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Western Canadian
Teacher Guide
Unit 2
Unit 1:
Sorting and Patterning
Unit 2: Number Relationships
Unit 3:
Time, Temperature, and Money
Unit 4:
Exploring Addition and Subtraction
Unit 5:
Data Management and Probability
Unit 6:
3-D Geometry
Unit 7:
Addition and Subtraction to 100
Unit 8:
Linear Measurement, Area, and Perimeter
Unit 9:
2-D Geometry and Patterning
Unit 10: Multiplication, Division, and Fractions
Unit 11: Mass and Capacity
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UNIT
2
“
A strategy is most useful
to children when it is
theirs, built on and
connected to concepts
and relationships they
already own.
”
—John A. Van de Walle,
Elementary and Middle School
Mathematics (4th Ed.), page 129
Number Relationships
Mathematics Background
What Are the Big Ideas?
This unit focuses on number relationships. Children learn and
practise approaches to counting, including grouping, skip counting,
counting on, and counting back.
■ Counting is a skill that is embedded in all of the activities in this
unit. Children move from counting by ones to counting groups.
The activities in this unit help children understand that larger
quantities can be more easily counted when they are partitioned
into smaller quantities. Children learn to skip count by 2s, 5s, 10s,
and 25s to 100 and beyond, and learn to look for patterns.
■ Children extend their understanding of the number relationships
of 1 or 2 more and 1 or 2 less, by counting forward and backward.
They use counting on and counting back as one strategy for
addition and subtraction. More and less relationships are also
explored with doubles and near doubles. When children know
doubles, they can extend that understanding to near doubles. Some
children will use doubles for other facts as well. Children will
continue to apply these skills in later units, and specifically in
Unit 3, where children apply their addition and subtraction
strategies to money problems.
FOCUS STRAND
Across the Strands
Number
Exploration of whole numbers and their relationships form the
foundation for conceptual understanding in mathematics across a
child’s grade 2 year. Explicit applications of counting will surface
again when the child encounters concepts in measurement (counting
non-standard and standard units, clustering standard units into
groups to facilitate counting larger numbers of units), data
management and probability (tallying experiment outcomes or
responses to survey questions), and geometry (counting objects or
figures that have been sorted according to selected attributes).
Children use concepts from the patterning strand as they work with a
variety of counting methods, and explore number relationships in
charts and tables.
SUPPORTING STRANDS
Patterns and Relations
Statistics and Probability
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Curriculum across the Grades
Grade 1
Grade 2
Grade 3
Children compare and
order numbers to 50.
Unit 2: Children read
and count to 1000.
Children build and
record addition and
subtraction facts.
Children build a variety
of number strategies to
support their recall of
addition and subtraction
facts.
Children extend place
value concepts to
numbers up to 1000.
Children identify number
patterns to 50.
Children compare,
order, and round whole
numbers up to 1000.
Children use materials to
count and represent
numbers to 100, and
explore number patterns
beyond 100.
Children develop a
variety of strategies for
adding and subtracting
two-digit and three-digit
numbers, including
mental math strategies.
Unit 4: Children develop
a variety of strategies to
find sums and differences
of two-digit numbers.
Children build and recall
multiplication facts to
7 x 7 and division facts
to 49 ÷ 7.
Unit 7: Children develop
paper-and-pencil methods
to find sums and differences
of two-digit numbers.
Unit 10: Children explore
repeated addition
(multiplication), sharing
(division), and fractions.
Preparing Materials
Make two-sided beans by spray painting one side of each bean, or use a
commercial set of two-colour counters.
The ten-frames, 100-charts, numeral cards, domino cards, and spinners
(LMs 3, 9–13, 17, 18, and 20) are best duplicated onto heavy paper and
laminated for durability. Once laminated, the numeral cards and dominoes
(LMs 9–13 and 17–18) can be cut and placed in resealable plastic bags
for children to use. Every child will need a copy of the number line and
100-charts, and 2 copies of the ten-frames. You can write the numbers and
symbols needed for a particular game on the spinners before laminating or
after, using washable markers. To use a spinner, children place a pencil tip
in the centre of the spinner and spin a partially unfolded paper clip.
Dot plates can be made using small paper plates and circular stickers. Copy
the pattern of dots shown on LM 6. Some patterns are made using two
colours of dots and these are shown on the Line Master in different shadings.
The dot patterns should be kept close together to allow for easy recognition.
LM – Line Master
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Curriculum Overview
Launch
Cluster 1: Number Relationships to 50
General Outcomes
Specific Outcomes
• Recognize and apply whole
numbers ...
• Identify, create, describe,
and translate numerical ...
patterns arising from daily
experiences in the school
and on the playground.
• Estimate, then count the
number of objects in a set
(0 to 100) ... and compare
the estimate with the actual
number.
• Read and write numerals to
100 ...
• Read and write number
words to 20.
• Identify and describe
patterns, including
numerical ... patterns.
• Round numbers to the
nearest ten.
Lesson 1:
Building Numbers to 20
Lesson 2:
Counting Collections
Lesson 3:
Counting on a Number
Line
Cluster 2: Addition and Subtraction to 18
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General Outcomes
Specific Outcomes
• Recognize and apply whole
numbers to 1000 ...
• Apply a variety of addition
and subtraction strategies on
whole numbers to 100 ...
and use these operations in
solving problems.
• Use an appropriate
calculation strategy or
technology to solve
problems.
• Demonstrate if a number
from ... is even or odd.
• Use manipulatives,
diagrams, and symbols to
demonstrate and describe
the processes of addition
and subtraction of numbers
...
• Apply and explain multiple
strategies to determine sums
and differences on 2-digit
numbers, with and without
regrouping.
• Apply a variety of
estimation and mental
mathematics strategies to
addition and subtraction
problems.
• Recall addition and
subtraction facts to 10.
Unit 2: Number Relationships
Lesson 4:
Number Facts
to 18
Lesson 5:
Related Facts
Lesson 6:
Doubles and Near
Doubles
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Activity Bank
• Classroom Collections
• A Show of Hands
• Dot Plates
Activity Bank
• Snap Cube Trains
• Hit the Target
• Trading for a Dime
Activity Bank
• Dot Plate Mysteries
• Adding on a Calculator
• All in the Family
Activity Bank
• Even Steven and Odd Todd
• Doubles Dominoes
• Building Doubles
• Odd and Even Numbers
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Curriculum Overview
Cluster 3: Number Relationships to 100 and Beyond
vi
General Outcomes
Specific Outcomes
• Recognize and apply whole
numbers up to ...
• Use an appropriate
calculation strategy or
technology to solve
problems.
• Identify, create, describe ...
numerical patterns arising
from daily experiences in the
school and on the
playground.
• Count to 1000 by 1s, 2s, 5s,
and 10s, and to 100 by 25s,
using starting points that are
multiples of 1, 2, 5, 10, and
25 respectively.
• Estimate, then count the
number of objects in a set
(0 to 100), and compare the
estimate with the actual
number.
• Recognize, build, compare,
and order sets that contain 0
to 100 elements.
• Represent and describe
numbers to 100 in a variety
of ways.
• Demonstrate, concretely and
pictorially, place-value
concepts to give meaning to
numbers up to 100.
• Read and write numerals to
100.
• Explore the representation of
numerals (0 to 100), using a
calculator or a computer to
display numerals.
• Demonstrate if a number
from 1 to 100 is even or
odd.
• Identify and describe
patterns, including numerical
... patterns.
• Create, extend, and describe
patterns including numerical
... patterns.
Unit 2: Number Relationships
Lesson 7:
Estimating Large
Numbers
Lesson 8:
Numbers to 100
Lesson 9:
Counting Patterns
beyond 100
Lesson 10:
Strategies Tool Kit
Lesson 11:
Show What You Know
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Activity Bank
• Drawing Stars
• Towers of 10s
• Ordering Collections
• Estimating and Counting Coins
Activity Bank
• Skip Counting on the Calculator • What’s My Pattern?
• Plotting People
• Neighbour Numerals
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Planning for Instruction
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Suggested Unit Time: 3 Weeks
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Planning for Instruction
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Suggested Unit Time: 3 Weeks
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Planning for Assessment
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Mathematics Centres
Making Numbers
Same Number, Different Ways
(appropriate for use after Lesson 2)
(appropriate for use after Lessons 3 and 8)
Materials: draw-and-stamp computer program
Resources and Materials: LM 3, LM 20; counters
■
Children work in pairs to create number
puzzles for each other. Each child uses a
computer draw-and-stamp program to
make a picture of up to 50 things. Children
stamp or copy and paste items on the
page and then print it.
■
On the reverse side, children record the
matching numeral.
■
Children can compare pages and predict
which shows more things. They then
exchange pages and count the number
of items.
■
Partners discuss whether their prediction
was correct and the different counting
methods they used.
Visual; Social
■
Children spin two different 4-part spinners to
determine the first and second digits of a number.
After lesson 3, use the numerals 1, 2, 3, and 4 on
the spinner for the first digit and 5, 0, 7, 8 on the
spinner for the second digit.
■
The child writes the numeral and represents it with
counters on ten-frames. The child then
records the number of tens and ones in the number.
■
Children compare their number with a friend’s
number. Whose is greater? How did they know?
■
Modify this Centre after Lesson 8 for numbers
beyond 50 by changing the numerals on the
spinners to 4, 7, 5, 8 and 6, 3, 9, 2. This time the
child can choose which numeral to use as the first
digit and which as the second.
Visual; Logical
Making Number Sentences
100-Chart Puzzles
(appropriate for use after Lessons 4
and 5)
(appropriate for use after Lesson 8)
Resources and Materials: LM 3,
LM 9; beans, beads, stickers, straws,
toothpicks, crayons, markers, paper
■
Children use materials to create and
record at least five different addition
and subtraction sentences for numeral
card 9.
■
The pages can be stapled together
to form a book “Addition and
Subtraction Sentences for 9”.
■
Throughout the course of the unit,
change the number and have children
create books for numbers 10 to 18.
Social; Logical
Resources: LM 8, copied onto colour paper, cut into a
variety of puzzle shapes along grid lines, and each set of
pieces placed in an envelope
■
■
Children work together in
pairs, or individually, to
assemble a 100-chart
puzzle.
24 25 26 27 28
38
48
58
While children work, ask
them to explain the strategies
23
they are using to connect the
33 34 35 36
pieces and order them by
44 45
tens and ones. This is a
valuable activity for assessing
children’s understanding of place value.
Logical; Visual
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UNIT
52
FOCUS
Demonstrate prior knowledge
of numbers to 20
MATERIALS
chart paper, collection of small
classroom objects (counters,
keys, shells, buttons)
PROGRAM RESOURCES
Big Math Book, page 5:
Numbers at the Grocery Store
Student page 27: Number
Relationships
Student page 28: Dear Family
Student page 29: How Many?
LM 1: Number Relationships
LM2: Dear Family
DIAGNOSTIC
ASSESSMENT
Provide a variety of concrete
counting opportunities for
children who have difficulty.
Engage them in counting
classmates (boys/girls;
sitting/standing), classroom
objects, items illustrated in
favourite books, and objects
they choose (pieces of
classroom games).
To guide your observations,
use Assessment Master 1:
Diagnostic Checklist.
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Launch
Ask children to share what they already know about numbers (e.g.,
counting, adding, and subtracting). Discuss with children when they
need to count numbers of things, such as when they count to see how
many things are in a collection, or count two collections to compare
how many.
Display Big Math Book, page 5. Ask:
■ What do you see on this page? (a grocery story, groceries, number of
objects)
■ What do you notice about the picture? (Items are in groups.)
Invite children to find examples of objects that represent numbers
from 1 to 10. For each example, discuss whether the child counted the
objects or how else she or he knew how many there were. Then have
children think of possible examples for numbers 11 to 20. Ask:
■ What can we add to the page to show 11? (11 cans of soup, 11 grapes)
■ What can we add to the page to show 12? (a carton of 12 eggs,
12 muffins)
Display a collection of small classroom
objects. Have a volunteer make a group of
up to 20 objects. Ask:
■ How many objects are in this group?
■ How do you know?
■ Does it make a difference where the
counting starts? Tell me about your
thinking.
■ What other way could you count the
objects? (skip count by 2s, 5s; make a group
of 5 and count on)
TEACHING TIP
Model the skills of
counting not only by
1s, but also by 2s, 5s,
and 10s. Think aloud
when demonstrating
these skills and have
children think aloud
when they count.
Provide support for children who are having difficulty. Touch each
object in the group as you count aloud.
Have children complete Student page 29. Bring them together to share
their work. Discuss the different ways of counting each group.
Some children may enjoy creating their own grocery store pictures.
Invite them to draw groups of grocery items and ask other children
to describe how many items there are in each group.
HOME CONNECTION
Send home Student pages 27 and 28 to introduce the Learning
Goals for this unit to family members. Alternatively, use LM 1 and
LM 2 to create a letter home.
