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Western Canadian
Teacher Guide
Unit 8
Unit 1:
Sorting and Patterning
Unit 2:
Number Relationships
Unit 3:
Time, Temperature, and Money
Unit 4:
Addition and Subtraction to 12
Unit 5:
Data Management and Probability
Unit 6:
3-D and 2-D Geometry
Unit 7:
Number Patterns
Unit 8:
Linear Measurement and Area
Unit 9:
2-D Geometry and Applications
Unit 10: Place Value and Number Applications
Unit 11: Mass and Capacity
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UNIT
“
8
Measurement involves a
comparison of an item that
is being measured with a
unit that has the same
attribute (length, volume,
weight, etc.). To measure
anything meaningfully,
the attribute must be
understood.
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Linear Measurement
and Area
Mathematics Background
What Are the Big Ideas?
Measurement
■
■
”
—John A. Van de Walle,
Elementary and Middle School
Mathematics, page 277
Measurement requires that children compare objects that share the
same attribute. When measuring, children first decide on the
attribute to be measured and then select a unit that has that attribute.
Young children need repeated experiences estimating, measuring,
and comparing, using non-standard units. Using a non-standard
unit, such as a paper clip or pencil, helps children build spatial
referents (pictures in the mind). Children use these spatial referents
when they estimate. Estimation helps children focus on the
attribute being measured and helps them become more familiar
with the attribute. These early experiences help build the
foundation for developing the need for a standard unit of measure.
Length
■
■
When making direct comparisons involving length, children will
discover that placing objects side by side along a common baseline
will make comparing and ordering lengths easier.
Children may already be familiar with many measurement terms
but may use words inaccurately. The language of measurement
and comparison should be developed and practised so terms can
be used accurately. Such words include longer/shorter, as tall as,
more/less, compare, far/near, and estimate.
Area
■
After children have had numerous experiences comparing lengths,
they move on to making direct comparisons of areas. When
comparing areas, children use non-standard units to cover, or tile,
different surfaces. These comparison activities help children
distinguish between area and length.
FOCUS STRAND
Across the Strands
Shape and Space
(Measurement)
This is an integrated unit, which incorporates both measurement and
data management (through a focus on attributes). The activities
further develop estimation and proportional (spatial) reasoning
fundamental to mathematical development across the strands. The
activities help reinforce counting and number sense. The results of
many activities can be represented in concrete graphs or picture
graphs, reinforcing expectations introduced in Data Management.
SUPPORTING STRANDS
Statistics and Probability
Number (Number Concepts)
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Curriculum across the Grades
Kindergarten
Grade 1
Grade 2
Children measure and
compare the lengths of
objects.
Children estimate,
measure, compare,
order, and record
lengths of objects using
non-standard units.
Children measure and
record linear
measurements using
both non-standard and
standard units (cm, m).
Children compare
areas using nonstandard units.
Children estimate,
measure, compare,
and record perimeters
and areas of twodimensional figures.
Preparing Materials
The Pattern Block shapes found on LM 11 can be copied onto heavy
paper, laminated, and then cut out. These can be placed in resealable
plastic bags for the children to use.
Unit 8: Linear Measurement and Area
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Curriculum Overview
Launch
Cluster 1: Comparing and Ordering Lengths
General Outcome
Specific Outcomes
• Estimate, measure and
compare, using whole
numbers and non-standard
units of measure.
• Select an appropriate nonstandard unit to measure
length.
• Estimate, measure, record,
compare and order objects
by length, height, and
distance around, using nonstandard units.
Lesson 1:
Comparing
Lengths
Lesson 2:
Estimating
Lengths
Lesson 3:
Ordering
Lengths
Lesson 4:
Choosing
a Unit
Lesson 5:
Strategies Tool Kit
Cluster 2: Area
2
General Outcome
Specific Outcomes
• Estimate, measure and
compare, using whole
numbers and non-standard
units of measure.
• Estimate the number of
uniform objects or shapes
that will cover the surface of
a design, and verify by
covering and counting.
• Estimate the number of
irregular shapes that will
cover a given area, and
verify by covering and
counting.
Unit 8: Linear Measurement and Area
Lesson 6:
Estimating and
Comparing Areas
Lesson 7:
Show What You Know
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Activity Bank
• Sorting by Length
• Length Hunt
• Comparing Lengths
• Will It Fit?
Activity Bank
• Box of Feet!
• Rolling Along
• About How Tall Are You? • I Spy!
Activity Bank
• Snakes Alive!
• Paper Airplane Flights
• Which Shoe Is Shortest?
• Who Is the Shortest?
Activity Bank
• Draw This!
• What’s My Line?
• How Many Will Fit?
• Choosing a Unit
Activity Bank
• Estimate and Cover
• Tangram
• Same Surface, Different Unit
• Conserving Area
Unit 8: Linear Measurement and Area
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Planning for Instruction
Lesson
Launch, page 11
Demonstrate prior knowledge of
linear measurement
Time
Lesson Materials
20–30 min
paper clips, crayons, Snap
Cubes, straws
Curriculum Cluster 1: Comparing and Ordering Lengths
Lesson 1: Comparing Lengths,
page 12
Compare lengths of objects to
one common referent
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Suggested Unit Time: 3 weeks
60–90 min
Activity Bank
Suggested Time: 8 to 10 days
unsharpened pencils,
classroom objects, word cards,
4 containers (3 small, 1 large)
„ Sorting by Length
„ Length Hunt
„ Comparing Lengths
„ Will It Fit?
Lesson 2: Estimating Lengths,
page 16
Estimate lengths using nonstandard units
60–90 min
straws, crayons, Snap Cubes
„ Box of Feet!
„ About How Tall Are You?
„ Rolling Along
„ I Spy!
Lesson 3: Ordering Lengths,
page 20
60–90 min
straws, ramps, toy vehicles,
books, masking tape
Order objects according to length
„ Snakes Alive!
„ Paper Airplane Flights
„ Which Shoe Is Shortest?
„ Who Is the Shortest?
Lesson 4: Choosing a Unit,
page 24
Determine a non-standard unit
appropriate to measure lengths
of objects
60–90 min
paper clips, straws, erasers,
crayons, string or yarn
„ Draw This!
„ What’s My Line?
„ How Many Will Fit?
„ Choosing a Unit
Lesson 5: Strategies Tool Kit,
page 28
“Use objects” to solve a problem
4
45–60 min
Unit 8: Linear Measurement and Area
a variety of materials for
measuring
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Activity Bank Materials
Program Resources
Big Math Book, page 40: Things We Measure
Student page 181: Linear Measurement and
Area
Student page 182: Dear Family
Student page 183: I Can Measure
20–100 min
materials of different length
lengths of string
Big Math Book, page 41: Measuring Lengths
Student page 184: Longer or Shorter?
Student page 185: Measurement Hunt!
LM 3: Compare Lengths
boxes, objects of different length
various objects, shirt or smock with a pocket
20–100 min
cut-outs of shoeprints, box
string or yarn, scissors, box or cup
Student page 186: Measure How Tall
Student page 187: Estimate, Measure, and
Record
LM 4: My Carrot Measurements
LM 5: Estimating
modelling clay, paper clips
straw, pencil, Snap Cubes, Lego
20–100 min
modelling clay, various objects to measure
paper airplanes, balls of different-coloured yarn, scissors
Big Math Book, page 42: Rolling Along
Student page 188: Ordering Lengths
LM 6: Measure the Distance
LM 7: Ordering Lengths
shoes
chart paper
20–100 min
a straw, paper, pencils, various classroom objects
classroom objects, paper clips, paper, pencils
Big Math Book, page 43: Make a Good Choice
Student page 189: Use Different Units
Student page 190: Choose a Unit
LM 8: Estimate with 5
LM 9: Estimate with 10
several samples of household objects, tape
paper clips, straws, strips of cardboard
Big Math Book, page 44: Who Went the
Farthest?
Student page 191: Who Went the Farthest?
Student page 192: Which Way Is Shorter?
LM 10: Estimate and Measure
LM – Line Master
(continued)
Unit 8: Linear Measurement and Area
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Planning for Instruction
Lesson
Time
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Lesson Materials
Curriculum Cluster 2: Area Suggested Time: 2 days
Lesson 6: Estimating and
60–90 min
newspapers, cards, Pattern
Comparing Areas, page 30
Blocks
Estimate and count the number
of objects needed to cover a
surface without gaps or overlap
Activity Bank
„ Estimate and Cover
„ Tangram
„ Same Surface, Different Unit
„ Conserving Area
Unit Assessment Suggested Time: 1 to 2 days
Lesson 7: Show What You
45–120 min
paper clips, toothpicks,
Know, page 34
crayons, straws
Demonstrate what has been
learned
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Unit 8: Linear Measurement and Area
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Time
20–100 min
Activity Bank Materials
building blocks
Tangram pieces
sheet of construction paper, variety of uni ts
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Program Resources
Student page 193: About How Many?
