates
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(e) Horizontal Axis Label: Classmates
(f) Vertical Axis Label: Number of Steps in Two Days
Questions
1. Tanya went to a strip mall's parking lot and recorded the colors of the various vehicles in the
lot at the time. She completed the tally portion of the tally and frequency chart.
Color
Tally
Number
of
Vehicles
Red
White
Black
Silver
Other
(a)
(b)
(c)
(d)
(e)
(f)
Complete the tally and frequency chart, and the bar graph above.
Is Tanya dealing with first-hand or second-hand data?
How many vehicles did Tanya observe at this time?
Which vehicle color appeared most frequently that day in the parking lot?
What label is being used on the vertical axis?
Can Tanya assume that black is generally the preferred color of vehicle in her town based
on this work?
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2. Complete the table that would have generated the following bar graph.
3. Below you will find data obtained from the Statistics Canada website on the average annual
rainfall of five Canadian cities. Samir created a bar graph using this data, which is shown on
the right.
City
Halifax
Fredericton
Montreal
Winnipeg
Vancouver
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Average Annual
Precipitation (mm)
1452
1143
979
514
1199
Is Samir dealing with first-hand or second-hand data?
Samir made a mistake when constructing the bar graph. What mistake did he make?
What is the title of this bar graph?
What scale is being used with the vertical axis?
Why would he have not used the scale where 1 tick mark would represent 1 millilmetre?
What label is being used on the vertical axis?
What label is being used on the horizontal axis?
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4. You will need two six-sided dice, both numbered 1 through 6. Roll the two dice,
find the sum of the two resulting numbers and record the information in the tally
and frequency chart below. Repeat this procedure until you have rolled the pair
of die 40 times.
Sum
2
Tally
Frequency
3
4
5
6
7
8
9
10
11
12
(a) Now that the chart is complete, draw a bar graph using the graph paper on the next page.
Do not forget to use include a title, labels and scale.
(b) Are you dealing with first-hand or second-hand data?
(c) Which sum occurred most frequently? Is this what you expected? Why or Why not?
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5. The same data was used to generate both of the bar graphs below. Both graphs are correct
but they may lead people to reach very different conclusions. Why is this so? Is this
something you should consider when reading bar graphs that you see in the media?
6. Data was collected regarding the eye color of students in a particular classroom. Your
mission is to fill in the missing pieces of this tally and frequency chart and this bar graph.
Eye
Color
Tally
Number
of
Students
Blue
Brown
13
Hazel
5
Green
1
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7. Take a paper cup, place it at the edge of a desk, push it off the desk, and record how the cup
lands on the ground (right-side up, upside down, or on its side). Repeat this process another
29 times. The data should be recorded in a tally and frequency chart and then a bar graph
should be constructed. Remember to include a title, labels and scale in your bar graph.
Tally
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Interpreting Bar Graphs
Now that you know how to collect data and create a bar graph, let's spend some time interpreting
bar graphs that are supplied to you. In the previous activity, we only looked at vertical bar
graphs, but now we will also look at horizontal bar graphs.
Example
Below you have been presented with both a vertical and horizontal bar graph. They are both
displaying the same information, which is, the sales of the top six small cars in Canada for May
2014. Use either one of these graphs to answer the questions below.
Vertical Bar Graph
Horizontal Bar Graph
(a) Why do you think numbers were supplied above or to the right of the bars?
(b) Which small car had the top sales for May 2014? How many were sold?
(c) How many more Corollas were sold in May 2014 compared to Volkswagen Jettas?
(d) What was the total number of sales of these six cars for May 2014?
(e) Are the combined number of sales of Cruzes and Jettas greater than those of Civics for May
2014?
Answers:
(a) Since the scale is so large (i.e. each tick mark represents 1000 vehicles sold), it is
impossible to accurately determine the exact length of each bar (i.e. the exact number of
sales that each bar represents). The numbers supplied with each bar correct this problem.
(b) Top Sales: Honda Civic with 7185 vehicles sold
(c) 6107 − 3412 =
2695
There were 2695 more Toyota Corollas sold in May 2014 than Volkswagen Jettas.
(d) 7185 + 6107 + 5628 + 4603 + 3760 + 3412 =
30695
In May 2014, the total number of sales for these six small cars was 30 695.
(e) No, the combined number of sales of Cruzes and Jettas (7172 sales) is slightly less than
those for the Civic (7185 sales).
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Questions
You may use a calculator when doing the following questions.
1. The following bar graph shows the relationship between the average annual earnings of Nova
Scotia citizens in 2006 in terms of their highest level of education.
Source: Statistics Canada
(a) What was the average annual earning of a Nova Scotian in 2006 if their highest level of
education was a high school diploma?
(b) What level of education generated average annual earnings of $50 889 for Nova Scotia
citizens in 2006?
(c) What was the difference in the average annual earnings of Nova Scotia citizens with less
than a complete high school education and citizens with a college education in 2006?
(d) Which level of education generated the highest average annual earnings in 2006, and
what was that average earning?
(e) On average in 2006, were the earnings of a couple where both people have less than a
complete high school education more than the earnings of a single individual with a postbachelor degree?
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2. The following bar graph shows the average high temperature in six Canadian cities for the
month of August. Use this graph to answer the questions below.
(a) What is the average high temperature for Montreal in the month of August?
(b) Which one of the five cities shown has an average high temperature in August closest to
that of Halifax?
(c) Which city has an average high temperature of 20oC for the month of August?
(d) Which one of the six cities has the highest average high tempearure in August?
(e) What is the difference between Yellowknife and Halifax's average high temperatures in
August?
(f) Which one of the five cities shown has an average high temperature in August closest to
that of Toronto?
(g) The scale on the horizontal axis starts at 14, rather than 0. Does this make the differences
between these cities' average tempeartures appear greater or smaller? Is this important to
recognize when reading a graph? Why or why not?
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3. The following bar graph shows the average life expectancy of citizens from seven different
countries.
Source: Infoplease.com
(a) Which one of the seven counties has the highest life expectancy? What is that life
expectancy in years?
(b) Which one of the seven countries has a life expectancy of 80 years?
(c) What is the difference between the average life expentency for Chad compared to that of
the Phillippines?
(d) Of the seven countries presented, which one has an average life expectancy closest to that
of Japan?
(e) Based on this bar graph, can we conclude that the standard of living in Canada is better
than that of the US? Explain.
(f) Does Haiti or the Phillippines have a higher average life expectancy?
(g) The scale on the vertical axis starts at 0 and goes up to 90. Do you think that this scale
allows readers to initially better understand the differences in life expectancies, as
opposed to scales that may start at 40 or 45? Explain.
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4. The following bar graph was created using data collected from US AT&T customers who
own and use smartphones. They were asked about their satisfaction level with their
smartphone. The score obtained for each smart phone is based on a 1000 point scale. That
is, if every customer using a particular smartphone gave it a perfect mark on every question,
then that smartphone would receive a final perfect score of 1000.
Source: J. D. Power 2013 US Wireless Smartphone Satisfaction Survey - Volume 2
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Which brand of smartphone had the lowest satisfaction score? What was that score?
How much higher was the satisfaction score for Apple compared to LG?
Which two brands of smartphones had scores that were almost identical?
Why do you think numbers were supplied to the right of the bars?
Did HTC or Motorola have the higher satisfaction score?
Which brand of smartphone has a satisfaction score closest to that of LG?
Can we conclude from this bar graph that more Apple smartphones were sold compared
to Nokia smartphones? Explain.
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Double Bar Graphs
A double bar graph is used to display two sets of data at once. By doing so, you can compare the
data sets.
Example 1
Anne tracked the additional time, in minutes, she spent outside of regular class time to work on
her five courses, over two days (Wednesday and Thursday). That information is displayed in the
graph below.
Minutes of Additional Work
40
35
30
25
Wednesday
20
Thursday
15
10
5
lo
gy
So
cio
to
ry
Hi
s
at
h
M
un
ica
t io
ns
Co
m
m
Bi
ol
og
y
0
(a) How much time did she spend on Thursday doing additional work in History?
(b) In what subject and on what day did she spend 25 minutes doing additional work?
(c) In what subject did she spend the same amount of time on Wednesday and Thursday doing
additional work?
(d) How much more time did she spend on Wednesday doing additional work in Math compared
to Thursday?
(e) How much more time did she spend on Thursday doing addition work in Biology compared
to History?
(f) How much time over the two days did she spend doing additional work in Biology and
Communications?
Answers:
(a) 10 minutes
(b) Math on Thursday
(c) Sociology (She spent 15 minutes each day)
(d) Math Wednesday: 30 minutes
Math Thursday: 25 minutes
30 - 25 = 5 minutes
(e) Biology Thursday: 20 minutes
History Thursday: 10 minutes
20 - 10 = 10 minutes
(f) 15 + 20 + 20 + 35 = 90 minutes or 1.5 hours
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Questions
Feel free to use a calculator with these questions.
1. The medal counts for the 2006 and 2010 winter Olympics for four countries have been
provided in the following graph.
2006 and 2010 Winter Olympic Medal Counts
(a) Of the four countries, which had highest medal count in 2006?
(b) What was the medal count for the United States in 2010?
(c) Which country had a medal count of 19 in 2006?
(d) How many more medals did Canada obtain in 2010 compared to 2006?
(e) In 2010, how many more medals did the United States get compared to Germany?
(f) What was the total medal count all four countries in 2010?
(g) What was the total medal count for both Germany and the United States over the 2006
and 2010 winter Olympics?
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2. Use the following double bar graph to answer the questions below.
Source: Desrosiers Automotive Reports
(a) Which one of the automobile companies should be concerned regarding their sales in
June during these two time periods? Why?
(b) Which of the six car companies had the greatest sales of vehicles in June and in what year
did that occur?
(c) How many more vehicles did Honda sell in June of 2014 in comparison to June of 2013?
(d) How many more vehicles did Toyota sell in June of 2013 compared to what Nissan sold
in the same month of the same year?
(e) How many vehicles in total did these six automotive companies sell in June of 2014?
(f) Are the combined sales of Toyota and Honda in June of 2013 greater than those of Ford
in the same month of the same year? Explain.
(g) Which one of these six automobile companies saw the largest increase in number of sales
when comparing sales for June 2013 to sales for June 2014?
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3. The following bar graph shows the number of new cases of specific cancers in Canada for
the year 2013. Use this graph to answer the questions below.
Source: Public Health Agency of Canada
(a) How many more new cases of colorectal cancer occurred in men as opposed to women in
2013?
(b) Of the five cancers presented, which had the greatest difference in terms of number
affecting men and the number affecting women in the year 2013?
(c) How many more new cases of thyroid cancer in females were there compared to the
number of new cases of stomach cancer in males in 2013?
(d) How many new cases in total of liver, stomach and thyroid cancer in both males and
females occurred in 2013?
(e) Is the combined number of new cases of stomach and thyroid cancer in both sexes greater
than the number of new cases of colorectal cancer in males in 2013? Explain.
(f) In 2013, were there more new cases of breast cancer or colorectal cancer? Explain.