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LESSON
1
CURRICULUM FOCUS
Represent whole numbers to
20 in different ways
N7, N8
MATH WORD WALL
zero to twenty
number
count
ten-frame
represent
MATERIALS
counters
PROGRAM RESOURCES
Student page 30: Numbers
to 20
LM 3: Ten-Frames
LM 4: Number Word Cards
(eleven to twenty)
LM 5: All about My Number
LM 9: Numeral Cards, 0
to 20
TEACHING TIP
Although counting to 20
may be second nature to
many children, the
concrete experience of
representing numbers with
counters and ten-frames
helps lay the foundation
for later place value work
with large numbers.
Breaking the numbers into
“10 and ____ more” may
also help some children
remember how to write
number words.
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Unit 2: Number Relationships
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Building Numbers to 20
BEFORE
Get Started
Draw a ten-frame on the board and invite a child to demonstrate how to
represent the number 6 on it. As the child shows the number, review the
procedures: only one counter is allowed in each section; the frame is
filled from left to right without skipping any sections; you start in the
top row; once the top row is full, you begin the next row. Ask:
■ Is 6 greater or less than 10? (Less) How do you know? (The ten-frame
is not full.)
■ How many counters do you have to add to fill the ten-frame? (4)
What does this tell you? (6 is 4 less than 10.)
Record the number word and numeral for 6, and how many less than
10 it is. Repeat for a ten-frame showing 9.
DURING
Explore
Have children count by 1s from 0 to 20 and back to 0. Ask:
■ What do you know about numbers that come between 10 and 20? (most
are teen numbers; all except 20 are written with a 1 and another numeral)
Problem Prompt
How can you use counters and ten-frames to represent numbers
between 11 and 20?
Provide each child with 2 ten-frames (LM 3), counters, and 2 copies of
LM 5. Make number word cards available for children who need help
writing the names. Write the numerals 11, 13, 16, and 17 on the board.
Have each child choose 2 of the numbers and complete the line masters.
Show and Share
For each of the 4 numbers, invite a volunteer to come to the board and
demonstrate how they represented and described the number. Some
children may fill one ten-frame and show the remaining counters
beside it, while others will use two ten-frames—both are valid
representations.
AFTER
Connect and Reflect
Have children refer to their completed masters and the samples
recorded on the board. Encourage them to consider the relationships
between the different ways of representing each number by asking:
■ What do the pictures we drew for each number have in common?
(there is 1 full ten-frame and some counters left over; each number was 10
and some more)
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What do the numerals have in common? (all begin with a 1, all end
with the number of left-over counters)
What do you notice about the end of the number names? (most end
in teen)
What do you notice about the start of the number names? (some start
with the number word or part of the number word for the left-over counters)
Invite a volunteer to come to the board and draw a representation for
20 using ten-frames. Ask:
■ How many groups of ten are there? (2)
■ How many counters are left over? (0)
Practice
Reinforcement
Review the directions for Student page 30 with the children. Make
counters, ten-frames, and number word cards available for children
who wish to use them.
Extra Support: ESL
ESL learners benefit from repeatedly seeing and using number words
in a variety of contexts. Provide them with lots of exposure to the
written number names by having them play “Number
Concentration” with a set of numeral cards and number word cards
for 11 to 20 (taken from LM 4 and LM 9). They mix up the cards, lay
them all out face down in rows, and turn over 2 at a time trying to
find matching pairs of numerals and words.
Extension
Provide children who are ready for a challenge with 5 ten-frames and
50 counters. Have them use counters to represent numbers between
20 and 50 on the ten-frames. They should draw a picture of each
arrangement and record the number of groups of tens and leftover
ones. Challenge them to develop a rule for representing numbers. Ask:
For a number like 34, what does the 3 tell you? (how many groups of 10)
What does the 4 tell you? (how many counters were left over)
Assessment for Learning
What to Look For
What to Do
Evidence that children
Continue to provide practice building sets with
concrete objects. Children having difficulty may
benefit from counting out the number of counters
first, then transferring the counters to ten-frames.
Ten-frame flash cards can promote instant
recognition of quantities without counting.
■
can represent numbers between 10 and 20 accurately
on ten-frames, with numerals, and number words
■
describe numbers between 10 and 20 as “10 and
____ more”
To guide observations and facilitate reporting, use
Assessment Master 3.1: Ongoing Observations
Checklist.
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LESSON
2
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Counting Collections
Get Started
CURRICULUM FOCUS
BEFORE
Estimate, count, and
represent numbers to 50
N2, N4, N7
Have 20 children stand in a line. Ask: “About how many children do
you think there are? Explain why you think so.”
MATH WORD WALL
Remind the children that estimating is about seeing how close you can
get to the actual number. Record their estimates. Then ask: “How can
we find out how many children there are?”
10s
left over
less
1s
more
estimate
MATERIALS
counters (beads, buttons,
paper clips), resealable
bags, ten-frames
PROGRAM RESOURCES
Big Math Book, page 6:
Estimating
Student page 31: Counting
Two Ways
Student page 32: Count the
Buttons
LM 3: Ten-Frame
LM 6: Dot Plates
Have the children count aloud from 1 to 5 as a child in the line steps
forward for each number. Pause and ask whether anyone wants to
change their estimate now that they have seen a group of 5 children.
After any revised estimates are made, have the children count on from
6 to 20. Compare the estimates with the counted result.
Display Big Math Book, page 6 and ask:
■ Do you think the squirrel has enough acorns for the winter?
■ About how many acorns do you think there are? Why do you think that?
■ How can we count them?
Use a counting method suggested by the class to count the number of
acorns aloud. Compare the estimates with the result (37). Record 37 on
the Big Math Book page and then ask:
■
How did we count the acorns? What other ways could they be counted?
■ Are some ways better than others? Explain. (some ways help you keep
track of the acorns that have been counted as you go)
■ How has 37 been shown? (as a picture, numeral)
■ What other ways can we show 37? (using materials, counters in a ten-frame)
With the children’s guidance, represent 37 by drawing counters on tenframes on Big Math Book, page 6.
DURING
Explore
Have children work in pairs. Provide each pair with a bag of up to 50
countable items. Tell children to work together to make an estimate,
explaining to their partners how they came up with a number.
Problem Prompt
How can you arrange the objects to make them easier to count?
Have children spill the contents of their bags, record their estimates,
and show different ways they counted the numbers on Student page 31.
Show and Share
Gather children together and ask:
What was your estimate?
■
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How many objects were in your collection?
How did you count the items in your bag?
Did anyone arrange the objects in groups? How did this help you?
AFTER
Connect and Reflect
Review different counting methods that children used. Ask:
■ Which way do you prefer when counting a large number of things?
Why? (I like to count by 10s; there are fewer groups to count.)
■ What different ways can we show numbers? (numerals, drawings,
number words, materials, counters in ten-frames)
Use the children’s suggestions about how to show numbers to create
a co-operative journal entry.
Practice
Reinforcement
Have children complete Student page 32, and share the ways they
counted the buttons. Activity Banks provide additional practice of
core concepts.
Extra Support: Procedures
Some children may need additional help with organizational skills
and strategies. Provide them with simple organizers, such as
10-frames, or a set of construction paper circles where they can place
objects as they are counted.
Children can practise and apply their counting skills at the
Mathematics Centres (see Making Numbers, page xiii).
Extension
Have each child in a pair represent a number under 50 using
countable materials. Children compare collections visually and
predict which contains more items, then check. Did the size of the
items in the collection affect their prediction? Challenge them to
work together to make a collection with few items that looks big and
a collection with many items that looks small.
Assessment for Learning
What to Look For
Evidence that children
■
make reasonable estimates of sets with 20 to 50 objects
■
form groups of the same size to count a collection
■
skip count by the number of objects in the smaller
sets to arrive at the total
To guide observations and facilitate reporting, use
Assessment Master 3.1: Ongoing Observations
Checklist.
What to Do
■
Invite children to think aloud for you as they
estimate so you can hear their reasoning.
■
Encourage children to count part way through
their set and then reflect on and adjust their
estimate if necessary. Explain that this is what
adults do when they estimate.
■
Provide additional practice with smaller sets.
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FROM THE LIBRARY
Alyssa Satin Capucilli, Mrs.
McTats and Her Houseful of
Cats (Aladdin, 2004)
Paul Giganti Jr., How Many
Snails? A Counting Book
(Harper Trophy, 1994)
Bruce McMillan, Counting
Wildflowers (William
Morrow, 1995)
Bruce McMillan, Jelly Beans
For Sale (Scholastic, 1996)
Rick Walton, How Many,
How Many, How Many
(Candlewick Press, 1996)
Niki Yektai, Bears At the
Beach: Counting 10 to 20
(Millbrook Press, 1996)
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LITERACY LINKS
Resources and Materials: Jerry Pallotta, Icky Bug Counting Book,
(Charlesbridge Publishing, 1992), large sheets of paper, crayons, coloured
pencils
Read the book aloud and have children find and count the number of
insects in the illustrations. As a group, decide on a different grouping
of animals (e.g. mammals) and create a different version of the book
using numbers from 1 to 26. Each child can write and illustrate a
page of the group Big Book.
Assign each child a number from 1 to 26. Have the children make
Big Book pages featuring the numeral and draw pictures of the
appropriate number of animals. Compile the pages together and title
the book “Icky ___ Counting Book.”
NUMBERS EVERY DAY
Have the children keep track of the number of days over time
by adding a Snap Cube each day, making towers of tens and ones.
Each day record the numeral represented by the cubes.
CROSS-CURRICULAR CONNECTION
Science
Materials: calendar
Ask children to think about what they wore to come to school. Have
them stand up if they wore a jacket, and count together. Continue
with appropriate outerwear for your climate (boots, umbrella,
gloves). Choose one type of clothing to track for a month and create
simple symbols (e.g., for footwear: runners, rubber boots, winter
boots; for hats: no hat; baseball hat; winter hat). Each day, determine
which of the options most children wore, and record it on the
calendar; this will provide additional practice counting and using
more/less. At the end of the month, have children count the number of
days with each type of symbol and create a pictograph showing the
results. Have children generate questions about their graph. For
example: what were most days like this month? How did the weather
change from the beginning to the end of the month? How do you
know?
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Activity Bank
Classroom Collections
Dot Plates
Materials: collection of countable objects that
children bring in (buttons, beads, bread tags),
container, paper, glue, and other materials for
organizing the collection
Materials: dot plates*, small circular
plates, dot stickers
■
Invite the children to begin a classroom collection.
Have the class choose a small, common,
household object that children can bring in and
contribute to the classroom collection.
■
Place a container in the classroom where children
can put their items.
■
When the container is almost full, ask children to
estimate how many items they have.
■
Have children suggest ideas for organizing the
collection so the number of items can be easily
counted, even if more are added.
■
Children at each table may enjoy making a
collection of items collected on the playground,
such as small stones or pebbles.
■
Display a dot plate very briefly. Have
children record the number they saw.
Ask: “How many dots did you see? How did
you know what number it was?”
■
Display the same plate again and have
several children explain their strategy for
counting the dots, or have them share in
pairs how they saw the number.
■
Repeat. Help children make connections
between strategies (seeing 5s, looking for
doubles, noticing shapes, looking for
domino patterns)
Some children may be interested in creating
dot plates with different arrangements of dots
for you to use in this activity.
Social; Kinesthetic
Visual; Logical
Whole Class
Whole Class/Partners
A Show of Hands
Resources and Materials: paper, markers, scissors, glue, chart paper
■
Have each child trace around her or his hands and cut out the tracings.
■
Place all the tracings together. Ask children to estimate how many there are and explain how they estimated.
■
Have children group and count the cutouts. Have them talk about their strategies (counting by 5s or by 10s).
■
Have the children organize the cutouts and glue them on large chart paper, circling each group and gluing any
leftovers beside the last group.
■
Children should use the prompt to write about their group:
■
“_______ groups of _____ and _______ left over. We have _______ hands.”
Visual; Verbal
Whole Class
* See Preparing Materials, page iii.
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LESSON
3
CURRICULUM FOCUS
Locate numbers on a number
line and use the number line
to skip count
N1, N4, N6, N7, P3
MATH WORD WALL
number line
skip count
MATERIALS
string, tape or paper clips,
chart paper, marker, counters
PROGRAM RESOURCES
Student page 33: What Is
Missing?
LM 7: Number Line, 0 to 50
LM 8: 100-Chart
LM 9–LM 11: Numeral
Cards, 0 to 50
Quit
Counting on a Number Line
BEFORE
Get Started
Distribute numeral cards 0 to 20 randomly to children in the class.
Challenge those with numerals 0 to 10 to stand in order to create a
number line. Secretly take two numeral cards away and ask:
■ Which numbers are missing?
■ How do you know? (6 is missing; it comes after 5 and before 7.)
Give back the numeral cards. Have the rest of the children with
numerals join the number line in the correct order. Choose a child in
this group and ask: “What number comes right before you? What
number is 2 after you?” Have children tape or clip their numeral cards
in order on a string to create a concrete number line and return to their
seats. Tell children since there aren’t enough people in the class to
build the line to 50, you will continue the line using part of a 100-chart.
Glue the first 2 rows cut from a 100-chart on chart paper to form a
number line, pointing out how they match the children’s number line.
Ask what numeral is missing (0) and add it at the beginning of the line.
Show the class the next 3 cutout rows. Ask a volunteer to come up and
add them to the line, explaining how they knew the correct order.
