SHAPE AND MEASUREMENT
A Mathematics Unit
Tanya Winship
UBC Teacher Candidate
Tanya Winship | 1
Table of
Contents
Unit Rationale
Assessment
Curricular Connections
Unit Timeline
Unit Overview
2
2
3
7
8
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Extensions and Adaptations
22
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Shape &
Measurement
Grade Level: 4/5
Timeline:
Unit Rationale
This unit is designed to cover a core aspect of the Mathematics curriculum for grades 4 and 5.
The ‘shape’ part of the unit includes the discovery and classification of 2-D and 3-D shapes
while measurement includes choosing appropriate units, measuring length and capacity, and
determining the perimeter, area, and volume. This unit will include a number of hands-on
activities to engage students in an active and meaningful way, including using manipulatives to
explore new concepts. There is also an experimental aspect to the unit as we explore capacity
and volume. The activities and lessons in this unit are designed to stimulate interest and
cement learning.
Assessment
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Students will be assessed in a number of ways throughout the unit. Participation in hands-on
activities and experiments are essential to students’ success in this unit. Students will complete
a variety of corresponding worksheets, a review package, and a unit test as summative
assessment for this unit. Formative assessment will be ongoing and will examine students’
ability to use manipulatives to demonstrate their understanding of topics and new concepts.
Curricular Connections
Mathematics – Grade 4
Prescribed Learning Outcomes
Suggested Achievement Indicators
It is expected students will be able to…
C3 demonstrate an understanding of area of regular and irregular
2‐D shapes by
 recognizing that area is measured in square units
 selecting and justifying referents for the units cm2 or m2
 estimating area by using referents for cm2 or m2
 determining and recording area (cm2 or m2)
 constructing different rectangles for a given area (cm2 or m2) in
order to demonstrate that many different rectangles may have the
same area
 describe area as the measure of surface recorded in square units
 identify and explain why the square is the most efficient unit for
measuring area
 provide a referent for a square centimetre and explain the choice
 provide a referent for a square metre and explain the choice
 determine which standard square unit is represented by a given
referent
 estimate the area of a given 2‐D shape using personal referents
 determine the area of a regular 2‐D shape and explain the
strategy
 determine the area of an irregular 2‐D shape and explain the
strategy
 construct a rectangle for a given area
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C5 demonstrate an understanding of line symmetry by
 identifying symmetrical 2‐D shapes
 creating symmetrical 2‐D shapes
 drawing one or more lines of symmetry in a 2‐D shape
 demonstrate that many rectangles are possible for a given area by
drawing at least two different rectangles for the same given area
 identify the characteristics of given symmetrical and nonsymmetrical 2‐D shapes
 sort a given set of 2‐D shapes as symmetrical and nonsymmetrical
 complete a symmetrical 2‐D shape given half the shape and its
line of symmetry
 identify lines of symmetry of a given set of 2‐D shapes and
explain why each shape is symmetrical
 determine whether or not a given 2‐D shape is symmetrical by
using a Mira or by folding and superimposing
 create a symmetrical shape with and without manipulatives
 provide examples of symmetrical shapes found in the
environment and identify the line(s) of symmetry
 sort a given set of 2‐D shapes as those that have no lines of
symmetry, one line of symmetry, or more than one line of
symmetry
Mathematics – Grade 5
Prescribed Learning Outcomes
Suggested Achievement Indicators
It is expected students will be able to…
C1 design and construct different rectangles given either
perimeter or area, or both (whole numbers) and draw
conclusions
 construct or draw two or more rectangles for a given perimeter
in a problem-solving context
 construct or draw two or more rectangles for a given area in a
problem-solving context
 illustrate that for any given perimeter, the square or shape
closest to a square will result in the greatest area
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 illustrate that for any given perimeter, the rectangle with the

C2 demonstrate an understanding of measuring length (mm) by
 selecting and justifying referents for the unit mm
 modelling and describing the relationship between mm and
cm units, and between mm and m units






C3
demonstrate an understanding of volume by
 selecting and justifying referents for cm3 or m3 units
 estimating volume by using referents for cm3 or m3
 measuring and recording volume (cm3 or m3)
 constructing rectangular prisms for a given volume








C4 demonstrate an understanding of capacity by
