Mathematics 7
Student E-Book
Semester 2
2014-2015
Table of Contents
List of Student Resources
Year-Round Problem Solving Process
Video Journaling Topics, Guidelines and Rubric
Exponents
a. Topics and Vocabulary
b. Exponents Assignments – Regular Track
c. Exponents Final Review
Linear Patterns and Graphing
a. Topics and Vocabulary
b. Patterns Activities - Regular Track including reviews for
c. Patterns – Compacting Assignments
quizzes
Manipulating Algebraic Linear Equations (ALE)
a. Topics and Vocabulary
b. ALE Assignments – Regular Track including reviews for quizzes
Speed, Rate, Ratios and Proportions
a. Topics and Vocabulary
b. SRRP Activities including reviews for quizzes
c. SRRP Compacting Assignments
Percent Operations
a. Topics and Vocabulary
b. Overview - Let’s see what you know before we start
c. Content is currently unprepared
******************* End of Semester 2 *********************
2
List of Student Resources
When you cannot find your notes,
When you don’t remember,
When you want to find the meaning of a math word,
When you want some help,
And when you want to learn something new….
Here are some places you might be able to find the answers to your
questions on any topic. Use the search engine of the following websites:
http://www.mathisfun.com
https://www.khanacademy.org/math
http://www.brainpop.com/math/
Username = asfmbp, Password = asfmbp
http://www.mathplayground.com/index.html
3
Year-Round Problem-Solving Process
When you’re confronted with a word problem that you need to solve, follow
the following steps and they will help you understand the problem and
figure out how to solve it.
1) Read the problem
2) Underline/highlight/circle the important information that will
help you solve the problem.
3) Know the answer to this question: What is the problem asking?
4) Pick a strategy that you think will help you come to the right answer:
i. Make a list
ii. Make a table/chart
iii. Draw a picture or build something
iv. Find a pattern
v. Guess and Check
vi. Work backwards
vii. Act it out!
viii. Make an equation or a number sentence
ix. Use another strategy that makes sense to you…
5) Solve the problem using the strategy you chose above.
6) Check your work and answers by looking over your work or using
another strategy to come to the same answer.
7) Write a sentence answering the question posed in the problem.
4
Semester 2 – Ongoing Content Review
Video-Journaling Topics, Guidelines and Rubric
1)
Each video must be maximum 3 minutes long.
2)
Make a video for each of the topics below. You must use the
vocabulary words in red, properly in your video.
***NOTE – Plan out your video before filming it.
You should figure out what you’re going to say and how you’ll use the
vocabulary words in red in each video. Make sure everything you want to
say, fits in 3 minutes for each video. Check the rubric at the end of this
document as you plan***
Topics:
Video 1:
Explain how to solve this problem: A plane is flying at 3,500m above sea level and
went up another 60m. Then the motors stop working and the plane crash in the middle
of the ocean and end up at 1700m below sea level. How far did the plane fall?
Vocabulary – Ascend, descend.
Video 2:
Show and explain how you would solve 8-3.
Vocabulary – base, exponent, negative, reciprocal, fraction, “to the power of”,
expanded notation.
Video 3:
Show how you add and subtract a mixed number fraction with a proper fraction.
Use different fractions for addition and different fractions for subtraction.
5
Vocabulary – numerator, denominator, mixed fraction, improper fraction, proper
fraction, equivalent fractions, common denominator, whole number.
Video 4:
Explain how to solve this problem: The perimeter of square A is 24 meters. The area
of square A is 4 times the area of square B. What is the area and perimeter of square B?
Vocabulary – dimensions, area, perimeter, length, width, quadrilateral.
Video 5:
Show and explain how you would compute the following:
43 +
|7−7∗4|
3
−3
2
5
÷6 =
Vocabulary – numerator, denominator, mixed fraction, improper fraction, proper
fraction, equivalent fractions, common denominator, whole number, exponent,
absolute value, multiply, divide, add, subtract.
Video 6:
Show and explain how you would find the missing angles in the picture below:
*** All triangles in the drawing are equilateral
6
Vocabulary – triangles, dimensions, area, perimeter, length, width, height, base,
polygons, quadrilateral
Video 7:
Show and explain how you divide a mixed number fraction with a proper fraction.
Use an example to demonstrate this.
Vocabulary – numerator, denominator, reciprocal, mixed fraction, improper
fraction
Video 8:
3
Show and explain how you would convert the fraction 3 to a percent and then to a
8
decimal.
Vocabulary – equivalent, denominator, numerator, whole number, percent,
fraction, decimal
Video 9:
Explain the difference between -42 and (-4)2 ?
Vocabulary – base, exponent, negative, multiply, “to the power of”
Video 10:
Formulate a word problem for this table of values and tell your audience how to come
up with an equation for the pattern.
Number of days that go by
0
1
2
3
Number of petals on the rose
25
22
19
16
Vocabulary – pattern, rate of change, equation, variable, decreasing.
Video Journal Rubric:
Categories
Level 4
Level 3
Level 2
Level 1
7
Use of red
vocabulary
words
All words are
used properly
in video.
Most words
are used
properly in
video.
Most ideas are
organized well
in the video.
Some words
are used
properly in
video.
Organization
All ideas are
Some ideas are
of ideas
organized
organized in
well in the
the video.
video. Video
Video does not
flows well.
flow well.
Mathematical All content is
Most content is Some content
accuracy
mathematicall mathematically is
y correct.
correct.
mathematically
correct.
Time limit and Video is
Video is 4
Video is more
completeness within 3
minutes long
than 4 minutes
minutes long
and complete.
long and
and complete.
complete.
Few to no
words are used
properly in
video.
Video makes
no sense.
Little or no
content is
mathematically
correct.
Video is
incomplete.
8
Unit 4 – Exponents
Topics to be covered in this unit:
1. Positive Exponential Powers
2. Negative Exponential Powers
3. Scientific Notation; Universe, Nano-Technology, Physics and
Computers
Math Lingo:
Word
Meaning (in your
Tell us how it’s used
own words). Give an in the real world.
example.
Base
Positive exponent
Negative exponent
Exponential notation
Expanded notation
Scientific notation
9
Exponents – Assignment 1 – Regular Track
Exploring Positive Exponents
Show your work for every question. You can copy and paste this assignment
into another word document and show your work in that document. You can
also show your work on paper or Bamboo Tablet. Upload the pictures for
your work into a folder called “Exponents-Assignment 1” on GoogleDocs
when you’re done.
Activity 1: The Rumor
Consider the following scenario:
One 7th grade student is born on January 30. She thinks about how great it would
be to not to have school on January 30. So, the seventh grade student decides to start a
rumor that ASFM will be closed on January 30.
On January 16th, she tells two of her friends. She tells each of them to tell two
more students on Jan. 17th and that each of the new students should tell two more on
Jan. 18th.
How many students would have heard the rumor by the January 20?
Answer the following questions in your notebook:
1) Highlight the parts of this problem that you think will help you reach the right
answer.
2) Choose one strategy that you will use to answer this question.
Draw a picture
Make a list
Make a table
Guess and check
Work backwards
Look for a pattern
Or another strategy you can think of…
3) Use the strategy and solve the problem. Show your work.
10
What is “Expanded Notation”?
What is “Exponential Notation”?
Fill out the following table: You can use a calculator
Day
Jan. 15
Jan. 16
Jan. 17
Jan. 18
Jan. 19
Jan. 20
Jan. 21
Jan. 22
Jan. 23
Jan. 24
Jan. 25
Jan. 26
Jan. 27
Jan. 28
Jan. 29
Jan. 30
The number
of new people
who hear the
rumor on a
given day
0
2
4
Expanded
Notation
Exponential
Notation
1
1X2
20
1X2X2
21
22
Total number of
people who have
heard the rumor
including the
initiator
1
3
7
Answer these last 3 questions using the table you just filled out:
1. How many students would have heard the rumor by the January 25th?
2. There are 2400 students at ASFM. By which day would all of the students have heard the
rumor?
3. Was the rumor started early enough for all the students to have heard that school will be closed
on January 30th?
11
Activity 2 – Making a million dollars
A man named Sam only has 1 dollar to his name. He goes to the casino one day because
he feels lucky. He bets the only dollar that he has to earn triple the amount that he
started off with. In the first round Sam wins 3 dollars. He feels luckier and so he
decides to bet all 3 dollars in the hopes that he will earn triple that amount. If Sam
keeps betting all the money he earns in every round and keeps winning every round,
how many rounds does Sam have to play to become a millionaire?
1) Highlight the parts of the problem that will help you answer the question.
2) Choose a strategy that you will use to solve this problem:
Draw a picture
Make a list
Make a table
Guess and check
Work backwards
Look for a pattern
3) Use the strategy and solve the problem in your notebook.
4) How can you use your knowledge of exponents to solve this problem in a shortcut manner?
12
Exponents – Assignment 2 – Regular Track
Introduction to Negative Exponents
Show your work for every question. You can copy and paste this assignment
into another word document and show your work in that document. You can
also show your work on paper or Bamboo Tablet. Upload the pictures for
your work into a folder called “Exponents-Assignment 3” on GoogleDocs
when you’re done.
THIS ASSIGNMENT MUST BE DONE BY ALL STUDENTS!!! DO NOT USE A
CALCULATOR!!
Activity 1 - Fast Growing Plant?
I recently purchased a new plant. When I bought the plant it was exactly one foot tall. I
noticed the plant was growing at a pretty fast rate, so after one month I decided to
measure its height. After one month my plant was two feet tall. I decided that I would
measure the height of my plant at the end of each month. As I give you the
measurements please fill in the data in the table below. After two months my plant was
four feet tall. After three months my plant was eight feet tall. We had to move the plant
out of my house at this point. We relocated it to a nearby office building. After four
months the plant was 16 feet tall and after five months the plant was 32 feet tall.