DURING
Explore
Have children play a number line game in pairs. Provide each pair
with a copy of LM 7 and 5 counters. Have them cut and glue the
pieces of the master to form a number line from 0 to 50. Present the
following problem to the class.
Problem Prompt
Create a number line mystery for your partner by hiding up
to 5 numerals with your counters.
Children take turns covering
numbers with counters and
identifying the missing numbers.
Children should explain to their
partner the clues they used to
determine the hidden numbers.
Allow time for each child to have
several turns at each part of the
activity. Encourage children to try
using a pattern to cover the numbers,
such as covering every third number
in a section of the number line.
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Unit 2: Number Relationships
TEACHING TIP
As children build a number line
from 0 to 50, talk about zero.
“Children at this age may not
realize that zero is also a
number. Children should
consider zero as a legitimate
number rather than the
absence of number.” Adding
It Up, (National Research
Council, 2001, page 111)
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Show and Share
Have children discuss the number line mysteries they created and
solved. Ask:
■ What were some of the clues you used to find missing numbers?
(looked at the number that came before or after)
■ What were the most difficult mysteries to solve? Why? (when
several numbers in a row were covered up)
■ What were the easiest mysteries to solve? Why? (when the hidden
numbers formed a pattern; because I could skip count)
Some children may find easy the type of mysteries others found
difficult. If this is the case, a discussion of the strategies these
children used may help others.
AFTER
Connect and Reflect
Have children refer to the completed number line. Ask:
■ What patterns do you see? (Numbers increase by 1s, numbers 0 to 9
repeat within each section.)
■ How could you use a number line to compare two numbers? (Look
at their positions on the line, the number on the left is smaller.)
■ How could you use the number line to count by 2s? (Say every
second number.)
■ How could you use the number line to count by 5s? (Say every fifth
number.)
■ How could you use the number line to count by 10s? (Say only the
decade numbers.)
Together with the class, skip count aloud by 2s from 0, then from 1,
and by 5s and 10s from 0.
The number line also provides a good opportunity for a visual
introduction to rounding. Ask children to identify “which 10 is closest”
while you name several numbers. For example:
■ 43 (40)
■ 18 (20)
■ 21 (20)
■ 35 (either 30 or 40)
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Practice
Reinforcement
Display the number line to 50 and have children complete Student
page 33 by recording missing numerals on partial number lines. After
the page has been completed, discuss children’s strategies for
determining the missing numbers.
Extra Support: Concepts
Using a number line constructed from LM 5, have a child touch each
number as he or she counts aloud. Have the child tell you her or his
favourite number on the line and place a counter on it. Then ask the
child to show you the numbers that are 1 less, 1 more, 2 less, 2 more,
10 less, and 10 more than the favourite. For each number they
identify, ask: “How did you know? Tell me about your thinking.”
Children can practise and apply their skills representing and
comparing numbers at the Mathematics Centres (see Making
Numbers and Same Number, Different Ways, page xiii).
Extension
Have children create “What’s My Number?” riddles. Children record
clues for numbers to 50 on index cards or small pieces of paper. The
answer should be written on the back of the card. For example: “I
have two digits. I come after 39 and before 41. What’s my number?”
(40) Collect the cards and make them available for children to use as
a game.
Assessment for Learning
What to Look For
Evidence that children
■
recognize numbers to 50
■
locate numbers on a number line, and predict the
numbers that come before/after
■
■
Have children order number cards in a pocket
chart or on a ledge, (forward and backward), with
various start points.
■
Play guessing games to develop fluency in number
order. These can be visual (covering a number on
a number line), or oral (saying a sequence while
children listen for a missing number or predict the
next one)
■
Have children join in counting songs and
chants. Try using various start numbers
(other than 1), or counting backward.
recognize a pattern while skip counting (visual
pattern or other)
To guide observations and facilitate reporting, use
Assessment Master 3.1: Ongoing Observations
Checklist.
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What to Do
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LESSON
4
CURRICULUM FOCUS
Identify and record addition
and subtraction stories to 18
N13, N16
MATH WORD WALL
number story
number sentence
addition story
addition sentence
subtraction story
subtraction sentence
MATERIALS
counters (10 per child), Snap
Cubes, beads, buttons
PROGRAM RESOURCES
Student page 34: Number
Sentences
Student page 35: Garden
Problems
LM 3: Ten-Frame
LM 9: Numeral Cards, 0 to 20
LM 14: Grid Paper
LM 15: To the Moon Game
Board
Quit
Number Facts to 18
BEFORE
Get Started
Present the following story problem to the class. You can draw simple
stick-people figures on the board if you wish. There are 9 people on an
elevator (or on a train, bus). At the next floor (station, stop), 4 more
people get on. Ask:
■ How can you find out how many people are on the elevator now?
(Add)
■ How many people are on the elevator? (13) Explain how you know.
(I started at 9 and counted 4 more; I know that 9 + 1 is 10 and there are
still 3 more to add.)
■ What addition sentence would you write for this story? (9 + 4 = 13)
■ At the next floor, 2 people get off the elevator. How can you find
how many people are left on the elevator? (Subtract)
■ How many people are on the elevator now? (11) Explain how you
know. (I counted back 2 from 13)
■ What subtraction sentence would you write for this story? (13 – 2 = 11)
■ The elevator stops again and some people get off. Six people are left on
the elevator. How many got off? (5) Explain how you know. (I asked
myself “6 and what is 11?” and I know that it is 5; I subtracted 6 from 11.)
■ What subtraction sentence would you write for this story? (11 – 5 = 6)
DURING
Explore
Provide small groups of children with as many sets of numeral cards
(0 to 9) (LM 9) as there are children in the group, a game board (LM
15), and small items to use as playing pieces. Make counters and
ten-frames available for children to model addition or subtraction.
Problem Prompt
How can you make and solve addition or subtraction sentences to
reach the moon on your game board?
The numeral cards are all shuffled and placed in a draw pile. Children
will take turns drawing 2 cards from the pile. They are to write and
solve one addition sentence and one subtraction sentence using the
numerals they draw. The other players verify the answers are correct.
For each correct sentence, a player can move 2 spaces on the game
board. If the player lands on a space with special instructions, they
must follow the instruction. The numeral cards are placed in a discard
pile to be shuffled and used again when the draw pile runs out. Play
continues until one child reaches the moon.
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Quit
Show and Share
Have children discuss the game they just played. Ask:
■ Did you enjoy the game? Are there any things about it you would
change?
■ Do you think it is possible to make an addition and subtraction
sentence for every pair of numbers you might have drawn? If not,
give an example. (It is possible. If children suggest an example where it
is not possible, ask a volunteer to write a sentence with the numbers.)
AFTER
Connect and Reflect
Gather the children together. Have them look at the number
sentences they wrote and talk about the strategies they used to
complete them.
■ Choose one of the addition sentences you wrote. Explain how you
solved it.
■ Choose one of the subtraction sentences you wrote. Explain how
you solved it.
Addition and
Subtraction Strategies
count on
Make a list of the strategies children describe.
If children do not suggest some of these addition and subtraction
strategies, you may wish to model them for the class. An example of
each is provided in the possible answers in the Get Started section.
count back
make a group of 10
think addition
Practice
Reinforcement
Provide counters for children to use as they complete Student pages 34
and 35. After page 35 has been completed, have children share the
number sentence for each problem and explain the strategy they used
to solve it. Invite children to present one of their stories from page 34
to the class and have the class write a number sentence for the story.
Does it match the number sentence the child wrote?
Extra Support: ESL
Story problems offer a way for ESL children to practise and extend
their language as well as their mathematical understanding. You could
provide word cards with small illustrations that they can use as they
create and share stories for Student page 35. (For example, a word card
for “butterfly” would include a small picture of a butterfly as well as
the word.)
Children can practise and apply their skills building addition and
subtraction number stories at the Mathematics Centres (see Making
Number Sentences, page xiii).
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Extension
Challenge pairs of children to play the “To the Moon” game using
one set of numeral cards from 0 to 20 rather than two sets of 0 to 9.
Ask the children to record one of their trickiest sets of clues,
something that nobody else would think of.
Assessment for Learning
What to Look For
Evidence that children
■
recognize whether to add or subtract to solve a
story problem
■
use a variety of strategies to complete addition or
subtraction problems
■
record addition and subtraction stories
To guide observations and facilitate reporting, use
Assessment Master 3.2: Ongoing Observations
Checklist.
What to Do
■
Modelling a story situation with counters will help
children decide whether they need to add or
subtract.
■
Children having difficulty to “make a group of 10”
would benefit from solving addition facts from 11
to 18 using counters and two ten-frames.
Demonstrate how to move counters from one frame
to fill the other and then count on for the total.
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FROM THE LIBRARY
LITERACY LINKS
Kate Duke, Twenty is Too
Many (Dutton, 2004)
Resources and Materials: Jon Scieszka, Math Curse (Viking, 1995)
Lynette Long, Dealing With
Addition (Charlesbridge
Publishing, 1998)
Lynette Long, Domino
Addition (Charlesbridge
Publishing, 1996)
Eve Merriam, 12 Ways to
Get to 11 (Simon & Schuster,
1996)
Stuart J. Murphy, Elevator
Magic (Harper Trophy,
1997)
Diane Ochiltree, Cats Add
Up (Scholastic, 1998)
Greg Tang, Grapes of Math:
Mind Stretching Riddles
(Scholastic, 2001)
Harriet Ziefert, A Dozen
Ducklings Lost and Found: A
Counting Story (Houghton
Mifflin, 2003)
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Unit 2: Number Relationships
Read the book aloud and discuss the story with the children. Ask
them to think about problems that involve mathematics in their own
lives. (How many times do they brush their teeth in a month?) Have
children write a story about how their own lives at times seem like
the girl’s in the book.
NUMBERS EVERY DAY
Explain that you will name a number and the children are to say
the number that comes 2 after it. Repeat for several numbers. Then
change so that children are to say the number that comes 2 before
your number. This will help children with counting on and counting
back strategies.
CROSS-CURRICULAR CONNECTION
Art
Materials: rulers, crayons, paper
On the chalkboard, draw a horizontal, a vertical, and a diagonal line
segment. Ask children to identify which line is horizontal; label it.
Repeat for the other types of lines. Challenge the children to create a
design by drawing 10 straight lines on a piece of paper and colouring
the spaces between the lines. They are to use only 2 of the types of
lines. Below the design they should write a story and an addition
sentence that describe how many of each type of line they used. For
example, “I used 6 horizontal lines and 4 vertical lines; 6 + 4 = 10.”
The children’s artwork can be displayed on a bulletin board in the
classroom. You can connect to the geometry strand by having
children investigate the types of figures that were created by their
intersecting lines.
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Activity Bank
Snap Cube Trains
Trading for a Dime
Resources and Materials: LM 14; Snap Cubes
for each child (two colours)
Resources and Materials: 20 pennies,
1 dime, LM 3, LM 20, (labelled 0, 1, 2, 3
and +, –, +, –)
■
■
■
Provide children with two colours of Snap Cubes to
build number trains. Explain that the same colour
cubes are to be kept together.
■
Each partner begins with a blank tenframe.
Have children find as many two-colour trains as they
can for 10. Once found, ask the children to arrange
the trains in order and colour each train on grid
paper. Ask:
■
Children take turns spinning both
spinners to find how many pennies to
add to or take away from their tenframes.
■
How many number trains did you build for 10?
(11 are possible)
■
The objective is to fill the ten-frame and
trade it for the dime.
■
What patterns do you see when your trains are in
order? (the colours form a “staircase” type of
pattern)
■
If a player has to remove more pennies
than are in the ten-frame, the child does
nothing and misses that turn.
■
What addition/subtraction stories can you tell
using the number trains?
■
Extension: Have each pair of children
work with 2 ten-frames.
■
Adaptation: change the objective to be
the first to empty the ten-frame.
Repeat this activity using Snap Cube trains for
8 (9 possibilities) and 9 (10 possibilities).
Visual; Logical
Logical; Social
Whole Class
Partners
Hit the Target
Materials: calculator
■
Provide pairs of children with a calculator and have them try to find as many ways as they can to reach the
target number 10. Explain that they can only use the 1, 2, 5, +, – keys.
■
You may wish to demonstrate or model this activity before the children try it on their own.
■
Have children in each pair take turns entering number sentences on the calculator and recording the number
sentences.
■
Set a time limit. Challenge children to find as many ways as they can to make 10.
■
Post the list of number sentences from the class for all to look at and check.
Visual; Logical
Partners/Whole Class
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LESSON
5
CURRICULUM FOCUS
Use two-colour counters to
explore fact families
N13, N14, N15, N16
MATH WORD WALL
related facts
fact families
MATERIALS
two-colour counters (14 per
pair), crayons, red and
yellow Snap Cubes
PROGRAM RESOURCES
Big Math Book, page 7:
Flying Geese
Student page 36: Snappy
Number Sentences
Student page 37: Add or
Subtract
LM 16: Fact Family Builders
(+ and –)
Quit
Related Facts
BEFORE
Get Started
Provide pairs of children with 14 two-colour counters to act out the
number sentences. Display Big Math Book, page 7 and talk about the
different groups of geese in each picture. Ask:
■ What addition story can you make up about the first picture?