Student page 194: Cover This Shape
Student page 195: Cover the Page
Student page 196: Choose a Unit
Student page 197: Roll and Cover
LM 11: Pattern Block Shapes
LM 12: Tangram
rectangular sheets of paper
Student page 198: Ordering My Objects
Student page 199: Choose, Estimate, and
Measure
Student page 200: My Journal
LM – Line Master
Unit 8: Linear Measurement and Area
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Planning for Assessment
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Purpose
Assessment Process
Recording and Reporting
Diagnostic
Launch
Diagnostic Assessment
Watch and listen during Launch
AM 1: Diagnostic Checklist
Conference and scaffold for selected children
(mid-unit)
AM 2: Diagnostic Conference for
Selected Children
Formative
End of Lesson
Assessment for
Learning
• What to Look For
• What to Do
Watch and listen during lessons; scaffold as
needed
AM 3.1 and AM 3.2: Ongoing
Observations Checklist
Question; conduct informal conferences and
interviews; provide feedback; scaffold as needed
(see GAM 11: Conference Prompts)
GAM 2: Inquiry Process Rubric or
GAM 3: Inquiry Process Checklist
GAM 9 and GAM 10: Observation
Records 1 and 2
Review Student pages and other practice work;
provide feedback; scaffold as needed; select key
pieces
GAM 12: Work Sample Record or
GAM 13: Collaborative Work
Sample Record
Prompt self-assessment
GAM 1: I Am a Problem Solver
Conduct performance assessment (Lesson 7)
AM 4: Performance Task Rubric
Prompt children’s self-assessment
GAM 4: What I Learned or GAM 5:
Looking Ahead
Review assessment rec ords
AM 5: Linear Measurement
and Area Rubric
AM 6: Unit Summary
Add unit results to ongoing rec ords
GAM 14: Summary Class Record:
Strands, GAM 15: Summary
Record: Achievement Categories,
or GAM 16: Summary Record:
Individual
Observe and record throughout unit
GAM 6: Attitudes and Dispositions:
Observation Record or
GAM 7: Attitudes and Dispositions
Checklist
GAM 8: Working Together
Summative
Show What You Know
Evaluating Student
Learning: Preparing to
Report, p. 36
Learning Skills
AM – Assessment Master
GAM – Generic Assessment Master
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Mathematics Centres
Measuring Lengths
Ordering Lengths
(appropriate for use after Lesson 1)
(appropriate for use after Lesson 3)
Materials: Link-Its or paper clips, small objects
Materials: containers, used crayons, paper,
shoebox lid
■
Ask children to use Link-Its or paper clips to
measure the lengths of different objects at
the centre.
■
Provide chart paper and have children
record their findings using pictures,
numbers, or words.
■
After several objects have been measured,
ask children to identify the longest or shortest
object and have them justify their responses.
■
Provide containers filled with crayons of
different lengths.
■
Children take a handful of crayons and put
them in order by length, from shortest to
longest, using the edge of a piece of paper
or the inside edge of a shoebox lid as a
baseline.
■
Have children record their findings by tracing
to show the length of each crayon.
Logical
Visual; Kinesthetic
Draw and Measure
Exploring Area with
Pattern Blocks
(appropriate for use after Lesson 2)
Materials: draw-and-stamp program, paper,
computers
■
■
■
Have children use a computer draw-andstamp program to draw a rectangle. Then
have them use the stamps (any image they
choose) to measure the length and width of
their rectangles.
They should record their findings by
indicating how many stamps long or wide
their rectangles are.
Have children “grow” a tree, using the tree
tool from the Paint Brush Pallet. Holding down
the shift key while clicking to grow a tree will
make the tree much taller! Children could
then measure the tree using the stamps.
Visual; Logical
(appropriate for use after Lesson 6)
Resources and Materials: LM 11; Pattern
Blocks, paper, outlines of Pattern Blocks
■
Ask children to explore using Pattern Blocks.
■
Prepare a set of Pattern Block outlines by
tracing actual blocks or use cut-out shapes
from LM 11.
■
Have children cover the outline using one
type of Pattern Block.
■
Encourage them to see that there may be
more than one correct answer depending on
the blocks they choose.
■
Have children identify and count the number
of each type of Pattern Block.
Visual; Kinesthetic
Unit 8: Linear Measurement and Area
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UNIT
FOCUS
8
Demonstrate prior knowledge
of linear measurement
MATERIALS
paper clips, crayons,
Snap Cubes, straws
PROGRAM RESOURCES
Big Math Book, page 40:
Things We Measure
Student page 181: Linear
Measurement and Area
Student page 182: Dear Family
Student page 183: I Can
Measure
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Launch
Tell children they are going to learn about measurement and invite
them to share what they already know (we measure things in
different ways, we measure time, my doctor measures how tall I am).
Display Big Math Book, page 40. Ask:
■ What are the people doing?
■ What are they finding out?
Begin a class chart and have children
suggest different things that are
measured for length at home and at
school. Record suggestions such as
bookcase and bulletin board on the chart.
Things We Measure
At School At Home
length of desk
bulletin board
bookcase
Display a classroom object, such as a book
or a box. Ask:
■ What parts of this could we measure?
(e.g., length, width, height)
Model measuring the object using a non-standard unit of
measurement (paper clip). Have children count the number of units
long, wide, and tall.
Give groups of children opportunities to practise measuring in the
same way.
After they have completed this
activity, ask:
■ What did you measure?
■ How did you measure it?
■ What did you find out?
DIAGNOSTIC
ASSESSMENT
Although children are familiar
with words such as tall, short,
big, and small, they may
use the word big to describe
any large object. Work
individually with children to
model the use of additional
measurement terms such as
shorter, longer, and measure.
To guide your observations,
use Assessment Master1:
Diagnostic Checklist.
TEACHING TIP
Model and reinforce use of terms
such as long, wide, tall.
Assign Student page 183 where
children draw pictures of
themselves measuring an object.
Consider the diversity of
children in the class. Note that
some children may not have
had previous experience
measuring. Ensure children
have opportunities to explore
the concept by having many
opportunities to measure
throughout this unit.
HOME CONNECTION
Send home Student pages 181 and 182 to introduce family members
to the Learning Goals for the unit.
Unit 8: Linear Measurement and Area
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LESSON
1
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Comparing Lengths
Get Started
CURRICULUM FOCUS
BEFORE
Compare lengths of objects
to one common referent
SS2
Tell children, “When we measure, we compare things.”
MATH WORD WALL
measure
long, longer
length
short, shorter
compare
MATERIALS
unsharpened pencils,
classroom objects, word
cards, 4 containers (3 small,
1 large)
PROGRAM RESOURCES
Big Math Book, page 41:
Measuring Lengths
Student page 184: Longer
or Shorter?
Student page 185:
Measurement Hunt!
Model comparing some classroom objects to an unsharpened pencil.
Use a common baseline.
Ask:
Is this object about as long as the pencil? (consider within width of
smallest finger “about as long”)
■ Is it longer or shorter?
■
Display Big Math Book, page 41.
■ Which of these objects are about the same length as the pencil?
■ Which ones are longer/shorter? How could we check?
Invite volunteers to check their predictions by comparing the length
of the pencil to the length of each object shown. Have the children
explain how they made their comparisons. Ask:
■ Why did you place one end of the pencil even with one end of the
cucumber? (easier to compare lengths)
Elicit from the children that objects are
easier to compare if they are lined up
along a common baseline.
DURING
TRY
THIS
Explore
Provide children with unsharpened
pencils all the same length.
See the
Literacy Links
on page 14.
You may want to
introduce the concept by
sharing one of these
stories with the children.
Problem Prompt
Look around the classroom. What objects can you find
that are about as long as your unsharpened pencil?
Allow time for children to find the objects and
place them in a container labelled “about as
long as.” Repeat for objects that are “shorter
than” and “longer than the pencil.” Ask
children to place these objects in containers
labelled “shorter than” and “longer than.”
TEACHING TIP
Begin a co-operative
journal on chart
paper to record what
children learn about
measuring length
and area.
Place the contents of all the containers in one
large bin. Randomly divide the contents of the
bin into four. Divide the class into four groups.
Provide each group with areas for sorting their collections into three
categories: about as long as, shorter than, and longer than the pencil.
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Show and Share
Have children visit the sorted collections. Ask:
■ How can we decide what belongs in the “shorter than” group?
(compare, estimate)
■ How can we check? (compare the lengths of objects with the
pencil, line up the objects along a baseline)
Use word cards for each group: shorter than, about as long as, and longer
than. Have volunteers place the cards with the appropriate groups.
AFTER
Connect and Reflect
Review with the children that objects such as a pencil or a straw
can be used to measure the lengths of other objects. Discuss the
importance of using the same pencil each time they compared lengths.
Practice
Reinforcement
Read directions and have children compare the lengths of objects on
Student page 184. Provide Snap Cubes for children to use when
completing Student page 185.
Extra Support: Procedures
Children can practise and apply their measuring skills at the
Mathematics Centres (see Measuring Lengths, page 9). Model and
review how to measure two objects using a baseline before they begin.