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4. The 5-year survival rates for six different types of cancers have been supplied in the graph
below.
Source: Canadian Cancer Registry
(a) What was the approximate survival rate for colorectal cancer between 1992 and 1994?
(b) What was the approximate survival rate for breast cancer between 2004 and 2006?
(c) By approximately how much did the survival rate for ovarian cancer improve from 19921994 to 2004-2006?
(d) Have survival rates for these six types of cancer improved over time? How can you tell?
(e) Can you conclude that there were fewer cases of brain cancer than prostate cancer based
on this graph? Why or why not?
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Introduction to Line Graphs
Fertility Rate
Line graphs are created by plotting data points and connected them with lines. These lines are
useful for showing trends; that is, how something changes in value as something else happens.
They are used when we have continuous numerical
4.5
data. Numerical data is continuous if the set of
4
possible values forms an entire interval on the number
3.5
line. For example, if soil samples were tested for
3
acidity, the pH could be reported with numbers like 4,
2.5
4.17, 4.173, or any other number in the interval.
Generally continuous data arises when observations
2
involve making measurements (e.g. weighing objects,
1.5
recording temperatures, recording time to complete
1
tasks,…). The graph on the right is a line graph which
0.5
shows how fertility rates amongst Canadian women
0
have changed since the 1950s.
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Before we can start working with line graphs, we have
to learn how we plot the points that make up a line graph.
Plotting Points
A line graph is formed from a collection of points. These points, which are described as pairs of
numbers called ordered pairs, are plotted on a rectangular coordinate system. This
coordinate system has two perpendicular number lines called axes. The axes cross at a point
called the origin. The vertical axis traditionally represents the y-axis and the horizontal axis
traditionally represents the x-axis. The axes form four quadrants which have been numbered I,
II, III and IV in the diagram below.
y-axis
5
4
II
I
3
2
origin
1
0
-5
-4
-3
-2
0
-1
1
2
3
4
5
x-axis
-1
-2
-3
III
-4
IV
-5
For this course, we are only going to be dealing with points in the first quadrant where both the x
and y-values are positive numbers.
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Consider the ordered pair (2, 4). The numbers in the ordered
pair are called components. The first component is 2 and the
second component is 4. To plot (2, 4), we start at the origin,
move horizontally 2 units to the right, move vertically 4 units
up, and make a dot. That dot is the point or ordered pair (2, 4).
(2,4)
We follow the same process to plot the ordered pair (3, 1). We
start at the origin, move horizontally 3 units to the right, move
vertically 1 unit up, and make a dot.
(3,1)
Sometimes people make the mistake of thinking that the scales
on the horizontal axis and the vertical axis have to be the same;
this is not the case. In the real world, we often have to use
different scales on the different axes because one set of
numbers is so much larger than the other. We can see such a
case when we plot the points (5, 180) and (15, 300) on the
coordinate system to the right.
(15,300
)
(5,180)
There are times when the origin (i.e. the point (0, 0)) is not
shown on the coordinate system. You will see this occur in the
example below.
Example
Anna recorded her daughter's height on every birthday starting at the age of 2 through 16. This
data is in the table below.
age (years)
height (cm)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
89
95
102
108
115
121
127
135
140
147
152
157
161
163
164
(a) Create a line graph using this data where the age is on the horizontal axis and height is on the
vertical axis.
(b) Between what two ages was growth the slowest based on the data presented?
Answers:
(a) The scales on the two axes should be
different. Most people would choose to
make one tick mark equal to 1 year on the
horizontal axis and make one tick mark
equal to 10 centimetres on the vertical axis.
Since the first height we are supplied with
is 89, it might be wise to start the vertical
axis at 80, rather than 0. This means the
origin, (0, 0), is not seen on the graph.
(b) Between the ages of 15 and 16
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Questions
1. (a) Plot the following ordered pairs on the coordinate
system shown on the right.
(6, 3), (2, 7), (1, 0), (3, 4), (0, 2) and (7, 5)
(b) Plot the following ordered pairs on the coordinate
system shown on the right.
(8, 100), (20, 0), (16, 275), (24, 150), (12, 200)
and (0, 125)
(c) Plot the following ordered pairs on the coordinate
system shown on the right. In this case, you will
have to approximate the location of some of the
points.
(60, 100), (25, 40), (40, 170), (8, 20), (52, 0),
(22, 156), (67, 163) and (0, 48)
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2. Two coordinate systems have been supplied below. Determine the coordinates of all of the
points labeled on these two coordinate systems. In some cases, you have to approximate the
coordinates.
F
G
A
H
B
C
I
D
J
E
Point A:
Point F:
Point B:
Point G:
Point C:
Point H:
Point D:
Point I:
Point E:
Point J:
Source: Statistics Canada
60
Percentage of Households Using Internet
3. The number of Canadian households using the
Internet changed significantly between 1998
and 2003. Create a line graph using the
coordinate system on the right and the ordered
pairs below. In the case of each ordered pair,
the first number represents the year and the
second number represents the percentage of
households using the internet.
(1998, 23), (1999, 29), (2000, 40),
(2001, 49), (2002, 51), (2003, 55)
50
40
30
20
10
0
1998
1999
2000
2001
2002
2003
Year
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4. Manish recorded his son's weight every two years from the ages of 2 through to 14.
Son's Age
Weight in Kilograms
2
13
4
17
6
21
8
28
10
35
12
45
14
56
(a) Create a line graph using this data. Choose a scale that you feel is most appropriate.
Also remember to label the axes.
(b) Are we dealing with discrete or continuous data? Why?
(c) Should the ordered pair (0, 0) also be plotted on this line graph? Why or why not?
(d) Although Manish did not record his son's weight at the age of five years, it can be
approximated using the line graph you created in part (a). What is a reasonable
approximation of his son's weight at the age of five?
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5. Kianna is planning a small party for her
daughter's high school graduation. She is
having the event at her house and ordering
in food. The graph on the right shows the
relationship between the number of people
who attend the party and the cost of hosting
the party.
(a) Why are the points not joined together?
(b) Would the data that was collected to
create this graph be considered discrete
or continuous?
6. (a) Working from the floor of your classroom, tilt a thin hard covered book or piece of wood
on its side so that it forms an incline. You are going to roll an object (e.g. marble, toy
car, pencil) down this incline and see how far it travels across the floor. Initially, you
will place the object 4 cm from the bottom of the incline and release it. Record the
distance the object travels along the floor in centimetres. Repeat this procedure but the
release position will increase by 4 cm reach time. Record the information in the table
below.
Release Position (Distance from
the Bottom of Incline in cm)
Distance Travelled Along the
Floor in cm
4
8
12
16
20
(b) Are we looking at discrete or continuous data?
(c) Create a graph using this data. Remember to include scales and label the axes.
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Interpreting Line Graphs
Example 1
Two pulleys are connected by a belt. As the larger pulley
turns, the smaller pulley connected to it also turns. The
graph and diagram illustrates this relationship.
(a) If the larger pulley makes 3 complete revolutions, how
many revolutions does the smaller pulley make?
(b) If the smaller pulley makes 8 complete revolutions,
how many revolutions does the larger pulley make?
(c) Why does the line graph pass through the point (0,0)?
Answers:
(a) The smaller pulley makes 6 complete revolutions.
(b) The larger pulley makes 4 complete revolutions.
(c) The line graph should pass through (0,0) because as the large pulley makes 0 revolutions
(i.e. does not turn), the smaller pulley, which is connected to the larger pulley, also makes
0 revolutions (i.e. does not turn).
Example 2
The following line graph shows how the
average price of a domestic flight from
Halifax changed between the first quarter of
2007 until the third quarter of 2010.
(a) What was the average price of a domestic
flight from Halifax in the fourth quarter
of 2008?
(b) In what year and what quarter was the
average price of a domestic from Halifax
approximately $176?
(c) Between what two quarters was the
greatest drop in the average price of a
domestic flight from Halifax?
(d) Between what two quarters was the greatest
increase in the average price of a domestic
flight from Halifax?
Source: Statistics Canada
Answers:
(a) The average price in the fourth quarter of 2008 is $200.
(b) In the third quarter of 2010, the average price is approximately $176.
(c) The greatest drop occurred between the fourth quarter of 2008 and the first quarter of
2009.
(d) The greatest increase occurred between the second quarter of 2008 and the third quarter
of 2008.
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Questions
1. A patient is hooked up to an intravenous bag (I.V.
bag) which continually supplies medicine to her
bloodstream. The amount of medication in the
bag, measured in milliliters, is recorded over a 12
hour period. The information is displayed in the
graph below.
(a) How much medication was initially in the bag?
(b) How long did it take to drain the I.V. bag?
(c) How many milliliters of medication were being
supplied to the patient every hour?
(d) How much medication was in the bag after 4
hours?
(e) At what time was there 400 ml of medication
in the I.V. bag?
(f) Would the data that was collected to create this graph be considered discrete or
continuous? Explain.
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2. The following graph shows the value of Canada's exports from January 2008 until November
2010. The values are expressed in billions of Canadian dollars.
Source: Statistics Canada
(a)
(b)
(c)
(d)
Name at least three periods when Canada's exports largely remained unchanged.
During what month and year did Canada's exports almost reach $45 billion dollars?
When were Canada's exports lowest between Jan-08 and Nov-10?
Approximately how much did exports drop by between October 2008 and January 2009?
Based on your knowledge of world events, why do you think this occurred?
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3. A soccer ball is kicked from ground level. Its
flight path is shown on the graph. The height of
the ball, in metres, is on the vertical axis. The
distance the ball travels horizontally, in metres, is
on the horizontal axis.
(a) What is the maximum height reached by the
ball?
(b) How far does the ball travel horizontally when
it reaches this maximum height?
(c) What’s the initial height of the soccer ball?
(d) How far will the ball travel horizontally before
it hits the ground?
(e) Approximate the height of the ball after it has
travelled 2 metres horizontally.
(f) Determine the horizontal distances that
correspond to a height of 3 metres.
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4. The value of stock changes over
time. The following line graph
shows how the Research in Motion
(RIM) stock changed over the
month of June in 2011. Notice that
the month is comprised of 22 days,
rather than 30. There were only 22
trading days in June 2011; stocks
are not traded on weekends.
Source: Nasdaq.com
(a) On what trading day was the
greatest single day loss in the
value of RIM shares during the
month of June? Approximate the amount that was lost per share on that day.
(b) By how much approximately did the stock drop by from the beginning of the month until
the end of the month?
(c) On what trading day was the greatest single day gain in the value of RIM shares during
the month of June? Approximate the amount that each share increased by on that day.
5. The following graph shows the number
of infant deaths in Canada from 1999 to
2007.
Source: Statistics Canada
What are your thoughts regarding the
scale used on the vertical axis of this line
graph?
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Geometry
(From 3D to 2D)
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Isoball
As an introduction to 3D geometry, we are going to be playing an online game in which you use
a limited number of geometric pieces and directional arrows to move a ball from a raised
position to a hole located at a specific point on the floor. This game is available at:
http://www.coolmath-games.com/0-isoball-3/index.html
(or Google Search: Coolmath Games Isoball)
Below we have shown the "before" and "after" images for one particular round of this game
Before
We were given 2 direction arrows, 4 wedges