(There are 8 geese floating on a pond and 6 more on the shore.)
■ What addition sentence would you write for this story? (8 + 6 = 14)
■ What other addition sentence can you write? (6 + 8 = 14)
■ What story can you make up for the second addition sentence?
(There are 6 geese on the bank of a pond and 8 more geese in the water.)
■ Does it matter what order you add the geese? (No, the answer is the
same.)
Write both addition sentences on the Big Math Book page. Then ask:
■ What subtraction story can you write about the second picture?
(There were 14 geese at a pond, 8 flew away. How many were left?)
■ What subtraction sentence would you write for this story? (14 – 8 = 6)
■ What other subtraction story and sentence could you write? (There
were 14 geese at a pond, and 6 stayed there. How many flew away?
14 – 6 = 8)
■ Does it matter which group of geese you subtract? (Yes, the answers
are different.)
Record both subtraction sentences (14 – 8 = 6 and 14 – 6 = 8) on the
Big Math Book page.
DURING
Explore
Present the following problem for
children to solve in pairs.
Problem Prompt
How can you use two-colour
counters to find addition and
subtraction sentences for 12?
Children gently toss 12 two-colour
counters. They draw the counters
and colour them to show which side
is facing upward. Then they use the
two colours in their drawings to
write addition and subtraction
sentences.
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Unit 2: Number Relationships
TRY
THIS
Use children to
model fact
families. Form a
group of 5 children.
Ask two to sit down while 3
stand up. Ask, “What addition
story could we write? What
addition sentence? What
subtraction story/subtraction
sentence?” Then ask children
to reverse positions and
repeat; have them suggest
other ways to arrange the
same number of children.
Continue, recording number
sentences as children stand
and sit — or do other actions
— in various combinations.
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Show and Share
Invite a pair to state how their counters landed and read the addition
and subtraction sentences they wrote. Record the information on the
chalkboard or chart paper as shown below. Tell the class that lists of
related facts like these are sometimes
called “fact families.” They are a way of
Addition and Subtraction
remembering which addition facts can
Stories for 12
help you with a subtraction sentence.
5 red and 7 yellow
After recording the list, ask:
5 + 7 = 12
■ Did any other pairs write the same
7 + 5 = 12
number sentences? (Answers will vary.)
■ If you did, did your counters land the
12 – 5 = 7
same way? (Some pairs may have tossed
12 – 7 = 5
the “opposite” combination of counters; for
the example above, 7 red and 5 yellow.)
Then ask for a pair that had a different result and repeat the
recording process. Continue until all sentences children have written
have been discussed.
AFTER
Connect and Reflect
Look at the number sentences the class has generated. Ask:
■ Are there any addition and subtraction sentences for 12 that we
haven’t included? (Probably the answer will be yes, since some
combinations of counters are unlikely to be tossed.)
■ Why do you think this happened? (No one tossed only 1 yellow counter.)
Work together to add any missing fact families for 12 to your
recording. There are 7 fact families for 12, including the double 6
(which has only 1 addition and 1 subtraction sentence) and facts
involving 0.
Discuss how to use related addition and subtraction facts to answer
subtraction questions. Ask:
■ Suppose you have to find 12 – 7. What question can you ask
yourself to use a related addition fact? (7 and what make 12?) What
is the answer? (5)
■ Suppose you have to find 12 – 4. What question can you ask
yourself to use a related addition fact? (4 and what make 12?) What
is the answer? (8)
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Practice
Reinforcement
Have children discuss the illustration at the top of Student page 36
and talk about the different number combinations. Provide Snap
Cubes for children to use as they record number sentences on Student
page 36. Remind children to use some of the strategies on the
strategies list as they work on Student page 37.
Extra Support: Concepts
Children can use the cards cut from LM 16 as guides for writing fact
families. Each card shows three numbers that can be used to create a
fact family. Children can use counters to verify that the number
sentences they write are correct. After they have completed a few of
these, invite them to make up cards of their own with 3 numbers that
can be used to create fact families, to be added to the class set of cards.
Children can practise and apply their skills building addition and
subtraction number stories at the Mathematics Centres (see Making
Number Sentences, page xiii).
Extension
Children can work in groups. Each group should choose a number
between 11 and 18 (except 12) and count out that many two-sided
counters. Challenge the group to write all the possible fact families for
the number and predict how many tosses it will take to have a picture
illustrating each fact family. The children toss counters, tally their
tosses, and draw pictures to check their prediction.
Assessment for Learning
What to Look For
Evidence that children
■
identify addition and subtraction sentences for a
given number
■
use the relationship between addition and
subtraction to identify related subtraction facts
To guide observations and facilitate reporting, use
Assessment Master 3.2: Ongoing Observations
Checklist.
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Unit 2: Number Relationships
What to Do
■
Have children use counters to model addition with
a sum less than 18. Talk with children about the
parts of the whole that they added together (the
addends), and record these on a card, along with
the total for the problem. From the card, the child
tells a story problem using the addends in the
opposite way. Work through these steps with a
subtraction problem.
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FROM THE LIBRARY
Eve Merriam, 12 Ways to
Get 11 (Simon & Schuster,
1996)
Stuart J. Murphy, Ready, Set,
Hop! (HarperCollins, 1996)
Dianne Ochiltree, Cats Add
Up (Scholastic, 1998)
Greg Tang, Math Appeal
(Scholastic, 2003)
Quit
LITERACY LINKS
Resources: Dick Gackenback, A Bag Full of Pups (Viking, 1995)
Read the book aloud with the children. Then, from page to page, as
the puppies are given away, have children track the number of
puppies left. With the children’s help record the subtraction stories.
(e.g., 12 – 1 = 11, 12 – 3 = 9)
NUMBERS EVERY DAY
Materials: dot plates or 10-frame flash cards
Hold up a dot plate or 10-frame flash card, asking “How many more
do we need to make 10?” (e.g., Flash a 7 plate or card. Children see it
and say “3.”)
CROSS-CURRICULAR CONNECTION
Science
Materials: container of water, small spoons such as teaspoons, shallow
pans, 12-cm-square samples of various materials to test for absorbency (e.g.,
paper towels, face cloths, dish towels, corrugated cardboard, various fabrics)
Have children conduct an experiment to compare the absorbency of
different materials. Before beginning, children can predict which
sample will absorb the most and explain their thinking. Place the first
sample to be tested in a shallow pan. They spoon water on it one
spoonful at a time, tallying each spoonful and stopping when the
sample will absorb no more water. They calculate and record the total
amount of water absorbed. Once they have tested all samples, children
order the samples from most to least absorbent. They can also use the
results to create and answer addition and subtraction questions. For
example: “How many spoonfuls of water did the paper towel sample
and dish towel sample absorb altogether?” “How many more
spoonfuls of water did the face cloth sample absorb than the paper
towel sample?”
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Activity Bank
Dot Plate Mysteries
All in the Family
Materials: dot plates*
Resources and Materials: LM 16,
paper bags, felts
■
■
■
■
Each pair or small group of children will set up a
“station” in the class. Groups will rotate through the
stations.
Each group selects two dot plates and records the
sum on a piece of paper. They turn over one dot
plate and move to another group’s station.
They use the sum and dot plate the other group left
face up to determine the missing addend. They
record their answer and turn over the dot plate to
check. Before leaving that station, they turn one dot
plate back over. It does not have to be the same one
turned over when they arrived.
After groups have rotated through all the stations,
have the children discuss the strategies they used to
find the missing addends. If any new strategies are
suggested, add these to the displayed list.
■
Place children in groups of three, and
give each group a card cut from LM
16. Each card has three numbers that
can be used to create a fact family.
■
Challenge children to invent and act out
a simple play about their fact family.
Who are the “people” in the family?
How do they go together? What
happens if one goes missing?
■
Children might like to make a simple
paper bag puppet as a prop for their
play, or act out the role themselves, or
they may find an alternative possibility.
■
Have children present their plays to
their peers.
Visual; Social
Kinesthetic; Verbal
Small Group/Whole Class
Small Group/Whole Class
Adding On a Calculator
Materials: calculators
■
Provide pairs of children with a calculator.
■
One child enters a number from 0 to 9 and the + key. The other
child enters a number that will produce a sum of 11.
■
The first child records the addition sentence.
■
Children switch roles and continue finding combinations for 11.
■
When pairs are finished, they share their combinations and
strategies (count on from the first number, think of related
addition fact, such as 2 and what number adds to 11) with
other pairs.
■
Vary the activity for sums 11 to 18.
Logical; Social
Partners
* See Preparing Materials, page iii.
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LESSON
6
CURRICULUM FOCUS
Use doubles to complete
number sentences
N11, N15, N16
MATH WORD WALL
double
near double
even number
odd number
MATERIALS
counters
PROGRAM RESOURCES
Big Math Book, page 8:
Domino Doubles
Student page 38: Seeing
Doubles
Student page 39: Using
Doubles
LM 14: Grid Paper
LM 17,18: Domino Cards
Quit
Doubles and Near Doubles
BEFORE
Get Started
Display Big Math Book, page 8. Ask:
■ What do you see in this picture? (dominoes showing groups of dots;
some show doubles)
■ What doubles do you see? (double 1, 2, 3, 4, and 6)
Circle the dominoes that show doubles on the Big Math Book page.
Then ask:
■ What is the sum of the dots on each double? (2, 4, 6, 8, and 12)
Record an addition sentence for each double on the board. Children
can refer to these during Explore. Explain that the sums of doubles
are called even numbers. Explain that the numbers between these
sums (1, 3, 5, 7, 9, 11, 13) are called odd numbers.
DURING
Explore
Provide counters for children
to use.
Problem Prompt
For each of the dominoes on
the Big Math Book page that is
not a double, find the sum of
the dots. When does knowing
the sum of a double help you?
TEACHING TIP
When introducing the words even
and odd, you may find it helpful to
use an example from everyday
life. Tell children to think about the
socks in their drawer at home.
When every sock has a partner,
you have an even number of
socks. When one sock is missing,
you have an odd number, and
“one odd sock.”
Show and Share
For each non-double domino, have a pair read their addition sentence
and state whether they used a double fact to help them. Ask:
■ What was the double and how did it help? (2 + 3 = 5; I know
2 + 2 = 4 and one more is 5.)
■ Did any one use a different double fact to find this sum? (2 + 3 = 5;
I know 3 + 3 = 6 and one less is 5.)
If no one suggests using doubles for a domino such as (4, 6), model
one way to do it: I know 5 + 5 = 10, the first number on the domino is
1 less than 5, the second is 1 greater, so my sum is the same.
For those dominoes, such as the (5, 2) domino, where children will
probably not use double facts to help, ask:
■ What other strategy did you use? (I counted on.)
■ Why do think double facts were not helpful? (the numbers were not
close to being doubles)
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AFTER
Quit
Connect and Reflect
Review with the children how a double fact can be used to find the
sum of a near double. Ask:
■ How would you describe a near double? (A near double has numbers
that are 1 or 2 apart.)
■ Suppose you have a near double where the numbers are 1 apart.
How would you find the sum? (Double the smaller number and add 1
or double the larger number and subtract 1.)
■ Suppose you have a near double where the numbers are 2 apart.
How can you find the sum? (Double the number between them.)
Practice
Reinforcement
Have children complete Student page 38 by drawing and recording
doubles. Have children explain which number is not the sum of a
double. On Student page 39, children identify the doubles that will
help find the answers to near doubles.
Extra Support: Concepts
To help children identify near doubles, use counters to represent a
sum like 3 + 4. Ask the children to find the “hiding double” by
arranging the counters to make a double with one left over. What is
the sum? Repeat for other addition facts to 18.
3 + 3 + 1
Another approach is to create a double number train with Snap
Cubes and break it into equal parts. Ask: “What is the double?” Add
a cube to one part. Ask: “What is the near double?” Repeat for other
doubles to 18.
Extension
Have children play this “Cover the Sum” game in small groups.
Provide each group with a set of standard double-six dominoes or
2 sets of domino cards (LM 17, 18) and some counters.
■
■
■
Each player draws a 3 by 3 grid on paper and writes a number
between 0 and 12 in each space. Players can use the same number
more than once. This is the player’s game board.
The players take turns drawing a domino or domino card,
mentally calculating the sum, and covering that number if it
appears on their game board. (If it appears more than once only
one is covered.) The used dominoes are placed in a discard area, to
be mixed up and reused if needed.
The first player to cover all the numbers on the game board wins.
The children can create new game boards or revise their old ones
after each game. After they have had a few chances to play the game,
ask: “What numbers are the best ones to write in the game board
spaces. Why?”
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Assessment for Learning
What to Look For
Evidence that children
■
can identify doubles
■
mentally add one-digit numbers (doubles)
■
use their knowledge of doubles to solve near
doubles
To guide observations and facilitate reporting, use
Assessment Master 3.2: Ongoing Observations
Checklist. To gather information about children who
are having difficulty, use Assessment Master 2:
Diagnostic Conference for Selected Children.
What to Do
■
Display an even number of counters; ask children
to separate them into two equal groups. Ask:
“What double fact do the groups show? What
addition sentence can you write?” Add a counter
to one group. Ask: “What is the near double?