Extension
Have children work in pairs and measure a chosen object, recording
its length using three non-standard units (paper clip, straw, crayon).
Children then play a guessing game, “What did we use to measure?”
where each pair shows the object and its measure. Others guess the
unit used to measure, and explain how they know.
Assessment for Learning
What to Look For
What to Do
Evidence that children
Many Grade 1 children have not yet developed the
concept of conservation of length, whereby they
recognize that the length of an object does not
change if the object is placed in a different position.
■
compare lengths accurately
■
compare each object with the referent
■
use a baseline when comparing the lengths
of objects
To guide observations and facilitate reporting, use
Assessment Master 2: Ongoing Observations
Checklist.
■
Focus children’s attention on the baseline as a
way to reinforce the concept.
■
Give children a “forced” baseline, such as a
shoebox lid, where they can use the raised edges
to position their objects accurately.
Unit 8: Linear Measurement and Area
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FROM THE LIBRARY
Eric Carle, Watch Out! A
Giant! (Simon and Schuster,
2002)
Hazel Hutchins, Two So
Small (Annick, 2000)
Loris Lesynski, Boy Soup or
When Giant Caught Cold
(Annick, 1996)
Marianna Mayer, The
Adventures of Tom Thumb
(SeaStar Books, 2001)
Eva Montanari, Thumbelina
(McGraw Hill, 2001)
Robert Munsch, David’s
Father (Annick, 1982)
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LITERACY LINKS
Resources and Materials: a version of Alice in Wonderland, Goldilocks
and the Three Bears, Clifford, the Big Red Dog, a collection of fairy tales;
paper, pencils, crayons
With help from the children, gather books about tall and short
characters. Over the next while, read aloud selected stories and
provide opportunities for children to browse through the collection.
Many stories have been written about the problems that tall
characters and short characters face. After reading these suggested
stories out loud, ask children to
■ describe the advantages and disadvantages that characters had by
being a different height. For example, Alice was able to go to many
exciting places when she was small, and Baby Bear had a chair
made just for him, but it wasn’t strong enough for Goldilocks.
■ talk about the comparative heights of some characters and the
significance of their size. Invite children to choose a character and
write and illustrate a story in which the character’s size plays
an important role.
NUMBERS EVERY DAY
There will be many “teachable moments” involving linear
measurement. Use these moments to connect linear measurement
concepts with counting activities, asking questions such as, “What
could we use to measure this? How many do you think it will take?”
CROSS-CURRICULAR CONNECTIONS
Art
Materials: paint, Snap Cubes, paper
In small groups, have children paint pictures of the Three Bears or
other story characters. When the paintings have dried, have them
estimate how many Snap Cubes tall each character is. Have a
volunteer write the estimate on a self-stick note on the painting.
Then have children measure to check how close their estimate was.
Social Studies
Children work with older buddies to compare
■ their finger, hand, arm, knee-to-heel, or foot lengths;
■ five big buddies with linked arms to “a chain” of five little
buddies with linked arms (challenge: link in groups of both big
and little buddies to make two chains of about the same length);
■ the width or thickness of a big buddy’s book with that of a little
buddy’s book.
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Activity Bank
Sorting by Length
Comparing Lengths
Materials: materials of different length
(e.g., paper clips, straws, pieces of string)
Materials: boxes, objects of different length
(pencils, crayons, small toys)
■
Provide each small group with a set of
materials. Ask: “How can we sort these
objects into three groups? What sorting rule
can we use?”
■
Have children sort their objects into three
groups according to their sorting rule.
■
Ask children to determine each group’s
sorting rule (e.g., “These things are shorter
than my finger.”).
■
Have pairs collect objects of various length.
■
Create several stations where a referent has
been placed.
■
Direct each pair to visit a station, sorting the
collected objects into groups that are about
as long as, shorter than, and longer than the
referent.
■
Ask each pair to share how it decided where
the objects belonged.
■
The sorted groups can be displayed as a
concrete graph.
Visual; Kinesthetic
Kinesthetic; Social
Small Group
Partners
Length Hunt
Will It Fit?
Resources and Materials: LM 3; lengths
of string
Materials: various objects, shirt or
smock with a pocket
■
Provide each pair of children with a length
of string.
■
Have each pair find two things that are
shorter than the string and draw pictures of
the objects on LM 3. Children then find two
things that are about the same length and
longer than the string and draw pictures of
these objects on LM 3.
■
Invite each pair to share its findings and
explain its choices. Ask: “How did you
choose objects to measure?” (compared
objects to length of string)
■
Ask: “Which objects will be too long for the
pocket? Which objects will fit in the pocket?”
Those objects that are too long extend
beyond the edges of the pocket.
■
Display objects one at a time and have
children make predictions.
■
Have volunteers test each suggestion and
create two groups: one group of items fits in
the pocket and one group is too long.
■
Ask: “When is it important to know if
something is too long or if it will fit?”
Kinesthetic; Verbal
Visual; Kinesthetic
Partners
Whole Class
Unit 8: Linear Measurement and Area
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LESSON
2
CURRICULUM FOCUS
Estimate lengths using
non-standard units
SS1, SS2
MATH WORD WALL
estimate
MATERIALS
straws, crayons, Snap Cubes
PROGRAM RESOURCES
Student page 186: Measure
How Tall
Student page 187: Estimate,
Measure, and Record
LM 4: My Carrot
Measurements
LM 5: Estimating
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Estimating Lengths
BEFORE
Get Started
Tell the children that they are going to learn to make estimates to
help find the lengths or heights of objects. Ask: “What have you
estimated before?” (e.g., length of time, numbers)
Have a volunteer stand. Raise a crayon in full view of the children
and ask: “About how many crayons do you think will be needed to
measure the height from the floor to Sam’s knee?”
Remind children to keep their estimates to themselves until asked.
Ask children to indicate their estimates and record them on a chart.
Have the class count the number of times the crayon can be placed
from the floor to the knee.
Think aloud as you measure using the crayon. “I put the crayon tip
on the floor next to the shoe (baseline). I use my finger to mark the
top of the crayon. Then I put the crayon at my finger mark. I do this
again and again, counting each time, then stop when I get close to
the knee.” Record the measure. Repeat, using another volunteer and
find the length from the wrist to the elbow.
DURING
Explore
Have children work in groups of four estimating their heights using
straws.
Problem Prompt
About how many straws do you think it will take to measure
your classmates’ heights?
On Student page 186, have children record the heights of four
classmates.
Show and Share
After completing Student page 186, children compare their estimates
with the results, noting any similarities or differences. Have children
explain how they made their estimates (e.g., tried to picture stacked
straws).
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AFTER
Quit
Connect and Reflect
Gather the children together to talk about estimating and measuring.
Ask:
■ How did you solve the problem? (e.g., placed straws on top of each
other, lay down to make measuring easier)
■ What helped you make your estimate? (e.g., tried to picture
number of straws, compared this height to previous
measurements, lay on the floor)
■ How did you make sure your measurements were accurate? (e.g.,
used a baseline, stacked straws, repeated measuring more than once)
Practice
Reinforcement
Provide children with Snap Cubes to complete the estimation and
measurement activity on Student page 187. Point out that they are to
measure the real objects shown, not the pictures. After children have
recorded their findings, ask them to share their results.
Extra Support: Concepts
Have children who require extra practice estimating complete
LM 4 and LM 5.
Extension
Have children work in pairs creating clues for a measurement hunt
game. Children provide a clue, such as, “Find something that is
about two crayons long.” Others look for objects, and the pair that is
closest provides the next clue.
Assessment for Learning
What to Look For
What to Do
Evidence that children
For children who are struggling, provide the
opportunity to use the sense of touch to generate
mental images and create spatial referents.
■
make reasonable estimates
■
can explain how they arrived at their estimates
■
place their non-standard units “nose-to-nose”
To guide observations and facilitate reporting, use
Assessment Master 3.1: Ongoing Observations
Checklist.
■
Show the child a straw 5 cm long. Place it in the
child’s hand and ask the child to feel its shape
and length.
■
Fill a bag with another 5-cm straw and four other
straws of various lengths. Have the child reach into
the bag, use touch to find the matching straw, and
remove it from the bag. Compare both straws.
■
Continue until the child becomes confident making
estimates.
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FROM THE LIBRARY
Tom Birdseye, Look Out,
Jack! The Giant Is Back!
(Holiday House, 2001)
Quit
LITERACY LINKS
Resources: versions of Jack and the Beanstalk, The Biggest Pumpkin Ever
Steven Kellogg, Jack and the
Beanstalk (William Morrow &
Company, 1991)
Read one of the stories aloud to the children and have them listen
for phrases that indicate the growth of the beanstalk or pumpkin
(“it reached up past the clouds”). Have them list all these references
to height.
Frances Minters, Cinder-Elly
(Penguin, 1997)
Resources and Materials: versions of Cinderella, Puss ‘n’ Boots, The
Elves and the Shoemaker; collection of different-sized shoes, boots, sandals
Read one of the stories with the children. Ask: “How can you tell if a
shoe will fit without trying it on?” Elicit suggestions such as
comparing the shoe and foot along a common baseline.