and 9 cubes that must be placed so that the ball
can move from the upper left to the hole on the
floor. All the objects must be used.
After
The objects have been correctly place. The
objects can be rotated by repeatedly clicking
on the item in the lower menu before placing it
in position.
Making sure that you have at least 45 minutes to work on this game, see how many rounds you
can complete successfully within that time. Periodically call your instructor over so that he/she
can see the progress you are making.
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Other Coolmath Games
Isoball is one of several excellent visual spatial reasoning games found on the Coolmath website.
We also recommend the following games. See how many rounds of each you can complete
within 45 minutes.
•
B-Cubed is a great game where individuals
slide the yellow cube around a course,
eliminating all of the grey cubes with the final
destination being the red cube. The yellow
cube is moved using the left, right, up, and
down arrows on the computer keyboard. The
first few rounds are fairly easy but the game
becomes progressively more challenging.
http://www.coolmath-games.com/0-bcubed/index.html
(or Google Search: Coolmath B-Cubed)
•
Bloxorz is a challenging game where
individuals topple a rectangular prism across
a plane in an effort to reach a desired hole. In
some rounds, the surface is made up of
different tiles where some tiles are strong and
others are weak. In other rounds you
encounter switches that are used to activate
bridges. The game provides directions
regarding both the tiles and switches. Again,
the arrows on the computer keyboard are used to move the prism.
http://www.coolmath-games.com/0-bloxorz/index.html
(or Google Search: Coolmath Bloxorz)
•
Water Drops is a fun problem solving game
where individuals construct ramps and use a
variety of tools to redirect water dripping
from a tap in an effort to water one or more
plants. You only have a limited amount of
water and time to complete the tasks.
http://www.coolmath-games.com/0-waterdrops/index.html
(or Google Search: Coolmath Water Drops)
For a hands-on visual spatial reasoning game, try Silhouettes. You use foam blocks to construct
an object based solely on the silhouettes (i.e. shadows) the mystery object casts on three surfaces.
This game was purchased for all CLOs.
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Orthographic Projections (A)
An orthographic projection is a method of representing a three-dimensional object in two
dimensions. One creates six basic views (top, bottom, right, left, front, and back views) that
together describe the original three-dimensional object.
Example 1
Suppose we took four hex-a-links (i.e. cubic building blocks) and attached them
together to form the letter “L” as shown in the accompanying diagram. We
want to create the orthographic projection for this L-shaped object.
Answer:
Front View
Back View
Right View
Left View
Top View
Bottom View
Example 2
Suppose we took six hex-a-links and attached them together to form the
following figure. Create the orthographic projection (i.e. six views) for this
object.
Answer:
Front View
Back View
Right View
Left View
Top View
Bottom View
Notice that some of the views have vertical and horizontal lines drawn across them. That is there
to indicate the certain faces/surfaces of the figure are closer or further away from you from that
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viewing position. If all of the faces/surfaces are the same distance away from your viewing
position, then there are no horizontal or vertical lines across the 2D drawing.
Questions
For each of the figures, draw the six views in the space provided. Feel free to use hex-a-links to
create a model of the figure.
1. This figure is comprised of four cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
2. This figure is comprised of five cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
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3. This figure is comprised of four cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
4. This figure is comprised of five cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
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5. This figure is comprised of five cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
6. This figure is comprised of six cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
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Orthographic Projections (B)
For each of the figures, draw the six views in the space provided. Feel free to use hex-a-links to
create a model of the figure.
1. This figure is comprised of five cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
2. This figure is comprised of five cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
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3. This figure is comprised of six cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
4. This figure is comprised of six cubes.
Front View
Back View
Right View
Left View
Top View
Bottom View
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Transfer Image to Dot Paper
In each case, transfer the image of the three dimensional figure to the dot paper. Two sample
questions are done for you so that you can see how the edges of the figure are formed by
connecting two points.
Image
Dot Paper
Image
e.g.
e.g.
1.
2.
3.
4.
5.
6.
Dot Paper
The images drawn on the dot paper are actually isometric projections. We will talk about these
in our next lesson and learn how to change an orthographic projection to an isometric projection,
and vice versa.
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Isometric Projections
In the previous section we learned about orthographic
projections; a series of drawing that showed the six perspectives
of a three dimensional object. There are other types of
projections called isometric projections or drawings. In these
projections the image of an object is presented from a skewed
direction such that more than one side of the object is viewed in
the same picture. Specifically the object's vertical lines are drawn
vertically, and the horizontal lines in the width and depth planes
are shown at 30 degrees to the horizontal.
30o
30o
Rather than using traditional drafting techniques (i.e. a 30o-60 o-90 o triangle and T-square), we
will be using isometric dot paper to accomplish the same task. Isometric dot paper is comprised
of a series of diagonal dots, that when joined can form isometric drawings.
Blank Isometric Dot Paper
Cube Drawn on Isometric Dot Paper
t
f
s
Notice that the front (f), side (s), and top (t) faces have been labeled on the cube above.
With the questions in the last section, you were supplied with isometric drawings of a figure and
then been asked to create the corresponding orthographic projections. In this section, we will be
supplied with the orthographic projections and asked to draw the corresponding isometric
diagram on the isometric dot paper. For these particular questions, we will be dealing with
simple figures where only three perspectives (front, right side, and top views) will be supplied.
Example
Front View
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Top View
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Questions
1.
Front View
Right Side
Top View
Isometric Drawing
2.
Front View
Right Side
Top View
Isometric Drawing
3.
Front View
Right Side
Top View
Isometric Drawing
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4.
Front View
Right Side
Top View
Isometric Drawing
5.
Front View
Right Side
Top View
Isometric Drawing
6.
Front View
Right Side
Top View
Isometric Drawing
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7.
Front View
Right Side
Top View
Isometric Drawing
8.
Front View
Right Side
Top View
Isometric Drawing
9.
Front View
Right Side
Top View
Isometric Drawing
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Orthographic Isometric Challenge
You need at least two learners to complete this activity and 26 cube-a-links (i.e. interlocking
cubes). Each person/team will create two challenging cube-a-links models, pass these models to
the opposing person/team, and then both people/teams will complete the isometric diagram and
orthographic projections for the models handed to them by the competition. The first model
must be comprised of only six cube-a-links, and the second of only seven cube-a-links.
Challenge #1
Isometric Diagrams for First Model Comprised of Six Cube-a-Links
Orthographic Projection for First Model Comprised of Six Cube-a-Links
Front View
Back View
Right View
Left View
Top View
Bottom View
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Challenge #2
Isometric Diagrams for First Model Comprised of Seven Cube-a-Links
Orthographic Projection for Second Model Comprised of Seven Cube-a-Links
Front View
Back View
Right View
Left View
Top View
Bottom View
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Edges, Faces and Vertices (A)
Faces: any flat surface
Edges: where two faces meet
Vertex: where edges meet
Example:
This figure has:
• 6 faces
• 12 edges
• 8 vertices
Questions:
Determine the number of faces, edges and vertices for each of these figures. Drawing on the
diagrams with colored pencils can be useful when trying to count edges and vertices (so that you
don't count the same vertex or edge more than once).
1.
2.
3.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
4.
5.
6.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
7.
8.
9.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
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Edges, Faces and Vertices (B)
Faces: any flat surface
Edges: where two faces meet
Vertex: where edges meet
Example:
This figure has:
• 8 faces
• 18 edges
• 12 vertices
Questions:
Determine the number of faces, edges and vertices for each of these figures.
1.
2.
3.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
4.
5.
6.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
7.
8.
9.
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
Number of Faces: _____
Number of Edges: _____
Number of Vertices: _____
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Construct the Geometric Figure
Learners can cut each of the following out, fold on the dotted lines, and using tape and/or glue
create the desired geometric figure. (Tabs have been included for pasting purposes.)
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Nets
The net of a solid is created by making cuts along some edges of a solid and opening it up to
form a plane figure. Based on this definition, a net can be folded up to create the original 3D
solid. On this activity sheet we want you to match the original object to its corresponding net.
Original Object
Matches
With
Net
1.
A
2.
B
3.
C
4.
D
5.
E
6.
F
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Draw the nets associated with each of these figures
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Describe the Faces
The faces of a three dimension object can be described using terms like triangles, quadrilaterals,
etc.
Triangles - three sided figures
Equilateral Triangles - all sides are of the
same length
Isosceles Triangles - two sides are of the
same length
Scalene Triangles - none of the sides are of Right Triangles - one of the interior angles
the same length
is right-angled (i.e. a 90o angle)
Quadrilaterals - four sided figures
Trapezoid - one pair of parallel sides
Parallelogram - two pair of parallel sides
Rhombus - two pair of parallel sides and
all sides are of equal length
Rectangle - two pair of parallel sides and
four right angles
Square - two pair of parallel sides, four
right angles, and all sides of equal length
Other Polygons - multi-sided figures
Pentagon - five sided figure
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Octagon - eight sided figure
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Questions:
1. Nets have been drawn for a variety of three dimensional objects. Indicate how many faces
we are dealing with, describe the faces of those objects using the appropriate terminology
(e.g. equilateral triangle, square, pentagon,…), and indicate whether some of the faces have
the same dimensions. If sides appear to be the same length, if sides appear parallel, or if
angles appear to be right angled, assume that this is the case.
e.g.
Answer:
There are a total of five faces.
• Two of the faces are identical isosceles triangles
• Two of the faces are identical rectangles.
• The last face is a rectangle.
(a)
(b)
(c)
(d)
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2. Isometric diagrams have been provided. You must identify how many faces you are dealing
with, describe those faces using the appropriate terminology, and indicate how many faces
have the same dimensions.
(a)
(b)
(c)
(d)
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(e)
(f)
(g)
(h)
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3. You will be given a figure and asked to state the number of faces, draw the individual faces
separately, include the dimensions of the faces, indicate the number of faces that have the
same dimensions, and describe those faces using the appropriate terminology term (e.g.
equilateral triangle, square, pentagon,…). Please note, if something looks like a right angle
in the diagram, just assume that it is. Similarly, if things look parallel, assume that they are.
e.g.
11 cm
11 cm
20 cm
8 cm
Answer:
Total Number of Faces: 5
Two Isosceles Triangle Faces