What is the new addition sentence?” Repeat with
other even numbers of counters to 18. Variations:
take one counter away from a group, or move a
counter from one group to another.
■
Play “doubles riddles,” posing questions such as:
“We are two kittens. How many paws do we
have?” “We are two space creatures. How many
eyes do we have?” Invite children to pose and
illustrate their own “double” riddles.
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FROM THE LIBRARY
David Birch, The King’s
Chessboard (Puffin, 1993)
Stuart J. Murphy, Double the
Ducks (HarperCollins, 2002)
Quit
LITERACY LINKS
Resource: Lily Toy Hung, Two of Everything: A Chinese Folktale (Albert
Whitman, 1993)
Share the story with the children. Discuss how the brass pot doubles
everything that goes inside. Ask: “When the two purses were pulled
out of the pot how many gold coins did Mr. and Mrs. Haktak have?”
Have children identify the double and record 5 + 5 = 10 on the board.
Brainstorm items that the children might enjoy putting in the pot and
have them identify the double each time.
Explain to the children that folktales often have a lesson to teach, and
ask them to identify the lesson in this folktale. Have the children
write a story about what happens when they find an ancient brass
pot in their garden.
NUMBERS EVERY DAY
Call out a near double, such as 7 + 8. Challenge children to
name the double they would use to help solve it. For example,
children could say 7 + 7 = 14 and 1 more is 15 or 8 + 8 = 16 and 1 less is
15. Give children a different near double each day.
CROSS-CURRICULAR CONNECTION
Art/Language Arts
Materials: construction paper, art supplies
Invite children to work in small groups to create a “Doubles Book.”
Have them write each double from 1 + 1 to 9 + 9 and illustrate it with
one double per page. Children could create a short rhyme for each
double. Have children make a cover and staple the pages together to
make their “Doubles Book.”
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Activity Bank
Even Steven and Odd Todd
Building Doubles
Resources and Materials: none
Resources and Materials: LM 14; two colours of
Snap Cubes, die, markers or crayons
■
Have children spread out throughout the
gym or playground.
■
Call out a number from 1– 18.
■
If the number is odd, children call out “Odd
Todd!” and run to the back of the gym,
where they freeze into an “odd” statue.
■
If the number is even, children call out “Even
Steven!” and run to the front of the gym. Ask
children what number doubled will make the
even number (for example, if you call out
10, then the number you doubled is 5).
Have children do that many jumping jacks,
hops on one foot, sit ups, and so on.
■
Provide each child with 9 domino cards or
9 dominoes in a paper bag.
■
Have children draw dominoes from the bag,
one at a time, and sort them into three groups
— dominoes that can be used to write a
double fact, dominoes that can be used to
write a near double fact, and dominoes that
don’t show doubles or near doubles.
■
When all 9 dominoes have been drawn
from the bag, ask children to place them in
order according to their sums.
■
Then have children write number sentences
for each domino.
■
Children can share their sentences.
One child rolls the die and makes two Snap Cube
trains, one in each colour, to represent the number.
The children snap the two trains together to make a
doubles tower.
■
The other child draws and colours the double on grid
paper, recording the matching number sentence.
■
The children then switch roles.
■
Extend the activity by having children build on the
towers to show the effect of “one more” or “one
less” than a double.
Partners
Whole Class
Resources and Materials: LMs 17 and
18; standard double-6 dominoes (sums 0 to
12), paper bags
Provide partners with Snap Cubes, a die, and LM 14.
■
Kinesthetic; Social
Kinesthetic; Logical
Doubles Dominoes
■
Odd and Even Numbers
Materials: Snap Cubes
■
Display figures of 1, 2, 3, 4, 5, and 6 Snap Cubes
like the ones shown below.
■
Ask:
■
What do you notice? (From left to right, each
figure has one more cube than the one before it.)
■
Which figures show doubles, or evens? (2, 4, and 6)
■
Which do not show doubles? (1, 3, and 5)
■
With children’s help, list odd and even numbers.
■
After listing the first six numbers, have children build
towers for 7 to 10. Ask them to predict whether the
number will be odd or even and then check by
seeing if the number is made up of pairs.
■
Add the numbers 7 to 10 to the list.
Kinesthetic; Logical
Logical; Visual
Independent
Whole Class
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LESSON
7
CURRICULUM FOCUS
Estimate using groups of 10s
N2, N3, N4, N5
MATH WORD WALL
estimate
MATERIALS
paper clips, 50 to 100
countable objects (counters,
buttons, shells, beads) for
each small group, containers
or resealable bags
PROGRAM RESOURCES
Student page 40: About How
Many?
Student page 41: Full of Beans
Student page 42: Counting
by 10s
LM 3: Ten-Frames
Quit
Estimating Large Numbers
BEFORE
Get Started
Place 57 paper clips on a tray or
overhead projector. Cover with a
piece of paper. Uncover the objects
briefly and ask: “Do you think there
are fewer than 50 or more than 50
paper clips?” Tally responses.
TRY
THIS
In order to have
sufficient materials
for counting, begin
a collection of items,
such as toothpicks, crayons,
or pennies. Choose materials
that are readily available and
ask children to bring a few of
each item. These objects can
then be used for estimation
and counting activities.
Uncover the clips again. Provide a
referent by making a group of 10
paper clips. Tell the children that this
is a group of ten. Ask “Does anyone
want to change her or his prediction about whether there are fewer
than 50 or more than 50 paper clips?” Make another tally and invite
children to share their reasoning as they make new predictions. Ask:
“How can we count the paper clips?” (by 1s, 2s, 5s, 10s)
Have a volunteer group the paper clips into 10s, and then ask the
children to count the groups of 10. Count the leftovers to arrive at the
total. Record the number of 10s and the leftover ones. Look back at
the children’s predictions. Discuss with the children how making a
group of 10 helped when predicting.
DURING
Explore
Provide small groups with 50 to 100 countable items in a container or
resealable bag.
Problem Prompt
How can you use what you know about making groups of 10 to
estimate, group, and count your collections?
First, children arrange one group of 10 using the materials in their
collections. They use this group of 10 to estimate the total number in
the collection, and record their estimates on Student page 40. Then
they make and count groups of 10s and leftover 1s.
Show and Share
Have children visit each other’s collections. Ask each group to share
its estimate and the number in its collection. Ask:
■ How did seeing one group of 10 help you make an estimate? (tried
to see other groups of 10)
■ How many groups of 10 do you have? How many left over?
■ How did you find the total?
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AFTER
Quit
Connect and Reflect
Ask:
■ How does grouping by 10s help you make an estimate? (It helps me
see how big a group of ten is and how it looks.)
■ Why does making groups of 10 help you count large numbers? (I can
count by 10s faster than by 1s, 2s, or 5s and I don’t lose track when I count.)
Practice
Reinforcement
Provide a large container of small countable items, such as beans or
counters, for children to use with Student page 41. Student page 42
offers practice in counting and recording numbers to 100 and asks
children to write about how grouping by 10s helps with counting.
Extra Support: Concepts
Children having difficulty may benefit from working with smaller
collections. They can do this at the Mathematics Centres (see Making
Numbers, page xiii).
Children can practise and apply their number skills at Mathematics
Centres (see Same Number, Different Ways, page xiii).
Extension
Make a selection of “Where’s Waldo” type books available to the
class. Children can work with a partner. They choose a page in one of
the books and develop a strategy for estimating the number of
people in the drawing on that page.
Assessment for Learning
What to Look For
Evidence that children
■
make reasonable estimates using a referent
of 10
■
accurately count and group 10s together
■
explain their estimating strategies
To guide observations and facilitate reporting, use
Assessment Master 3.3: Ongoing Observations
Checklist.
What to Do
■
When making groups of 10, some children need to
use blank ten-frames or other guides.
■
For children to use 10 as a referent, they need a
strong sense of “10-ness.” Provide opportunities for
children to “see 10” in a variety of different contexts:
10 children, 10 pennies; 10 objects; 10 pictures.
■
Practice visualizing 10, then larger numbers: have
children look at one penny, then close their eyes and try
to “see” that penny in their mind’s eye. Then, ask them to
“see” 10 pennies. Have them open their eyes and look
at a small collection of pennies quickly. Ask: “Are there
more than the 10 you saw with your mind’s eye or
fewer?” Practise with other objects and larger collections.
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LITERACY LINKS
Resources: Stuart J. Murphy, Betcha! (HarperCollins, 1997)
FROM THE LIBRARY
Jack Beers, Bears, Ten by Ten,
Addison Wesley Mathematics
Little Books, Early Level
(Addison Wesley, 2002)
Stephanie Calmenson,
Dinner At the Panda Palace
(HarperCollins, 1995)
Rebecca Dickinson, The 13
Nights of Halloween
(Scholastic, 1996)
Betsy Franco, Time to Estimate
(Capstone Press, 2002)
Wanda Gag, Millions of
Cats (Putnam, 1997)
Bill Grossman, My Little Sister
Ate One Hare (Bantam
Doubleday Dell, 1998)
Leo Lionni, Swimmy (Alfred A.
Knopf Inc., 1973)
Margaret Mahy, 17 Kings and
42 Elephants (Dial, 1987)
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Unit 2: Number Relationships
Read the story to the children and ask them to describe what is
happening in each picture. Brainstorm a list of real-life situations
that require estimation (e.g., ordering pizza for a party, buying fruit).
Have the children pick one of the situations and choose an
estimation question to answer. Children can play the “Betcha” game
with a partner. Help children to think of different strategies to
consider for making estimates (e.g., use a referent, look for a group
of 10).
NUMBERS EVERY DAY
Materials: up to 100 counters, overhead projector
Place 40 to 50 counters on the overhead projector and turn it on
briefly. Ask children to estimate the number of counters they saw to
the nearest ten. Now organize the counters into groups of 10 and
turn the projector on and off quickly. Provide children with an
opportunity to revise their estimates. Ask children their reasons for
making or not making revisions. Have the children count the
counters by 10s and then count on for the remaining counters. Ask:
“How did organizing the counters help you make an estimate?”
CROSS-CURRICULAR CONNECTION
Social Studies
Materials: reference books, the Internet
Have small groups of children choose a country and investigate the
number words used in that country. Children whose families speak a
language other than English could take a leadership role in a group
by teaching the other children number words in their language. If
you post a world map on a bulletin board, each group can identify
its country on the map and post a list of some number names used
there.
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Activity Bank
Drawing Stars
Ordering Collections
Materials: drawing paper, crayons or markers
Materials: clear resealable bags filled with small
objects (beans, counters, buttons), paper
■
■
■
■
Ask: “How many stars do you think you could
draw in one minute?” Have children record
their estimates. Then time them while they
draw.
When the time is up, children circle groups of
10 stars and count and record the number of
groups and leftovers.
Ask: “Did you draw more or fewer stars than
your estimate? How many stars do you think
you could draw in two minutes? Let’s check.”
Time children as they draw.
After children have counted their stars, ask:
“Was your estimate closer this time? If so,
why?”
■
Have each pair take 3 bags of different
objects. They try to order the bags from least to
greatest number of objects by looking at the
contents without opening the bags.
■
They then spill the contents onto the surface of a
desk or table one bag at a time. The pairs
group the objects by 10s, record the number of
10s, the leftover ones, and the total number.
■
Did they predict the order correctly?
■
Suggest that children repeat the procedure,
using three other bags of objects.
Visual; Kinesthetic
Pairs
Visual; Logical
Individual
Towers of 10s
Resources and Materials: pennies and
dimes
■
Provide groups of children with 60 to 100
pennies.
■
Have them arrange the pennies into “towers
of 10” and count by 10s and leftover 1s to
find the total amount.
■
Confirm that each group of 10 pennies is the
same as one dime. Ask children to substitute
dimes for pennies and tell the total amount.
■
Establish that it is the same. Children can
count by 10s to check.
Estimating and
Counting Coins
Resources and Materials: LM 3; collection of
pennies, paper, pencils
■
Have children work in groups. Tell each group
that in your imaginary store, juice packs cost
50¢ each.
■
Place a collection of pennies on the table. Ask
“Does your group have enough money to buy a
juice pack from my store?” Have children
estimate the number of pennies and record as
more than 50 or fewer than 50. Then children
fill the ten-frames with the coins and place any
extras on the table.
■
Children count by 10s, and then count on to
find the total.
■
Were there enough pennies to buy a juice pack?
Visual; Kinesthetic
Kinesthetic; Social
Small Group
Small Group
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LESSON
8
CURRICULUM FOCUS
Identify, compare, and order
numbers to 100
N3, N7
MATERIALS
numeral cards (1–100),
pocket chart
PROGRAM RESOURCES
Student page 43: Be a
Number Detective
Student page 44: Missing
Number Mysteries
LM 8: 100-Chart
LM 9–LM 13: Numeral
Cards, 0 to 100
Quit
Numbers to 100
BEFORE
Get Started
Display numeral cards 1 to 50, in order in a pocket chart. In random
order, distribute numeral cards from 51 to 60 for children to add to
the chart. As each child comes up, ask:
■ Where does your number belong?
■ How do you know you have placed it correctly?