NUMBERS EVERY DAY
Select an object such as a box. Place a large paper clip beside it
and ask children to estimate and measure its height in paper clips.
Ask a volunteer to count to measure its height. Compare estimates to
the measure. If desired, estimate and measure the width and length
of the box as well.
CROSS-CURRICULAR CONNECTION
Science
Materials: paper towels, clear plastic cups, mung beans, small Lego cubes
Place damp paper towels inside clear plastic cups and a mung bean
against the side of each cup. Have children keep the paper towels
damp. As beans sprout and grow, direct children to estimate and
measure the heights of their plants by making towers from small
Lego cubes. Children record their estimates and the actual growth
on individual T–charts. This activity can be conducted over
several weeks.
18
Week
Estimate
Measure
1
1 cube
0 cube
2
1 cube
2 cubes
3
3 cubes
4 cubes
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Quit
Activity Bank
Box of Feet!
Rolling Along
Materials: cut-outs of shoeprints, box
Materials: modelling clay, paper clips
Trace a child’s shoe, make copies, and cut out
the tracings. Place the cut-outs in a “box of feet.”
■
Have children work in pairs. One child
makes a roll of modelling clay while the other
estimates its length using paper clips.
■
Have both children check the roll’s length by
counting the number of paper clips used and
compare the result to the estimate. Have
children switch roles.
■
After repeating the activity several times, talk
about how their estimates are getting closer
to the actual measurement. Have children
suggest possible reasons (e.g., I can make a
picture in my mind of a paper clip).
■
■
■
Ask about how many shoeprints it will take to
measure the length of the carpet (counter or
width of a hall). Note: Ensure all distances
are less than 20 shoeprints.
Have each child make an estimate; arrange
for children to measure in small groups.
Deepen the activity by choosing a different
shoeprint, such as a teacher’s or an infant’s.
Ask which unit requires more to measure the
same distance, and why (you need more
smaller units).
Visual; Kinesthetic
Kinesthetic; Social
Partners
Small Group
I Spy!
About How Tall Are You?
Materials: string or yarn, scissors, box or cup
■
Children work in pairs, measuring their
heights with string: one child lies down on
the floor while the other cuts a matching
length of string.
■
Then divide the class into groups of three or
four. Have children in each group place their
strings into a box or cup.
■
Discuss: “Your task, as a group, is to match
each string to its owner.”
■
Encourage children to talk about their solutions
(e.g., match the longest string to the tallest
child/shortest string to the shortest child; line
up strings from shortest to longest and match
the strings to the line up of children).
Materials: straw, pencil, Snap Cubes, Lego
■
Play a variation of “I Spy” using length. Give
pairs of children a unit of length, or let them
choose their own. Provide time for them to
secretly choose, estimate, and measure an
object, recording the name of the object and
its measurement (box is about two erasers tall).
At first, suggest they choose objects whose
sizes can be measured in one to three units.
■
Children then take turns posing their “I Spy”
challenges. For example, “I spy something
that is two straws long.” Others try to identify
the object. When the object is correctly
identified, the pair who identified it poses the
next challenge.
■
Ask children who correctly identify an object
to explain how they did it.
Logical; Visual
Visual; Kinesthetic
Partners/Small Group
Partners
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LESSON
3
CURRICULUM FOCUS
Order objects according to
length
SS2
MATH WORD WALL
far, farther, farthest
shortest
longest
order
MATERIALS
straws, ramps, toy vehicles
(cars, trucks), books (to
support ramps), masking tape
PROGRAM RESOURCES
Big Math Book, page 42:
Rolling Along
Student page 188: Ordering
Lengths
LM 6: Measure the Distance
LM 7: Ordering Lengths
Quit
Ordering Lengths
BEFORE
Get Started
Tell children they are going to learn to place different lengths in order.
Show children Big Math Book, page 42. Ask:
■ What are the children doing?
■ So far, which car has travelled farther? How can you tell?
■ The children are about to send another car down the ramp. How
can they find out which car travels the farthest? (use a
measurement device)
DURING
Explore
Divide children into small groups of no more than four children. Provide
each group with a ramp, three toy vehicles, masking tape, and straws. Tell
children they have to use these materials to solve the following problem.
Problem Prompt
How can you find out which of these three toys
travels the farthest past the ramp?
Ensure the groups understand their task. Explain that they are to
measure the distances the toys travel from the end of the ramp to
where they stop. To facilitate measuring, suggest children use
masking tape to mark the stopping point of each car. Have children
measure the distances using straws and record the distances on LM 6.
Note: Remind children not to push their toys down the ramp, but
merely release them.
Show and Share
Have each group share their procedures
and results. Choose one group’s results
and record the distances on chart paper:
Car
Distance rolled
(number of straws)
Car 1
5
Car 2
4
Car 3
8
Ask:
■ Which car rolled the farthest? How do you know?
■ How can we put these distances in order, from longest to shortest?
Discuss children’s suggestions. Then have children work in groups
ordering and recording the distances from longest to shortest on LM 6.
AFTER
Connect and Reflect
Focus children’s attention on the different methods they used to order
the distances. Ask:
20
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■
Quit
How did your group order the distances? (e.g., order the number of
straws, order the numerals from greatest to least)
Have the children note that they all started the cars from the same
place at the top of the ramp (baseline). As children compare three or
more objects or distances, remind them to use words such as shortest
and longest. Add to the co-operative journal what the children know
about ordering lengths.
Practice
Reinforcement
Have children cut out the pictures from LM 7, arrange them, and
then glue them in order onto Student page 188.
Extra Support: ESL
Support children in learning words that describe size by providing
word cards that they can associate with their concrete activities and
oral discussions (e.g., long, longer, longest). Sentence frames can help
them express comparisons that they discover by measuring (e.g., The
pencil is ___________ than the crayon.). Children who are learning
English benefit from hearing and seeing key comparative words in a
variety of contexts. Listening to and acting out simple stories (e.g.,
Goldilocks and the Three Bears), viewing pictures where size is
exaggerated, and relating measurement to their own experiences and
possessions can help to reinforce the language they are learning.
Extension
Children can experiment with the effects of changing the height of a
ramp. Children predict what will happen, test using three toy vehicles,
and record how they changed the ramp and their results. Encourage
children to explain why changing the height of the ramp has an effect
on the distance.
Assessment for Learning
What to Look For
Evidence that children
■
use appropriate language (shortest, longest )
■
are able to compare the lengths and place them
in order
■
identify the longest and the shortest length
To guide observations and facilitate reporting, use
Assessment Master 3.1: Ongoing Observations
Checklist. To gather information about children
who are having difficulty, use Assessment Master 2:
Diagnostic Conference for Selected Children.
What to Do
■
Model and reinforce appropriate use of comparative
language (e.g., farther, farthest, shorter, shortest,
longer, and longest). Consider using word cards
to help children label their results.
■
Children who are having difficulty ordering more
than two objects may benefit from listening and
watching as you think aloud to share your
strategies (using the process of elimination or
comparing to extremes first).
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Quit
LITERACY LINKS
With the children’s assistance, choose three to five words of varying
lengths from your Math Word Wall. Have the children order the
word cards from longest to shortest and from shortest to longest.
NUMBERS EVERY DAY
Choose three children. Have them stand and order
themselves from shortest to tallest. Ask children to identify
the first, second, and last in line. Choose another three children, but
this time have them order themselves from tallest to shortest. Repeat
with four or five children.
CROSS-CURRICULAR CONNECTION
Physical Education
■
■
■
22
In the gym, have children line up with their toes against a line to
begin playing “Red Light/Green Light.” The goal is to cross the
room to the next line. The one who does it first becomes the next
“caller.”
The teacher calls out: “You may take 10 giant steps.” The children
wait to hear red light or green light and make their moves
accordingly. Use any form of steps to get the children across the
room (e.g., baby steps, hopping steps, sliding steps).
The child who moves against the light or takes more than the
required number of steps is sent back to the line to begin again.
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Activity Bank
Snakes Alive!
Which Shoe Is Shortest?
Materials: modelling clay, various objects to
measure
Materials: shoes
■
Working in pairs, each child uses modelling
clay to make three snakes of different lengths.
■
Have children compare and order their
partner’s snakes.
■
Ask children to explain to each other how
they decided what order to put the snakes in.
■
Have children form small groups; each child
places one shoe in the middle.
■
Together, children look at the shoes and
predict which one is shortest and which one
is longest. They record their predictions.
■
Children work together to order the shoes by
length and check their predictions.
■
Have each group share their strategies for
putting the shoes in order.
■
Encourage children to share their thoughts
when they made their predictions.
Visual; Kinesthetic
Visual; Social
Partners
Small Group
Paper Airplane Flights
Who Is the Shortest?
Materials: paper airplanes, balls of differentcoloured yarn, scissors
Materials: chart paper
■
Record the following problem on chart paper
and read it aloud. Have children work in pairs
or small groups to solve the problem:
■
Make a simple paper airplane for each group
of children.