Months
owned
Height in
feet
0
1
2
3
4
5
1. If my plant keeps growing at this rate, how can you find the height of my plant after
eight months? Add this height to the table.
2. If my plant keeps growing at this rate, how can you find the height of my plant for
any number of months? Think of a couple of different ways that the height could be
found for any number of months.
13
3. Write an equation that gives the height of plant in feet for any number of months.
Explain your equation in the context of this story.
4. I recently went back to the store where I bought my plant and I found out that the
plant was alive for a long time before I bought it and that the store owner believes it
was growing at the same rate, even before it was one foot tall. Assuming this is the case,
and that my plant was doubling in height each month, how tall was plant (in feet) one
month before I purchased it?
5. How tall was my plant (in feet) two and three months before I purchased it? What
math are you doing to find the height a year earlier?
6. You should have noticed that in your equation in problem three the exponent
represents the number of months that you owned the plant. What exponent value
would it make sense to use in your equation to model when I bought the plant? How
about 1, 2 and 3 months before I owned the plant?
7. Fill in the table below to include the plant’s height for months before and after I
purchased the plant.
Months
-4
-3
-2
-1
0
1
2
3
4
owned
Height in
feet
8. Based on questions 4 – 7, describe in words what happens when we take a positive
number and raise it to a negative power.
9. Describe any patterns or anything you notice in the table in problem number seven.
10. Based on what you learned think about the value of the following powers of two. If
it helps think about them in the context of my plant:
2-6 =
2-7 =
26 =
27 =
14
Exponents – Assignment 3 – Regular Track
Positive & Negative Exponents Worksheet
(Review for Quiz 1)
Show your work for every question. You can copy and paste this assignment
into another word document and show your work in that document. You can
also show your work on paper or Bamboo Tablet. Upload the pictures for
your work into a folder called “Exponents-Assignment 4” on GoogleDocs
when you’re done.
Solve:
1) Evaluate 45
2) Evaluate 123
3) Evaluate (-10)2
4) Evaluate 100-2
5) Evaluate 9-2
6) Evaluate 7-3
7) Evaluate 8-1
8) Evaluate 4-2
9) Evaluate 10
10)Evaluate 120
Evaluate – You may use a calculator:
a) 27 =
b) 63 =
c) 106 =
d) 1.62 =
e) 0.14 =
f) 2.33 =
g) 0.54 =
Expanded Form:
11) Write this expression in expanded form: 375
12) Write this expression in expanded form: 9-3
13) Write this expression in expanded form: (101)-3
Problems:
15
1) Suppose a certain forest fire doubles in size every 12 hours. If the
initial size of the fire was 1 acre, how many acres will the fire cover in
2 days?
2) Suppose that a dollar placed into an account triples every 12 years.
How much will be in the account after 60 years?
3) Suppose a bacterium splits into 2 bacteria every 15 minutes. How
many bacteria will there be in 3 hours?
4) The number 81 can be written as 92 or as 34. Write each of the
following numbers as a power with an exponent greater than 1 in 3
ways:
a) 256
b) 1 000 000
5) Express the number of wheels on 16 cars as:
a. A power of 8
b. A power of 4
c. A power of 2
17) negative exponent questions need to be added here…
Show your work for every question.
1551 =
8–2 =
190 =
(-6)4 =
(-9)3 =
(-8)-3 =
(-4)-2 =
-53 =
-25 =
-43 =
-12-2 =
-5-4 =
16
Exponents – Assignment 4 – Regular Track
Scientific Notation
Show your work for every question. You can copy and paste this assignment
into another word document and show your work in that document. You can
also show your work on paper or Bamboo Tablet. Upload the pictures for
your work into a folder called “Exponents-Compacting” on GoogleDocs when
you’re done.
All students must complete this assignment!!!
Watch these videos:
Brainpop:
http://www.brainpop.com/math/numbersandoperations/standardandscientificnotation/preview.we
ml
username = asfmbp
password = asfmbp
Watch this video too:
www.youtube.com/watch?v=AWof6knvQwE
After watching the videos, answer these questions in this file on the computer:
What is scientific notation and why do we need it?
How does scientific notation work for big numbers?
17
How does scientific notation work for small numbers?
Practice scientific notation by completing the following questions on your computer:
Write each number in scientific notation.
1. 7,900 = __________________________ 2. 0.0468 = ____________________
3. 314,000 = __________________________
4. 0.00731 = ____________________
5. 63,000 = __________________________
6. 50,400,000 = __________________
7. 8,100,000,000 = ____________________ 8. 77,250,000 = __________________
9. 0.00000073 = ______________________
10. 0.000903 = __________________
11. 0.00631 = _________________________
12. 555,900,000 = ________________
13. 2,103,000 = _______________________
14. 0.00000342 = ________________
15. Which shows 833,000 in scientific notation?
A 8.33 x 103
B 8.33 x 104
C 8.33 x 105 D 8.33 x 106
18
16. What is 0.000000765 written in scientific notation?
A 7.65 x 10–9
B 76.5 x 10–8
C 7.65 x 10–7
D 7.65 x 10–6
17. A piece of paper has a thickness of about 0.0032 inch. Write this
measurement in scientific notation.
18. An aircraft carrier weighs 75,000,000 pounds. Write this weight in scientific
notation.
19. In 2000, there were approximately 281,000,000 people in the United States.
Which of the following is not another way of expressing the number 281,000,000?
A 28.1 million
B 0.281 billion
C 28.1 x 107
D 2.81 x 108
Write each number in standard form.
1. 7.4 x 103 = ________________________
2. 4.35 x 10–4 = __________________
3. 5.94 x 107 = ________________________
4. 7.2 x 10–3 = ___________________
5. 2.104 x 10–3 = ______________________
6. 1.2 x 105 = ___________________
Compute the following:
1. (3.2 x 105) + (8.1 x 103)
2. (5 x 10–1) + (9.8 x 10–3)
19
Do the following questions using a calculator and show your work:
1. The body of a 150 lb person contains 2.3 x 10-4 lb of copper. How much copper is
contained in the bodies of 1200 such people?
2. The speed of light is approximately 3 x 108 m/s. How far does light travel in 6.0 x 101
seconds?
3. A computer can perform 4.66 x 108 calculations per second. How many calculations can
this computer perform in one minute?
4. The size of the Indian Ocean is 2.7 x 107 square miles. The Arctic Ocean is 1/5 the
size of the Indian Ocean. How big is the Arctic Ocean?
5. The speed of light is 3 x 108 m/s. If the sun is 1.5x 1011 meters from earth, how many
seconds does it take light to reach the earth?
20
Exponents – Review for Quiz 2 with Solutions
Compute the following and show your work:
1322 =
9-3 =
-23 =
(-8)3 =
(-6)-2 =
-4-2 =
(-3)-3 =
-2-5 =
-123340 =
(-345)0 =
(-89)1 =
-671 =
(-976)-1 =
-875-1 =
Use the calculator to compute the following and show your work:
1324 =
9-4 =
(-15)-4 =
-18-4 =
-143 =
(-43)3 =
(-21)-5 =
-8-5 =
Write the following in standard notation:
2.104 x 10–3 = ______________________
1.2 x 105 = ___________________
21
8.071 x 10–2 = ______________________
1.3064 x 10–4 = _________________
The United States has a total of 1.2916 x 107 acres of land reserved for state parks. Write
this number in standard form.
Write the following in scientific notation:
53,300,000 = __________________
0.000000702 = _______________
In the United States, 15,000,000 households use private wells for their water supply. Write
this number in scientific notation.
Use a calculator to compute the following. Leave your work and answers
in scientific notation if the numbers are too big or too small.
1) The bedroom of our house is 1,200 cubic meters. We know that there are
3.4 x 109 particles of dust per cubic meter. Write how many particles of dust
are present in the bedroom of our house?
2) Find out the weight of 6 billion dust particles, if a dust particle has a mass of
7.53 x 10-10 g.
3) Last month, my friend bought a computer. If it can perform 2.796 x 1011
calculations per minute. How many calculations can the computer perform in
one second?
Solve the following problems. Show your work.
1) 25 marbles are arranged in the form of a square. How many marbles
are along the length of the square?
22
2) There are 216 oranges arranged in a cube box. How many oranges are
arranged along the length of the box?
3) If the sum of all edges in a cube is 60cm, what is the volume of the cube?
4) If the area of a square is 100m2, what is the perimeter of the square?
5) If the perimeter of one square face on a cube is 12cm, what is the
volume of the cube?
6) A bacterial cell doubles every hour. If you start with one cell, at the end
of one hour you would have 2 cells, at the end of two hours you have 4
cells, and so on. How many cells you would have after five hours? Show
all your work.
23
Solutions to Exponents Review for Quiz 2:
Compute the following and show your work:
1
1322 = 17424
1
9-3 = 729
1
-23 = − 8
(-8)3 = -512
(-6)-2 = 36
-4-2 = − 16
1
(-3)-3 = − 27
1
-2-5 = − 32
-123340 = -1
(-345)0 = 1
(-89)1 = -89
-671 = -67
1
1
1
(-976)-1 = − 976
-875-1 = − 875
Use the calculator to compute the following and show your work:
1324 = 303595776
1
(-15)-4 = 50625
1
9-4 = 6561
1
-18-4 = − 104976
-143 = -2744
(-43)3 = -79507
1
(-21)-5 = − 4084101
1
-8-5 = − 32768
Write the following in standard notation:
2.104 x 10–3 = _____0.002104_____________
1.2 x 105 = ___120000________________
24
8.071 x 10–2 = ____0.08071_____________
1.3064 x 10–4 = ______0.00013064______
The United States has a total of 1.2916 x 107 acres of land reserved for state parks. Write
this number in standard form.