11 cm
Two Rectangle Faces
11 cm
11 cm
20 cm
8 cm
One Rectangle Face
8 cm
20 cm
(a) Assume that all four interior angles on the base are right angled.
6 cm
6 cm
14 cm
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(b) Assume that all four interior angles on the base are right angled.
10 cm
6 cm
8 cm
10 cm
(c) Assume that all four interior angles on the base are right angled.
24 mm
24 mm
15 mm
15 mm
(d) Assume that all four interior angles on the base are right angled.
4m
16 m
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(e)
11 cm
11 cm
7 cm
7 cm
7 cm
(f) Assume that all four interior angles on the base are right angled.
6m
4m
5m
9m
9m
(g) Assume that all four interior angles on the base are right angled.
8 cm
30 cm
8 cm
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(h). Assume that all four interior angles on the base are right angled
13 cm
13 cm
4 cm
4 cm
10 cm
10 cm
(i) Assume that all four interior angles on the base are right angled
5m
5m
2m
5m
(j)
10 cm
10 cm
6 cm
6 cm
8 cm
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(k) Assume that all four interior angles on the base are right angled. Also note that all edges
on this figure measure 2 metres.
2m
(l) Notice that the back face and front face are not the same size.
4 cm
10 cm
2 cm
4 cm
8 cm
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Geometry Terminology Crossword
1.
2.
3.
4.
5.
6.
7.
8.
9
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Across
1. a point where edges meet
4. a four sided figure
8. a type of projection used to represent a three dimensional object which shows six basic views
(top, bottom, right, left, front, and back) of the object
10. a triangle with a 90o angle
11. a triangle where two sides are of the same length
15. a triangle where the three sides are of different lengths
16. any flat surface on a three dimensional solid.
17. an eight sided figure
18. a six sided figure
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19. created when two faces meet
Down
2. a triangle where all sides are of the same length
3. a representation of a three dimensional solid created by cutting along the edges of the solid
and opening it up to form a plane figure
5. a type of projection used to represent a three dimensional object which shows the object from
a skewed direction such that more than one face is visible in the picture
6. a five sided figure
7. a four sided figure with two pair of parallel sides
9. a four sided figure with two pair of parallel sides and four sides of equal length
12. a four sided figure with only one pair of parallel sides
13. a four sided figure with two pair of parallel sides, sides of equal length, and four right angles
14. a four sided figure with two pair of parallel sides and four right angles
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Reflections (A)
Draw the reflected image on the isometric dot paper.
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Reflections (B)
Draw the reflected image on the isometric dot paper.
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Reflections (C)
Draw the reflected image on the isometric dot paper.
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Base Ten Blocks
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What's the Number?
What number is represented by each of these sets of base ten blocks?
(a)
Number: ____________
(b)
Number: ____________
(c)
Number: ____________
(d)
Number: ____________
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(e)
Number: ____________
(f)
Number: ____________
(g)
Number: ____________
(h)
Number: ____________
Scrambled Answer Key (In no particular order)
2308
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3406
2247
3080
147
524
1420
1358
4019
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Express the Number Different Ways
In each case, determine the number represented by the base ten blocks. Then write the number
in its expanded form and write the number out using words. An example has been provided.
e.g.
Number: 3257
Expanded Form: 3000 + 200 + 50 + 7
Using Words: Three thousand, two hundred fifty-seven
(a)
Number:
Expanded Form:
Using Words:
(b)
Number:
Expanded Form:
Using Words:
(c)
Number:
Expanded Form:
Using Words:
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(d)
Number:
Expanded Form:
Using Words:
(e)
Number:
Expanded Form:
Using Words:
(f)
Number:
Expanded Form:
Using Words:
(g)
Number:
Expanded Form:
Using Words:
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Express with the Fewest Number of Manipulatives
Example 1
In the example below, we have used 38 manipulatives (base ten blocks) to represent a number.
This same number can be expressed using a fewer number of manipulatives.
We can use a fewer number of manipulatives by recognizing that 10 ones tiles (unit tiles) are
equal to 1 tens tile (rod), that 10 tens tiles are equal to 1 hundreds tile (flat), and that 10 hundreds
tiles are equal to 1 thousands tile (block). We have to do some regrouping.
Above, we have regrouped things so that we have a set of 10 rods (equivalent to 1 flat) and two
groups of 10 unit tiles (each group being equivalent to a rod). Below we have replaced the 10
rods with a flat, and the 20 unit tiles with 2 rods.
The two tables below show how the number of manipulatives (base ten blocks) changed between
our original representation and our final one. We went from using 38 manipulatives (1 +13 +
24) to 11 manipulatives (2 + 5 + 4) by regrouping.
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
13
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
24
2
5
4
Both of these base ten block representations represent the same number, 254.
Questions
1. For each base ten block representation, regroup the tiles to create a new, yet equivalent,
representation that uses the fewest number of manipulatives. Draw or use Base Ten Stamps
(available from your instructor) to create this new representation. Once this is done,
complete the two tables showing how the manipulative count changed from the original
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representation to the new representation. Also identify what number is represented by the
base ten blocks.
(a) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
(b) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
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(c) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
(d) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
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(e) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
(f) Original Representation:
New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
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Example 2
In example 1, we used regrouping and base ten blocks to create our new representation and we
ended up creating the following two tables showing how the number of manipulatives changed
from one representation to another.
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
13
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
24
2
5
4
Let's consider the following question. Could we have gone directly from the first table to the
second table without ever drawing or physically handling the base ten blocks? The answer is
yes. We do it by regrouping within the first table. Below we have created the table for original
representation again but now we have also expressed the number of rods as 10 + 3, and the
number of unit tiles as 20 + 4. The 10 rods can be exchanged for 1 flat, and the 20 unit tiles for 2
rods (see arrows below).
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
13
(10 + 3)
Moves over as 1 flat
24
(20 + 4)
Moves over as 2 rods
Once this exchange (i.e. regrouping) is complete, we get the new representation.
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
(1+1)
2
(2+3)
5
4
So the number that was originally represented by 1 flat, 13 rods, and 24 unit tiles is more
efficiently represented by 2 flats (2 hundreds), 5 rods (5 tens), and 4 unit tiles (ones). The
number represented is two hundred fifty-four (254).
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Questions
2. Look at the original representation then complete the two tables of values where the second
table would correspond to the representation that uses the fewest number of manipulatives.
Also identify the number we are working with. Please note that you do not need to draw or
use base ten blocks to complete this question.
(a) Original Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
(b) Original Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
(c) Original Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
Number: ______________
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3. This question is very similar to question 2 but we have not provided a diagram of the original
representation. For this reason, we have had to complete the table for the original
representation. Your mission is to complete the second table that corresponds to the
representation that uses the fewest number of manipulatives. Also identify the number we
are working with.
(a)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
5
14
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
17
Number: ______________
(b)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
23
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
19
Number: ______________
(c)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
6
31
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
13
Number: ______________
(d)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
3
16
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
27
Number: ______________
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(e)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
15
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
38
Number: ______________
(f)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
5
24
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
25
Number: ______________
(g)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
6
22
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
34
Number: ______________
(h)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
32
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
27
Number: ______________
(i)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
3
33
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
18
Number: ______________
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Adding
1. Write out the addition problem and its answer based on the base ten blocks that have been
provided.
Example 1
Tens
Example 2
Tens
Ones
Ones
Answer:
Answer:
3 2
5 3
+ 2 5
+ 1 1
5 7
6 4
(a)
(b)
Tens
Ones
Tens
Ones
Answer:
Answer:
(c)
(d)
Tens
Ones
Tens
Answer:
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(e)
(f)
Tens
Ones
Tens
Answer:
(g)
Hundreds
Tens
Ones
Answer:
Ones
Answer:
(h)
Hundreds
Tens
Ones
Answer:
Look back at your answers. Do you see a pattern? Hopefully you recognize that you align the
numbers so that you can add the ones, the tens, and the hundreds. By doing so, you end up with
the answer. Please note that we only presented addition problems that do not require regrouping;
that is, that the totals for the ones, tens, or hundreds digits was never greater than 9. We will
learn how to handle questions that involve regrouping in the next section.
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2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial
representation of these addition problems. Also complete the addition problem.
(a)
Tens
Ones
Tens
Ones
Tens
Ones
3 1
+ 5 4
(b)
(c)
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+ 6 6
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Hundreds
(d)
Tens
Ones
1 2 6
+ 1 3 3
3. Complete the following addition problems. You do not have to use the base ten blocks.
(a)
1 3
+ 7 2
(b)
4 2
+ 3 6
(c)
(d)
4 3
+ 4 5
(e)
5 6
+ 3 3
(f)
2 9
+ 2 0
(g)
1 3 4
+ 1 5 2
(h)
2 1 6
+ 1 4 2
(i)
1 2 8
+ 3 7 1
(j)
2 8 1
+ 5 0 3
(k)
7 4 0
+ 2 4 3
(l)
4 2 1
+ 3 2 5
(m)
1 3 2 1
+ 1 4 6 5
(n)
1 4 3 1
+ 2 0 6 8
(o)
3 1 5 4
+ 2 0 1 4
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Adding with Regrouping
On the previous activity sheet, we learned how to add multi-digit numbers with and without base
ten blocks. All of the questions in the previously activity were special in that none of them
required one to do regrouping. Regrouping occurs when totals for a place value (ones, tens, or
hundreds digits) is greater than 9.
Example 1:
Original Question:
3 5
+ 2 7
The problem is that when
we look at the base ten
blocks we have 12 ones
Tens
Ones
Next Step:
Break the 12 ones into
two groups. One group
will be made up of 10
ones, and the other will
be made up of 2 ones.
Tens
Ones
Final Step:
Exchange the 10 ones for
a rod (which is equal to
10 ones)
1
3 5
+ 2 7
6 2
Tens
Ones
Questions
1. Provide a written description for each step providing the original question and the final
answer for each three step process involving the base ten blocks.
(a)
Tens
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Ones
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Step 1 (Original Question)
Step 2 (Next Step)
Step 3 (Final Step)
(b)
Tens
Ones
Next Step:
Tens
Ones
Final Step:
Tens
Ones
Step 1 (Original Question)
Step 2 (Next Step)
Step 3 (Final Step)
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(c)
Tens
Ones
Next Step:
Tens
Ones
Final Step:
Tens