 describing the relationship between mL and L
 selecting and justifying referents for mL or L units
 estimating capacity by using referents for mL or L
 measuring and recording capacity (mL or L)



smallest possible width will result in the least area
provide a real-life context for when it is important to consider
the relationship between area and perimeter
provide a referent for one millimetre and explain the choice
provide a referent for one centimetre and explain the choice
provide a referent for one metre and explain the choice
show that 10 millimetres is equivalent to 1 centimetre using
concrete materials (e.g., ruler)
show that 1000 millimetres is equivalent to 1 metre using
concrete materials (e.g., metre stick)
provide examples of when millimetres are used as the unit of
measure
identify the cube as the most efficient unit for measuring
volume and explain why
provide a referent for a cubic centimetre and explain the choice
provide a referent for a cubic metre and explain the choice
determine which standard cubic unit is represented by a given
referent
estimate the volume of a given 3-D object using personal
referents
determine the volume of a given 3-D object using manipulatives
and explain the strategy
construct a rectangular prism for a given volume
explain that many rectangular prisms are possible for a given
volume by constructing more than one rectangular prism for
the same given volume
demonstrate that 1000 millilitres is equivalent to 1 litre by
filling a 1 litre container using a combination of smaller
containers
provide a referent for a litre and explain the choice
provide a referent for a millilitre and explain the choice
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 determine which capacity unit is represented by a given


C5 describe and provide examples of edges and faces of 3-D
objects, and sides of 2-D shapes that are
 parallel
 intersecting
 perpendicular
 vertical
 horizontal







C6 identify and sort quadrilaterals, including
 rectangles
 squares
 trapezoids
 parallelograms
 rhombuses



referent
estimate the capacity of a given container using personal
referents
determine the capacity of a given container using materials that
take the shape of the inside of the container (e.g., a liquid, rice,
sand, beads) and explain the strategy
identify parallel, intersecting, perpendicular, vertical, and
horizontal edges and faces on 3-D objects
identify parallel, intersecting, perpendicular, vertical, and
horizontal sides on 2-D shapes
provide examples from the environment that show parallel,
intersecting, perpendicular, vertical, and horizontal line
segments
find examples of edges, faces, and sides that are parallel,
intersecting, perpendicular, vertical, and horizontal in print and
electronic media such as newspapers, magazines, and the
internet
draw 2-D shapes or 3-D objects that have edges, faces and sides
that are parallel, intersecting, perpendicular, vertical, or
horizontal
describe the faces and edges of a given 3-D object using terms,
such as parallel, intersecting, perpendicular, vertical, or
horizontal
describe the sides of a given 2-D shape using terms, such as
parallel, intersecting, perpendicular, vertical, or horizontal
identify and describe the characteristics of a pre-sorted set of
quadrilaterals
sort a given set of quadrilaterals and explain the sorting rule
sort a given set of quadrilaterals according to the lengths of the
sides
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according to their attributes
 sort a given set of quadrilaterals according to whether or not
opposite sides are parallel
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Unit Timeline
MONDAY
TUESDAY WEDNESDAY THURSDAY
FRIDAY
April 28 – Lesson 1:
Shapes
May 5th – Lesson 5:
Building Geometric
Models
May 12th – Lesson 10:
Measuring Length
April 29 – Lesson 2:
Sorting 3-D Solids
May 6th – Lesson 6: Lines
of Symmetry
April 30 – Lesson 3:
Constructing 3-D Models
May 7th – Lesson 7: Lines
of Symmetry (cont’d)
May 1 – Lesson 4:
Nets
May 8th – Lesson 8:
Problem Solving
May 2nd – NO
SCHOOL
May 9th – Lesson 9:
Review/Mini-Test
May 13th – Lesson 11:
Units of Measure
May 14th – Lesson 12:
Perimeter
May 15th – Lesson 13:
Introducing Area
May 19th – NO
SCHOOL
May 26th – NO
SCHOOL
June 2nd – Unit Test
May 20th – Lesson 15:
Calculating Area
May 27th – Lesson 19:
Units of Measurement
May 21st – Lesson 16:
Surface Area
May 28th – Conversion
May 22nd – Lesson 17:
Volume
May 29th – Review
May 16th – Lesson
14: The Area Stays
The Same
May 23rd – Lesson
18: Capacity
May 30th – Review
th
th
th
st
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Unit Overview
Topic
1
The Classification and
Identification of Shapes
Learning
Outcomes
(SWBAT)
- name and identify a
variety of 2-D and 3D shapes
- define key vocab,
including vertices and
faces
Activities
Materials
Show students a number of shapes on the
SMARTBoard, ranging from easily identifiable to
difficult, including both 2-D and 3-D shapes. Ask
students if they can identify the shape.