■
Tell children they can use their airplane for
“test flights.”
Jason is taller than Katie.
Have children take turns releasing the plane
and measuring distances using differentcoloured lengths of yarn.
Who is the shortest? (Tamara)
■
■
■
After each child in a group has had a turn,
ask each group to order the lengths of yarn.
Ask: “Will we get the same results if we fly the
planes again? Why? Why not?”
Have children find out by making a second
test flight using the same planes.
Katie is taller than Tamara.
■
Ask each pair or group to share their strategies
and demonstrate how they solved the problem
(e.g., ask children to model, use objects, or
draw pictures).
■
Have children make up their own problems
about who is taller and shorter.
Kinesthetic; Visual; Social
Logical; Verbal
Small Group
Partners/Small Group
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LESSON
4
Quit
Choosing a Unit
Get Started
CURRICULUM FOCUS
BEFORE
Determine a non-standard unit
appropriate to measure
lengths of objects
SS1, SS2
Show children a straw and a paper clip. Ask:
■ Which object would be better to use to measure the length of your
nose? (paper clip because it is shorter)
MATH WORD WALL
measure
long, longer
length
short, shorter
compare
MATERIALS
paper clips, straws, erasers,
crayons, string or yarn
Display Big Math Book, page 43. Ask:
■ Should we use a straw or a paper clip to
measure the length of the goldfish? Why?
(paper clip; straw is longer than the fish)
TRY
THIS
See the
Literacy Links
on page 26.
You may want
to begin the lesson by
sharing and discussing
The Measurement
Mysteries with children.
Direct attention to the hamster and ask:
“What do you think we can use to measure
the length of the hamster?”
Record the suggested non-standard units in a
chart. For each unit, ask:
■ About how many units long do you think the hamster is?
■ Is it longer than five?
PROGRAM RESOURCES
Big Math Book, page 43:
Make a Good Choice
Student page 189: Use
Different Units
Student page 190: Choose
a Unit
LM 8: Estimate with 5
LM 9: Estimate with 10
Objects
Longer than 5?
eraser
yes
no
paper clip
yes
no
DURING
Estimate
Measure
Explore
Have children work in pairs to solve the problem.
Problem Prompt
Look at the lizard. What do you think is the best object to use to
measure its length? How many units long is it?
Discuss the different objects children can use as non-standard units.
Show and Share
Bring children together and have them share their results. Ask: “What
did you use to measure the lizard? Why did you choose it?”
Have children look at the chipmunk. Ask: “What object would you use
to measure its length?” Talk about whether the length includes the tail,
and the need for material that will bend, such as string or yarn. Have a
volunteer trace the chipmunk’s length with a piece of string, then cut
to match. Measure the string using a unit such as straws.
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AFTER
Quit
Connect and Reflect
Ask:
■ What do you notice about the object and the unit you chose to
measure? (e.g., unit is shorter than the object)
■ If we choose an even smaller unit, what happens to our
measurement? (e.g., it takes more small units to fill the same distance)
Practice
Reinforcement
Direct children to select a classroom object to measure using different
units. Have them record the object, the units, their estimates, and
measurements on Student page 189. Have children also complete LMs
8 and 9. Read Student page 190 together before children complete it
independently.
Extra Support: Concepts
Children who have difficulty choosing an appropriate unit may not
understand that measuring involves repeatedly using one unit to
“fill” the length of another. They may benefit from exploring ways of
measuring the same length with different units. For example, provide
a large book or a mat, and invite them to measure its length with at
least three different units. Ask: “How many cubes did it take to match
this length? How many pencils? What would happen if we used both
cubes and pencils at the same time?” Support children by thinking
aloud (e.g., “No, that won’t work. We have to use the same unit over
and over again to find out how many it takes to match the length.”).
Extension
Toss a skipping rope loosely onto the floor. Challenge children to
estimate, then measure, its length using a unit of their choice.
Assessment for Learning
What to Look For
What to Do
Evidence that children
Support children by
■
choose an appropriate measuring unit (smaller
than the object; repeatable)
■
place units nose-to-nose, using fingers as
placeholders
To guide observations and facilitate reporting,
use Assessment Master 3.1: Ongoing
Observations Checklist.
■
thinking aloud as you demonstrate choosing and
applying a unit (e.g., “Let’s see. If I am going to
measure the length of this truck, first I have to
choose something smaller – this book wouldn’t
work, because it is longer than the truck. . . .”)
■
making a masking tape line beside the object
being measured, or providing practice with units
that link together (e.g., paper clips or Snap Cubes.)
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Quit
LITERACY LINKS
Resources and Materials: Adria Klein, The Measurement Mysteries,
Addison Wesley Mathematics Little Books, Early level (Addison Wesley, 2002);
paper clips
FROM THE LIBRARY
Jonathan Allen, Chicken
Licken (Voyager, 1999)
Jan Brett, The Gingerbread
Baby (G.P. Putnam’s Sons,
1999)
Gail Hartman, As the Crow
Flies (Bradbury Press, 1993)
H. Werner Zimmermann,
Henny Penny (Scholastic,
1996)
Discuss how the front cover and title page photographs are related.
Read pages 2 and 3 together to find out what “mystery” must be
solved. Guide children through pages 4 to 15, talking about the
illustrations and using them to answer the text questions. Elicit that
the graph on page 16 summarizes and compares what the children
found out. In response to the final question, children may consider
comparing the length of lettuce and carrots on page 13 or the lengths
of the animals’ ears.
Other possible discussion questions:
■ How is Russell trying to measure the goat on the front cover? Is this
way better than using paper clips? Why or why not?
■ Why is it important to measure everything using the same object?
■ Why is each animal “about” so many paper clips long? Why is it
difficult to measure animals exactly?
NUMBERS EVERY DAY
When children are lining up to visit the library or when they
are going out for recess, ask them to line up in order from shortest
to tallest or tallest to shortest.
CROSS-CURRICULAR CONNECTIONS
Social Studies
Materials: notepads or clipboards
■
■
Take children to the school playground or a nearby park. Ask them
to choose a few pieces of equipment and, walking heel to toe, pace
off how far apart these pieces are from one another.
Ask: “Why are some pieces of equipment, such as swings, farther
away from the others?” (safety reasons)
Science
Materials: pencils, black paper, white paper, scissors, an assortment of
large non-standard units (e.g., string, straws, box lids, envelopes)
Have children work in pairs to measure the size of each other’s
shadows at different times of the day, using a unit of their choice. You
may want to have children paste their shadows around a circle to
show the connection to the sun and eventual connection to the clock.
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Quit
Activity Bank
Draw This!
How Many Will Fit?
Materials: a straw, paper, pencils, various
classroom objects (paintbrush, chalk)
Materials: several samples of
household objects (books, packages, cereal
boxes), tape
■
■
■
■
Hold up a straw. Ask children to look at it
closely and then close their eyes and try to
picture its length.
Provide paper and have children draw a line
that they think is about the same length as the
straw.
Have them check their estimates by
comparing their lines to the straw. Ask: “How
did making a picture of the straw in your
mind help?”
■
Place a length of tape on the floor to create a
horizontal line (shelf).
■
Provide each group with several boxes or
packages.
■
Have children estimate the number of boxes
that will fit along the “shelf.”
■
Have groups share their findings and explain
how they solved the problem.
■
Ask children who might do this kind of activity
(e.g., storekeeper stocking shelves, family
putting groceries in cupboard at home).
Repeat with other objects.
Visual; Intrapersonal
Visual; Social
Individual
Small Group
What’s My Line?
Choosing a Unit
Materials: classroom objects, paper clips,
paper, pencils
Materials: paper clips, straws, strips of
cardboard
■
Select 10 classroom objects of different
lengths. Display them on a tray or table.
Each object must be no longer than a
letter–sized piece of paper.
■
Have each child choose and measure an
object without showing it to others.
■
Children then draw a line on paper that is the
same length as the chosen object. On the back,
they record the name or a picture of the object.
■
Have children take turns showing their lines
while others guess the secret object. The
answers can be checked by looking at the
reverse side of the paper.
■
Give each group three non-standard units of
varying lengths: a paper clip, a straw, a strip
of cardboard (equivalent to about two straws).
■
Children find, measure, and record three
classroom objects (or parts of the body) using
three different units.
■
Bring the class together to compare the
results and what they chose to measure with
each unit. Encourage children to explain
their choices.
I found that ________ is _____ paper clips long.
Visual; Social
Visual; Logical
Whole Class
Partners/Small Group
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LESSON
5
CURRICULUM FOCUS
“Use objects” to solve a
problem
Quit
Strategies Tool Kit
BEFORE
Understand the Problem
Tell the children they are going to work together to solve a problem
about length. Show them Big Math Book, page 44.
MATERIALS
a variety of materials for
measuring (pencils,
toothpicks, cubes, pieces of
string or yarn)
PROGRAM RESOURCES
Big Math Book, page 44:
Who Went the Farthest?
Student page 191: Who
Went the Farthest?
Student page 192: Which
Way Is Shorter?