Ones
Step 1 (Original Question)
Step 2 (Next Step)
Step 3 (Final Step)
2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial
representation of these addition problems. Please combine steps one and two (i.e. Original
Question and Next Step which involves grouping). Also complete the addition problem.
Steps 1 and 2
Tens
(a)
Ones
Step 3
Tens
Ones
3 6
+ 2 9
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Steps 1 and 2
Tens
(b)
Ones
Step 3
Tens
Ones
Ones
Step 3
Tens
Ones
2 5
+ 1 8
Steps 1 and 2
Tens
(c)
3 9
+ 4 7
Example 2:
Now let's drop the base ten blocks, and see if we can come up with a rule for adding two digit
numbers where regrouping is required. We go back to our original example 35 + 27.
We start by stacking the numbers such that the ones digits line up and the tens digits line up.
3 5
+ 2 7
Now we only look at the ones digits, the 5 and 7. We know that when these digits are added, we
get 12, where the tens digit is 1, and the ones digit is 2. That tens digit (1) will be added to the
tens digits in our original question (We are regrouping here.), and the ones digit (2) will be go in
the ones spot. All we left to do is add the tens. Our final answer is 62.
1
5
7
3 5
+ 2 7
1 2
6 2
+
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In the last, we showed the ones digits being added separately and then fitted back into the
original question. Typically this addition with the ones digits is done in your head.
Example 3:
Work out 65 + 25
Answer:
1
6 5
+ 2 5
9 0
In your head you add the 5 and 5. This gives you 10. The tens
digit of 1 is regrouped so that it goes with the other tens digits
(6 and 2). The ones digit of 0 stays in the ones spot. All we
have left to do is add the tens. Our final answer is 90.
Example 4:
Work out 39 + 48
Answer:
1
3 9
+ 4 8
8 7
In your head you add the 9 and 8. This gives you 17. The tens
digit of 1 is regrouped so that it goes with the other tens digits
(3 and 4). The ones digit of 7 stays in the ones spot. All we
have left to do is add the tens. Our final answer is 87.
Example 5:
Work out 73 + 52
Answer:
1
5 2
7 3
+
1 2 5
In your head you add the 3 and 2. This gives you 5, therefore
no regrouping needs to be done here. The tens digit of 5 is
then added to the tens digit of 7. This gives us 12. The 1 will
become a hundreds digit (regrouping) and the 2 will remain a
tens digit. Our final answer is 125.
If you were to think of this in terms of base ten blocks, it would look like this.
Steps 1 and 2
Tens
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Step 3
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166
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Ones
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Questions:
3. Add the following. All of these require some regrouping.
(a)
(b)
3 7
4 6
+ 1 5
(d)
(c)
+ 2 3
(e)
5 6
+ 2 8
(g)
4 9
+ 4 7
(f)
2 8
+ 2 5
(h)
6 2
+ 7 5
(i)
7 7
3 6
9 5
+ 1 5
+ 4 4
+ 3 1
4. Add the following. Not all of these require regrouping.
(a)
(b)
6 2
+ 8 3
(d)
7 7
3 2
+ 1 9
+ 2 4
(e)
1 5
+ 3 6
(g)
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(c)
(f)
3 5
+ 5 5
(h)
4 6
+ 2 7
(i)
6 3
3 4
+ 4 5
+ 6 1
167
7 8
+ 8 5
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Subtracting
1. Write out the subtraction problem and its answer based on the base ten blocks that have been
provided.
Example:
Tens
Ones
Answer:
6 4
− 2 1
4 3
Tens
Ones
(a)
Answer:
Tens
Ones
(b)
Answer:
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Tens
Ones
(c)
Answer:
Tens
Ones
(d)
Answer:
Tens
Ones
(e)
Answer:
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Hundreds
Tens
Ones
(f)
Answer:
Hundreds
Tens
Ones
(g)
Answer:
2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial
representation of these addition problems. Also complete the addition problem.
Tens
(a)
Ones
7 4
− 5 2
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Tens
(b)
(c)
Ones
8 6
− 3 6
Hundreds
Tens
Ones
Hundreds
Tens
Ones
2 7 9
− 1 2 6
(d)
2 5 8
−
4 3
Look back at your answers to questions 1 and 2. Do you see a pattern? Hopefully you recognize
that you align the numbers so that you can subtract the ones, the tens, and the hundreds
separately. By doing so, you end up with the answer. Please note that we only presented
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subtraction problems that do not require regrouping; that is, that the digit that that is taken away
from the corresponding digit is always smaller or equal to the corresponding digit. We will learn
how to handle questions that involve regrouping in the next section.
3. Complete the following subtraction problems. You do not have to use the base ten blocks.
(a)
7 6
(b)
− 2 3
(d)
9 3
(c)
− 8 1
5 8
− 3 2
8 6
− 3 6
(e)
(g)
6 7
− 1 5
(h)
2 6
− 2 4
(i)
4 7
− 3 7
(j)
2 5 4
− 1 1 2
(k)
5 7 6
− 3 4 1
(l)
6 7 8
− 5 2 1
(m)
9 8 3
− 5 0 1
(n)
7 4 3
− 2 4 0
(o)
8 9 4
− 8 3 2
(p)
3 8 7 5
− 1 4 6 0
(q)
7 4 4 8
− 2 0 1 6
(r)
6 8 9 0
− 4 8 2 0
(s)
7 9 8 5
3 6 5
−
(t)
8 6 4 9
− 7 6 0 6
(u)
5 7 8 1
−
4 2 0
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9 8
(f)
− 2 7
172
7 9
− 5 0
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Subtracting with Regrouping
Sometimes when we are doing a subtraction question using base ten blocks, we are unable to
take away the necessary blocks. Such is the case with the question below, 65 - 39. The problem
is that we have to take away 9 one blocks, but there are only 5 one blocks present.
Tens
Ones
6 5
− 3 9
We get around this is by regrouping. In this case we exchange 1 ten block for 10 one blocks.
Tens
Ones
−
5
15
6
3
5
9
Now the subtraction can be completed. (See below.) The final answer is 26.
Tens
Ones
−
5
15
6
3
5
9
2 6
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Let's try another question where regrouping is required. Such is the case with 218 - 147. We
don't have enough ten blocks. We only have 1 ten block but we need to remove 4 ten blocks.
Hundreds
Tens
Ones
2 1 8
− 1 4 7
We will regroup. In this case we exchange 1 hundred block for 10 ten blocks.
Hundreds
Tens
Ones
1
−
11
2
1 8
1
4 7
Now the subtraction can be done. (See below.) The final answer is 71.
Hundreds
Tens
Ones
1
−
2
1
11
1 8
4 7
7 1
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Questions
1. With each of the following questions, regrouping will have to be done. A second chart has
been provided where you can draw in the blocks after the regrouping has taken place, and
then complete the subtraction by crossing out the appropriate blocks. (Do not spend a lot of
time drawing the blocks; very rough sketches will do.) Make sure that you also supply the
final answer.
Tens
Ones
(a)
8 6
− 3 8
Tens
Ones
8 6
− 3 8
Tens
Ones
(b)
7 4
− 5 7
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Tens
Ones
7 4
− 5 7
Tens
Ones
(c)
9 2
− 6 8
Tens
Ones
9 2
− 6 8
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Hundreds
Tens
Ones
(d)
2 3 6
− 1 5 2
Hundreds
Tens
Ones
2 3 6
− 1 5 2
Hundreds
Tens
Ones
(e).
2 4 7
−
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Hundreds
Tens
Ones
2 4 7
−
Hundreds
Tens
8 1
Ones
(f).
2 8 4
− 2 3 5
Hundreds
Tens
Ones
2 8 4
− 2 3 5
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2. The following questions are partially completed. Although we are not using base ten blocks,
we can see that the regrouping was required. Complete each of the questions.
(a)
(d)
−
−
7
14
8
2
4
9
7
12
8
2
2
5
(b)
6
3
(e)
−
−
8
11
9
7
1
6
3
15
4
2
5
6
(c)
6
6
(f)
−
5
13
6
3
3
8
7
− 5
8
16
9
6
6
9
3. Complete the following questions. Please note that some questions involve regrouping,
while others do not.
(a)
6 6
− 1 8
(b)
5 1
− 3 7
(c)
7 8
− 4 3
(d)
9 4
− 6 8
(e)
6 7
− 2 3
(f)
7 2 9
− 3 6 1
(g)
5 6 9
− 3 9 0
(h)
4 9 6
− 2 6 5
(i)
6 8 3
− 6 5 8
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Answers
How Much Do They Have? (A) (page 2)
Anne’s Money: 50¢ or $0.50
Jake’s Money: 90¢ or $0.90
Ryan’s Money: $3.80
Yoshi’s Money: $4.65
Meera’s Money: $2.45
How Much Do They Have? (B) (page 3)
Dave’s Money: 95¢ or $0.95
Shelly’s Money: 65¢ or $0.65
Jun’s Money: $4.30
Lei’s Money: $5.50
Maurita’s Money: $1.80
How Much Do They Have? (C) (page 4)
Andrew’s Cash: $70
Mary’s Cash: $45
Montez’s Cash: $120
Shima’s Cash: $140
Kara’s Cash: $50
How Much Do They Have? (D) (page 5)
Hamid’s Cash: $55
Tanya’s Cash: $40
Mark’s Cash: $135
Hatsu’s Cash: $175
Samir’s Cash: $80
How Much Do They Have? (E) (page 6)
Sasha’s Money: $8.25
Hinto’s Money: $11.70
Tiva’s Money: $7.40
Meera’s Money: $53.30
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Lisa’s Money: $24.20
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Emptying the Junk Drawer (pages 7 and 8)
Bills or Change
Number of Each
Value in Dollars
$20 bills
1
20
$10 Bills
1
10
$5 Bills
3
15
Toonies ($2 coins)
4
8
Loonies ($1 coins)
3
3
Quarters (25¢ coins)
7
1.75
Dimes (10¢ coins)
10
1.00
Nickels (5¢ coins)
12
0.60
Total:
59.35
If you found three more nickels, five more quarters, and four more loonies, how much would you
have in total? Answer: $64.75
Least to Most Expensive (page 12)
1.
Two Slice Toaster
Litre of Milk
Refrigerator
Electric Fry Pan
2
1
4
3
Silver Earrings
Leather Jacket
Pair of Socks
Pencil
3
4
2
1
Power Drill
Winter Gloves
Fingernail Clippers
Mattress (Queen)
3
2
1
4
Hardcover Book
Birthday Card
Prescription Glasses
Pair of Winter Boots
2
1
4
3
Coffee Table
Kitchen Stove
Can Opener
Electric Kettle
3
4
1
2
Four Winter Tires
20 inch Television
DVD Player
Four Litres of Oil
4
3
2
1
2.
3.
4.
5.
6.
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7.
Small Flashlight
Delivery Pizza
Reclining Chair
Table Lamp
1
2
4
3
Hair Dryer
Coffee Mug
Chocolate Bar
Toaster Oven
3
2
1
4
Paperback Novel
Big Concert Ticket
Spring Jacket
Bus Toll
2
4
3
1
Love Seat
Dish Soap
10 kg Turkey
Four Litres of Milk
4
1
3
2
8.
9.
10.
What Are the Three Items Worth? (page 13)
1.
3.
5.
Item:
Hammer
Florescent Light Bulb
Can of Pop
Price
$10
$3
$1
Item:
Sofa
A Pair of Sunglasses
Microwave Oven
Price
$600
$20
$150
Item:
A Man's Haircut
Loaf of Bread
An Adult Bicycle
Price
$25
$2
$250
2.
4.
6.
Item:
Box of Cereal
A Pair of Jeans
T-shirt
Price
$6
$50
$12
Item:
Fast-food Hamburger
A Pair of Work Boots
Knapsack for School
Price
$3
$90
$40
Item:
Tube of Toothpaste
Small Waste Paper Basket
Winter Coat
Price
$3
$15
$120
What Is It Worth? (A) (page 14)
Item
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Ride-on Lawn Mower
DVD/Blu-ray Player
Toaster
HD Video Camera
Compact Car
42 inch Flat Screen TV
Tank of Gas (Compact
Car)
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Approximate
Price (Number)
$2149
$99
$17
$329
$14 900
$549
$50
182
Approximate Price
(Words)
Two thousand, one hundred forty-nine
Ninety-nine
Seventeen
Three hundred twenty-nine
Fourteen thousand, nine hundred
Five hundred forty-nine
Fifty
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What Is It Worth? (B) (page 15)
Item
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Washing Machine
Hair Dryer
Minivan
Fast Food Meal for One
Gasoline Push Mower
Child's Bicycle
Four Person Hot Tub
Approximate
Price (Number)
$469
$21
$22 900
$8
$239
$69
$3599
Approximate Price
(Words)
Four hundred sixty-nine
Twenty-one
Twenty-two thousand, nine hundred
Eight
Two hundred thirty-nine
Sixty-nine
Three thousand, five hundred ninetynine
Paying With Cash (pages 16 to 19)
1. (a) Using the fewest number of bills and coins, make $3.65.
- you need zero $5 bill(s)
- you need one $2 coin(s)
- you need one $1 coin(s)
- you need two 25¢ coin(s)
- you need one 10¢ coin(s)
- you need one 5¢ coin(s)
(b) Using the fewest number of bills and coins, make $7.95.
- you need one $5 bill(s)
- you need one $2 coin(s)
- you need zero $1 coin(s)
- you need three 25¢ coin(s)
- you need two 10¢ coin(s)
- you need zero 5¢ coin(s)
$2.00
$1.00
$0.50
$0.10
$0.05
$3.65
$5.00
$2.00
$0.75
$0.20
$7.95
(c) Using the fewest number of bills and coins, make $13.30.
- you need one $10 bill(s)
- you need zero $5 bill(s)
- you need one $2 coin(s)
- you need one $1 coin(s)
- you need one 25¢ coin(s)
- you need zero 10¢ coin(s)
- you need one 5¢ coin(s)
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$10.00
$2.00
$1.00
$0.25
$0.05
$13.30
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(d) Using the fewest number of bills and coins, make $16.40.
- you need one $10 bill(s)
- you need one $5 bill(s)
- you need zero $2 coin(s)
- you need one $1 coin(s)
- you need one 25¢ coin(s)
- you need one 10¢ coin(s)
- you need one 5¢ coin(s)
2. (a) Using the fewest number of bills and coins, make $4.85.
- you need zero $10 bills
- you need zero $5 bills
- you need two $2 coins
- you need zero $1 coins
- you need three 25¢ coins
- you need one 10¢ coin
- you need zero 5¢ coins
$10.00
$5.00
$1.00
$0.25
$0.10
$0.05
$16.40
$4.00
$0.75
$0.10
$4.85
(b) Using the fewest number of bills and coins, make $11.70.
- you need one $10 bill
- you need zero $5 bills
- you need zero $2 coins
- you need one $1 coin
- you need two 25¢ coins
- you need two 10¢ coins
- you need zero 5¢ coins
$10.00
$1.00
$0.50
$0.20
$11.70
(c) Using the fewest number of bills and coins, make $19.80.
- you need one $10 bill
- you need one $5 bill
- you need two $2 coins
- you need zero $1 coins
- you need three 25¢ coins
- you need zero 10¢ coins
- you need one 5¢ coin
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$10.00
$5.00
$4.00
$0.75
$0.05
$19.80
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3. (a) Using the fewest number of bills and coins, make $8.20.
- you need zero $10 bill(s)
- you need one $5 bill(s)