SMARTBoard with
variety of shapes
After students have identified each shape, classify each
shape (how many sides does it have, faces, dimensions,
corners, edges, etc.) Use this opportunity to review
key vocabulary and explain the properties of shapes
(vertices, faces, etc.)
Copies of orksheet
Give students one block shape (prisms, cylinders,
pyramids) per two students. Students will work in
pairs to examine their shape and complete the
accompanying worksheet to name and describe the
item. Ask students to share their findings.
Students will then complete a set of independent
activities further exploring shapes and their properties.
Wood 3-D solids
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2
Topic
Learning
Outcomes
(SWBAT)
Sorting 3-D Solids
- sort shapes and
solids using different
classifications
- identify solids as
having specific
number of faces,
edges, or vertices
Activities
Display a collection of 3-D solids. Place two hula
hoops on top of a large sheet of paper (representing
the outside set, where items not belonging to either
hula hoop set are placed). Sort the 3-D solids without
telling students what your rule is (select a rule such as
solids with at least one circular face/solids with no
circular faces, etc.) Ask students to, as you sort, record
their ideas about your sorting rule. Once you have
sorted all the solids, have students share their answers.
Allow students to come up and sort the items, one at a
time, provide the sorting rule and have the students
sort the objects. Record the rules on index cards (solids
with eight vertices, no vertices, no faces, four faces,
etc).
Continue the activity by giving students the
opportunity to choose their own sorting rule and sort
the solids while their classmates try and guess the rule.
Be sure the volunteer records their sorting rule first
and double-checks it with you so you can guide the
sorting.
What patterns do students notice? Are there prisms
that are similar? Different? Explain that all rectangular
prisms have rectangular faces and all triangular prisms
have triangular faces. Create a table to examine the
Materials
Wood 3-D solids
2 hula hoops
Index cards with
sorting rules
Table on whiteboard
Copies of prisms and
non-intersecting
Venn Diagrams
Scissors and glue
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Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
number of faces, edges, and vertices (with prism and
base as other headings). Have students examine
prisms and contribute. Students should copy table into
their books.
3
Constructing Models of
3-D Solids
- construct 3-D
models of solids and
prisms using a variety
of materials
- draw and describe 3D prisms
Provide students will copies of small pictures of prisms
and blank non-intersecting Venn Diagrams. Have
students cut and paste the prisms into the appropriate
categories or create their own.
Divide class into groups of 4 and provide each group
with one 3-D solid and some modelling clay. Have
each group first examine, and discuss their solid,
focusing on the number and shape of its faces as well
as the number of edges and vertices. Have students use
the clay to build a model of their solid. Once all
students in the group have built their models, they
may choose another 3-D solid and build a new model.
Repeat until each group has built a minimum of 3
solids.
Have a student collect the modelling clay and solids
while you distribute several sets of pattern blocks.
Pose the question, Can you use several pattern blocks
to build a larger 3-D solid? Challenge the groups to
discuss and determine a way to use the pattern blocks
to build a 3-D solid. Review students’ solutions by
having each group display their 3-D solid. Continue to
Wood 3-D solids
Modelling clay
Pattern blocks
Copies of worksheet
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Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
develop this by guiding students, can they build a
triangular prism? A rectangular prism?
4
Exploring Nets
- define nets
- examine nets to
predict and determine
the 3-D solid it
represents
Students should return all materials and independently
practice drawing 3-D solids with accompanying
worksheet.
Show students a net of a triangular prism on the
SMARTBoard and ask students what they think it is.
Review the term net, explaining that it is a twodimensional figure created by opening up and
flattening a three-dimensional object. Ask students
what 3-D solid they think this net will make and why.