Once all the numbers are filled for that row, ask:
■ Except for the last number, how are the numbers in this row the
same? (All begin with 5.) What does that tell you about each number?
(it has 5 tens; we could fill 5 ten-frames with that many counters)
Distribute the numeral cards for 61 to 100 randomly to the class. Ask:
■ Who has a number that belongs in the next row? How do you
know? (All except the last number will begin with 6 and will have 6 tens,
the last will be 70.)
Have children with cards for the 60s row come up and place their
numeral cards on the chart. The rest of the class should watch and
verify the placement. Continue in this manner until all the rows are
full. Direct children’s attention to the completed 100-chart. Tell them
that a vertical line of numbers on a chart is called a column. As you
run your hand down the 4s column of the chart, ask:
■ How are the numbers in this column the same? (All end in 4.)
■ What does this tell you about each number? (It has 4 ones left over
after we fill as many ten-frames as we can.)
Ask a volunteer to show another column on the chart and describe
the numbers in it. Then remove numeral cards 67 and 83 without
showing them. Ask:
■ Which numbers have been removed? Tell me what you know
about each number from its position on the chart. (67 is before 68
and after 66, it is 10 more than 57 and 10 less than 77, it has 6 tens and 7
ones; 83 is before 84 and after 82, it is 10 more than 73 and 10 less than
93, it has 8 tens and 3 ones.)
DURING
Explore
Model “What’s My Number?” Provide clues and have children refer
to the 100-chart, trying to identify the number. Some examples: “My
number is 10 more than 81. What is my number?” “My number is
two after 64. What is my number?” “My number is between 91 and
100 and has 7 ones. What is my number?” Discuss with the children
the strategies they used to locate the numbers.
Have children play “What’s My Number?” in pairs.
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Problem Prompt
What clues can you write so your partner can find your mystery
number? How can you use your partner’s clues to guess her or
his number?
Children take turns choosing a number, and then offering clues for
their partner to guess the number.
Show and Share
Ask the children to share the clues they wrote and their strategies for
determining the numbers.
AFTER
Connect and Reflect
Choose one of the children’s clues and then ask:
■ What helped you find the number? (using a 100-chart, counting on/back)
■ How did the 100-chart help if a clue included “more than”?
(counted on) “less than”? (counted back)
■ How did the 100-chart help if a clue included “ten more than”?
(looked below the numeral) “ten less than”? (looked above the numeral)
■ What advice would you give others if they were playing this game?
Practice
Reinforcement
Have children complete Student page 43 by recording missing
numerals on pieces of 100-charts. On Student page 44, they create a
number mystery for a friend to solve by filling in a few numerals, but
leaving others blank.
Children can practise and apply their skills ordering numbers at the
Mathematics Centres (see Ordering Numbers, page xiii).
Extra Support: Communication/ESL
Some children may need additional opportunities to practise the
language of ordering and comparing (more, fewer, before, next, after,
row, column, count on, count back.) Simple riddles and oral games can
help build and reinforce this vocabulary. Children can use flash cards
to show their answers; for example, use cards for 2 more and 2 fewer;
as you point to 53, then 55, children show their cards for “2 more.”
Extension
Challenge children to create more open-ended “What Are My
Numbers?” problems that have several numbers as answers. Some
examples: “My numbers are greater than 47, less than 55, and are
even. What are my numbers?” (48, 50, 52, 54) “My numbers are
greater than 80 and have 5 ones. What are my numbers?” (85 and 95)
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Assessment for Learning
What to Look For
Evidence that children
■
can count to 100
■
recognize numerals 1 to 100
■
can predict the number that comes before or after
in a sequence
To guide observations and facilitate reporting, use
Assessment Master 3.3: Ongoing Observations
Checklist.
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Unit 2: Number Relationships
What to Do
■
Provide guided opportunities for children to build
consecutive numbers using concrete materials.
■
Have children play Number Line Hop! Make a
partial number line on the floor using masking
tape and large number cards. Pose a problem: 2
more than 53. A child starts at 53, then hops two
spaces and announces the answer. Use smaller
numbers for children who are having difficulty.
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LESSON
9
CURRICULUM FOCUS
Skip counting beyond 100
N1, N10, N11, P3, P4
MATERIALS
transparency of 100-chart
and 100-chart (101–200),
transparent coloured
counters, overhead projector
PROGRAM RESOURCES
Student page 45: 100-Chart
(101–200)
Student page 46: Odd and
Even Numbers
Student page 47: Counting
Patterns
LM 7: Number Line, 0 to 50
LM 8: 100-Chart
LM 19: 100-Chart
(101–200)
Quit
Counting Patterns beyond 100
BEFORE
Get Started
Display a number line to 50 made from LM 7. Ask:
■ What do you remember about a number line? (The numbers are
placed in order from least to greatest.)
■ How did we use the number line to practise counting by 2s? (Said
every second number.) By 5s? (Said every fifth number.) By 10s? (Said
every decade number.)
Display a 100-chart transparency on the overhead projector and
discuss the similarities and differences between it and a number line.
Then have the class begin counting aloud by 2s starting at 26. As they
say each numeral, cover it with a transparent counter. Ask:
■ What pattern do you see? (26, 28, 30, and so on; every even number
from 26 on is covered.)
Remove the counters. Have children identify patterns counting by 10
from various start numbers; for example, count by 10s, starting at 4. Ask:
■ What pattern do you notice in the final digits? (They are all the same.)
■ How can you count by 10s on the 100 chart?” (Just count down a column)
Use the 100-chart transparency to practise counting by 5s, covering 5, 10,
15, 20, and 25 with one colour of transparent counters. Ask children to
identify the numerals that will come next. Then have children count by
5s from 11, covering the numbers with a different colour of counters. Ask:
■ What pattern do you notice in the final digits? (The final digits
alternate 1, 6, 1, 6, and so on.)
■ Why does this pattern happen? (Because 2 jumps of 5 make 10.)
Finally, use the 100-chart to practise counting by 25s, covering 25, 50,
75, and 100 with one colour of transparent counters. Then have
children count by 25s from 5 (5, 30, 55, 80) or 10 (10, 35, 60, 85),
covering the numbers with a different colour of counter each time.
DURING
Explore
Display a 100-chart. Ask: “Can we make a 100-chart for numbers
greater than 100? Explain your thinking.”
Place a 100-chart (101–200) transparency on the overhead projector.
Have the children count aloud by 1s from 101 and point to each
number until children reach 200. Ask:
■ How is this 100-chart the same as the 100-chart with numbers 1 to
100? (Numbers across the rows increase by 1; numbers in the columns
increase by 10.)
■ How are the charts different? (One chart shows numbers from 1 to 100
and the other shows numbers from 101 to 200.)
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Problem Prompt
What number patterns can you find on a 100-chart that shows
101–200?
Provide pairs with LM 19. Challenge children to find at least two
patterns and record them on Student page 45.
Show and Share
Have children choose one pattern to share and describe to the class.
Ask children to identify a number that would not belong in their
pattern and explain why.
AFTER
Connect and Reflect
Talk about using the 100-chart (101–200) to practise counting by 5s.
Have the children count aloud and cover the numerals with a
transparent coloured counter. Ask:
■ “What pattern would we get if we started counting from 112 by 5s?”
(Every fifth number is covered, numbers end in either 2 or 7 alternately.)
■ What would the pattern look like if we started at 12 on a typical
100-chart? (The hundreds would be different, but the patterns would
appear in the same boxes.)
Continue to use the 100-chart (101–200) to practise counting by 2s, 5s,
10s, and 25s from start numbers that are multiples of 1, 2, and 5.
Practice
Reinforcement
Use the activity Skip Counting on the Calculator, on page 37, to help
develop technology skills. Children investigate patterns in odd and
even numbers on Student page 46. Provide children with copies of LM 8
and LM 19 to refer to when completing Student page 47. After they have
completed the pages, have children talk about the patterns they found.
Extra Support: ESL
Bring together a small group of children in a circle. Give each child a
number from 0 to 50. Hold up a number card (e.g., 22) and give a
direction “hold up your card if it is less than mine” Emphasize the key
word. If children are comfortable with 0–50, play the same game with
numbers to 100, then to 200. Children can take turns being leader and
giving the direction.
Extension
Children work with a partner. One child spins a 4-part spinner
(LM 20) labelled 2, 5, 10 and 25. The other child chooses a starting
number on a 100-chart (101–200) and covers it with a counter. The first
child skip counts by the number on the spinner, starting at the covered
number. They then switch roles.
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Assessment for Learning
What to Look For
Evidence that children
■
count beyond 100 by 1s, 2s, 5s, 10s, and 25s
■
recognize and extend counting patterns
■
describe patterns they find
To guide observations and facilitate reporting, use
Assessment Master 3.3: Ongoing Observations
Checklist.
What to Do
■
Provide more hands-on opportunities for children to
count collections of objects by grouping. They
could also count objects that naturally come in
groups, such as the number of eyes or fingers in
the class.
■
Provide a spinner marked 1-more, 1-fewer, 1-up,
1-down for games where children move on a
100-chart. Give players a start number. They take
turns spinning and moving their counter. For each
move, players must say the number they are
starting on, how they are moving, and where they
end (28, one up is 38.) If they can’t move, they
lose a turn. The game ends when one player gets
to 100 or to 1.
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FROM THE LIBRARY
Mary Chalmers, Six Dogs,
Twenty-Three Cats, Forty-Five
Mice and One Hundred
Sixteen Spiders
(HarperCollins, 1986)
Hitz Demi, One Grain of
Rice: A Mathematical Folktale
(Scholastic, 1997)
Tana Hoban, 26 Letters and
99 Cents (HarperCollins,
1995)
John V. Lord, The Giant Jam
Sandwich (Houghton Mifflin,
1991)
Edward Packard, Big
Numbers: And Pictures That
Show Just How Big They Are!
(Millbrook Press, 2000)
Marjorie Weinman Sharmat,
The 329th Friend (Marcel
Dekker, 1992)
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LITERACY LINKS
Resources: Adria Klein, Feet Go Two by Two and Jack Beers, Fingers Go
Five by Five, Addison Wesley Mathematics Little Books, Early Level (Addison
Wesley, 2002)
Put an assortment of books about skip counting, including Addison
Wesley Little Books, on display for children to read independently.
Talk about how counting by 2s, 5s, and 10s are shown. Children may
wish to draw pictures extending the patterns. For example, children
can draw a picture of the pairs of feet for 10 children or the number
of fingers on 6 children.
NUMBERS EVERY DAY
Each day, cover up one or more numbers on a 100-chart.
Ask children to identify which number or numbers are covered.
Have them explain how they know. Daily practice will help children
see the repetitive patterns and the place-value patterns in larger
numbers.
CROSS-CURRICULAR CONNECTION
Physical Education
Have small groups of children practise skip counting by 2s as they
participate in a jump rope competition. Explain that the children are
to continue skip counting after a child misses a jump or finishes his
or her turn. They should record the number they end at when the last
child’s turn ends. The group that got the greatest number is the
“winner” of that round. This will be of assistance to those children
who have difficulty skip counting from different start numbers. In
the next rounds, groups should skip count by 5s and then 10s.
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Activity Bank
Skip Counting on the Calculator
What’s My Pattern?
Materials: four function calculators, overhead calculator
(optional)
Resources and Materials:
LM 8, LM 19; counters
■
Provide each child or pair of children with a calculator.
Have the class work as a group to practise skip counting.
Say: “Press ON/C to clear the display. What do you
see? (0) Press + , press 5 , now press = . What do you
see? (5) What will you see if you press = again?” (10)
■
Have children continue to press = as the class reads
aloud the numbers that appear on the displays. Record
the pattern on the board. Then ask: “What is the pattern
here?” (Counting by 5s)
■
Have children explore ways to count by 5s on the
calculator starting from numbers other than 0. They
should record the number patterns they create.
■
Then have children explore counting by 10s and 25s on
the calculator from a variety of starting numbers.
■
■
On a large outdoor paved area, create a 10 x 10
grid in chalk, and number the squares from
101–200. Squares must be big enough for a child
to stand in.
In small groups (4–5), ask children to find a pattern
on the chart (counting by 5s for example) and to
keep their pattern a secret. One group at a time,
children come and stand on the squares to show the
first 4–-5 terms of the pattern. The remaining
children guess the pattern, and if they guess
correctly, come and stand on the next spaces until
the pattern is complete.
TIP: Children can play at this on their own at recess!
Kinesthetic, Visual
Small group/Whole class
■
Ask children to describe their
strategies for finding a pattern rule
and then switch roles.
Partners
Whole Class/Individual or Partners
Resources and Materials: Chalk, large outdoor
paved area
Working in pairs, have one child
shade or cover three to five
numerals on a 100-chart
(101–200) to show a number
pattern, such as 116, 121, 126,
131, and 136. Then have the child
read the shaded numbers aloud.
The other child identifies the pattern
rule and suggests three numbers
that follow the same pattern, such
as 141, 146, and 151.
Visual, Verbal
Visual; Logical
Plotting People!
■
Neighbour Numerals
Resources and Materials: LM 8, LM 19;
crayons, pencils
■
Provide children with LM 8 and have
them shade a target numeral, such
as 12.