LM 10: Estimate and Measure
STRATEGIES TOOL KIT
Look for a pattern
Make a model
Act it out
Use objects
Guess and check
Make a graph
Choose a strategy
Problem Prompt
Who went the farthest?
Pose questions to determine whether the children understand
the problem. Ask:
■ What is the problem you have to solve? (find the animal that went
the farthest)
■ What do we already know? (where the animal paths start and end)
■ What will you need to get started? (items that can be used to
measure the paths)
DURING
Make a Plan
Help children make a plan to solve the problem; possibilities include
measuring the winding path with a unit that can curve and
comparing the lengths. Discuss the children’s plans with them.
Tell the children that they will work together (in pairs or small
groups) to solve the problem. Have each group discuss and then
agree on a plan to solve the problem. Children may use whatever
materials they need to carry out their plans.
Carry Out the Plan
Make available a variety of materials for measuring such as pencils,
toothpicks, cubes, and pieces of string or yarn. Children use a suitable
non-standard unit. Allow time for each group to find a solution to the
problem: Who is farthest from home?
AFTER
Look Back
Invite a volunteer from each group to share its solution. As a class,
discuss the various solutions and look back at the problem to see if
the solutions are reasonable.
Have each child record the solution to the problem on Student page 191.
Emphasize that children solved the problem by using objects to
measure the length of the path at various points.
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Quit
Practice
Reinforcement
Read the directions on Student page 192 with the children and have
them complete the page.
Extra Support: Problem Solving
Provide children who had difficulty estimating lengths with LM 10
and ask them to explain how they approach each problem. Scaffold
by asking questions (e.g., “Does the second one look shorter, about
the same, or longer? If you coloured the part of the second one that
matches the first one, how much would be left over?”). Model by
thinking-aloud so that children can see how a skilled estimator
thinks. Have children make and check one estimate at a time so that
they can use the knowledge they are developing to approach the
next question.
Extension
Have children work in pairs to create their own “Which one is
longest/shortest?” problems using curved lines. Children can
exchange paths and solve the problems.
Assessment for Learning
What to Look For
Evidence that children
■
are able to rephrase the problem in their own
words
■
ask questions and make predictions
■
explain their solutions logically in pictures or
words
■
justify their strategies and their solutions
To guide observations and facilitate reporting, use
GAM 2: Inquiry Process Rubric or GAM 3: Inquiry
Process Checklist.
What to Do
■
Observe children’s ability to make and carry out a
plan to solve the problem. As children make their
plans, have them justify their reasoning.
■
Listen for problem-solving language (Here’s what
we can do ... I know another way ... I think that
would work. Let’s try). Provide feedback to let
children know that using appropriate language
shows that they are good problem solvers and that
positive and constructive language is valued.
■
For children who have difficulty with problemsolving activities, provide extensive modelling,
exploration, and reinforcement:
■
model using speculative language as you work (I
wonder ... What if ...? It might ... I think I’ll try ...)
■
create collaborative charts that list problemsolving strategies that children discovered and
used; revisit and discuss the lists regularly
■
prompt children to explain how and why they
approached a problem the way they did
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LESSON
6
CURRICULUM FOCUS
Estimate and count the
number of objects needed to
cover a surface without gaps
or overlap
SS3, SS4
MATH WORD WALL
cover
area
surface
MATERIALS
newspapers, cards (index
cards, cards made from
manila tags), Pattern Blocks
PROGRAM RESOURCES
Student page 193: About
How Many?
Student page 194: Cover
This Shape
Student page 195: Cover
the Page
Student page 196: Choose
a Unit
Student page 197: Roll
and Cover
LM 11: Pattern Block Shapes
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Estimating and
Comparing Areas
BEFORE
Get Started
Review that children have been learning about length, width, and
height. Prompt them to think about how they might measure a
surface, such as a tabletop or a rug.
Point to an obvious surface in the classroom, such as an area rug.
Hold up a sheet of newspaper and ask: “About how many pieces of
newspaper will it take to cover the rug?” Record estimates on the board.
With the children, cover the surface. Think aloud as you work,
placing the newspaper close together without gaps or overlap.
Explain that covering a surface in this way helps to find its area.
Have children count aloud the number of pieces of newspaper used.
Record the count on the board and compare it to the children’s
estimates.
Note that you are using a unit that is always the same size.
DURING
Explore
Provide pairs of children with about 20 uniform cards.
Problem Prompt
About how many cards will it take to cover the surface of one
of your chair seats? Note: Chairs must have a flat seat.
Ask each pair to record their estimates on Student page 193. Have
children check their estimates by covering the seats of their chairs and
then count and record the number of cards they used.
Next, give each pair a large piece of recycled paper. Ask:
Do you think it will take more or fewer cards to cover this paper
than it did to cover your chair?
■ About how many cards do you think it will take?
■ How could we find out? (e.g., cover the paper with the same cards
we used for our chairs, see if the paper fits over the seat of the chair)
■ Have children choose other objects and estimate the number of cards
they think it will take to cover each object. Have them record the
results on Student page 193.
■
Show and Share
Bring children together to share their findings. Ask:
■ Which surface took more cards? How do you know?
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AFTER
Quit
Connect and Reflect
Discuss the methods children used to cover the surfaces. Ask:
■ How can we measure a surface? (cover it with objects the same size
and count them)
■ How can we compare two surfaces? (cover them with the samesized objects and compare the number used)
Explain the importance of placing the units closely together. Ask:
■ When we covered our chair seats, did we all get the same results?
■ Why were some answers different? (e.g., placed the cards in a
different orientation, we left spaces between them)
■ How did the results from covering a chair seat help when
estimating the number of cards that could cover the paper?
Practice
Reinforcement
Provide Pattern Blocks (or copies of cut-out shapes from LM 11) and
read directions before having children complete Student page 194.
Distribute materials and read directions before having children
complete Student page 195 and Student page 196.
Extra Support: Concepts
Simple covering games can help children understand the concept of
covering a surface. Provide two children with a number cube, a regular
surface, and several small cards or blocks of uniform size (e.g., Pattern
Blocks or Lego). Children roll the cube in turn and place cards or blocks on
the surface equal to the number rolled. If they are playing co-operatively,
they simply keep track of how many rolls it took to “fill” the surface, then
try to “beat the record.” Student page 197 provides a playing surface.
Extension
Have children create a Pattern Block design, then estimate and measure
to find how many triangle blocks are needed to cover the design.
Assessment for Learning
What to Look For
What to Do
Evidence that children
When there is unfilled surface area, scaffold by
posing questions:
■
fit objects so that there is no unfilled space
■
use language such as full, left over, empty,
to/over the edge, spaces between
■
make reasonable estimates when filling a surface
To guide observations and facilitate reporting, use
Assessment Master 3.2: Ongoing Observations
Checklist.
■
Tell me what you see when you look at this area.
What do you notice about the cards? about the
surface?
■
Why do you think this happened? (e.g., cards
aren’t edge to edge)
■
What could we do to fill this space? (place the
cards tightly together)
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FROM THE LIBRARY
Joanne C. and Paul
Galdone, The Three Little Pigs
(Houghton Mifflin, 1979)
Patricia Seibert, The Three
Little Pigs (McGraw-Hill,
2001)
Quit
LITERACY LINKS
Resources and Materials: a version of The Three Little Pigs; cardboard
milk cartons, 2 cm x 1 cm cardboard “bricks,” drawing paper, crayons,
Tangram pieces, large square pieces of heavy cardboard “floor”
Read the story to the class. Show a milk carton, pretending that it is the
little pig’s brick house. Ask children to estimate the number of bricks
they think would cover one side of the house; record their estimates.
Have each child decorate the floor of the pig’s house. Using the large
square pieces of heavy cardboard, provide a choice of pattern blocks.
Let each child create a floor pattern entirely out of one shape with all
edges touching.
NUMBERS EVERY DAY
Have two children start at the same place and count the number
of steps it takes them to reach the exit door. One child walks, and the
other child takes giant steps. Discuss the differences in number.
CROSS-CURRICULAR CONNECTION
Art
Materials: magazines, index cards, scissors, heavy paper
■
■
32
Have children remove pages from magazines that show peoples’
faces. Using an index card as a tracer, have them cut out eyes, noses,
mouths, and hair from the pictures.
Have them sort the pieces according to facial parts. The children will
have fun making funny faces by using these pieces to tile faces on
paper.
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Activity Bank
Estimate and Cover
Same Surface, Different Unit
Materials: building blocks
Materials: sheet of construction paper, variety
of units (e.g., building blocks, counters, dry
macaroni)
■
■
■
Have children work in small groups using
blocks. Ask: “About how many blocks do
you think will cover the surface of your desk
or table?”
Ask children to make their estimates first and
then use blocks to check. Compare the
estimates with the results.
Encourage children to suggest other surfaces
they could cover with blocks. Repeat the
activity.
■
Have one child measure the area of the
paper with the building blocks. Record
the result.
■
Have a different child measure the paper
using the counters, then other objects.