Distribute copies of net A and have students cut out
their nets and fold them into a 3-D solid. Ask students
what solid it made and what they know about
triangular prisms (# of faces, base shapes, etc.)
Repeat process with another triangular net (net B).
How are they alike? How are they different?
Distribute copies of activity sheet and have students
draw diagrams of their nets and corresponding 3-D
solids.
SMARTBoard with
nets
Copies of nets A, B,
C, and D
Copies of
worksheets
Scissors and tape
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Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
Provide students with the net C and net D (a cube and
a rectangular prism) and have them assemble each.
How are they alike? How are they different?
Distribute activity sheet and have students draw
diagrams of their nets and corresponding 3-D solids.
5
Building Geometric
Models
- build geometric
models using cubes
- examine pictures of
geometric shapes to
determine how it is
created and identify
its key features
- draw geometric
models using
isometric paper
Students will conclude by investigating a final net
without building it, but rather by predicting the solid
it will make and writing a paragraph on their
understanding.
Use six interlocking cubes to build a rectangular prism
as show it to students. Turn the shape so that they can
see it from different perspectives. Ask students if they
can name the solid, how many cubes were used, how
many cubes long is the solid, how many cubes wide,
and how many cubes high.
Distribute interlocking cubes to students and have
them use the cubes to build a rectangular prism just
like yours.
Build another solid, more complicated. Show students
from different perspectives. Ask students to describe
the solid and then build it themselves with
interlocking cubes. Have students compare their
completed shapes with their classmates.
Interlocking cubes
Copies of activity
sheet
Isometric dot paper
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Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
Divide the class into partners. Have each student use
five interlocking cubes to make another solid. Ask
partners to exchange shapes and then use another five
cubes to replicate their partners’ solids to make sure
the two solids are the same. Repeat four-five times.
Distribute activity sheet and have students use
interlocking cubes to build the solids shown. Complete
the first one together with students. Ask how many
cubes do you need to build the solid, how many cubes
are on the bottom layer, how are they arranged, how
many cubes are on the second layer, and so on.
6
Lines of Symmetry
- define line of
symmetry
- use mirrors to
determine if an object
or picture is
symmetrical
Students will then complete the remaining solids,
using interlocking cubes to build the solid. Students
should also use isometric dot paper to draw 3-D
models of each solid.
Ask students to define symmetry. Explain that when
an object can be divided into two parts that are exactly
the same, the object is symmetrical. The line that
divides the shape into equal parts is called the line of
symmetry. The parts of the object or shape on each
side of the line of symmetry are congruent, or
identical in shape and size. Show students a variety of
images and ask them if they are symmetrical or not
Miras or small,
plastic mirrors
Copies of activity
sheet and table
Scissors and glue
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Topic
Learning
Outcomes
(SWBAT)
- use geoboards to
create or re-create
symmetrical shapes
Activities
and why they think so. Ask students if they can think
of things that are symmetrical.
Materials
Geoboards with
elastic bands (or
iPads with app)
Provide students with Miras or small plastic mirrors
and copies of the activity sheet. Have students
examine the pictures on the activity sheet and predict
which ones they think are symmetrical. Demonstrate
how students may use a mirror to determine if the
object is symmetrical. Have students test each object
and cut out, sort, and glue the pictures onto the chart.
Have them draw a line of symmetry through each
picture they sort into the “symmetrical” column.
7
Lines of Symmetry
(cont’d)
- apply knowledge of
symmetry to answer
basic questions about
objects
- determine the
number of lines of
symmetry in any
given shape
Have students use GeoBoards to create symmetrical
shapes. Have students record their images on graph
paper and draw the lines of symmetry.
Ask students take out a piece of paper and have
students examine it. Ask what shape the piece of paper
is, whether they think it is symmetrical, and how they
know. Have students fold their sheet of paper in half
vertically and then open it. Ask whether this proves it
is symmetrical, what does the fold represent, and
whether there is another way you could fold your
rectangle into two parts that are equal in size and
shape (congruent).
Paper
Copies of activity
sheets
Pattern blocks
Graph paper
T a n y a W i n s h i p | 17
Topic
Learning
Outcomes
(SWBAT)
- classify shapes as
symmetrical or
asymetrical
Activities
Materials
Can shapes have more than one line of symmetry? Can
they have only one line? Have students share their
ideas and record them on the board.