12916000
Write the following in scientific notation:
53,300,000 = _____5.33 x 107_____________
0.000000702 = __7.02 x 10-7_____________
In the United States, 15,000,000 households use private wells for their water supply. Write
this number in scientific notation.
1.5 x107
Use a calculator to compute the following. Leave your work and answers in scientific
notation if the numbers are too big or too small.
1) The bedroom of our house is 1,200 cubic meters. We know that there
are 3.4 x 109 particles of dust per cubic meter. Write how many particles
of dust are present in the bedroom of our house?
4.08 x 1012 dust patricles
2) Find out the weight of 6 billion dust particles, if a dust particle has a
mass of 7.53 x 10-10 g.
4.518g
3) Last month, my friend bought a computer. If it can perform 2.796 x 1011
calculations per minute. How many calculations can the computer perform in
one second?
4.66 x 109 calculations per second
25
Solve the following problems. Show your work.
7) 25 marbles are arranged in the form of a square. How many marbles
are along the length of the square?
5 marbles along the length.
8) There are 216 oranges arranged in a cube box. How many oranges are
arranged along the length of the box?
6 oranges are arranged along the length of the box.
9) If the sum of all edges in a cube is 60cm, what is the volume of the cube?
125cm3
10)
If the area of a square is 100m2, what is the perimeter of the
square?
40cm is the area of the square.
11)
If the perimeter of one square face on a cube is 12cm, what is the
volume of the cube?
27cm3
12)
A bacterial cell doubles every hour. If you start with one cell, at
the end of one hour you would have 2 cells, at the end of two hours you
have 4 cells, and so on. How many cells you would have after five hours?
Show all your work.
25 = 32 cells after 5 hours
26
Unit 5 – Linear Patterns and Graphing
Topics to be covered in this unit:
1. Patterns - Increasing, Decreasing and Fractional rate of
change
2. Rate of change – Focus on linear patterns with a constant
rate of change (challenge - logarithmic)
3. How to make a table of values and formulate an equation
from the data provided in a table and/or graph.
4. Introduction to variable expressions (one step and two step
linear equations)
Math Lingo:
Word
Meaning (in your
own words)
Find/draw a
picture that
describes the
word or give an
example
Pattern
Rate of change
Increasing pattern
Decreasing pattern
Equation
Variable
27
Patterns – Activity 1 – Regular Track
Intro to Increasing Patterns
The Flickerbill Problem
28
29
Patterns – Activity 2 – Regular Track
Increasing Pattern - Building Patterns with
Wooden Blocks
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity2” on GoogleDocs when you’re done. Also upload
the GeoSketchpad document that contains your graph to the same
folder.
1) Watch the video with Ms. Khare to figure out what you need to do for
this activity.
2) First decide on which blocks you’re going to use to make the basic
structure of your pattern.
3) Fill in this table:
Number of basic structures in the
pattern
Perimeter (cm) of your pattern
4) What is the rate of change of your pattern?
5) DO NOT BUILD THIS: If your pattern consisted of 8 basic structures,
what would its perimeter be? How did you figure that out?
30
6) Make an equation that finds the total perimeter for any number of basic
structures in your pattern. Write it down!
7) If your pattern consisted of 96 basic structures, what would its
perimeter be? How did you figure that out?
8) Make the graph for your pattern using Geometer’s Sketchpad.
31
Patterns – Activity 3 – Regular Track
Increasing Patterns and Making Equations
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity3” on GoogleDocs when you’re done.
Pattern 1: My friend David went apple picking in the
middle of winter and the table describes what he was able to
find in the 5 hours he spent there.
Number of Hours
1
2
3
4
5
100
Number of apples picked
1
4
7
10
1) What is the rate of change?
2) Come up with an EQUATION for this pattern:
Pattern 2: There is a jump-rope competition happening at
ASFM. The first 5 students to complete 500 jumps will
represent the school and compete with students in other
schools in Monterrey. Beba recorded her number of jumps
and time in the following table:
32
Time passed (minutes)
1
2
3
4
100
Number of Jumps
completed
70
140
210
1) What is the rate of change?
2) Come up with an EQUATION for this pattern:
3) Between which minutes will Beba complete her 500
jumps?
Pattern 3: (USE A CALCULATOR FOR THIS ONE)
Ana Paula had 500 beads. She started by making one
bracelet out of 16 beads and then decided to make only
necklaces. The table below shows how many beads Ana
Paula used up over time.
Time passed in minutes
1
2
3
Number of beads used to
make jewelry
16
48
80
33
4
5
100
112
1) What is the rate of change?
2) What is the size of each necklace Ana Paula is making?
3) Come up with an EQUATION for this pattern:
4) BONUS: How many beads will Ana Paula use up in 15
minutes?
34
Patterns – Activity 4 – Regular Track
Review for Increasing Patterns Quiz 1 Solutions
Note: This review will be given out on paper in class. These are the
solutions to the review.
Activity 1 – Order of Operations
3/7 + 9/8 – 1/3 =
5/6  1/7 ÷ 2/3 =
205
168
=1
37
168
15
84
1/6 – 2-2  3-2 + 10 = 10
5
36
=
365
36
Activity 2 – A Pattern with Graphing Practice
Sandra discovered a forest in which there were 15 trees. She alone
planted trees in that forest, such that at the end of 1 year there were
22 trees in total, at the end of 2 years there were 29 trees in total,
and at the end of 3 years there were 36 trees in total.
1) Fill out this table using the information above:
# of Years
0
1
2
3
4
# of trees
15
22
29
36
43
35
2) If the pattern continues, how many trees will there be in the
forest at the end of 9 years? How did you figure that out?
78 trees
3) Find an equation that calculates the total number of trees in
the forest by the end of any number of years.
# of years X 7 +15 = Total # of Trees
4) Make a graph for this pattern on graph paper.
5) How many trees will there be in the forest after 25 years?
# of years X 7 +15 = Total # of Trees
25 X 7 +15 = 190 trees
6) For how many years has Sandra been planting trees, if there
are a total of 162 trees in the forest?
Sandra has been planting trees for 21 years because:
21 X 7 +15 = 162 trees
36
Patterns – Activity 5 – Regular Track
Increasing Pattern - Bees and their honey
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity5” on GoogleDocs when you’re done. Also upload
the GeoSketchpad document that contains your graph to the same
folder.
WORK WITH FRACTIONS IN THIS ASSIGNMENT!!! DO NOT TURN
FRACTIONS INTO DECIMALS!!!
There are 2 ml of honey in a hive at the beginning. Bees are then
added to the hive to produce more honey. Each bee makes 1/5 ml of
honey in a hive throughout its lifetime.
1) Fill out the following table showing the relationship between
the number of bees and the total amount of honey produced in
the hive.
Number of bees
0
Amount of honey in the hive
(ml)
2ml
37
2) How much honey will be in the hive if 10 bees are present?
How did you figure that out?
3) Write an equation that tells us the total amount of honey in the
hive for any number of bees. Use variables in your equation
and explain what those variables represent.
4) Make a graph of the data in your table on GeoSketchpad.
5) How much honey will be in the hive if 60 bees are present?
6) How much honey will be in the hive if 154 bees are present?
7) How many bees will be needed to have at total of 27ml of
honey in the hive?
8) How many bees will be needed to have at least 90 ml of honey
in the hive?
9) How many bees will be needed to have at least 103 ml of
honey in the hive?
38
Patterns – Activity 6 – Regular Track
Decreasing Patterns – The Rose Problem
Note: This assignment will be given to you on paper in class.
The Rose Problem
In the town of Laughton, a witch created an enchanted rose. On the
day the rose was created it had 35 petals. After one day, the rose
had 32 petals and after 2 days it had 29 petals.
1) Fill in this table to show the relationship between the number
of days that go by and the number of petals on the rose.
2) What is the rate of change of this pattern?
3) Write an equation that tells us the number of petals left on the
rose after any number of days. Use VARIABLES in your
equation and explain what the variables mean.
39
4) How many petals will be left on the rose after 9 days? How did
you figure that out?
5) Make a graph of the information in your table on paper.
6) After how many days will there be no petals left on the rose?
How did you figure that out?
40
Patterns – Activity 7 – Regular Track
Decreasing Patterns and Solving for the
Variable in 1- and 2-step equations
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity7” on GoogleDocs when you’re done.
Note: All students must complete this assignment.
Activity 1 – Eugenio’s Jellybeans
Eugenio gets a bag of 300 Jellybeans for his birthday. On the first day
after his birthday, Eugenio notices that someone has eaten some of his
jellybeans. There are 296 left in the bag. On the second day after his
birthday, Eugenio notices the thief has eaten more. There are only 292
Jellybeans left in the bag. On the third day there are 288 Jellybeans left
in the bag.
a) Fill out the following table with information from the problem:
b) What is the rate of change of this pattern?
41
c) How many Jellybeans are left in the bag 10 days after Eugenio’s Bday?
How did you figure this out?
d) Write an equation that tells you the number of Jellybeans left in
Eugenio’s bag, any number of days after his birthday. Use variables in
your equation and explain what the variables represent.
e) Use your equation to determine the number of Jellybeans left in
Eugenio’s bag, 21 days after his birthday.
f)
How many Jellybeans are left in Eugenio’s bag 35 days after his
birthday? Use your equation to figure this out.
g) If there are only 12 Jellybeans left in Eugenio’s bag, how many days
have gone by? Use your equation to figure this out.
h) After how many days will there be no Jellybeans left in Eugenio’s bag?
Activity 2: Solving Equations 2
Play the game on this website:
http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/equations2.shtml
Record your work and answers for 20 questions.
Activity 3 - Order of Operations (APEMDAS)
Show your work on another piece of paper, take a picture and insert it
under each problem.
42
2−3 ÷ 40 −
3
=
4
3 1
3− ∗ =
5 6
1
3
5
÷ ( − 3−2 ) + 2 =
4
43
Patterns – Activity 8 – Regular Track
Decreasing Patterns – Pay Attention!!!