■
Compare the results: Which measures were
more accurate? Why? (e.g., area measures
are most accurate when the units of measure
fit closely together on the surface; counters
and macaroni won’t give a close estimate
because of the gaps between items)
Logical; Kinesthetic
Visual; Kinesthetic
Small Group
Whole Class
Tangram
Conserving Area
Resources and Materials: LM 12; Tangram
pieces
Materials: rectangular sheets of paper
■
Provide each pair of children with a set of
Tangram pieces (or cut-out shapes from
LM 12). Ask: “About how many small
triangles do you think will fit in the
large triangle?”
■
Have children make their estimates and then
check using the Tangram pieces.
■
Encourage children to create their own
Tangram designs by putting pieces together
and tracing their outlines.
■
Have other children discover which Tangram
pieces were used by finding the figures that
will cover the outline.
■
Provide each child with a rectangular piece
of paper. Demonstrate how to fold the paper
on the diagonal; cut along the fold.
■
Have children discuss the resulting shapes
(two triangles). Ask: “How could you use
these triangles to make a rectangle?”
■
Hold up the two pieces to show the shape of
the original rectangle. Ask: “How do you
know the two triangles cover the same
amount of space as the rectangle?” (trace the
original piece of paper and place the two
triangles on top)
■
Encourage children to see that the rectangle
and the two triangles cover the same area.
Logical; Kinesthetic
Logical; Visual
Partners
Whole Class
Unit 8: Linear Measurement and Area
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LESSON
7
FOCUS
Demonstrate what has been
learned
MATERIALS
paper clips, toothpicks,
crayons, straws
PROGRAM RESOURCES
Student page 198: Ordering
My Objects
Student page 199: Choose,
Estimate, and Measure
Student page 200: My
Journal
Quit
Show What You Know
BEFORE
Get Started
Display any class charts or the co-operative journal, and have
children recall their favourite activities. You may wish to make a list
of measurement activities.
Tell the children they will work on
their own to show what they have
learned. Children will
■ put objects in order of length from
shortest to longest
■ measure three objects
They will need to choose a unit of
measure, estimate, and measure
each object.
DURING
TRY
THIS
Ask children to
bring in four
objects from
home that are
different lengths. Remind
them the objects must be
able to fit onto a student
page. Hold up a student
page to show the size.
Explore
Part 1
Provide each child with a paper clip, toothpick, a crayon, and a straw,
or provide a larger collection of objects to allow them to choose their
four objects. Ask children to put the four objects in order from
shortest to longest. Have them turn to Student page 198 and record
their results by tracing the objects.
Part 2
Have children turn to Student page 199. Tell children they should
choose four objects and draw a picture of each one.
Emphasize that for each object, the children should circle the nonstandard unit they think will be best to measure the lengths. Ask
them to estimate the number of units they need to measure the
lengths. Have them record their estimates on the chart, measure the
objects, and record their answers.
Show and Share
Have children work in pairs to share their results and talk about
what they found out. Ask:
■ Were your results the same as or different from your partner’s?
■ What did you remember about measuring that helped you?
34
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AFTER
Quit
Connect and Reflect
Invite children to talk about what they did and what they found out,
talking about one object at a time. Where two children used different
units for the same object, ask: “How did you choose? What answer
did you get? Are the answers the same? Why or why not?” Also ask:
■ What did you do to help estimate how many you needed for each
object? (e.g., I made a picture in my mind.)
■ Which of your estimates was closest? What helped you make a
close estimate? (e.g., It looked about the same length as ________.)
■ What is one important thing your work shows about your learning?
(e.g., I know how to make a baseline. I can make good estimates.)
Review with the children what they learned in this unit. Have them
record their responses in pictures, numbers, or words or work with a
scribe to complete Student page 200.
Assessment Check
✓
Look for evidence that children
❏
❏
❏
❏
❏
❏
Choose an appropriate unit to measure each object.
Show understanding by explaining their choices.
Make reasonable estimates for the objects.
Order lengths accurately.
Measure lengths accurately using a non-standard unit.
Use appropriate language related to comparing and measuring
lengths.
Refer to Assessment Master 4: Performance Task Rubric and Assessment
Master 6: Unit Summary.
Unit 8: Linear Measurement and Area
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Evaluating Student Learning:
Preparing to Report
This unit provides an opportunity to report on a child’s progress related to
the Shape and Space (Measurement) strand. Assessment Master 6:
Unit Summary provides a comprehensive format for recording and
summarizing evidence teachers have 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: SHAPE AND SPACE
(MEASUREMENT)
Ongoing
observations
Strategies Tool Kit
(Lesson 5)
Notes
with support, seems to
understand basic concepts
and knows what to do; has
problems with fine motor
skills that interfere with
nose-to-nose measuring
worked with
group
Adequate
Not assessed at
individual level
Portfolio or work
samples; conferences
needs support but shows
Adequate
evidence of basic concepts;
uses some basic terms. Work
samples hard to interpret.
Performance task
(Lesson 7)
needed some prompting;
Adequate
made reasonable estimates.
Fine motor issues caused
accuracy problems
Achievement Level
for reporting
36
Most Consistent Level
of Achievement
Unit 8: Linear Measurement and Area
Meets expectations
(minimal level)
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Recording
How to Report
Ongoing
observations for
each cluster
Teachers who have used AM 3.1 and AM 3.2:
Ongoing Observations Checklist can determine the most
consistent level achieved and enter it in the chart.
Observations are particularly important in this unit,
where much of student learning is demonstrated when
they are making measurements. Teachers can choose
whether to summarize information by achievement
category, or simply enter an overall level. Observations
from later in the unit should be weighted more heavily.
Performance on
problem-solving
tasks
Teachers who used GAM 2: Inquiry Process Rubric or
GAM 3: Inquiry Process Checklist with Strategies Tool
Kit (Lesson 5) can transfer the results to the summary
form. Because this rating comes from a single activity, it
should not play a major role in determining overall
achievement. In some cases, particularly where children
work together on the problem, teachers may choose not
to record an individual level.
Portfolio or
work samples;
conferences
Use AM 5: Linear Measurement and Area Rubric to
make decisions about achievement. Work that was
completed near the end of the unit should be weighted
more heavily than that done earlier. Because
measurement involves hands-on activities, children’s
written work, by itself, may not offer much information
about their progress. Observations, conferences or brief
interviews where they demonstrate, explain, or show
their thinking are often necessary in order to understand
their work samples.
Unit performance
task
Because this occurs at the end of the unit (Lesson 7) it
should offer a useful snapshot of children’s achievement.
It draws primarily on expectations associated with linear
measurement (cluster 1). 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 am good
measuring.” “I like using Snap Cubes because you can
put them together without marking with your finger.”
“Marking with your finger is hard.” “My favourite is
measuring things that are very, very long.”
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 Checklist.
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.
Unit 8: Linear Measurement and Area
37
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Unit 8: Linear Measurement and Area
Name:
Assessment Master 1
Date:
Diagnostic Checklist
During Launch activities, use this form to note observations about children who appear to have difficulty.
Name
Connects to
measuring
activities at
home and
school
Uses simple
measurement
language
Recognizes that
measuring
involves
comparing
Describes
attributes such
as length, width,
height
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Unit 8: Linear Measurement and Area
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 3). 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
Reasoning and applying concepts
Provide two similar objects and ask:
• How are these the same?
• How are they different?
• Which of these do you think is longer?
• How could we find out?
Notice the child’s confidence and ability to
• identify and compare attributes of two objects
• estimate which is longer
• explain a simple measurement process
Problem-solving strategies
Introduce a third object and ask:
• How could we find out which of these is longest?
• Is there another way we could find out?
Notice the child’s confidence and ability to
• adjust to the added complexity
• generate a possible solution
• consider more than one approach
Accuracy of procedures
Offer the following prompt:
• Show me how you could find out which one is longer.
Notice the child’s confidence and ability to
• use a baseline
• identify differences in length
Communication
Offer the following prompts:
• Show me your results.
• Explain to me how you decided which one was longest.
Notice the child’s confidence and ability to
• display results
• use appropriate language to explain strategies and results (compare,
measure, longer, same, different, taller)
Note: Ask ESL children to demonstrate rather than explain.