■
Ask the children to circle all of the
numeral’s “neighbours.” (Neighbours
are numerals directly to the left, to the
right, above, and below the target
numeral.)
■
What do children notice about the
numerals that are neighbours?
■
Have children find the neighbour
numerals for 112 on LM 19 and
compare with the neighbours for 12.
■
Repeat using different target numerals.
Visual; Logical
Independent
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LESSON
10
CURRICULUM FOCUS
Use “look for a pattern” to
solve a problem
MATERIALS
counters, calculators (class set)
PROGRAM RESOURCES
Student page 48: Reaching 41
Student page 49: Reaching 62
LM 7: Number Line, 0 to 50
LM 8: 100-Chart
STRATEGIES TOOL KIT
Look for a pattern
Make a model
Act it out
Use objects
Guess and check
Make a chart
Draw a picture
Choose a strategy
TEACHING TIP
Remind children how to use the
automatic constant feature on
the calculator. Review how to
turn the calculator on and off,
how to display numbers, and
how to clear the display.
Demonstrate how to count
forward using the constant
feature. For example, press
+ 1 = = = . The
automatic constant feature
helps reinforce counting
sequences and helps children
notice patterns.
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Strategies Tool Kit
BEFORE
Understand the Problem
Have children work in pairs to solve this problem about numbers.
Make available a variety of materials, such as calculators, 100-charts,
counters, and number lines. Then pose the following problem. To
foster flexible thinking have children make a prediction before
solving the problem.
Problem Prompt
Will you reach 41 if you count by 5s beginning at 6?
Before children get started, make sure they understand the problem:
Ask:
■ What are you supposed to do or find out?
■ What do you already know? (We are to begin at 6, then count by 5s to
see if we reach 41.)
■ What materials can you use? (calculators, number line, 100-chart)
■ Do you think the answer will be yes or no? Why?
DURING
Make a Plan
Tell children they will work in pairs. Ask them to talk to a partner
about ways they might be able to solve this problem. Have pairs
share their ideas with the class. Ask:
■ How can you use a calculator to solve the problem? (We can enter 6
on a calculator and keep adding 5 to see if we get to 41.)
■ How can you use a 100-chart? (Place a counter on 6 and count on
by 5, putting a counter on each number counted.)
Carry Out the Plan
Remind children that they can use any materials they want. When
they are happy with their solution or answer, they can show their
thinking on Student page 48, using pictures, numbers, or words.
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AFTER
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Look Back
Ask volunteers to share how they solved the problem. Elicit from the
children that while there are many ways to solve the problem, 41 will
be reached when counting by 5s from 6. Explain to the children that
they solved the problem by using a pattern.
You may wish to have children complete Generic Assessment Master 1:
I Am a Problem Solver and add it to their portfolios.
Practice
Reinforcement
Have children complete another similar problem on Student page 49.
Extra Support: Problem Solving
Repeat the problem-solving activity independently or in a small,
guided group with the teacher.
Extension
Challenge children to create and record their own “Will you
reach …?” problems and then share them with the class.
Assessment for Learning
What to Look For
What to Do
Evidence that children
Listen for the language of problem solving: “Here’s
what we can do.” “I know another way.” “I think that
would work.” Provide feedback to let the children
know that using appropriate language helps to show
that they are good problem-solvers and that you
value positive and constructive language.
■
rephrase the problem in their own words
■
use appropriate language to communicate ideas
for problem solving
■
explain their solution and can model it for others
To guide observations and facilitate reporting, use
GAM 2: Inquiry Process Rubric or GAM 3: Inquiry
Process Checklist.
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LESSON
11
CURRICULUM FOCUS
Demonstrate what has been
learned about number
relationships
MATERIALS
counters
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Show What You Know
BEFORE
Get Started
Review with children the different objects and materials they used to
build numbers and solve problems (e.g., counters, ten-frame,
calculators). Ask:
■ How did these materials help you learn about numbers?
Display class charts or the co-operative journal and have children
recall their favourite activities.
PROGRAM RESOURCES
Big Math Book, page 9:
Dragon Boats
Big Math Book, page 10:
Dragon Boat Stories
Student page 50: How Many
Paddles?
Student page 51: Dragon
Boat Stories
Student page 52: My Journal
LM 3: Ten-Frames
LM 7: Number Line, 0 to 50
LM 8: 100-Chart
DURING
Explore
Invite children to share what they know about dragon boats. Explain
that dragon boats first came from China. Now, people all over the
world have learned to paddle and have dragon boat races. There are
festivals in many communities in Canada. Each boat has a dragon’s
head, and a drummer to help paddlers keep a steady pace.
Tell children they are going to look at a picture of a dragon boat race
for just a moment, to estimate the number of paddles. (If necessary,
review what paddles are.)
Display Big Math Book, page 9, for only a moment. Have the children
estimate the number of paddles they saw: are there more than 50 or
less than 50? Have them record their answers on Student page 50.
Invite them to share their strategies for estimating.
Display the picture again, and ask: “What are some different ways
you could count the paddles to check your estimate?” (by 1s, 2s, 5s,
10s, and counting on). Have the children complete Student page 50.
Invite children to closely examine Big Math Book, page 10 and talk
about what they see (paddlers, birds, dragon heads/teeth)
Have them look at the illustration on Student page 51. Provide
materials and have children use their own ideas to create number
stories about the dragon boat race. Then have them share their stories.
Show and Share
Have children tell their number stories and explain the strategies
they used to solve them. As children complete each task, ask:
■ How did you think of your story?
■ Can you find someone whose story is like yours? Someone whose
story is very different from yours?
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AFTER
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Connect and Reflect
Review with children what they have learned in this unit. Then have
children record what they learned in pictures, numbers, or words on
Student page 52.
Take It Further
Children may enjoy acting out a dragon boat race. Work together to
find out how many paddlers there can be (there must be an equal
number on each side, with another person to steer and one to drum
and chant.) What if you wanted to have two boats? How many
paddlers would there be in each boat? What if another class joined
you — then how many paddlers would there be in two boats?
Assessment Check
✓
Look for evidence that children
❏
❏
❏
❏
❏
❏
❏
Make reasonable estimates and describe their strategies
Use counting strategies (e.g., skip count, count on)
Represent numbers in more than one way
Compare numbers
Write addition and subtraction sentences
Create and solve addition and subtraction problems
Show and describe a number more than one way.
Refer to Assessment Master 4: Performance Task Rubric and Assessment
Master 6: Unit Summary
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Evaluating Student Learning:
Preparing to Report
This unit provides an opportunity to report on the Number (Number
Concepts and Number Operations) strand. Assessment Master 6:
Unit Summary provides a comprehensive format for recording and
summarizing evidence teachers may have already collected. In completing
the Unit Summary, teachers may choose to record a grade/numeric rating
and/or a comment, according to local reporting requirements.
Here is one example of a completed summary chart for this unit:
Strand: NUMBER
(NUMBER CONCEPTS
AND NUMBER
OPERATIONS)
Notes
Most
Consistent
Level of
Achievement*
Ongoing observations
Shows an emerging sense of number
and number relationships. While this
seemed slow to develop in early parts
of the unit, recent activities,
particularly with the 100-chart, have
shown understanding of number
patterns (skip counting).
Adequate/
Proficient
Portfolio or work
samples; conferences
Had difficulty telling and writing
number stories, particularly those
that involved separating
(subtraction).
Adequate
Performance task
(Lesson 11)
Needed support to connect the tasks Adequate
to previous activities and learning.
Needs frequent opportunities to
connect number relationships and
patterns to real-life activities and
stories.
Achievement Level for reporting on this strand
Meets
expectations
at a minimal
level (with
support)
*Use locally or provincially approved levels, symbols, or numeric ratings as appropriate.
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Recording
How to Report
Ongoing
observations
Teachers who have used AM 3.1, AM 3.2, and AM
3.3: Ongoing Observations Checklist can determine
the most consistent level of performance.
Performance on
problem-solving
tasks
Teachers who have used GAM 2: Inquiry Process
Rubric or GAM 3: Inquiry Process Checklist with
Strategies Tool Kit (Lesson 10) can transfer the results
to the summary form.
Portfolio or
work samples;
conferences
Use AM 5: Number Relationships Rubric to make
decisions about achievement. Children’s work
towards the end of this long unit should be weighted
more heavily than that from earlier in the unit.
Conferences or brief interviews where children
explain or show their thinking are often necessary in
order to understand their work samples.
Performance task
Because this occurs at the end of the unit (Lesson 11),
it can offer a useful snapshot of children’s
achievement. Use AM 4: Performance Task Rubric.
Children’s
self-assessment
Opportunities to quote a child’s oral or written words
about his or her own progress may come from
conferences, in-class discussions, journals, or other
written reflections. For example: “I like big numbers.
I can count way more than a hundred.”
Learning Skills
Ongoing Records
Ongoing throughout a reporting
period, rather than being broken
down by units or strands. Use
GAM 6: Attitudes and Dispositions:
Observation Record and
GAM 7: Attitudes and Dispositions
Record evaluations of children’s
achievement over several clusters, a
reporting period, or a school year.
Use GAM 14: Summary Class
Record: Strands; GAM 15: Summary
Class Record: Achievement
Categories; and GAM 16: Summary
Record: Individual.
Checklist
Unit 2: Number Relationships
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Unit 2: Number Relationships
Date:
Assessment Master 1
Diagnostic Checklist
During Launch activities, use this form to note observations about children who appear to have difficulty.
Name
Recognizes
opportunities
to use number
in real-life
situations
Suggests more
than one way
to count
Counts
accurately
(correct
sequence;
one-to-one)
Prints
numerals
(to 20)
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Unit 2: Number Relationships
Name:
Assessment Master 2
Date:
Diagnostic Conference for Selected
Children
This outline is intended for use with children whose progress is a concern at the midway point of
the unit (e.g., Lesson 6). It can be used with an individual child or a small group of children
who appear to be having difficulty with basic concepts and procedures.
CATEGORIES
OBSERVATIONS AND COMMENTS
Place a collection of two types of counters or other small objects in a plastic
bag (e.g., butterfly counters and bird counters.); 30-40 counters in all.
Reasoning and applying concepts
Estimate and count
Ask the child to examine the bag and feel it. Ask:
• What can you tell me about the objects in this bag? (they’re different
shapes, there are lots of them)
• Do you think there are more than 10? Tell me about your thinking. Do you
think there are more than 20? (if child says yes, ask: More than 50? If child
says yes, ask: More than 100?)
Invite the child to empty the bag and count the objects. Ask:
• What are some ways we could count these?
• What is your favourite way to count?
Compare
Say: Let’s separate these into two groups (separate two types of counters.)
Which group has more? How could we check? (by counting)
Use doubles; count-on
Make two sets of 4s each, and ask: What can you tell me about these sets?
(they are doubles, they show 8) Invite the child to make a set of doubles. Say:
• What number sentence could we make about these? (3 + 3 = 6)
• If I add one to this set, how many will there be altogether? (7) How did you
know? (counted on)
• What if I take two counters away? (5—counted back)
Notice the child’s confidence and ability to:
• Make reasonable estimates
• Count in more than one way
• Compare quantities
• Use doubles and counting on/back to solve combining problems
Problem-solving strategies
Model making an addition story using the counters, and invite the child to
solve it. Then say:
• Now it’s your turn. Make an addition story for me to solve.
If the child successfully makes an addition problem and models its solution,
invite a subtraction story.
Notice the child’s confidence and ability to:
• solve and create addition and subtraction stories
• create more than one story for the same number
• recognize the relationship between addition and subtraction
• use strategies such as doubles or counting on/back
Accuracy of procedures
As children work with the objects, notice how accurately they:
• count, add, and subtract
Communication
Say: “Thank you for your hard work and thinking! Let’s make a list together of
everything we did and what we found out.” [Allow student to retell the
activities freely; prompt if stuck.]
