Grade 3, Module 5
Core Focus
• Working with division by reviewing “fair share” concepts and introducing
the division symbol
• Connecting multiplication and division
• Working with the tens and fives division facts, and the twos and fours division facts
• Exploring 2D shapes and the relationships between rectangles, rhombuses,
and quadrilaterals
Division
Ideas for Home
• Multiplication and division receive major attention in third grade. It is very important for
students to understand how these operations are closely related.
• Practice the twos and
fours doubling facts, e.g.
“What is 4 x 7?” Instead of
stopping at “28,” ask your
child to explain the doubling
strategy: “I know that double
7 is 14 and double 14 is 28,
so 4 x 7 is 28.”
• “Fair shares” is familiar well before working with division symbols. E.g. 20 marbles
shared fairly among 4 children means each child gets the same number (5). The number
sentence 20 ÷ 4 = 5 represents the “fair share.” The related multiplication is 4 × 5 = 20.
This sharing mat shows how 20 can be divided into four groups of 5.
• Because multiplication and division are so closely related, students use what they know
about multiplication facts when they think about division. This strategy is emphasized
for tens and fives facts.
To solve a division fact it is often easier to think of the related multiplication fact.
see
40
4
think
÷
×
4
?
=
?
=
40
Glossary
What multiplication fact could you use to figure out 50 Ö 5?
In this lesson, students are introduced to the tens division facts by thinking about
the related tens multiplication facts.
• In Module 3, students focused on doubling for twos multiplication facts and doubling
doubling for fours multiplication facts. Now students think about twos and fours division
facts as halving and halving halving.
5.7
• Add the practice of division
facts, “What is 28 ÷ 4?”
Instead of stopping at 7,
ask your child to explain the
halving strategy: “I know half
of 28 is 14 and half of 14 is 7,
so 28 ÷ 4 = 7.”
Partially covered arrays
show the total and either
the number of groups or the
number in each group to
represent division.
a.
30 dots
in total
Introducing the Twos and Fours Division Facts
•
These marbles are shared equally between two friends.
How many marbles are in each share?
Dividing by 2 is the same
as halving. Half of 16 is 8.
3×
16 marbles
= 30
30 ÷ 3 =
b.
20 dots
in total
Imagine the same bag of marbles is equally shared among four friends.
© ORIGO Education.
How could you figure out the number of marbles in each share?
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Layla used a halving strategy.
×2
×2
8
÷2
16
James thought of the related
multiplication fact.
× 10 = 20
20 ÷ 10 =
× 4 = 16
÷2
In this lesson, students work with twos and fours division facts by using halving
and related multiplication strategies.
1
Grade 3, Module 5
• An arrow diagram reinforces the relationship between multiplication and division of
the × 2 and × 4 facts and ÷ 2 and ÷ 4 facts. The inner arrows show how “double double”
is the same as × 4 and “half half” is the same as ÷ 4; the top and bottom outer arrows.
4
×2
×2
4
4
8
÷2
Ideas for Home
• Cut out a wide variety of
four-sided polygons, and
practice categorizing them
using the labels shown in the
tree diagram (see example
5.12). Ask your child to defend
their decisions and explain
their thinking.
• Play “I Spy” with geometric
shapes when running errands,
looking at books, or going on a
walk. “I spy with my little eye a
quadrilateral that has four equal
sides” etc.
÷2
4
Geometry
• In Grades K–2, students have been introduced to a variety of two-dimensional
geometric shapes, including various straight-sided figures (polygons), and
especially four-sided polygons (quadrilaterals).
• In this module, students explore the similarities and differences of four-sided figures
and use tree diagrams to illustrate relationships among various types of quadrilaterals.
5.12
Glossary
A rhombus is any four-sided
figure with all sides the
same length.
Exploring Quadrilaterals
What do you know about these shapes?
What is the same about them? What is different?
A
B
C
What shape families do the shapes
belong to?
D
Shape A is a quadrilateral because it has
4 straight sides. It is also a square, which
is a type of rhombus because all its sides
are equal. It is also a type of rectangle
because all its corners are the same size.
This tree diagram shows how quadrilaterals are related.
A rectangle is a quadrilateral
with four right angles, also
known as a non-square
rectangle. Squares (also
known as square rectangles)
are special rectangles with all
sides the same size.
quadrilateral
rhombus
non-square rhombus
rectangle
square
other quadrilaterals
non-square rectangle
© ORIGO Education.
In this lesson, students examine shapes whose properties allow them to belong
to more than one shape family.
•
A square is a special
rhombus with four right
angles.
Every square is both a
special rhombus and a
special rectangle.
2
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