- you need one $2 coin(s)
- you need one $1 coin(s)
- you need zero 25¢ coin(s)
- you need two 10¢ coin(s)
- you need zero 5¢ coin(s)
$5.00
$2.00
$1.00
$0.20
$8.20
(b) Using the fewest number of bills and coins, make $12.45.
- you need one $10 bill(s)
- you need zero $5 bill(s)
- you need one $2 coin(s)
- you need zero $1 coin(s)
- you need one 25¢ coin(s)
- you need two 10¢ coin(s)
- you need zero 5¢ coin(s)
$10.00
$2.00
$0.25
$0.20
$12.45
(c) Using the fewest number of bills and coins, make $13.95.
- you need one $10 bill(s)
- you need zero $5 bill(s)
- you need one $2 coin(s)
- you need one $1 coin(s)
- you need three 25¢ coin(s)
- you need two 10¢ coin(s)
- you need zero 5¢ coin(s)
$10.00
$2.00
$1.00
$0.75
$0.20
$13.95
4. (a) $3.15 one $2 coin, one $1 coin, one 10¢ coin, and one 5¢ coin
(b) $6.75 one $5 bill, one $1 coin, and three 25¢ coins
(c) $12.55 one $10 bill, one $2 coin, two 25¢ coins, and one 5¢ coin
(d) $18.85 one $10 bill, one $5 bill, one $2 coin, one $1 coin, three 25¢ coins and one 10¢
coin
Cash Purchases (page 20)
1.
Toaster
$15.49 (before tax)
$17.81 (after tax)
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How much cash do you have?
$19
Is it enough?
Yes
If so, how much change will you receive?
$1.29
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2.
3.
4.
5.
Blu-Ray Movie
$22.99 (before tax)
$26.44 (after tax)
Alarm Clock
$27.99 (before tax)
$32.18 (after tax)
Blouse
$47.95 (before tax)
$55.14 (after tax)
Video Game
$61.99 (before tax)
$71.29 (after tax)
How much cash do you have?
$26
Is it enough?
No
If so, how much change will you receive?
N.A.
How much cash do you have?
$33
Is it enough?
Yes
If so, how much change will you receive?
$0.82
How much cash do you have?
$57
Is it enough?
Yes
If so, how much change will you receive?
$1.86
How much cash do you have?
$72
Is it enough?
Yes
If so, how much change will you receive?
$0.71
Unit Price (pages 23 to 26)
1. (a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
0.388¢ per gram or $0.00388 per gram
0.314¢ per gram or $0.00314 per gram
$1.53 per litre
0.763¢ per gram or $0.00763 per gram
53.6¢ per container or $0.536 per container
$12.85 per kilogram
$0.345 per metre or 34.5¢ per metre
$69 per cubic metre
$0.224 per pencil or 22.4¢ per pencil
2. Which one of these products is the best buy based solely on the unit price?
• 475 millilitres of Brand A salad dressing; Unit Price: 1.11¢ per millilitre
• 700 millilitres of Brand B salad dressing; Unit Price: 0.93¢ per millilitre ← Best Buy
• 350 millilitres of Brand C salad dressing; Unit Price: 1.08¢ per millilitre
3. Which one of these is the best buy based solely on the unit price
• 250 grams of Brand A margarine; Unit Price: 0.92¢ per gram
• 500 grams of Brand B margarine; Unit Price: 0.90¢ per gram
• 1 kilogram of Brand A margarine; Unit Price: 0.66¢ per gram ← Best Buy
• 2 kilograms of Brand B margarine; Unit Price: 0.69¢ per gram
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4. (a) 180 gram bag of popular brand; Unit Price: 1.3¢ per gram
245 gram bag of popular brand; Unit Price: 1.1¢ per gram
245 gram bag of no-name brand; Unit Price: 1.0¢ per gram
(b) 245 gram bag of no-name brand
(c) 245 gram bag of popular brand
5. (a) $9.23
(b) $9.53
(c) $37.84
6. (a) Pickseed Town & Country Grass Seed (10 kg bag) with a unit price of $8.70 per
kilogram
(b) Pickseed Shade Grass Seed (1 kg bag) with a unit price of $9.99 per kilogram
Which Measurement Is Reasonable? (page 33)
1. The length of an adult's arm: (a) 65 centimetres
2. The length of three city blocks: (d) 1 kilometre
3. The amount of lemonade that could be held in a pitcher: (c) 2 litres
4. The weight of a ten year old boy: (b) 34 kilograms
5. The amount of water in a drinking glass: (c) 350 millilitres
6. The height of a three-story apartment building: (a) 12 metres
7. The weight of a compact car: (b) 1800 kilograms
8. The length of a man's fingernail on his pinkie finger: (d) 1 centimetre
9. The distance from Halifax, Nova Scotia to Truro, Nova Scotia: (d) 100 kilometres
10. The amount of gasoline that can be held in a compact car's gas tank: (c) 40 litres
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What's the Appropriate Temperature? (page 34)
1
Body Temperature of a Human
2.
Boiling Temperature of Water
3.
A Hot Summer's Day in Nova Scotia
4.
5.
Temperature at the North Pole in the
Middle of Winter
Freezing Temperature of Water
6.
Temperature of Molten Iron
7.
A Comfortable Room Temperature
8.
A Cold Winter's Day in Nova Scotia
9.
The Serving Temperature of a Cup of
Coffee
3.
28oC or 84oC
6.
1200oC or 2192oF
8.
-20oC or -4oF
9.
70oC or 158oF
2.
100oC or 212oF
4.
-40oC or -40oF
5.
0oC or 32oF
7.
20oC or 68oF
1.
37oC or 98oC
Measurement; Insert the Appropriate Number (page 35)
1. The distance between Halifax and Sydney is 425 km. It takes approximately 5 hours to
travel this distance and you would likely use 30 L of gasoline to complete this trip by car.
2. The 2 L container weighs 2300 g when it is full of orange juice. John, who is thirty years old
and weighs 85 kg, usually drinks a container of OJ each week.
3. The cupcake recipe requires 750 mL of flour. It also states that the oven must be at a
temperature of 180 oC, and that the cupcakes must be baked for 15 minutes.
4. A 5 kg stuffed turkey takes 420 minutes to cook in the oven, assuming that the oven is set at
165 oC.
5. Nashi is running a 10 km road race. She expects that it will take her 50 minutes and that she
will drink 500 mL of fluid during the race.
6. The college basketball player is approximately 2 metres tall and weighs 93 kg. He usually
plays much of the 40 minute game.
7. The baseball bat that Jun uses is 95 centimeter(s) long and weighs 1 kilogram(s). The nine
inning baseball games that Jun plays typically lasts for 3 hour(s).
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8. Cathy's dishwasher heats the water up to 55 oC; hot enough to kill any bacteria. The
dishwasher is 88 centimetres tall and weighs 38 kilograms.
9. Kadeer likes to use 10 grams of ground coffee to make 150 millilitres of coffee. He also
likes the coffee to be served at 70 oC.
10. The average adult giraffe is 5 metres tall and weighs 1100 kilograms. The body temperature
should be approximately 41 oC.
Metric Measures for Length (pages 36 to 40)
1. (a) 2.8 cm
(c) 3.7 cm
(e) 3.2 cm
(b) 6.5 cm
(d) 5.9 cm
(f) 1.1 cm
2. (a) 71 mm
(c) 37 mm
(e) 59 mm
(b) 24 mm
(d) 63 mm
(f) 6 mm
3. (a) length = 64 mm or 6.4 cm
(b) length = 53 mm or 5.3 cm
width = 15 mm or 1.5 cm
width = 21 mm or 2.1 cm
4. (a) 72 mm or 7.2 cm
(b) 101 mm or 10.1 cm
6. (a)
(c)
(e)
(g)
metres
millimetres
metres
centimetres
(b)
(d)
(f)
(h)
centimetres
kilometres
kilometres
millimetres
7. (a)
(c)
(e)
(g)
98 mm
2100 mm
9 mm
450 cm
(b)
(d)
(f)
(h)
14.5 cm
1.3 cm
12.29 cm
630 mm
8. (a) 4 km
(c) 7 km
(e) 500 m
(b) 60 cm
(d) 12 m
(f) 49 km
Converting Metric Measures for Length (pages 41 to 43)
1. (a) To convert 80 metres (m) to centimetres (cm), we move down two step(s) on the diagram.
That means we need to multiply the 80 by 10 two time(s). Therefore, 80 metres is equal
to 8000 centimetres.
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(b) To convert 5600 millimetres (mm) to metres (m), we move up three step(s) on the
diagram. That means we need to divide the 5600 by 10 three time(s). Therefore, 5600
millmetres is equal to 5.6 metres.
(c) To convert 70 kilometres (km) to metres (m), we move down three step(s) on the
diagram. That means we need to multiply the 70 by 10 three time(s). Therefore, 70
kilometres is equal to 70 000 metres.
(d) To convert 320 centimetres (cm) to decimetres (dm), we move up one step(s) on the
diagram. That means we need to divide the 320 by 10 one time(s). Therefore, 320
centimetres is equal to 32 decimetres.
(e) To convert 93 kilometres (km) to hectometres (hm), we move down one step(s) on the
diagram. That means we need to multiply the 93 by 10 one time(s). Therefore, 93
kilometres is equal to 930 hectometres.
2. (a)
(c)
(e)
(g)
(i)
320 cm = 3200 mm
72 000 m = 72 km
4 km = 4000 m
140 cm = 14 dm
70 hm = 7000 m
3. (a) 2 m
(c) 7 m
(e) 6 km
(g) 1 km
(b)
(d)
(f)
(h)
(j)
800 mm = 80 cm
83 m = 8300 cm
320 cm = 3.2 m
29 dm = 2900 mm
60 000 dm = 60 hm
(b)
(d)
(f)
(h)
5000 m
150 cm
800 cm
500 mm
Metric Measures for Liquid Capacity and Weight (pages 44 to 47)
1.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
NSSAL
©2012
Situation
the length of a coil of rope
the weight of a gorilla
the amount of milk that can be poured into a coffee cup
the distance between Halifax and Amherst
the amount of salt in a serving of potato chips
the width of a small river
the amount of oil that can be pumped into a home heating oil tank
the thickness of a pane of glass
the weight of a chocolate bar
the dimensions of a building
the weight of a small boulder
the amount of water in a bathtub
the distance covered on a two day bike trip
length of your foot
the amount of cooking oil added to a recipe
the amount of fat in a cookie
190
Unit
m
kg
mL
km
g
m
L
mm
g
m
kg
L
km
cm
mL
g
Draft
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(q)
(r)
(s)
(t)
(u)
(v)
3. (a)
(c)
(e)
(g)
(i)
(k)
the dimensions of a postage stamp
the amount of weight a pair of snowshoes can support
the amount of fuel a jet airplane burns in an hour
the height of a flagpole
the amount of water needed to fill a bottle cap
the length of a hockey stick
8.2 kilograms
7800 millilitres
27 000 millilitres
12 900 grams
64 900 millilitres
0.75 litres
(b)
(d)
(f)
(h)
(j)
(l)
mm
kg
L
m
mL
cm
86 litres
123 000 grams
0.98 kilograms
1.2 litres
300 grams
18.5 kilograms
Perimeter and Area (pages 48 and 49)
1. Perimeter = 6 cm, Area = 2 cm2
2. Perimeter = 10 cm, Area = 4 cm2
3. Perimeter = 10 cm, Area = 6 cm2
4. Perimeter = 10 cm, Area = 5 cm2
5. Perimeter = 14 cm, Area = 6 cm2
6. Perimeter = 16 cm, Area = 8 cm2
7. Perimeter = 12 cm, Area = 8 cm2
8. Perimeter = 14 cm, Area = 8 cm2
9. Perimeter = 16 cm, Area = 7 cm2
10. Perimeter = 18 cm, Area = 9 cm2
11. Perimeter = 18 cm, Area = 8 cm2
12. Perimeter = 18 cm, Area = 11 cm2
True or False (a) False
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(b) False
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Approximately How Much Time Will It Take? (page 50)
1. 3 to 6 months
2. 10 to 25 minutes
3. About 1 hour
4. 7 to 14 days
5. 15 to 20 minutes
6. 2 to 3 seconds
7. 1 hour
8. 1.5 to 2 hours
9. 2 weeks
10. 3 months
11. 35 to 40 hours
12. 3 to 4 minutes
13. 13 to 20 seconds
14. 30 to 40 minutes
Telling Time (A) (page 51)
(a) 4:50
(d) 7:25
(g) 3:35
(b) 11:00
(e) 1:15
(h) 12:05
(c) 2:00
(f) 9:55
(i) 6:05
(b) 2:15
(e) 11:05
(h) 5:10
(c) 10:10
(f) 3:45
(i) 12:15
(b) 1:30
(e) 3:50
(h) 10:20
(c) 9:00
(f) 12:20
(i) 7:55
(b) 12:35
(e) 11:25
(h) 8:10
(c) 9:15
(f) 5:45
(i) 6:40
Telling Time (B) (page 52)
(a) 7:40
(d) 1:20
(g) 8:50
Telling Time (C) (page 53)
(a) 5:20
(d) 11:15
(g) 2:25
Telling Time (D) (page 54)
(a) 4:10
(d) 2:40
(g) 10:30
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Telling Time (E) (page 55)
(a) 5:50
(d) 4:15
(g) 2:50
(b) 6:20
(e) 6:30
(h) 10:40
(c) 1:45
(f) 9:10
(i) 8:15
(b) 10:45
(e) 5:55
(h) 7:15
(c) 4:30
(f) 12:50
(i) 1:55
Telling Time (F) (page 56)
(a) 3:10
(d) 8:25
(g) 9:35
How Much Time Hass Passed? (A) (pages 59 and 60)
(a) Start Time: 6:20
Finish Time: 6:30
Time Passed: 0 hour(s), 10 minutes
(b) Start Time: 2:00
Finish Time: 2:40
Time Passed: 0 hour(s), 40 minutes
(c) Start Time: 4:15
Finish Time: 4:30
Time Passed: 0 hour(s), 15 minutes
(d) Start Time: 9:10
Finish Time: 10:10
Time Passed: 1 hour(s), 0 minutes
(e) Start Time: 11:00
Finish Time: 12:15
Time Passed: 1 hour(s), 15 minutes
(f) Start Time: 2:00
Finish Time: 3:45
Time Passed: 1 hour(s), 45 minutes
(g) Start Time: 4:15
Finish Time: 5:45
Time Passed: 1 hour(s), 30 minutes
(h) Start Time: 10:30
Finish Time: 12:15
Time Passed: 1 hour(s), 45 minutes
How Much Time Hass Passed? (B) (pages 61 and 62)
(a) Start Time: 11:05
Finish Time: 11:40
Time Passed: 0 hour(s), 35 minutes
(b) Start Time: 9:35
Finish Time: 10:40
Time Passed: 1 hour(s), 5 minutes
(c) Start Time: 6:50
Finish Time: 9:10
Time Passed: 2 hour(s), 10 minutes
(d) Start Time: 5:20
Finish Time: 7:40
Time Passed: 2 hour(s), 20 minutes
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(e) Start Time: 1:45
Finish Time: 4:10
Time Passed: 2 hour(s), 45 minutes
(f) Start Time: 6:40
Finish Time: 8:25
Time Passed: 1 hour(s), 45 minutes
(g) Start Time: 11:00
Finish Time: 1:30
Time Passed: 2 hour(s), 30 minutes
(h) Start Time: 11:15
Finish Time: 2:40
Time Passed: 3 hour(s), 25 minutes
How Much Time Hass Passed? (C) (pages 63 and 64)
(a) Start Time: 3:10
Finish Time: 3:50
Time Passed: 0 hour(s), 40 minutes
(b) Start Time: 5:45
Finish Time: 8:15
Time Passed: 2 hour(s), 30 minutes
(c) Start Time: 4:15
Finish Time: 6:50
Time Passed: 2 hour(s), 35 minutes
(d) Start Time: 12:20
Finish Time: 4:15
Time Passed: 3 hour(s), 55 minutes
(e) Start Time: 11:40
Finish Time: 12:50
Time Passed: 1 hour(s), 10 minutes
(f) Start Time: 10:30
Finish Time: 1:15
Time Passed: 2 hour(s), 45 minutes
(g) Start Time: 10:45
Finish Time: 2:50
Time Passed: 4 hour(s), 5 minutes
(h) Start Time: 9:15
Finish Time: 12:35
Time Passed: 3 hour(s), 20 minutes
What is the likelihood that the outdoor temperature in Nova Scotia will
be cold enough to freeze water on March 1?
What is the likelihood that you or a family member will
get in an accident today?
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Certain