Notice the child’s confidence and ability to:
• use appropriate language related to 10s and 1s, groups, counting, and
number stories
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Unit 2: Number Relationships
Date:
Assessment Master 3.1
Ongoing Observations Checklist
Cluster 1: Lesson 1
Name
shows
numbers
10 to 20
on 10frames
writes
numerals
and
number
words
describes
numbers
as “10
and __
more”
Cluster 1: Lesson 2
estimates
sets of 10
to 50
forms
groups to
count
skip
counts
Cluster 1: Lesson 3
orders
numbers
to 50
locates
numbers
on a
number
line
recognizes
a pattern
when skip
counting
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Unit 2: Number Relationships
Date:
Assessment Master 3.2
Ongoing Observations Checklist
Cluster 2: Lesson 4
Name
chooses
to add or
subtract
uses
addition/
subtraction
strategies
records
number
stories
Cluster 2: Lesson 5
explores
whole
numbers
records
number
sentences
uses one
fact to
find
another
Cluster 2: Lesson 6
identifies
doubles
mentally
adds
one-digit
numbers
uses
doubles to
solve near
doubles
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Unit 2: Number Relationships
Date:
Assessment Master 3.3
Ongoing Observations Checklist
Cluster 3: Lesson 7
Name
uses
reference
of 10 to
estimate
counts
and
groups
10s
explains
estimating
strategies
Cluster 3: Lesson 8
recognizes
numerals
to 100
compares
and
orders
numbers
uses
clues to
identify a
number
on a 100chart
Cluster 3: Lesson 9
counts
and skip
counts
beyond
100
recognizes
and
extends
counting
patterns
describes
patterns
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Unit 2: Number Relationships
Name:
Assessment Master 4
Knowledge/Skills
Reasoning and
applying concepts
• shows understanding
of number concepts
by
– making reasonable
estimates and
explaining his or
her thinking
– counting and
representing
numbers in more
than one way
Accuracy of
procedures
• counts accurately
• writes numerals and
number sentences
accurately
• compares numbers
accurately
Problem-solving
strategies
• uses appropriate
strategies to create
addition- and
subtraction-story
problems
Date:
Performance Task Rubric
Not Yet Adequate
(needs assistance)
Adequate
Proficient
(limited assistance)
Excellent
shows very limited
understanding of
number concepts;
needs one-to-one
assistance to
– make reasonable
estimates
– count and
represent numbers
in more than one
way
shows some
understanding of
number concepts;
with prompting and
support, able to
– make reasonable
estimates (may
have difficulty
explaining his or
her thinking)
– count and
represent numbers
in at least two
simple ways (e.g.,
1s and 2s)
shows basic
understanding of
number concepts;
able to
– make reasonable
estimates and
explain his or her
thinking
– count and
represent numbers
in more than one
way
shows in-depth
understanding of number
concepts; independently
able to
– make reasonable
estimates and explain
this or her thinking;
may have an innovative
strategy
– count and represent
numbers in more than
one way; may
introduce some
complexity into the task
(e.g., count in a way
that has not been
modelled)
needs one-to-one
help; makes frequent
errors in
– counting
– writing numerals
and number
sentences
– comparing
numbers
partially accurate;
makes some errors
in
– counting
– writing numerals
and number
sentences
– comparing
numbers
generally accurate;
may make a few
minor errors in
– counting
– writing numerals
and number
sentences
– comparing
numbers
accurate; very few or no
errors in
– counting
– writing numerals and
number sentences
– comparing numbers
needs one-to-one
assistance to create
simple additionand/or subtractionstory problems
creates simple
addition- and
subtraction-story
problems; may need
support for the
subtraction problem
creates simple
addition- and
subtraction-story
problems
creates addition- and
subtraction-story
problems that show some
complexity or innovation
explains his or her
reasoning and
procedures clearly
explains his or her
reasoning and
procedures clearly,
confidently, and with
some precision
Communication
• explains his or her
unable to explain his partially explains his
reasoning and
or her reasoning and or her reasoning and
procedures clearly,
procedures
procedures
including appropriate
terminology
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Name:
Assessment Master 5
Date:
Number Relationships Rubric
This rubric can be used to assess and summarize children’s achievement of unit expectations.
Knowledge/Skills
Reasoning and applying
concepts
• shows understanding
and reasoning with
number concepts by
– representing and
describing numbers to
100 in various way
(including 10s and 1s)
– making reasonable
estimates of objects in a
set and counting to
compare
– building and comparing
sets
– demonstrating placevalue concepts
concretely and
pictorially with twodigit numbers
– demonstrating and
describing processes of
addition and subtraction
Accuracy of
procedures
• compares and orders
numbers (including
locating numbers on a
number line)
• counts beyond 100 (by
1s, 2s, 5s, 10s)
• reads and writes
numerals to 100; number
words to 10
• recalls addition and
subtraction facts
to 10
Problem-solving
strategies
• chooses and carries out a
range of estimation and
problem-solving strategies
(e.g., concrete objects,
pictures, mental
mathematics, number
patterns, modelling,
calculators, number line,
100-chart, grouping) to
solve and create problems
Not Yet Adequate
(needs assistance)
Adequate
(limited assistance)
Proficient
Excellent
with assistance, shows
very limited
understanding and/or
reasoning with number
concepts; may be
unable to
– represent and
describe numbers
(various ways)
– make reasonable
estimates and count
to compare
– build and compare
sets
– demonstrate placevalue concepts
– demonstrate and
describe processes
of addition and
subtractions
shows some
understanding and
ability to reason with
number concepts, able
to do some of the
following:
– represent and
describe numbers
(various ways)
– make reasonable
estimates and count
to compare
– build and compare
sets
– demonstrate placevalue concepts
– demonstrate and
describe processes
of addition and
subtractions
shows basic
understanding and
reasoning with number
concepts; able to do
most of the following:
– represent and
describe numbers
(various ways)
– make reasonable
estimates and count
to compare
– build and compare
sets
– demonstrate placevalue concepts
– demonstrate and
describe processes
of addition and
subtraction
shows in-depth
understanding and
reasoning; able to do
most of the following
consistently and in a
variety of contexts:
– represent and describe
numbers (various
ways)
– make reasonable
estimates and count to
compare
– build and compare sets
– demonstrate placevalue concepts
– demonstrate and
describe processes of
addition and
subtraction
needs ongoing
assistance; little
accuracy; major errors/
omissions in
– comparing and
ordering numbers
– counting beyond 100
(1s, 2s, 5s, 10s)
– reading and writing
numerals to 100;
number words to 10
– recalling addition and
subtraction facts to 10
somewhat accurate;
minor errors/
omissions in
– comparing and
ordering numbers
– counting beyond
100 (1s, 2s, 5s, 10s)
– reading and writing
numerals to 100;
number words to 10
– recalling addition
and subtraction
facts to 10
generally accurate;
few errors/ omissions
in
– comparing and
ordering numbers
– counting beyond
100 (1s, 2s, 5s, 10s)
– reading and writing
numerals to 100;
number words to 10
– recalling addition
and subtraction
facts to 10
accurate; very few or no
errors/omissions in
– comparing and ordering
numbers
– counting beyond 100
(1s, 2s, 5s, 10s)
– reading and writing
numerals to 100;
number words to 10
– recalling addition and
subtraction facts to 10
needs assistance to
choose and carry out
appropriate strategies
to create and solve
problems
with limited
assistance, chooses
and carries out some
appropriate strategies
to create and solve
simple problems in
familiar contexts
chooses and carries
out appropriate
strategies to create
and solve problems in
familiar contexts
chooses and carries out
appropriate and effective
strategies to create and
solve increasingly
complex problems in a
variety of contexts; may
be innovative
Communication
• explains his or her
unable to explain his or
reasoning and procedures her reasoning and
clearly, including
procedures
appropriate terminology
partially explains his or explains his or her
her reasoning and
reasoning and
procedures
procedures clearly
explains his or her
reasoning and procedures
clearly, confidently, and
with some precision
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Unit 2: Number Relationships
Name:
Assessment Master 6
Date:
Unit Summary
Review assessment records to determine the most consistent achievement level achieved for each
of the following during this unit. Notes can be included as needed.
Strand:
NUMBER (NUMBER
CONCEPTS AND NUMBER
OPERATIONS)
Ongoing observations
Notes
Most
Consistent
Level of
Achievement*
Portfolio or work samples;
conferences
Performance task
(Lesson 11)
Achievement Level for reporting on this strand
*Use locally or provincially approved levels, symbols, or numeric ratings as appropriate.
Self-assessment:
Strengths:
Needs:
Next steps:
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 1
Unit 1:
Number Relationships
We can count
by 2s, 5s, 10s,
and 25s.
Sorting
and Patterning
Unit 2: Number
Relationships
Unit 3: Time, Temperature,
and Money
Unit 4: Exploring Addition
and Subtraction
We can use
a calculator.
Unit 5: Data Management
and Probability
Unit 6: 3-D Geometry
Unit 7: Addition and
Subtraction to 100
Unit 8: Linear Measurement,
Area, and Perimeter
Unit 9: 2-D Geometry and
Patterning
Unit 10: Multiplication, Division,
and Fractions
We can build large
numbers. We can
record numbers as
tens and ones.
We use adding and
subtracting to solve
number problems.
Unit 11: Mass and Capacity
52
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 2
Dear Family
Your child is learning about number relationships. Your child
can practise these concepts at home by doing the following
activities.
Gather 20 small objects
such as buttons or bread
tags. Show your child a
group of 10 items and up
to 8 more. Ask: “How
many? What number is
two more? What number
is one less?”
Share addition and
subtraction story
problems about things
in your neighbourhood.
For example, “There are
15 houses on our street.
9 of them have a
garage. How many do
not have a garage?”
Gather a collecti
on of
small objects for
your
child to count, s
uch as
raisins or pennie
s. Have
your child show
about 40
small objects. A
sk your
child to count th
e
collection by gro
uping the
objects in differe
nt ways.
Have your child build a
set of 11 to 15 pennies
and then add 1, 2, or
3 pennies. Have your
child count on from that
number to get the total.
Repeat the activity for
subtraction.
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 3
Ten-Frames
✃
✃
54
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
twenty
sixteen
fifteen
nineteen
fourteen
thirteen
seventeen eighteen
twelve
Number Word Cards
eleven
Line Master 4
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 5
All about My Number
My number __________
This is how I showed it.
__________ is 10 and __________ more.
The number word is __________________________________.
56
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 6
Dot Plates
1
2
3
4
5
6
7
8
9
10
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Name: __________________________ Date: _________________________
42 43 44 45 46 47 48 49 50
41
34 35 36 37 38 39 40
31
22 23 24 25 26 27 28 29 30
21
20
18
17
19
16
15
14
13
12
11
10
9
8
7
6
5
4
3
1
0
2
58
32 33
Number Line, 0 to 50
Line Master 7
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Name: __________________________ Date: _________________________
Line Master 8
100-Chart
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 9
0
Numeral Cards, 0 to 20
1
2 3
4 5 6 7
8 9 10 11
12 13 14 15
16 17 18 19 20
60
✃
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 10
Numeral Cards, 21 to 40
21 22 23 24
25 26 27 28
29 30 31 32
33 34 35 36
37 38 39 40
✃
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 11
Numeral Cards, 41 to 60
41 42 43 44
45 46 47 48
49 50 51 52
53 54 55 56
57 58 59 60
62
✃
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 12
Numeral Cards, 61 to 80
61 62 63 64
65 66 67 68
69 70 71 72
73 74 75 76
77 78 79 80
✃
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 13
Numeral Cards, 81 to 100
81 82 83 84
85 86 87 88
89 90 91 92
93 94 95 96
97 98 99 100
64
✃
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Name: __________________________ Date: _________________________
Line Master 14
Grid Paper
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Line Master 15
66
To The Moon Game Board
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Unit 2: Number Relationships
Name: __________________________ Date: _________________________
Fact Family Builders (+ and –)
18
7
8
15
7
5
14
13
9
9
16
9
15
9
6
7
9
16
8
6
8
14
8
6
5
4
9
10
4
12
7
2
13
9
12
7
8
7
4
11
8
13
3
3
12
5
11
9
11
5
2
10
6
4
8
3
3
6
10
7
10
5
5
7
8
11
8
3
4
9
3
4
Line Master 16
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Name: __________________________ Date: _________________________
Line Master 17
Domino Cards
Cut along the solid lines.
68
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Name: __________________________ Date: _________________________
Line Master 18
Domino Cards
Cut along the solid lines.
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Name: __________________________ Date: _________________________
Line Master 19
70
100-Chart (101 to 200)
101
102 103 104 105 106
107
108 109
110
111
112
116
117
118
120
121
122 123 124 125 126
127
128 129 130
131
132 133 134 135 136 137 138 139 140
141
142 143 144 145 146
147
148 149 150
151
152 153 154 155 156
157
158 159 160
161
162 163 164 165 166
167
168 169
171
172
177 178 179 180
181
182 183 184 185 186 187 188 189 190
191
192 193 194 195 196 197 198 199 200
113
114
115
173 174 175
176
119
170
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Name: __________________________ Date: _________________________
Line Master 20
Four-Part Spinners
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Page OBCII
Home
Program Authors
Carole Saundry
Sharon Jeroski
Heather Spencer
Michelle Jackson
Maureen Dockendorf
Sandra Ball
Maggie Martin Connell
Jill Norman
Linden Gray
Susan Green
Program Consultants
Craig Featherstone
Maggie Martin Connell
Trevor Brown
Assessment Consultant
Sharon Jeroski
Primary Mathematics and
Literacy Consultant
Pat Dickinson
Elementary Mathematics Adviser
John A. Van de Walle
British Columbia Early Numeracy Adviser
Carole Saundry
Ontario Early Math Strategy Adviser
Ruth Dawson
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Copyright © 2005 Pearson Education Canada Inc.
All Rights Reserved. This publication is protected by
copyright, and permission should be obtained from
the publisher prior to any prohibited reproduction,
storage in a retrieval system, or transmission in any
form or by any means, electronic, mechanical,
photocopying, recording, or likewise. For
information regarding permission, write to the
Permissions Department.
The information and activities presented in this
book have been carefully edited and reviewed.
However, the publisher shall not be liable for any
damages resulting, in whole or in part, from the
reader’s use of this material.
Brand names that appear in photographs of
products in this textbook are intended to provide
students with a sense of the real-world applications
of mathematics and are in no way intended to
endorse specific products.
Complete Teacher Guide ISBN 0-321-12094-9
Printed and bound in Canada
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