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity8” on GoogleDocs when you’re done. Also upload
the GeoSketchpad document that contains your graph to the same
folder.
NOTE: All students must complete this assignment.
From the time a teacher calls on students to pay attention, the
percentage of students actually paying attention to the teacher
starts to decrease in a linear manner. At the beginning, 100% of the
class is paying attention. After 3 minutes 76% of the class is still
interested in what’s being explained. After 4 minutes, 68% of the
class is paying attention. After 5 minutes, 60% of the class is paying
attention.
a) Fill out the following table with information from the
problem:
Time that goes by (minutes)
Percent of students paying
attention
44
b) What is the rate of change of this pattern?
c) What percent of students are paying attention after 10
minutes?
d) Write an equation that tells you the percent of students
paying attention after any number of minutes. Use
VARIABLES in your equation and explain what the variables
represent.
e) Make a graph of the information in your table on Geometer’s
Sketchpad.
f) If this trend continues, after how many minutes do all
students stop paying attention to the teacher?
g) Based on your answer to question e), after how many minutes
should a teacher call student’s attention back or how long
should a teacher’s entire lesson be? (Hint: There are many
answers to this question but you have to support your
answer with good reasons.)
45
Patterns – Activity 9 – Regular Track
Graphing and Solving for Variable in
1- and 2-step Equations
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Activity9” on GoogleDocs when you’re done. Also upload
a picture of the paper that contains your hand-made graph to the
same folder.
Note: This assignment will serve as a review for Patterns Quiz 2.
Activity 1:
Sandra decides to go for a walk. She travels 25m and then decides
to pace herself. One minute after pacing herself, she has traveled
60m total. Two minutes after pacing herself, she has travelled 95m
total. 3 minutes after pacing herself, she has travelled 130m total.
1) What is Sandra’s walking pace (rate of change)?
2) Make a table of values that shows the relationship between
the time that passes by and the distance Sandra has travelled
in meters.
3) Find an equation that tells you the total meters that Sandra
has walked given any amount of time. Use variables in your
equation and mention what the variables represent.
46
4) Use your equation to figure out how far would Sandra walk in
15 minutes.
5) If Sandra walked 1075m and then stopped to drink some
water. How much time has gone by? Use your equation to
figure this out.
6) Make a graph to represent this pattern on paper.
Activity 2:
There are 427 people living in a village. A disease hits the village
and the next month only 422 people are alive. 2 months after, only
417 people are alive. 3 months after, only 412 people are alive.
1) What is the death rate (rate of change) in this village?
2) How many people died by the end of month 5?
3) How many people are still alive by the end of month 5?
4) Write an equation that tells you the number people that are
still alive after any given number of months. Use variables in
your equation and mention what the variables represent.
47
(Hint: Make a table of values before you try to figure out what
the equation for this pattern is.)
5) Use your equation to tell us how many people are still alive
after 2 years?
6) If 327 people are still alive, how much time has gone by? Use
your equation to answer this question.
7) If people continue to die at the same rate, after how many
months will everyone be dead?
8) Make a graph of this pattern on paper.
Activity 3: Solve for the Variable
1) 16 − 𝑐 = −4
2) −25 + 𝑓 = −8
3) 6𝑔 + 7 = −29
4)
8
9
𝑦 = 24
48
5)
2
6)
2
5
6
𝑗 = 15
𝑑 + 2 = 10
49
Patterns – Compacting 1
Introduction to Number Patterns
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Compacting1” on GoogleDocs when you’re done.
Activity 1:
http://www.bbc.co.uk/bitesize/ks2/maths/number/numbe
r_patterns/play/
Type up the numbers and “rule” for each pattern.
Activity 2:
http://www.funbrain.com/cracker/
(Pick “hard” or “super hard”)
Type up the numbers and “rule” for each pattern.
Activity 3:
a. Can you work out how to make this pattern?
b. What are the next 10 numbers in this pattern?
50
c. Read this webpage for more information and write 3
new things that you learned about the Fibonacci
sequence.
http://www.mathsisfun.com/numbers/fibonaccisequence.html
51
Patterns – Compacting 2
Increasing Patterns - Ferrari California
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called
“Patterns-Compacting2” on GoogleDocs when you’re done.
USE A CALCULATOR FOR THIS ACTIVITY:
Sandra bought a Ferrari California on Sunday and she travelled
45km in it. Sandra’s job causes her to travel long distances
everyday.
The numbers in the table below describe her daily driving habits
from the day she bought the car. Find the pattern and fill out the
rest of the table.
Number of Days
1
2
3
4
5
Number of Kilometers
travelled
45
195
345
10
N
1) What is the rate of change for this pattern?
52
2) Write an equation that tells us how many kilometers Sandra has
travelled after “N” days. Tell us what every variable in your
equation means.
3) How many kilometers will Sandra have traveled after 1 year?
4) Graph Sandra’s first 5 days of travel by hand and hand it in with
this completed assignment. Label your axis.
Bonus Question: A car generally needs an oil change after every
5000km travelled. After how many days will Sandra’s car need an
oil change?
53
Patterns – Compacting 3
Increasing Patterns with a Fractional Rate of
Change & Solve for Variable in 2-step
Equations
Show your work for every question. You can show your work on
paper or Bamboo Tablet. Upload the pictures for your work into a
folder called “Patterns-Compacting3” on GoogleDocs when you’re
done. Also upload the GeoSketchpad document that contains your
graph to the same folder.
Activity 1 – Order of Operations
3/7 + 9/8 – 1/3 =
5/6  1/7 ÷ 2/3 =
1/6 – 2-2  3-2 + 10 =
Activity 2 – Some of the money goes to charity!!
Mavy is selling friendship bracelets at ASFM to raise money for the
Smile Foundation in South Africa. She and a group of friends make
3
the bracelets themselves and sell each bracelet for 1$. of each
5
2
dollar Mavy makes goes to the Smile Foundation and she keeps of
5
every dollar to cover the costs of making the bracelets.
54
1)
Fill in the following table so that it shows the relationship
between the amount of bracelets Mavy sells and the amount
of money that goes to charity.
2)
Find an equation that describes the relationship between
the number of bracelets sold and the amount of money that
goes to charity. Use variables in your equation and tell us
what each variable in your equation means.
3)
If Mavy sells 1324 bracelets, how much money will be given
to the Smile Foundation?
4)
If Mavy wants to donate $5000 to the Smile Foundation,
how many bracelets will she have to sell?
5)
If Mavy wants to keep $80 for herself (to cover the cost of
making bracelets), how many bracelets will she have to sell?
6)
Graph this pattern (for the first six bracelets) using
Geometer’s Sketchpad.
55
Activity 3: Solve for the variable – Show your work on another
paper
1)
H=
1
B+2
12
In the equation above “H” represents the “total teaspoons of
honey made” and B represents the “number of honey bees”.
1
Each honey bee makes teaspoon of honey in her life. We
12
start with 2 teaspoons of honey in the hive.
a)
b)
c)
2)
How much honey would 48 bees make?
How much honey would 65 bees make?
How many bees would it take to make 52 teaspoons of
honey in the hive?
Solve for the variable in the equation:
a. 5x – 12 = 43
b. 400 – 8x = 0
1
c. b – 11 = 31
7
d. If the perimeter of the square below is 60cm. What is the
value of “z”?
4z + 3
56
Patterns – Compacting 4
Decreasing Patterns – Chilaquiles Problem
Note: Your teacher will give you this problem on paper.
Chilaquiles at School
Juan Diego had 500 pesos in his pocket on February 1st, 2013. He decided that every day he
would buy Chilaquiles at school and he would only use the money in his pocket to do that.
Chilaquiles costs 30 pesos at the school.
1) Make a table that shows the relationship between the number of days that go by and
the amount of money that Juan Diego has left in his pocket.
2) How much money does Juan Diego have left in his pocket at the end of 9 days? How
did you calculate that?
3) Find an equation that will tell you the amount of money left in Juan Diego’s pocket
at the end of any number of days. Use VARIABLES in your equation and explain
what the variables mean.
4) Make a graph of the information in your table on paper.
5) On what day will Juan Diego not have enough money left to buy Chilaquiles?
57
Patterns – Compacting 5
Graph Analysis Assignment
& Solve for Variable in 2-step equations
Show your work for every question. You can copy and paste this assignment into another
word document and show your work in that document. You can also show your work on
paper or Bamboo Tablet. Upload the pictures for your work into a folder called “PatternsCompacting5” on GoogleDocs when you’re done.
Activity 1:
58
The graph above shows the changes in the population size of a
village in south India over many years.
1) What is happening to the population of the village in the first
3 years?
2) What is the rate of change of the population in the first 3
years?
3) Make an equation that describes how to find the population of
the village in the first 3 years of it’s existence. Use variables in
your equation and mention what each variable stands for.
4) What is happening to the population of the village between
year 3 and year 8? Why do you think the population of a
village would change this way between years 3 and 8?
5) What is the rate of change of the population between years 3
and 8?
6) Make an equation that describes how to find the population of
the village between years 3 and 8. Use variables in your
equation and mention what each variable stands for.
7) What do you think would cause the population of a village
change the way it does between years 8 and 12?
59
8) Make an equation that describes how to find the population of
the village between years 8 and 12. Use variables in your
equation and mention what each variable stands for.
9) If violence struck this village and people began to die at a rate
of 7 people per year and no new people were born, in how
much time would there be no more people left living in the
village?
Activity 2:
Hector ran a marathon in Monterrey yesterday. The graph
below shows how far Hector ran over time.
1) How far did Hector run in total? How do you know?
60
2) How long did he run in total? How do you know?
3) Did Hector run at a same speed throughout the entire
marathon? How do you know?
4) How many stops did Hector make and how long was each stop?