What is the likelihood that a metal bolt will sink when
dropped into water.
What is the likelihood that one of the learners in an adult education
class will be 15 years old?
Possible and
Likely
Possible but
Unlikely
Impossible
Likelihood; Part 1 (pages 66 and 67)



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C. D. Pilmer

What is the likelihood that you will be struck by lightning
within your lifetime?

What is the likelihood that you will experience at least one high tide in
the Bay of Fundy within a 24 hour period?

What is the likelihood that at least a three children will be absent from
the local elementary school on Monday?
What is the likelihood that a Nova Scotia campground will
be fully occupied in December?
Certain
Possible and
Likely
Possible but
Unlikely
Impossible
What is the likelihood that an office administrator at a major
landscaping company would receive at least twenty calls a day?


What is the likelihood that the sun will rise tomorrow?

What is the likelihood of obtaining a 2 with a single roll of the die?


What is the likelihood of obtaining a number less than 5 with a single
roll of the die?

What is the likelihood of randomly selecting a blue marble on a single
draw from the marble bag?

What is the likelihood of obtaining the letter "A" on a single spin of
the spinner?

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Certain

What is the likelihood of randomly selecting a green marble on a
single draw from the marble bag?
What is the likelihood of obtaining the letter "D" on a single spin of
the spinner?
Possible and
Likely
Possible but
Unlikely
Impossible
Likelihood; Part 2 (pages 68 and 69)
Draft
C. D. Pilmer
What is the likelihood of obtaining a 7 with a single roll of the die?


What is the likelihood of obtaining the letter "A" or letter "C" on a
single spin of the spinner?

What is the likelihood of obtaining a 6 with a single roll of the die?
What is the likelihood of randomly selecting a purple marble on a
single draw from the marble bag?


What is the likelihood of obtaining the letter "A", "B" or "C" on a
single spin of the spinner?

What is the likelihood of obtaining an even number with a single roll
of the die?
What is the likelihood of obtaining a 1 and a 2 with a single roll of the
die?
What is the likelihood of randomly selecting an orange or green
marble on a single draw from the marble bag?
What is the likelihood of obtaining the number 1 or greater with a
single roll of the die?
Certain
Possible and
Likely
Possible but
Unlikely
Impossible
What is the likelihood of randomly selecting an orange, green or blue
marble on a single draw from the marble bag?




Likelihood; Part 3 (page 70)
Answers will vary.
1. Blue Marbles: largest number (possibly 13 to 17 marbles)
Yellow Marbles: next largest number (possibly 3 or 4 marbles)
Green Marbles: next largest (possibly 1 to 3 marbles)
Red Marbles: 0 marbles
2. Letter "E" Section: largest section (45% to 55%)
Letter "D" Section; next largest section (35% to 40%)
Letter "A" and "C" Sections: smallest and equal (5% to 10% each)
Letter "B" Section: none
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Is It What You Expect? (pages 71 and 72)
Predictions:
Certain

Likelihood of obtaining a 4 with a single roll of the die


Likelihood of obtaining a 3 or more with a single roll of the die.
Likelihood of obtaining an odd number with a single roll of the die
Likelihood of obtaining a 9 with a single roll of the die.
Possible and
Likely
Possible but
Unlikely
Impossible
Part 1: Six-sided Die


Likelihood of obtaining a 6 or less with a single roll of the die.

Likelihood of obtaining a diamond with one draw from the deck.

Likelihood of obtaining an even number with one draw from the deck.
Likelihood of obtaining a king with one draw from the deck.


Likelihood of obtaining a 6 or less with one draw from the deck.
Likelihood of obtaining a 5 with one draw from the deck
Certain
Possible and
Likely
Possible but
Unlikely
Impossible
Part 2: Eight Playing Cards

Most learners should find that the experiments and predictions match up reasonably.
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Data and Data Collection (pages 73 to 76)
 Yes
 No
Flawed
How many hours of television do you typically watch in one week? ___
Appropriate
What is your favorite team sport to play?
 Hockey Soccer  Football  Basketball  Other
Appropriate
Doctors recommend that school-age children should get approximately
ten hours of sleep each night. How many hours of sleep do your schoolage children typically get each night? ___
Flawed
How many hours of sleep do your school-age children typically get each
night? ___
Appropriate
Numerical
1.
(a)
(b)
(c)
(d)
(e)
NSSAL
©2012
First-hand
Flawed
Categorical
What is your favorite team sport to play?
 Hockey Soccer  Football  Baseball
Second-hand
Do you watch a lot of television?
Six hundred randomly selected adults were asked, "How many
hours of sleep do you typically get on a weeknight?" This
data was collected by a polling company and the data was
given to you for analysis.
   
You randomly selected forty adults and asked them, "From
which retailer (e.g. Sobeys, Superstore, Costco, etc.) do you
buy most of your groceries?"
   
You went to the Statistics Canada website and downloaded
the data regarding the average household income of
Canadians for 2014.
   
You got to the ESPN website and record the goals saved by
Josh Harding (NHL goalie) in each of his first eight years in
the league.
You ask the fifty-eight members of your local legion hall,
"What percentage of your income do you send on
entertainment (e.g. movies, concerts, restaurants, etc.)?"
198
   
   
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Second-hand
First-hand
Categorical
Numerical
(f)
Prior to the federal election, a polling company asked 1500
randomly selected adults the following. "Which federal party
will you be voting for in the upcoming election? You decided
to use this data in a paper you were doing for school.
   
You need to pick up coffee for a large staff meeting. You can
choose from Tim Hortons, Starbucks, Second Cup and Jim's
Specialty Coffee. You ask each of the staff members which
one of the four they would prefer.
   
(h)
You roll two dice forty times. Each time you record the sum
of the two numbers rolled on the two dice.
   
(i)
The local children's hospital records the weight of all
newborns. They supply you with this data.
   