Distribute activity sheet to students. Have students cut
out each shape, fold it to see if it is symmetrical, and
then sort, and glue it onto the chart based on whether
it has one line of symmetry, more than one line of
symmetry, or no lines of symmetry. Have students
draw the lines of symmetry on each picture. When
students have completed the activity, have them share
their findings.
8
Problem Solving with
Pattern Blocks
- use manipulatives to
answer a problem
solving question
involving lines of
symmetry
Have students use pattern blocks to create a set of
symmetrical shapes (with a list of specific
requirements) and record their findings on graph
paper. How many different shapes can we make as a
class? Have students share their findings.
Give students a problem solving question that requires
them to use pattern blocks and explore lines of
symmetry.
Students will work independently to answer the
question. Students are encouraged to use
manipulatives to work through the question.
Copies of problem
Pattern blocks
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Topic
9
10
Shape Review
Measuring Length
Learning
Outcomes
(SWBAT)
- illustrate sound
understanding of
shape
- use a variety of
items, non-standard
and standard, to
measure
Activities
Have students complete a short review package or quiz
to conclude the shape portion of this unit and assess
understanding of concepts.
Discuss rules of measurement. Ask students “how”
they measure? Where do you start when using a ruler?
(0 or the end of the ruler?) What if it’s longer than the
ruler? What units can we measure in? What can we
use to measure?
Copies of review
package/quiz
Have students practice measuring length with nonstandard units. Complete activity chart and scavenger
- estimate length prior hunt. Have students practice estimating and choosing
to measuring
appropriate units.
- use measuring tools
to accurately measure Complete measurement worksheets.
a variety of objects
- determine the unit
What unit of measure do we use for length? How long
of measurement
is a centimeter? Have students use a cm cube to find
required to measure a things that are around the same length. Complete
variety of items (cm,
Length 19 and Length 20 sheets to measure with cm
m, mm)
cubes.
Copies of activity
sheets
- demonstrate proper
use of measuring tools
11
Units of Measure: Length
and Height
Materials
Ask students to define a meter. What is it? How do
they know? Use cm cubes to determine the length of a
meter. Compare to a meter stick. Complete Length 14
– Length 16 activity sheets in groups.
Ruler
Pencils, paper clips,
cubes, or other nonstandard measures
Centimeter cubes or
rods
Meter sticks
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Topic
12
Perimeter
Learning
Outcomes
(SWBAT)
- demonstrate a
variety of ways to
determine perimeter
- define perimeter
- use a formula to
determine the
perimeter of a variety
of shapes
13
Introducing Area
- use manipulatives or
grid paper to calculate
area
Activities
Ask students to predict what a millimeter is. How do
they know? Look at a ruler. Complete activity sheets
measuring with centimeters and millimeters.
Ask students to brainstorm and write down ways they
could measure the distance around their desk (use a
string, trundle wheel, measure each side and add). Ask
students if they can define ‘perimeter’. Explain that
the distance around the outside of any shape is the
perimeter.
Materials
Copies of activity
sheets
Rulers
Give students perimeter shapes sheets and ask them to
recreate the shapes and determine the perimeter.
Students should label each side and determine the
total perimeter. Students will repeat this process with
the shapes on the second sheet, but should also draw
the shapes on graph paper as well as label each side
and determine the total perimeter.
Complete find the perimeter worksheets.
Ask students to define area. What is area? Why is it
used? What purpose do we have for calculating area?
Students should write down their ideas, share with a
partner, and add to their own ideas. Students should
then contribute to class discussion of area and add to
their own ideas with those of others.
Geoboards and
elastic bands (or
iPads with app)
Copies of activity
sheets
1cm grid paper
T a n y a W i n s h i p | 20
Topic
Learning
Outcomes
(SWBAT)
Activities
Materials
Demonstrate on the board how we can find area by
counting the regions (i.e. cubes). Have students
complete activity sheet to find areas of shapes.
Students will then use GeoBoards to complete exercise
exploring different sizes of the same shape and how
the area may change.