5) How fast did Hector run (in kilometers per hour) between
3:30pm and 4:30pm?
6) a) Between which times did Hector run the fastest? What was
his speed in kilometers per hour?
b) How do you know where Hector ran the fastest from the
shape of the graph?
Activity 3: Solve for the Variable
7) 16 − 𝑐 = −4
8) −25 + 𝑓 = −8
9) 6𝑔 + 7 = −29
61
8
10) 𝑦 = 24
9
2
11) 𝑗 = 15
5
2
12) 𝑑 + 2 = 10
6
62
Patterns – Compacting 6
Patterning in Computer Programming
PROGRAMMING IN JAVA
There are 3 basic parts to computer programming:
1) Write the instructions (or the algorithm) in the form of a
computer program that you want the computer to complete
using a computer language.
2) Get the computer to compile your algorithm. This means check
to see if you have any spelling or grammar mistakes in your
instruction file.
3) Get the computer to execute the instructions that you typed
out.
Now that you have developed a method or procedure for calculating
the number of squares in a grid of 25 squares, you need to learn a
little bit about the Java language so that you can use this language to
get the computer to calculate the number of squares in a grid of 25
little squares.
Variables:
Variables are words or letters that are used as symbols to represent
numbers or letters or words.
For this project you’ll be using “integer” type variables.
int c = 10; //This means “c” is an “integer” type of variable and it’s
value is 10.
63
Java Statements:
I’m going to show you how to use 3 different types of statements in
Java. In the end, you’ll use these statements to program the
computer with your instructions.
The “if-then” and “if-then-else” Statements
The if-then Statement
The if-then statement is the most basic of all the control flow
statements. It tells your program to execute a certain section of code only
if a particular test evaluates to true.
The following program, IfElseDemo, assigns a grade based on the value
of a test score: an A for a score of 90% or above, a B for a score of 80%
or above, and so on.
class IfElseDemo {
public static void main(String[] args) {
int testscore = 76;
// “grade” is a letter-type of variable.
char grade;
if (testscore >= 90) {
grade = 'A';
} else if (testscore >= 80)
grade = 'B';
} else if (testscore >= 70)
grade = 'C';
} else if (testscore >= 60)
grade = 'D';
} else {
grade = 'F';
}
System.out.println("Grade =
{
{
{
" + grade);
}
}
64
The output from the program is:
Grade = C
The “while” Statement
The while statement continually executes a block of statements while a
particular condition is true. Its syntax can be expressed as:
while (expression) {
statement(s)
}
The while statement evaluates expression, which must return a boolean
value. If the expression evaluates to true, the while statement executes
the statement(s) in the while block. The while statement continues
testing the expression and executing its block until the expression
evaluates to false. Using the while statement to print the values from 1
through 10 can be accomplished as in the following WhileDemo program:
class WhileDemo {
public static void main(String[] args){
int count = 1;
while (count < 11) {
System.out.println("Count is: " + count);
count++;
//”count++” means add 1 to the value of the variable count.
}
}
}
The for Statement
The for statement provides a compact way to iterate over a range of
values. Programmers often refer to it as the "for loop" because of the
way in which it repeatedly loops until a particular condition is satisfied.
The general form of the for statement can be expressed as follows:
65
for (initialization; termination;
increment) {
statement(s)
}
When using this version of the for statement,
keep in mind that:
6.
The initialization expression initializes the loop; it's executed once,
as the loop begins.
7. When the termination expression evaluates to false, the loop
terminates.
8. The increment expression is invoked after each iteration through
the loop; it is perfectly acceptable for this expression to increment
or decrement a value.
The following program, ForDemo, uses the general form of the for
statement to print the numbers 1 through 10 to standard output:
class ForDemo {
public static void main(String[] args){
for(int i=1; i<11; i++){
System.out.println("Count is: " + i);
}
}
}
The output of this program is:
Count
Count
Count
Count
Count
Count
Count
Count
Count
Count
is:
is:
is:
is:
is:
is:
is:
is:
is:
is:
1
2
3
4
5
6
7
8
9
10
66
It’s your turn!!!
Use your knowledge of variables and the different JAVA statements
above to write out your own computer program that calculates the
total number of squares in a grid of 25 little squares.
1) Start by making a procedure that sums up all types of squares
in a systematic way for a grid of 25 squares. Write this
procedure on a piece of paper. (Theoretically, if your
procedure works for a grid of 25 squares, it should also work
for a grid of 100 squares.)
2) Pick out a “JAVA statement” from above that you would use to
code your program.
3) Talk to the teacher about your procedure to see if it could
work as a program, if it makes sense and if there are no errors
in your math.
4) Go to this website:
http://www.compileonline.com/compile_java_online.php
5) Ask the teacher how to use this website to type out, compile
and run your computer program.
67
Patterns – Compacting 7
Independent Study Project
1) Find a pattern in the real-world (i.e. in nature, in board games
or outdoor games that you play with your friends, in computer
games, etc.) that you want to analyze.
2) Enact the pattern and set up a table of values that compares 2
variables that depend on each other in some manner.
3) Try to come up with an equation that relates one variable with
the other in your table of values. (Hint: Think about what’s
happening in the pattern in real life to do this. It will be easier
for you to find the equation that way.)
4) Make sure that your equation works by testing it with at least
3 different rows on your table of values.
5) Make a graph that illustrates what is happening as your
pattern continues.
6) Make up interesting/complex questions to do with your
pattern and use your data, graph and/or equation to find the
answers to these questions.
68
Unit 6 – Manipulating Algebraic Linear Equations (ALE)
(Simplifying many forms of One- and Two-Step Equations)
Topics to be covered in this unit:
1. Combining like terms
2. Distributive property
3. One-step equations (applied in the form of simple real-life
problems)
4. Two-step equations (applied in the form of simple real-life
problems)
5. Solving for the variable in one- and two-step equations after
combining like-terms and/or using the distributive property.
Math Lingo:
Word
Meaning (in your
own words)
Find/draw a
picture that
describes the
word or give an
example
One-step equation
Two-step equation
Combine Liketerms
Distributive
Property
Linear equation
Variable
69
ALE – Assignment 1 - Regular Track
Solve for the Variable
Show your work for every question. You can show your work on
paper or Bamboo Tablet. Upload the pictures of your work into a
folder called “ALE-Assignment1” on GoogleDocs when you’re done.
Solve for the variable
One-step Equations:
1) 6g = 36
2) 15 – x = 9
3) b + 28 = 45
3
1
5
10
4) w – =
2
5
3
6
5) + y =
3
6) b = 75
4
1
7) r = 70
5
8) 9 – y = -7
3
3
8
4
9) 𝑥 + = −
70
Two-step Equations:
10)
2𝑧 + 3 = 9
11)
5r – 6 = 19
12)
20 – 3u = 11
13)
45 + 7p = 59
14)
1
15)
3
16)
10 − ℎ = 6
17)
8 + 𝑛 = 11
18)
12 − 𝑐 = −2
2
5
𝑘 − 2 = 18
𝑛 + 2 = 20
1
4
1
3
2
7
71
ALE – Assignment 2 - Regular Track
Introduction to Combining Like-Terms
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called “ALEAssignment2” on GoogleDocs when you’re done.
Activity 1: Combining Like Terms
Watch this video if you were not in class the day we learned how to “Combine Like
Terms” or if you still don’t understand how to “Combine like terms”:
http://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/manipulating-expressions/v/combining-like-terms
Go to the link below, do all questions in it and show your work:
http://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/manipulating-expressions/e/combining_like_terms_1
Activity 2: Do this activity and show all your work. Take a picture of the
graph you make and upload it onto GoogleDocs.
There are 500 iPhones in a store. Eight iPhones are sold every minute.
1) Fill out a table that shows the number of iPhones still in the store as minutes pass by.
Time (Minutes)
Number of iPhones in store
2) Write an equation that allows you to determine how many iPhones are left in the store
after any number of minutes.
72
3) Make a graph of this pattern on graph paper. Remember to label your axes.
Activity 3: Solve for the variable and check that your answer is right.
Show all your work!!!
1) 4𝑦 − 9 = 7
3)
5
6
𝑦 = 30
2) 25 − 3𝑧 = −5
4)
2
7
𝑏 − 6 =8
3
5) 30 − 8 𝑟 = 6
73
ALE – Assignment 3 - Regular Track
Combining Like-Terms 2
Note: Your teacher will give you a paper copy of this assignment.
74
75
76
77
ALE – Assignment 4 - Regular Track
Combining Like-Terms 3
(Review for Quiz)
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called “ALEAssignment4” on GoogleDocs when you’re done.
Activity 1: Combining Like terms in long complicated Equations
Watch the following video if you don’t understand how to do
the questions below:
http://www.khanacademy.org/math/algebra/solving-linearequations-and-inequalities/manipulatingexpressions/v/combining-like-terms-3
Complete the following questions:
1. 15m + (– 5m) =
2. –2 + t + 10 =
3. 5 + m + m + m =
4. 5y + 8y + 4z =
5. 8x2 + 2x2 + 7x =
6. 6xy + 3xy + 3x =
7. 8x + 6 + 7x –10 –5x + 8 =
8. 6x2y – 2x2y – 10x2y + 8x2y =
9. 2x – 6y + 7x + 2y =
10. 6s2 – 3x2 + 4t – 6s2 =
78
11. 8a2 + 4ab + 6a – 8a2 =
12. 7x2y + 8 –5x2y + 4 =
13. 5a + 3b + 4c + 2a =
14. 6x3 + 9x + 10x3 + 4x2 =
15. 10x4 – 8x3 + 4x3 –5x2 + 3x =
Activity 2: Combining Like Terms and expressing perimeter
Express the perimeter of each of these shapes as a smaller and simpler equation.