(g)
2. Answers will vary. (We've supplied at least one acceptable answer in each case.)
(a) Most days how do you get to school?
 Drive in A Car/Truck
 Ride a Bicycle
 Drive a Motorcycle
 Walk
 Take Public Transit
 Other
(b) Typically how many hours of moderate to vigorous aerobic exercise do you get each
week?
(c) "Quality family time" is time spent doing an activity that is meaningful to the parent and
child. It is time when family members really engage with each other. This could include
discussions at meal time, participating together in physical activities (e.g. biking, hiking,
etc.), and/or playing board games.
How many hours of quality family time do you typically have in one week?
(d) Which one of the following is your favorite type of television show?
 Comedy
 Documentary
 Home Improvement
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 Drama
 Sports
 Travel
199
 Reality Show
 News
 Other
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3. Answers will vary.
Which one of the following is your favorite type of music?
 Classic
 Pop
 Rap
 Rock
 Jazz
 Country
 Hard Rock
 Blues
 Other
Gathering Data and Creating Bar Graphs (pages to )
1. (a)
Color
Red
Number
of
Vehicles
6
White
8
Black
10
Silver
5
Other
7
(b)
(c)
(d)
(e)
(f)
2.
Tally
First-hand Data (Tanya collected the data herself.)
36 vehicles
Black
Vertical Axis Label: Number of Vehicles
No, she only looked at 36 vehicles in one particular parking lot.
Animal
Fox
Mouse
Deer
Bear
Rabbit
Squirrel
Life Expectancy
in Years
14
4
27
40
9
20
3. (a) Second-hand Data (Obtained from Statistics Canada website)
(b) Mistake: Winnipeg's annual precipitation appears to be a little more than 600 mm on the
bar graph, even though it supposed to be 514 according to the table.
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(c)
(d)
(e)
(f)
(g)
Title: Average Annual Precipitation for Five Canadian Cities
Scale: Every tick mark represents 200 mm
The graph would have to ridiculously tall if that scale was used.
Vertical Axis Label: Annual Precipitation in Millimetres
Horizontal Axis Label: Canadian Cities
4. (a) Answers will vary but generally looks like a normal distribution (i.e. bell-shaped)
(b) First-hand Data
(c) Typically it’s the sum of 7 because it can be generated with 1 and 6, 2 and 5, and 3 and 4.
5. The second graph initially gives the impression that Swedes and Australians view very little
television per day. However, when you realize that the vertical scale on the second bar graph
starts at 140, you recognize that the viewing habits amongst people from these different
countries are not as different as you initially suspected.
6.
Eye
Color
Tally
Blue
Number
of
Students
8
Brown
13
Hazel
5
Green
3
Grey
1
7. Answers will vary.
Interpreting Bar Graphs (pages 85 to 89)
1. (a)
(b)
(c)
(d)
(e)
$31 749
Bachelor Degree
$8624
Post-Bachelor Degree, $63 998
no
2. (a) 25oC
(b) Vancouver
(c) St. John's
(d) Toronto
(e) 5oC
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(f) Montreal
(g) greater, yes
3. (a)
(b)
(c)
(d)
(e)
(f)
(g)
Monaco, 90 years
US
23 years
Canada
No; this graph is dealing with average life expectancies, not standard of living.
Phillippines
Yes
4. (a) Blackberry, 778
(b) 51 points
(c) Nokia and Samsung
(d) Since the scale is so large (i.e. each tick mark represents 20 pints), it is impossible to
accurately determine the exact length of each bar (i.e. the exact score that each bar
represents). The numbers supplied with each bar correct this problem.
(e) HTC
(f) Pantech
(g) No; this bar graph shows satisfaction scores, not total sales.
Double Bar Graphs (pages 90 to 94)
1. (a)
(b)
(c)
(d)
(e)
(f)
(g)
Germany
37 medals
Norway
2 medals
7 medals
116 medals
121 medals
2. (a) General Motors; sales dropped from 24 707 to 21 007
(b) Ford, 2014
(c) 1311 vehicles
(d) 8856 vehicles
(e) 97 885 vehicles
(f) Yes, their combined sales of 30 468 vehicles is greater than Ford's 28 703 vehicle sales
(g) Nissan
3. (a) 2600 new cases
(b) Breast Cancer
(c) 2300 new cases
(d) 10 990 new cases
(e) No; 5340 new cases isn't even close to 13 200 new cases
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(f) Breast, but only slightly; 24 000 new cases for breast cancer compared to 23 800 new
cases for colorectal cancer.
4. (a) 56%
(b) 87%
(c) 4%
(d) Yes; the second bar for every type of cancer is taller.
(e) No, The graph does not show the number of cases. It only shows survival rates.
Introduction to Line Graphs (pages 95 to 100)
1. (a)
(b)
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(c)
2. Point A: (5, 7)
Point B: (9, 6)
Point C: (0, 4)
Point D: (4, 1)
Point E: (8, 0)
Point F: (17, 39)
Point G: (90, 40)
Point H: (45, 30)
Point I: (83, 11)
Point J: (30,7)
3.
4. (a)
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(b) Continuous; his son continues to grow (i.e. increase in weight) between this recorded data
points.
(c) No; when his son is born, he will not weigh 0 kg.
(d) approximately 18 to 19 kg
5. (a) In terms of the number of people attending, you can only be dealing with whole numbers.
For example 6 people could attend, but 6.3 people cannot attend.
(b) Discrete
6. Answers will vary.
(b) Continuous
Interpreting Line Graphs (pages 101 to 105)
1. (a) Initially there was 1000 ml of medication in the bag.
(b) It took 10 hours to drain the I.V. bag.
(c) If it took 10 hours to drain 1000 ml, then the medication was going into the patient at a
rate of 100 ml/hr.
(d) After 4 hours, there was 600 ml of medication in the I.V. bag.
(e) There was 400 ml of medication in the I.V. bag after 6 hours.
(f) Continuous
Any time we are dealing with a line graph we are also dealing with continuous data.
2. (a) Jan - Feb 08, Aug - Sept 08, Jan - Feb 09, Jan - Feb 10, Oct - Nov 10
(b) Oct 08
(c) May 09
(d) $15 billion
3. (a)
(b)
(c)
(d)
(e)
The ball reaches a maximum height of 4 metres.
To reach its maximum height, the ball must travel 6 metres horizontally.
The initial height of the soccer ball is 0 metres.
The ball travels 12 metres horizontally before it hits the ground.
After the ball has travelled 2 metres horizontally, it reaches an approximate height of 2.2
metres.
(f) The ball is at a height of 3 metres at two instances; as the ball goes up and as it comes
down. This will occur when the horizontal distances are 3 metres and 9 metres.
4. (a) 13th day, $7.40
(b) $11.40 per share
(c) 15th day, $2.50 per share
5. The scale used makes one initially feel that there were drastic fluctuations in the number of
infant deaths between 2004 and 2007. This is not the case.
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Orthographic Projections (A) (pages 109 to 112)
1.
2.
3.
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
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4.
5.
6.
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
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Orthographic Projections (B) (pages 113 and 114)
1.
2.
3.
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
Front View
Back View
Right View
Left View
Top View
Bottom View
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4.
Front View
Back View
Right View
Left View
Top View
Bottom View
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Isometric Projections (pages 116 to 119)
1.
2.
3.
4.
5.
6.
7.
8.
9.
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Edges, Faces and Vertices (A) (page 122)
1.
2.
3.
4.
5.
6.
7.
8.
9.
Faces
5
5
6
4
7
8
6
8
9
Edges
9
8
12
6
15
18
10
12
17
Vertices
6
5
8
4
10
12
6
6
10
Edges, Faces and Vertices (B) (page 123)
1.
2.
3.
4.
5.
6.
7.
8.
9.
Faces
9
6
10
7
7
8
8
9
11
Edges
16
12
24
15
12
18
13
21
27
Vertices
9
8
16
10
7
12
7
14
18
Nets (pages 129 and 130)
1. F
2. C
3. B
4. E
5. A
6. D
The diagrams below have been scaled down.
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Describe the Faces (pages 131 to 139)
1. (a) Six Faces
Two of the faces are identical parallelograms.
Two of the faces are identical squares.
Two of the faces are identical rectangles.
(b) Five Faces
Four of the faces are identical isosceles triangles.
Last face is a square.
(c) Six Faces
Four of the faces are identical rectangles.
Two of the faces are identical rhombuses.
(d) Five Faces
Three of the faces are identical squares.
Two of the faces are identical equilateral triangles.
2. (a) Six Faces
Four of the faces are identical rectangles.
Two of the faces are identical squares.
(b) Five Faces
Two of the faces are identical isosceles right triangles.
The three remaining faces are rectangles but they are not of the same size.
(c) Six Faces
Two of the faces are identical parallelograms.
Two of the faces are identical rectangles.
The last two faces are identical rectangles.
(d) Six Faces
Two of the faces are identical rectangles.
Another two faces are identical rectangles.
The last two faces are identical rectangles.
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(e) Five Faces
Two of the faces are identical rectangles.
Two of the faces are identical isosceles triangles.
The last face is a square.
(f) Six Faces
Two of the faces are identical trapezoids.
Three of the faces are rectangles but they are not of same size.
The last face is a square.
(g) Five Faces
Two of the faces are identical scalene right triangles
Two of the faces are rectangles but they are not of the same size
The last face is a square.
(h) Six Faces
Four of the faces are identical trapezoids.
The two remaining faces are squares but they are not of the same size
3. (a) 4 identical rectangles
6 cm
14 cm
2 identical squares
6 cm
6 cm
(b) 2 identical scalene right triangles
6 cm
10 cm
8 cm
1 square
10 cm
10 cm
2 rectangles, but of different sizes
6 cm
10 cm
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8 cm
10 cm
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(c) 4 identical isosceles triangles
24 mm
24 mm
15 mm
1 square
15 mm
15 mm
(d) 2 identical rectangles
4m
9m
2 more identical rectangles
9m
16 m
2 more identical rectangles
4m
16 m
(e) 3 identical isosceles triangles
11 cm
11 cm
7 cm
1 equilateral triangle
7 cm
7 cm
7 cm
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(f) 2 identical trapezoids
6m
5m
4m
9m
1 square
9m
9m
3 rectangles but of different sizes
4m
9m
5m
9m
6m
9m
(g) 2 identical hexagons
(All edges are 8 cm long.)
8 cm
6 identical rectangles
8 cm
30 cm
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(h) 4 identical isosceles triangles
13 cm
13 cm
10 cm
4 identical rectangles
4 cm
10 cm
1 square
10 cm
10 cm
(i) 2 identical equilateral triangles
5m
5m
5m
2m
3 identical rectangles
5m
(j) 3 identical isosceles triangles
10 cm
10 cm
6 cm
Another 3 identical isosceles triangles
8 cm
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8 cm
6 cm
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(k) 2 identical octagons
(All edges are 2 m in long.)
2m
8 identical squares
2m
2m
4 cm
(l) 2 identical trapezoids
10 cm
10 cm
8 cm
Another 2 identical trapezoids
2 cm
10 cm
10 cm
4 cm
2 rectangles, but of different sizes
4 cm
2 cm
4 cm
8 cm
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C. D. Pilmer
Geometry Crossword (pages 140 and 141)
V
E
R
T
E
X
Q
Q
U
N
A
D
R
I
L
A
T
I
I
L
S
A
O
R
T
E
R
A
T
P
H
O
G
R
A
P
M
E
E
R
T
A
M
R
L
B
T
R
H
I
C
H
I
S
O
I
S
U
C
Q
S
F
A
S
C
E
E
A
E
L
E
R
H
C
L
E
E
N
P
C
O
Z
X
A
P
E
A
N
R
U
G
C
S
T
G
L
O
R
E
N
E
L
C
O
T
A
G
N
A
I
G
M
D
L
218
H
L
R
N
G
A
A
O
I
A
E
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L
D
G
O
N
E
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C. D. Pilmer
Reflections (A) (page 142)
Very Challenging (Only give to your strongest learners)
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Reflections (B) (page 143)
Very Challenging (Only give to your strongest learners)
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C. D. Pilmer
Reflections (C) (page 144)
Very Challenging (Only give to your strongest learners)
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What's the Number? (page 146 and 147)
(a)
(c)
(e)
(g)
2247
3132
4019
1420
(b)
(d)
(f)
(h)
1358
524
2308
3080
Express the Number Different Ways (pages 148 and 149)
(a) Number: 1435
Expanded Form: 1000 + 400 + 30 + 5
Using Words: one thousand, four hundred thirty-five
(b) Number: 2561
Expanded Form: 2000 + 500 + 60 + 1
Using Words: two thousand, five hundred sixty-one
(c) Number: 5214
Expanded Form: 5000 + 200 + 10 + 4
Using Words: five thousand, two hundred fourteen
(d) Number: 4186
Expanded Form: 4000 + 100 + 80 + 6
Using Words: four thousand, one hundred eighty-six
(e) Number: 6042
Expanded Form: 6000 + 40 + 2
Using Words: six thousand, forty-two
(f) Number: 1709
Expanded Form: 1000 + 700 + 9
Using Words: one thousand, seven hundred nine
(g) Number: 3470
Expanded Form: 3000 + 400 + 70
Using Words: three thousand, four hundred seventy
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Express with the Fewest Number of Manipulatives (pages 150 to 157)
1. (a) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
2
11
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
16
3
2
6
Number: 326
(b) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
22
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
18
3
3
8
Number: 338
(c) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
3
10
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
29
4
2
9
Number: 429
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(d) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
0
26
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
23
2
8
3
Number: 283
(e) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
16
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
8
5
6
8
Number: 568
(f) New Representation:
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
20
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
31
3
3
1
Number: 331
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2. (a)
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
3
17
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
13
4
8
3
Number: 483
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
2
22
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
18
4
3
8
Number: 438
Original Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
1
25
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
32
3
8
2
Number: 382
3. (a)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
6
5
(b)
7
6
Number: 657
(c)
2
(d)
3
9
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
Number: 923
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4
Number: 649
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
9
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
8
7
Number: 487
225
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C. D. Pilmer
(e)
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
5
8
(f)
8
7
Number: 588
(g)
5
(h)
4
5
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
7
Number: 854
(i)
6
Number: 765
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
8
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
4
7
Number: 747
New Representation
Flats
Rods
Unit Tiles
(Hundreds)
(Tens)
(Ones)
6
4
8
Number: 648
Adding (pages 158 to 161)
1.
(a)
1 5
+ 3 3
(b)
4 8
(e)
3 4
+ 4 2
7 6
NSSAL
©2012
4 2
+ 4 3
(c)
7 3
(f)
3 2
+ 3 2
5 1
+ 2 2
(d)
7 3
(g)
6 4
1 2 2
+ 1 4 6
2 6 8
226
2 6
+ 2 3
4 9
(h)
1 3 4
+
2 4
1 5 8
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C. D. Pilmer
2.
(a)
Tens
Ones
Tens
Ones
Tens
Ones
3 1
+ 5 4
8 5
(b)
2 5
+ 4 3
6 8
(c)
1 2
+ 6 6
7 8
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Hundreds
(d)
Tens
Ones
1 2 6
+ 1 3 3
2 5 9
3. (a) 85
(d) 88
(g) 286
(j) 784
(m) 2786
(b)
(e)
(h)
(k)
(n)
78
89
358
983
3499
(c)
(f)
(i)
(l)
(o)
48
49
499
746
5168
Adding with Regrouping (pages 162 to 167)
1.
(a)
Step 1
4 6
+ 3 8
Step 2
Step 3
Break the 14 ones
Exchange 10 ones for
into a group of 10
a rod.
ones and a group of 4
ones.
1
4 6
+ 3 8
8 4
(b)
1 9
+ 3 4
Break the 13 ones
Exchange 10 ones for
into a group of 10
a rod.
ones and a group of 3
ones.
1
1 9
+ 3 4
5 3
(c)
4 5
+ 2 6
Break the 11 ones
Exchange 10 ones for
into a group of 10
a rod.
ones and a group of 1
ones.
1
4 5
+ 2 6
7 1
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2.
(a)
1
Steps 1 and 2
Tens
Ones
Step 3
Tens
Ones
Steps 1 and 2
Tens
Ones
Step 3
Tens
Ones
Steps 1 and 2
Tens
Ones
Step 3
Tens
Ones
3 6
+ 2 9
6 5
(b)
1
2 5
+ 1 8
4 3
(c)
1
3 9
+ 4 7
8 6
3. (a) 61
(d) 84
(g) 92
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(b) 60
(e) 53
(h) 80
(c) 96
(f) 137
(i) 126
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4. (a) 145
(d) 51
(g) 108
(b) 96
(e) 90
(h) 95
(c) 56
(f) 73
(i) 163
Subtracting (pages 168 to 172)
1.
(a)
(e)
8 8
5 6
(c)
7 5
(d)
6 7
− 5 4
− 1 3
− 3 4
− 4 2
3 4
4 3
7 3
2 5
5 3
− 2 3
3 0
2.
(a)
(b)
(f)
2 6 9
(g)
− 1 3 5
2 8 7
− 2 1 6
1 3 4
7 1
Tens
Ones
Tens
Ones
7 4
− 5 2
2 2
(b)
8 6
− 3 6
5 0
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(c)
Hundreds
Tens
Ones
Hundreds
Tens
Ones
2 7 9
− 1 2 6
1 5 3
(d)
2 5 8
−
4 3
2 1 5
3. (a) 53
(d) 50
(g) 52
(j) 142
(m) 482
(p) 2415
(s) 7620
(b)
(e)
(h)
(k)
(n)
(q)
(t)
12
71
2
235
503
5432
1043
(c)
(f)
(i)
(l)
(o)
(r)
(u)
26
29
10
157
62
2070
5361
Subtracting with Regrouping (pages 173 to 178)
1.
(a)
−
7
16
8
6
3
8
4 8
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(b)
−
6
14
7
5
4
7
1 7
231
(c)
−
8
12
9
6
2
8
2 4
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C. D. Pilmer
(d)
−
(e)
1
13
2
3
6
1
5
2
2.
(a)
−
(d)
−
7
14
8
2
4
9
5
5
7
12
8
2
2
5
(a)
−
5
16
6
1
6
8
(b)
−
(e)
6
3
−
−
8
14
9
6
4
8
4
7
8
1
2
− 2
(c)
8
11
9
7
1
6
1
5
3
15
4
5
6
2
6
6
(b)
−
−
−
4
16
5
3
6
9
8
3
4
5
13
6
3
3
8
2
5
8
16
7
9
6
− 5
6
9
2 2 7
(c)
4
11
5
1
7 8
− 4 3
3
7
3 5
1 4
(e)
6 7
− 2 3
(f)
−
4 4
6
12
7
3
2
6
9
1
3 6 8
(h)
9
0
4 9 6
− 2 6 5
2 3 1
1 7 9
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14
5
(f)
2 6
(g)
7
4 9
1 9 0
4 8
(d)
2
1 6 6
5 7 3
3.
14
−
8 4
(f)
1
(i)
6
− 6
7
13
8
5
3
8
2 5
232
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