14
15
The Area Stays The Same
Calculating Area
- understand and
explain that shape
does not determine
area, but rather size
does
- use a number of
formulas to accurately
calculate the area of
different shapes
Have students trace their hands on 1cm grid paper and
count the regions to determine the area of their hand.
Begin class by discussing the unit of measure used for
calculating area. Why is this the unit? Use
manipulatives to illustrate.
Squares cut to 10cm
x 10cm
Scissors
Have students cut a square (or pre-cut squares) that are
10cm x 10cm (100cm2). Students should determine the
area by laying it on a 1cm grid paper and trace the
shape. Students should then cut their square into
pieces and re-arrange the pieces to make a new shape.
Have students place this shape on the grid paper and
trace. They should then calculate the “new” area. Have
students write a paragraph explaining their findings.
Have students hypothesize how they could find area
without counting squares. What formula can we use?
What about shapes that are not squares or rectangles?
1cm grid paper
Geoboards with
elastic bands (or
iPads with app)
T a n y a W i n s h i p | 21
Topic
Learning
Outcomes
(SWBAT)
- use manipulatives to
explain and
understand the
various formulas for
area
16
17
Surface Area
Volume
- determine the
surface area of 3-D
objects
- determine the
volume of specific
solids
Activities
Have students use GeoBoards and ask them to make a
triangle. Compare this to the area of a square. What
formula could we use?
Materials
Copies of worksheet
or textbook
Introduce the standard formulas for rectangles,
squares, parallelograms, triangles, and trapezoids. Have
students complete textbook work or workbook with
practice questions.
Challenge students to find the area of unusual shapes
and record their methods.
How do we find the area of 3-D objects? What is it
called? Introduce the topic of surface area.
Give students a 3-D object or prism. How can we find
the surface area of the object? Have students
brainstorm ways to figure out surface areas. Introduce
formula for surface area.
Have students complete the worksheets on surface
area.
What is volume? How is it determined? Introduce the
formula for volume.
Copies of
worksheets
Wood 3-D solids
Textbooks
SMARTBoard
Have students practice finding the volume of a variety
of shapes, starting together as a class.
Complete textbook work independently.
T a n y a W i n s h i p | 22
Topic
18
19
Capacity
Units of Measurement
Learning
Outcomes
(SWBAT)
- determine how
capacity and volume
are different
- sort units of
measurement by their
purpose (area,
volume, length, mass)
- choose appropriate
units of measurement
for various purposes
Activities
Materials
Are capacity and volume the same thing? What is
capacity?
Two glasses with the
same capacity
Show students two different size glasses. Do they hold
the same amount of water? Which one is bigger?
Which one holds more? Have students predict which
glass holds more? Pour the water from one cup into
the other. Does it hold the same amount?
Water
Give students varying sizes of containers. Ask students
to determine the volume using standard
measurements. They will then choose a “filler” and
predict the capacity, i.e. how many grains of rice or
how many marbles will it hold. Students will then
carry out their experiment.
Provide students with cards labelled with units of
measurement (kg, g, lb, cm, cm3, cm2, etc.) Students
need to find their “group” by sharing their unit and
looking for those who have things in common,
grouped by weight, volume, area, length, etc. These
will include both units and key terms associated with
each category. Students should discuss what they have
in common and be prepared to share.
Independently, students will complete activity sheets
focused on choosing appropriate units of measure.
Containers, different
shapes and sizes
Fillers (a variety of
materials)
Cards labelled with
units of
measurement
Copies of
worksheets
T a n y a W i n s h i p | 23
Topic
20
Conversion
Learning
Outcomes
(SWBAT)
- complete basic
conversion and
demonstrate an
understanding of
conversion
Activities
Materials
Ask students to name all the units of measurement
they can think of and categorize them. What is the
difference between a mm, cm, and m?
SMARTBoard with
copy of conversion
chart
Show students how to convert using multiplication
and division.
Textbook
Have students complete textbook work on conversion.
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Extensions &
Adaptations
This unit contains themes for both grades 4 and 5. There are
also a number of students who have IEPs. In order to
address the need for adaptations, students will have reduced
workloads with modified questions where necessary.
Students who need an additional challenge will be given
challenge questions, aimed at furthering their investigation
into the topic and extending their knowledge. Advanced
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students may also begin to explore how to calculate the area
of circles.