3 – 2x
x
3ab + 4a2
4z + 3
4z + 3
7+y
2a
2a
6b2 – 5ab
7 + 3x
3x - 4
3x - 4
7 – 2x
7 – 2x
5x + 5
3a - b
5x – 2
3a - b
3a - b
Activity 3: Solve for the variable. Show all your work.
1)
5c + 7 = 52
2)
2
4
− 𝑢 = −5
15
79
3)
7
4)
28 −
5
5)
6)
9
𝑡=2
8
4
𝑢
9
3
7
𝑛 = 19
1
21
𝑦 − 5 = 20
5
− 7 = 11
Activity 4: Combine like-terms and then solve for the variable
1) 4b + 9 - 2b = 21
2) 9 – 2h + 5h -12 = 0
Combining Like-Terms 3 (Review Solutions)
Activity 1:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10m
t+8
3m + 5
13y + 4z
10x2 + 7x
9xy + 3x
10x + 4
2x2y
9x - 4y
80
10)
11)
12)
13)
14)
15)
-3x2 + 4t
4ab + 6a
2x2y + 12
7a + 3b + 4c
16x3 + 4x2 + 9x
10x4 - 4x3 - 5x2+3x
Activity 2:
1)
10-x+y
2)
16z+12
3)
-2ab + 4a2 + 6b2 + 4a
4)
7x +11
5)
16x+10
6)
9a-3b
Activity 3:
1)
2)
c=9
14
𝑢=
3)
𝑡=
4)
n= 21
5)
y=1
6)
𝑢=
15
72
14
738
7
Activity 4:
1)
b=6
2)
h=1
81
ALE – Assignment 5 - Regular Track
Distributive Property Game
There is a link on Edu2.0 that explains how to play the game
including the materials that you need. Your teacher will go over it
with you in class. You will hand in your work and your partners
work together in class.
82
ALE – Assignment 6 - Regular Track
Distributive Property Workshop
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo
Tablet. Upload the pictures for your work into a folder called “ALEAssignment6” on GoogleDocs when you’re done.
Activity 1: Solve for the variable (Hint: You might want to
combine like-terms or use the distributive property before
solving for the variable)
1) 5c – 3 = 22
4
3
5
10
2) − v =
3) -6v – 3 = 33
3
4) 19 – r = 13
5
5
5) y + 3 = 13
6
6) 4m + 4 − 2m = 12
1
1
3
2
7) n − 4 + n = 11
8) 8k – 3 + 7 – 3k = 39
9) 4(3v+2) = 20
10)
3(2r-2) = 24
83
Activity 2: Use the distributive property to express the area of the
following shapes as the smallest and simplest equation. Combine
like-terms after that if necessary.
3x
x-5
2c
3y - 2
Bonus Question below is worth 3 extra points!!!
y-2
10
3y
84
ALE – Assignment 7 - Regular Track
Use the Distributive Property, Combine LikeTerms and Solve for the Variable
Show your work for every question on paper and hand it in.
COPY THESE QUESTIONS ONTO PAPER IN AN ORGANIZED WAY AND SHOW YOUR
WORK AND ANSWERS FOR EVERY QUESTION:
Solve for the variable in 2-step Equations with Fractions and Negatives
3
1) 10 − 5 𝑘 = 1
5
2) −7 + 6 𝑏 = 53
5
3) − 7 ℎ + 25 = −15
4
5
4) − 12 + 𝑔 = 6
5)
5
8
𝑦 − 4 = −10
3
6) − 4 𝑤 + 6 = 32
𝑦
7) −32 + = 9
3
8)
2
9)
5
9
2
2
5
𝑘−3=9
3
𝑎−8=4
85
10)
4
2
− 3 𝑢 = −2
5
Combine Like-Terms and solve for the variable
11) 4𝑏 − 12 + 3 − 10 + 5𝑏 = 12
12) 3𝑐 − 4 − 5𝑐 + 10 − 2𝑐 = −13
1
13) 2𝑐 − 3 + 𝑐 + 3 − 12 = 24
3
2
14) 8 − 5 𝑣 + 10 + 3𝑣 = 12
4
15) −6 + 3𝑟 − 4 − 2𝑟 + 5 𝑟 = −10
Use the distributive property and combine like-terms to express these equations in
shortest and simplest form
16) 3(4𝑤 + 21 − 3𝑑) =
17) 4𝑓(3 + 5𝑒) =
18) 3(3ℎ − 7𝑦 + 4) =
19) 6(5𝑘 − 2𝑐 + 3𝑘) =
20) 5 + 3(4𝑟 − 7) − 20 =
21) 6 − 2(𝑔 − 4) + 5𝑔 − 10 =
22) 9 − 15 + 3(𝑦 − 8 + 4) =
86
Use the distributive property, combine like-terms and then solve for the variable
23) 5(𝑐 − 2) + 10 − 3𝑐 = 24
24) 7 + 2(3𝑑 − 4) + 4𝑑 − 15 = 30
25) −4(ℎ − 5) + 2ℎ + 5(ℎ − 2) = 5
26) −3(5 − 𝑦) + 12 − 6𝑦 = 10
87
ALE – Review for Quiz + Solutions
1) There is a class Jeopardy game in a “Notebook” file that you
can play as a class with your teacher as a form of review or
extra practice. Your teacher has the file containing this
review.
2) You should complete the following review for your quiz on
your own:
Show your work for every question. You can show your work on
paper or Bamboo Tablet.
Activity 1: Jeopardy (Part 1)
http://www.quia.com/cb/173353.html
Copy and paste the link above into a browser. Play the game and
show your work and answers.
Activity 2: Jeopardy (Part 2)
Go to Edu2.0 and download the PowerPoint file called “JeopardyMath Variables” from the news section.
Play the game and show your work and answers.
88
Activity 3: Calculating Perimeter with variables
Show your work on a separate piece of paper.
a) Express the perimeter of the following shape as the simplest and
shortest equation:
x
3x-2
3x-2
10-x
10-x
40 + x
b) If the perimeter of the shape above is actually 74cm, use your
equation to solve for the variable “x”.
c) What is the actual length of each side of the shape?
Activity 4: Calculating Area with variables
Show your work on a separate piece of paper.
1a) Express the area of the following shape as the simplest and
shortest equation:
35+7-3x
2x
b) If x = 5, what is the actual area of the rectangle? Use your
equation from a) to figure this out.
89
2a) Express the area of the following shape as the simplest and
shortest equation:
3r + 25
16
10r - 2
b) If the actual area of the triangle is 144cm2, solve for the variable
“r” using your equation.
c) What is the length of each side of the triangle?
90
ALE Review Solutions
ACTIVITY 1:
The answers to the Jeopardy show up as you play the game online. Show your work and
answer for every question.
ACTIVITY 2:
One-Step Equations
4
100: u= 9
200: b=24
300: v = 40
400: g = 14
Two-Step Equations
100: k = 24
200: h = 30
300: c = 18
400: n = 20
Solve (1)
100: w = 3
200: p = 2
300: c = 9
400: q = 8
Solve (2)
100: u = 5
200: x = 4
91
300: p = 6
400: u = 6
ACTIVITY 3:
a) 6x + 56 = perimeter
b) x = 3
c)
3cm
7cm
7cm
7cm
7cm
43cm
Note: The dimensions of this shape are not geometrically
correct. Discuss this with the teacher.
ACTIVITY 4:
1a) 84x – 6x2 = area
b) 270cm2
2a) 80r-16 = area
b) r = 2
c)
16cm
31cm Note: The dimensions of this triangle are not geometrically
correct. Discuss this with the teacher.
18cm
92
Unit 7 – Speed, Rate, Ratios and Proportions (SRRP)
Topics to be covered in this unit:
1. Scaling and equivalency in terms of units (mm to cm, cm to
m, m to km, ml to L, etc)
2. Rate - explored heavily through speed, distance and time
problems. Other applications also discussed.
3. What are ratios and proportions?
4. Working with ratios and proportions in real life
Math Lingo:
Word
Write the
meaning or
describe the
relationship (in
your own words)
Find/draw a
picture that
describes the
word or give an
example
Speed
Rate
Kilometer (km) and
meter (m) and
centimeter (cm)
Kilogram (kg) and
gram (g)
Liter (L) and
milliliter (ml)
Ratio
Proportion
93
SRRP – Activity 1 - Regular Track
Speed Challenge
Note: Your teacher will give you this assignment on paper in class.
All students must do this assignment.
Objective – In this activity you will investigate speed as a rate of change.
You need to work in partners for this activity!!! Only 2 students per team!!!
Step 1: Gather your materials!
Each team needs 1 timer, 1 measuring tape and your assignment paper.
Step 2: Create your “race” track.
Find a spot outside away from other groups. You need to make 1 racetrack. Your
racetrack should be between 11 and 20 meters. Mark the start and finish line of the
racetrack.
Step 3: Go for it!
Collect That Data!
Record your data from this experiment in the chart. Then use the information to
calculate the distance per unit of time (speed) for each task. Round answers to the
nearest hundredth if needed.
TASK
Run Backwards
DISTANCE
(meters)
TIME
Student 1)
Student 1)
Express your
“speed” as the
number of meters
you travelled per
second
Student 1)
Student 2)
Student 2)
Student 2)
94
Hop Forward
Student 1)
Student 1)
Student 1)
Speed Walk
Student 2)
Student 1)
Student 2)
Student 1)
Student 2)
Student 1)
Sprint
Student 2)
Student 1)
Student 2)
Student 1)
Student 2)
Student 1)
Student 2)
Student 2)
Student 2)
Student 1
Think About It!
1. Which task and distance resulted in the fastest speed?
Task = ____________ Distance = ____________ Speed = ____________
2. Which task and distance resulted in the slowest speed?
Task = ____________ Distance = ____________ Speed = ____________
3. How far could you speed walk in 10 minutes based on your speed? Show your work!
4. How long would it take you to hop 30 meters based on your speed? Show your work!
5. How far could you travel running backwards for 15 minutes based on your results? Show
your work!