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Unit 8: Linear Measurement and Area
Date:
Assessment Master 3.1
Ongoing Observations Checklist
Cluster 1: Lesson 1
Name
compares compares
objects
lengths
with
referent
Cluster 1: Lesson 2
makes
uses
reasonable
a
baseline estimates
places
explains
estimates units
nose-tonose
Cluster 1: Lesson 3
compares, finds
longest,
orders
shortest
lengths
length
uses
comparative
language
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Unit 8: Linear Measurement and Area
Date:
Assessment Master 3.2
Ongoing Observations Checklist
Cluster 1: Lesson 4
Name
places units
chooses an
nose-to-nose
appropriate
measuring unit
Cluster 2: Lesson 6
makes
reasonable
estimates
uses
fits objects
with no unfilled appropriate
language (e.g.,
area
full, space)
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Unit 8: Linear Measurement and Area
Name:
Assessment Master 4
Knowledge/Skills
Reasoning and
applying concepts
• shows
understanding by
choosing and
measuring with
appropriate units
and explaining his
or her choices
Accuracy of
procedures
• orders objects
accurately
• measures
accurately (e.g.,
uses baseline;
measures nose-tonose; counts units)
• records results
accurately
Problem-solving
strategies
• uses one or more
appropriate
estimating
strategies
Communication
• explains his or her
work, using
appropriate
mathematical
language (e.g.,
measure, long,
longer)
Date:
Performance Task Rubric
Not yet adequate
(needs assistance)
Adequate
(limited assistance)
Proficient
Excellent
with 1:1 help, may
be able to choose
and use an
appropriate unit for
some objects
with support,
chooses and uses
appropriate units
for most objects
chooses and uses
appropriate units
for each object
chooses and uses
appropriate and
efficient units for
each object
gives explanations
that show very
limited
understanding of
linear
measurement
gives explanations
that show partial
understanding of
linear
measurement
gives explanations
that show
understanding of
linear
measurement
gives explanations
that show in-depth
understanding of
linear
measurement
makes several
major errors in
- ordering objects
- measuring
objects
- recording results
makes some minor
errors in
- ordering objects
- measuring
objects
- recording results
makes few
errors in
- ordering objects
- measuring
objects
- recording results
makes very few or
no errors in
- ordering objects
- measuring
objects
- recording results
needs one-to-one
guidance to use a
strategy for
estimating length
with limited
prompting, uses a
reasonable
strategy for
estimating length
uses a reasonable
strategy for
estimating length
uses an effective
strategy for
estimating length
unable to describe
procedures and
results
with prompting,
uses some
appropriate
language to
describe
procedures and
results
clearly describes
procedures and
results, using
some appropriate
language
clearly and
confidently
describes
procedures and
results, using
appropriate
language
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Unit 8: Linear Measurement and Area
Name:
Assessment Master 5
Date:
Linear Measurement and Area
Rubric
This chart can be used to make decisions about children’s achievement of unit outcomes.
Knowledge/Skills
Not yet adequate
(needs assistance)
Adequate
(limited assistance)
Proficient
Excellent
shows very limited
understanding that
- measuring involves
comparing
- measuring involves
repeating the same
unit
- dimensions of
objects can be
compared,
measured, and
recorded
shows partial
understanding that
- measuring involves
comparing
- measuring involves
repeating the same
unit
- dimensions of
objects can be
compared,
measured, and
recorded
shows understanding
that
- measuring involves
comparing
- measuring involves
repeating the same
unit
- dimensions of
objects can be
compared,
measured, and
recorded
shows in-depth
understanding, in a
variety of contexts, that
- measuring involves
comparing
- measuring involves
repeating the same
unit
- dimensions of objects
can be compared,
measured, and
recorded
often makes major
errors/omissions in
- measuring linear
dimensions (nonstandard units)
- recording measures
- ordering and
comparing
- covering a surface
- counting shapes that
cover a surface
makes frequent minor
errors/omissions in
- measuring linear
dimensions (nonstandard units)
- recording measures
- ordering and
comparing
- covering a surface
- counting shapes that
cover a surface
makes few
errors/omissions in
- measuring linear
dimensions (nonstandard units)
- recording measures
- ordering and
comparing
- covering a surface
- counting shapes that
cover a surface
rarely make
errors/omissions in
- measuring linear
dimensions (nonstandard units)
- recording measures
- ordering and
comparing
- covering a surface
- counting shapes that
cover a surface
needs assistance to
use appropriate
strategies to
- make estimates
- choose units
- solve measurement
problems
with limited assistance,
uses some appropriate
strategies to
- make estimates
- choose units
- solve measurement
problems
uses appropriate
strategies to
- make estimates
- choose units
- solve measurement
problems
uses appropriate, often
innovative, strategies to
- make estimates
- choose units
- solve measurement
problems
unable to describe
measuring activities
and results
with prompting,
describes measuring
activities and results,
using some appropriate
language; tends to be
vague
clearly describes
measuring activities
and results, using some
appropriate language
clearly and confidently
describes measuring
activities and results,
using appropriate
language
Reasoning and
applying concepts
• shows understanding by
explaining and
demonstrating basic
measurement concepts
(non-standard units)
Accuracy of
procedures
• accurately measures,
records, compares, and
orders objects by length,
height, distance around
(non-standard units)
• covers a surface or area
with regular and
irregular figures and
counts the result
Problem-solving
strategies
• uses appropriate
strategies to
- make reasonable
estimates of length,
height, and distance
around
- choose appropriate
non-standard units to
measure length
- solve problems
related to their own
environment
Communication
• explains or
demonstrates measuring
activities clearly, using
appropriate language
(e.g., long, high, around,
cover)
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Unit 8: Linear Measurement and Area
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: SHAPE AND SPACE
(MEASUREMENT)
Notes
Most Consistent Level
of Achievement*
Ongoing observations
Strategies Tool Kit
(Lesson 5)
Portfolio or work samples;
conferences Performance task
(Lesson 7)
Achievement level for reporting
*Use locally or provincially approved levels, symbols, or numeric ratings.
Self-assessment:
Strengths:
Needs:
Next steps:
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 1
Unit 1:
Linear Measurement and Area
Sorting
and Patterning
Unit 2: Number
Relationships
We are learning to
measure length and
height by counting
units.
Unit 3: Time, Temperature,
and Money
Unit 4: Addition and
Subtraction to 12
Unit 5: Data Management
and Probability
Unit 6: 3-D and 2-D
Geometry
Unit 7: Number Patterns
Unit 8: Linear Measurement
and Area
We can estimate
and compare the
lengths of different
objects.
Unit 9: 2-D Geometry and
Applications
Unit 10: Place Value and
Number Applications
Unit 11: Mass and Capacity
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 2
Dear Family
Your child is learning about how to measure length and area.
You can help your child practise at home using these activities.
Choose a unit, like a spoon,
and find objects that are
shorter, longer, and about
the same length. Choose a
different unit and measure
the same items. Ask: “Why
did we get different
answers?”
,
Using straws
ing,
pencils, or str
r
work with you
ate
child to estim
each
the height of
er.
family memb
ild
Have your ch
heck
measure to c
.
the estimates
46
Cut a sho
rt length o
f
string. Wit
h your
child, find
three
things tha
t are
curvy, and
use the
string to m
easure
which is t
he longes
t
and which
is the
shortest.
With your child, find
examples in your home of
surfaces that are covered
by tiles, such as a
bathroom wall or a kitchen
floor. Ask your child to
estimate and count the
number of tiles.
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 3
Compare Lengths
My object ___________________________________________
Draw 2 objects that are shorter.
Draw 2 objects that are about the same length.
Draw 2 objects that are longer.
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 4
My Carrot Measurements
Use a carrot to measure objects in the class.
Object
Estimate
Measure
Chair
about
Newspaper
about
Friend
about
✃
48
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 5
Estimating
Use Snap Cubes to estimate and measure.
Object
Estimate
My hand
about
My foot
about
My arm
about
My smile
about
Measure
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 6
Measure the Distance
How far did each car travel?
Car 1
________ straws
Car 2
________ straws
Car 3
________ straws
Which car travelled the longest distance? Car ________
Which car travelled the shortest distance? Car ________
Record the distances in order from longest to shortest.
Car ________
50
Car ________
Car ________
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 7
Ordering Lengths
✃
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 8
Estimate with 5
I used ___________________________________ to measure.
Choose 3 objects.
Object
52
Longer than 5?
Estimate
yes
no
about
yes
no
about
yes
no
about
Measure
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 9
Estimate with 10
I used ___________________________________ to measure.
Choose 3 objects.
Object
Longer than 10?
Estimate
yes
no
about
yes
no
about
yes
no
about
Measure
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 10
Estimate and Measure
Circle your estimates.
1. This string is 4
long.
About how long is this piece of string?
2
3
2. This string is 2
5
7
long.
About how long is this piece of string?
2
3
3. This string is 5
4
5
long.
About how long is this piece of string?
2
4
5
Check your estimates. Use
.
54
3
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 11
Pattern Block Shapes
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Unit 8: Linear Measurement and Area
Name: __________________________ Date: _________________________
Line Master 12
56
Tangram
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Cover Gr1_TG_U8_west
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Page OBCII
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Author Team
Michelle Jackson
Sharon Jeroski
Carole Saundry
Cathy Anderson
Maureen Dockendorf
Brenda Lightburn
Maggie Martin Connell
Michelle Skene
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Copyright © 2004 Pearson Education Canada Inc.,
Toronto, Ontario
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.
Heather Spencer
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.
Donna Beaumont
Complete Teacher Guide ISBN 0-321-12076-0
Lynn Bryan
Jennifer Travis
Printed and bound in Canada
1 2 3 4 5 WC 08 07 06 05 04
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
Project Adviser
Carole Saundry
Ontario Early Math Strategy Adviser
Ruth Dawson