95
6. How long would it take you to sprint 1 kilometer (or 1,000 m) based on your speed? Show
your work!
Student 2
Think About It!
1. Which task and distance resulted in the fastest speed?
Task = ____________ Distance = ____________ Speed = ____________
2. Which task and distance resulted in the slowest speed?
Task = ____________ Distance = ____________ Speed = ____________
3. How far could you speed walk in 10 minutes based on your speed? Show your work!
4. How long would it take you to hop 30 meters based on your speed? Show your work!
5. How far could you travel running backwards for 15 minutes based on your results? Show
your work!
6. How long would it take you to sprint 1 kilometer (or 1,000 m) based on your speed? Show
your work!
96
SRRP – Activity 2 - Regular Track
Scaled Speed Worksheet
Note: Your teacher will give you this assignment on paper in class.
All students must do this assignment.
Speed:
1) A car travels 300km in 5 hours. What is the speed of the car?
2) A plane travels 2500km in 2 hours. What is the speed of the plane?
3) Patricio finishes 5 pages of homework in 2 hours. At what rate (speed) is Patricio
finishing his homework?
Distance:
1) If Cynthia skates 45km/hr and she does this for 2 hours, how many kilometers has
she skated?
2) If a puck on an air hockey table moves at a speed of 3m/s and it moves for 15
minutes, what distance does it move in total?
3) Ms. Khare rides a bike at a speed of 15km/hr. If she rides a bike for 20 minutes,
how much distance will she cover?
Time:
1) A duck swims in the pond at a rate of 3m/s. In how much time will the duck swim
27m?
97
2) David rides a tricycle at a speed of 8m/s. How long will David take to ride 2km?
3) A train travels at a speed of 60km/hr. The next station is 480m away. How much
time will it take the train to get to the next station? (YOU CAN USE A CALCULATOR
FOR THIS QUESTION!!!
SRRP – Activity 3 - Regular Track
WebQuest – World’s Fastest and Slowest
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper. Upload the
pictures for your work into a folder called “SRRP-Activity3” on
GoogleDocs when you’re done.
Note: All students must do this assignment.
Google each “category” and find the name and calculate the speed. Then answer
question 1 and question 2 for each category. Show your work and answer. YOU CAN
USE A CALCULATOR FOR THESE QUESTIONS.
Category
Name
Speed (with
units)
Question 1:
Question 2:
World’s
fastest car
How far could
this car travel
in 3 hours?
How long
would it take
this car to
travel 915km
(Monterrey to
Mexico City)?
World’s
fastest man
How far could
this man run
in 20 minutes?
How long
would it take
this man to
run 1km
98
(1000m)?
World’s
fastest
woman
How far could
this man run
in 20 minutes?
How long
would it take
this woman to
run 1km
(1000m)?
World’s
fastest animal
How far could
this animal
move in 2
hours?
How long
would it take
this animal to
move 1km
(1000m)?
World’s
slowest
animal
How far could
this animal
move in 2
minutes?
How long
would it take
this animal to
move 10
99
meters?
World’s
fastest roller
coaster
How far could
this roller
coaster travel
in 30 minutes?
How long
would it take
for this roller
coaster to
travel 1km?
Order of Operations:
1)
3
2)
1
5
2
4
− 7 (3-2  2)
2
∙ 3 3 + (23 - | -5| )
100
SRRP – Activity 4 - Regular Track
Three-Legged Man Activity
Note: Your teacher will give you this assignment on paper in class.
THREE-LEGGED MAN ACTIVITY
1) Get into partners.
2) Find a spot outside and measure out 20 meters for a racetrack.
3) Be sure to mark your start point and your end point.
4) One partner should tie one of his legs to a leg of the other partner at the start line.
5) Both partners should run on 3 legs from the start line to the finish line and time
themselves.
6) If one of the partners falls, step 5 should be repeated until both partners get it right.
7) Fill out the FIRST ROW of the following table:
Names
Distance
(meters)
Time
(seconds)
Speed
Team A:
Team B:
8) Fill out the second row of the following table using another team’s data.
101
Follow-up Questions:
1) Which team would finish 1st if both teams had a 3-legged man race?
2) If no one got tired, how far could Team A travel in 30 minutes?
3) How much time would it take Team B to travel 2km as a 3-legged man?
4) If one team started at the finish line and another team started at the start line:
a. At what distance from the finish line would both teams pass each other
on the racetrack?
(Hint: Draw a picture of this problem and then try to solve it!)
b. After how much time would both teams pass each other on the
racetrack?
102
SRRP – Activity 5 – Regular Track
Review for Quiz on Speed and Rate
You can copy and paste this assignment into another word
document and show your work in that document. You can also
show your work on paper.
Note: All students must do this assignment.
Speed and Rate Review
You can use a calculator! SHOW ALL YOUR WORK (EVEN THE WORK YOU DO ON THE
CALCULATOR)!!
1) A plane travels 700km in 3 hours. What is the speed of the plane?
2) John drives at a speed of 60km/hr for 7 hours. How far did he go?
3) A train travels 70km/hr for 490km. How much time does it take?
4) Sandy can do 80 jumping jacks in 2 minutes. How many jumping jacks will she do
in 15 minutes if she doesn’t get tired?
5) A machine takes 12 minutes to fill up 200 bottles of soda. At this rate, how many
minutes will it take for the machine to fill 500 bottles of soda?
103
6) A car gets 50km per gallon of gasoline. How many kilometers could the car travel on
4.5 gallons of gasoline?
7) Jimena runs 54m/minute. If Jimena didn’t get tired, how long would it take her to
run 367m?
8) The world’s fastest typist types 150 words per minute. How many words can she
type in 10 seconds? How many words can she type in 1 second?
9) Willy read a 200-page book in 10 hours. At that rate, how long would it take him to
read a 320 page book?
10)A duck flew at 16km/hr for 4 hours, and then 12km/hr for 3 hours. How far did the
duck fly in all?
11)Stephanie is reading a 456-page book. During the past 7 days she has read 168
pages. If she continues reading at the same rate, how many more days will it take
her to complete the book?
12)A parking meter takes a dollar for every 10 minutes. How much does it cost to park
for 2 hours?
13)If the world’s fastest man runs 10.44m/s, how long would it take him to run 1km?
(1km = 1000m)
14)If the worlds fastest land animal (cheetah) runs 112km/h, how much distance will it
cover in 5 minutes?
15)Ms. Khare runs 9m/s. If she doesn’t get tired, how far can she run in 25 minutes?
104
16) Tania and Steven are 15km away from each other. Tania is at the pond and Steven
is at the cabin. Tania walks 2km/hr. Steven walks 3km/hour. They are walking
towards each other.
a) After how much time will Tania and Steven meet? (Hint: Make a picture of the
race track and make the pond 0 and the cabin 15 and track Tania’s and
Steven’s distance towards each other).
b) How far from the pond will Tania and Steven be when they meet?
Solutions to Speed and Rate Review
1) 233.33km/hr
2) 420km
3) 7hr
4) 600 jumping jacks
5) 30 minutes
6) 225 km
7) 6.80 minutes
8) 25 words in 10 s. 2.5 words/s
9) 16 hours
10)100 km
11)12 days
12) 12 dollars
13)95.79s
14)9.33km
105
15)13500m
16) a) 3hr
b) 6km from the pond.
SRRP – Activity 6 – Regular Track
Introduction to Ratios
Show your work and answers on paper and hand in your paper at
the end of class.
Ratio Word Problems
1) The ratio of bananas to peaches in a fruit basket is 11 to 5.
If there are 99 bananas then how many peaches are there?
2) The ratio of doves to parrots in a cage is 11 to 8. If there
are 44 doves then how many parrots are there?
3) The ratio of bananas to peaches in a fruit basket is 6 to 7.
If there are 104 bananas and peaches in the fruit basket
altogether then how many bananas are there?
4) The ratio of cubes to spheres in a geometry box is 5 to 8. If
there are 20 cubes then how many spheres are there?
5) The ratio of doves to parrots in a cage is 9 to 8. If there are
64 parrots in the cage then how many doves and parrots
are there altogether?
6) The ratio of cars to vans in a parking lot is 13 to 12. If
there are 108 vans then how many cars are there?
7) The ratio of blue marbles to red marbles in a box is 7 to 13.
If there are 100 blue marbles and red marbles in the box
altogether then how many blue marbles are there?
106
8) The ratio of doves to parrots in a cage is 1 to 5. If there are
40 parrots then how many doves are there?
9) The ratio of cubes to spheres in a geometry box is 7 to 11.
If there are 72 cubes and spheres in the geometry box
altogether then how many cubes are there?
10) The ratio of apples to oranges in a fruit basket is 8 to 7. If
there are 64 apples then how many oranges are there?
107
SRRP – Activity 7 – Regular Track
More Practice with Ratios
(Review for the Ratios Quiz)
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper. Upload the
pictures for your work into a folder called “SRRP-Activity7” on
GoogleDocs when you’re done.
1) Write each ratio in simplest form:
a) 5:10 =
b) 18:6
c) 14:35
d) 120:50
2) What is the missing number?
a)
b)
4
7
=
12
=
5
c)
16
d)
2
36
3
14
15
=
=
4
15
108
3) What is the missing number?
a. 1:6 = ______ : 54
b) 6:8 = 3: _______
c) 5:20 = ______ : 4
d) _______ :4 = 8:16
4) There are 100 passengers on the train at the start of the route. The
train stops at a station and 36 passengers get off.
a. Write the ratio, in simplest form, that compares the number of
passengers remaining on the train to the total number at the start.
b. Look at your answer for a). Is that a part-to-part ratio or a partto-whole ratio? Explain how you know.
5) Tami makes her own oil and vinegar dressing. Her recipe needs 150ml
of olive oil and 200ml of vinegar.
a) Write the ratio, in simplest form, to compare the amounts of the 2
ingredients.
b) Look at your answer for a). Is that a part-to-part ratio or a part-towhole ratio? Explain how you know.
c) What amount of vinegar is needed to mix with 270ml of olive oil?
109
d) If Tami wants to make 700ml of dressing, what quantity of each
ingredient does she need?
6) A recipe for 2-cheese lasagna calls for 200 grams of ricotta cheese and
300 grams of mozzarella.
a. Write a ratio, in simplest form, to compare the amounts of the 2
cheeses.
b. What amount of mozzarella is needed to make lasagna that
contains 800 grams of ricotta?
c. What amount of each cheese is needed to make lasagna that
contains 1 kg of cheese in total?
7) At a soccer tournament, one team’s win-loss record was 12:8. A second
team had a win-loss record of 15:5. Both teams had no ties.
a. Express each ratio in simplest form.
b. How many games did each team play?
8) A baseball team’s win-loss record is 20:15.
a. Write this ratio in simplest form and explain what this ratio tells
you.
b. If this trend continues, how many losses would you expect the
team to have once they have won 60 games? (You can use a
calculator for this one)
110
c. Approximately how many games would you expect the team to
win over a 161-game season? (You can use a calculator for this
one)
9) The ratio of the length to the width of the Canadian flag is 2:1.
a. The flag on the cover of the Canadian atlas is 8cm wide. How long
is it?
b. One Canadian flag has a perimeter of 2.7m. What is its length?
(You can use a calculator for this one)
Bonus!!! Use the table below to answer the next few questions.
Headliners
The Howlin’ Paulinas
Virtual Elizondos
Lalo’s Monkeys
3-left feet
Supporting Acts
Moondancer
CU L8er
ASFM rocks
Math is the best!
Tania DLG aka MathWizard
Charlie and his chocolate
A concert lasts 10 hours. Each headliner plays twice as long as each
supporting act. Each band gets 25 minutes to set up.
a) What is the ratio, in simplest from, of the number of headliners to the
number of supporting acts?
b) How much total time is used for:
i. Band set-up?
ii. Playing time?
111
c) Write the ratio, in simplest form, to compare total set-up time to total
playing time.
d) Determine how many minutes:
i. Each supporting act gets to play.
ii. Each headliner gets to play.
Solutions to Review for Ratios Quiz
1) Write each ratio in simplest form:
a) 5:10 = 1:2
b) 18:6 = 3:1
c) 14:35 = 2:5
d) 120:50 = 12:5
2)What is the missing number?
a)
4
b)
4
c)
16
d)
2
7
5
=
=
36
3
8
14
12
15
=
=
4
9
10
15
3) What is the missing number?
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a. 1:6 = ___9___ : 54
b) 6:8 = 3: ___4____
c) 5:20 = __1____ : 4
d) ___2____ :4 = 8:16
4) There are 100 passengers on the train at the start of the route. The
train stops at a station and 36 passengers get off.
a. Write the ratio, in simplest form, that compares the number of
passengers remaining on the train to the total number at the start.
64:100 = 16:25
b. Look at your answer for a). Is that a part-to-part ratio or a partto-whole ratio? Explain how you know.
Part-to-whole
5) Tami makes her own oil and vinegar dressing. Her recipe needs 150ml
of olive oil and 200ml of vinegar.
a) Write the ratio, in simplest form, to compare the amounts of the 2
ingredients.
3ml olive oil: 4ml vinegar
b) Look at your answer for a). Is that a part-to-part ratio or a part-towhole ratio? Explain how you know.
Part-to-part
c) What amount of vinegar is needed to mix with 270ml of olive oil?
360ml of vinegar
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d) If Tami wants to make 700ml of dressing, what quantity of each
ingredient does she need?
300ml olive oil: 400ml vinegar
6) A recipe for 2-cheese lasagna calls for 200 grams of ricotta cheese and
300 grams of mozzarella.
a. Write a ratio, in simplest form, to compare the amounts of the 2
cheeses.
2g ricotta :3g mozzarella
b. What amount of mozzarella is needed to make lasagna that
contains 800 grams of ricotta?
1200g mozzarella
c. What amount of each cheese is needed to make lasagna that
contains 1 kg of cheese in total?
400g ricotta : 600g mozzarella
7) At a soccer tournament, one team’s win-loss record was 12:8. A second
team had a win-loss record of 15:5. Both teams had no ties.
a. Express each ratio in simplest form.
12:8 = 3:2 and 15:5 = 3:1
b. How many games did each team play?
20 games
8) A baseball team’s win-loss record is 20:15.
a. Write this ratio in simplest form and explain what this ratio tells
you.
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4:3
b. If this trend continues, how many losses would you expect the
team to have once they have won 60 games? (You can use a
calculator for this one)
45 losses
c. Approximately how many games would you expect the team to
win over a 161-game season? (You can use a calculator for this
one)
92 games won
9) The ratio of the length to the width of the Canadian flag is 2:1.
a. The flag on the cover of the Canadian atlas is 8cm wide. How long
is it?
16cm long
b. One Canadian flag has a perimeter of 2.7m. What is its length?
(You can use a calculator for this one)
Length = 0.9m
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SRRP – Compacting 1
Worm vs. Snail & Superman vs. Lois Lane
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper or Bamboo.
Upload the pictures for your work into a folder called “SRRPCompacting1” on GoogleDocs when you’re done.
Part 1: The Worm vs. The Snail
Worm and Snail Problem. A worm starts at the oak tree and moves
away, heading for the elm tree at a constant rate of 13 meters per
hour (m/h). At the same time, a snail starts at the elm tree and
moves toward the oak tree at a constant rate of 17 m/h. The two
trees are 100 m apart. Let x be the number of hours the two
creatures have been creeping.
a.
Draw a diagram showing the two trees 100 m apart and the
worm and snail somewhere between the trees. Draw arrows
marking each creature’s distance from the oak tree.
b.
Write the definition of x . Then write an equation for the worm’s
distance from the oak tree. Write an equation for the snails
distance from the oak tree.
c.
Who is closer to the oak tree after 2 hours? How much closer?
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d.
Who is closer to the oak tree after 4 hours? How much closer?
e.
When do they pass each other?
f.
How far are they from the oak tree when they pass each other?
Part 2: Lois Lane vs. Superman
Lois Lane leaves Metropolis driving 50 km/h. Three hours later
Superman leaves Metropolis to catch her, flying 300 km/h. When
does Superman catch up with Lois? How far are they from
Metropolis then?
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SRRP – Compacting 2
Human Proportions - Vitruvian Man Lab
Show your work for every question. You can copy and paste this
assignment into another word document and show your work in
that document. You can also show your work on paper. Upload the
pictures for your work into a folder called “SRRP-Compacting1” on
GoogleDocs when you’re done.
Problem:
Can we identify physical proportions that are shared by all humans?
Hypothesis:
I think I (CAN / CANNOT) find a pattern in the development of the human body.
Materials:
Measuring tape
Procedure:
1) Make the following measurements as indicated below and record them in your
data table for you and your partner. Write all your measurements in
centimeters!!!
Height: With back against the wall and shoes removed, measure from the tip of the skull to
the heel.
Arm Span: Extend arms horizontally and measure from the fingertip on one hand to the
fingertip on the other hand.
Head width: Measure from the top of the tip of one ear, across the face, to the top of the tip
of the other ear.
Shoulder width: Measure from one shoulder tip to the other shoulder tip across the back.
Head length: Measure a line from the top of the forehead to the tip of the chin.
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Forearm: Measure from the elbow to the wrist.
Hand-length: Measure from the wrist to the tip of the longest finger.
Hand-width: With the hand flat on the table, measure the width of the four fingers of the
hand when they are touching each other.
Shin: measure from the knee to the bottom of your ankle bone.
Foot length: Measure from the heel to the tip of the longest toe.
Head circumference: Measure the perimeter above your ears around your skull.
Ear length – Measure from the top tip of your ear to the bottom of your ear lobe.
2) If you’re a boy, get information from another 3 girls and 1 boy to fill up the other
columns of your data table. If you’re a girl, get information from another 3 boys
and 1 girl to fill up the other columns of your data table. DON’T FORGET UNITS!!!
Data Table
Body Part
Me
Partner
Other
Person 1
Other
Person 2
Other
Person 3
Other
Person 4
Height
Arm Span
Head width
Shoulder
width
Head Length
Forearm
Hand-length
Hand-width
Shin
Foot Length
Head
Circumference
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Ear Length
Results and Discussion: Answer the following 2 questions
1) Look at the measurements on your data table and calculate the average ratio
between the following pair of measurements. Fill out the table below to do this. The
first row of the table is an example of how the rest of the table should be filled out.
Body Part
1
Body Part
2
Ratio
(body part 1 : body part2)
for each person surveyed
Reduced ratios
of each person
surveyed
Average
reduced
ratio
Conclusion
Head
width
Ear
length
24cm:6cm
22cm:5cm
32cm:8cm
28cm:7cm
25cm:6cm
19cm:5cm
24:6 = 4:1
22:5 = 4.4 :1
32:4 = 4:1
28:7 = 4:1
25:6 = 4.2 :1
19:5 = 3.8 :1
4.1 :1
So earlength
fits into
head
width 4
times for
all 7
graders
at ASFM.
(All of these
ratios are really
close to 4:1)
Height
Shoulder
width
Foot
Length
Forearm
Height
Armspan
Head
width
Hand
Width
Hand
length
Head
Length
2) An artist relies upon certain proportions of the body in order to accurately portray a
human figure. What do you think might be the most important measurement from
which an artist will base all of the other measurements on a human drawing?
3) Through this experiment, can you see a pattern of human development that can be
recognized as human in nature?
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******************** End of Semester 2 ***************************
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