Grade 4, Module 10
Core Focus
• Relating multiplication and division to divide whole numbers
• Dividing two-, three-, and four-digit numbers by one-digit divisors and solving
word problems
• Learning the foundational geometry concepts of points, parallel and perpendicular
lines, line segments, and rays
• Exploring symmetry through reflecting shapes across a line of symmetry and
identifying lines of symmetry
Multiplication and Division
• Students extend their skill with division by building on what they already know about
how multiplication and division are related. Just like multiplication, division can
be represented using a rectangular area model.
• In the problem below, students use what they know about the area model formula
(L × W = A) to split the total area (60) into parts that can easily be divided (60 + 3)
by the known W dimension (3) to find the missing L dimension (21).
Three friends share the cost of this gift.
$63
Nina used this strategy. She followed these steps.
Step 1
Step 2
She drew a rectangle to
show the problem. The
length of one side becomes
the unknown value.
She split the rectangle into
two parts so that it was
easier to divide by 3.
3
63
3
60
Step 3
3
She thought:
3 × 20 = 60
3×1=3
then 20 + 1 = 21
60
3
?
20
1
In this lesson, area models are used to split two-digit dividends into parts
that are easily divisible by one-digit divisors.
• All of the lessons build on this “splitting” idea to make division easier.
The key is to choose convenient ways to split numbers, so the division becomes easy
to perform.
Jamal paid for this laptop in 3 monthly payments.
He paid the same amount each month.
I would break 639 into parts
that are easier to divide.
3
600
30
9
10 +
3
What is special about the numbers 600, 30, and 9?
© ORIGO Education.
What amount does Jamal pay each month?
The dividend is the number
that is split into smaller
equal parts when division
is performed.
The divisor is the number
that indicates how many
parts the dividend is to be
split into, or the number in
each part.
The quotient is the missing
information in a division
problem (the answer)
What amount did he pay each month? How do you know?
Describe how this rectangle has been split.
• Take turns practicing mental
division problems while
traveling or walking. Use
multiples of the divisor to
come up with problems like
336 ÷ 3. This problem can
be mentally decomposed to
become 300 ÷ 3 and 36 ÷ 3,
which equals 100 + 12, which
equals 112. Try 245 ÷ 5,
648 ÷ 6, 819 ÷ 9, etc…
Glossary
3
+
Ideas for Home
200
+
In this lesson, area models are used to split three-digit dividends into
parts that are easily divisible by one-digit divisors.
The standard division
algorithm is the paper/pencil
procedure for long division
that most adults were taught
exclusive to any other
method. It will be taught in
Grade 5 and mastered by
Grade 6.
1
Grade 4, Module 10
• Place-value strategies keep students focused on the whole number (54 tens
and 6 ones), not just parts of it (54 and 6). They are better able to decide if answers
are reasonable and are less likely to make the procedural errors that the standard
long division algorithm invites (skipping steps, misaligning numbers, etc.).
Alisa’s laptop was $546. She paid the same amount each month for 6 months.
546
It's easier to divide if you think
of 546 as 54 tens and 6 ones.
54 tens
6 ones
540 ÷ 6 =
amount that she paid each month.
6÷6=
546 ÷ 6 =
Use this strategy to figure out 279 Ö 3.
• While it is tempting to show students the standard division algorithm, it is important
that students develop a firm foundation in the place-value strategies for division
before learning the procedure for the long division algorithm.
Geometry
• Students are formally introduced to the fundamental building blocks of geometry:
points, lines, segments, rays, and parallel/perpendicular lines. These lessons focus
on identifying and naming these important geometric features. The figures below
show examples.
A
A
B
C
D
D
E
The figure on the left shows points, lines, segments, and rays. Figures on
the right show parallel and perpendicular lines.
• Reflectional symmetry and lines of symmetry are geometry concepts that are simple,
but interesting, and can be found everywhere in our everyday lives, in art, and in nature.
10.12
Identifying Lines of Symmetry
Draw a line of symmetry on each shape so that one
side of the shape is a mirror image of the other.
© ORIGO Education.
• Look around your community
or home for examples of
parallel and perpendicular
line segments. Railroad tracks
(parallel), the side and top of
a door frame (perpendicular),
roads, fences, and tiles are
good for discussing geometry
with your child..
• To explore reflections and
symmetry, spread some paint
on paper, then fold and unfold
the paper. This will create a
painting that is the same on
both sides of the fold (which is
the line of symmetry).
• Write the alphabet in capital
letters, and examine it for
symmetry. Some letters (like
A and T) have vertical lines
of symmetry; some (like B
and E) have horizontal lines
of symmetry; some (like H
and X) have both vertical and
horizontal lines of symmetry.
F
C
B
Ideas for Home
A line of symmetry splits a
whole shape into two parts
that are the same shape
and the same size.
• Try to find common words
or names that have lines
of symmetry. E.g. OBOE has
a horizontal line of symmetry,
and MAT, written vertically,
has a vertical line
of symmetry.
Glossary
A line of symmetry is drawn
to divide a shape into two
parts that are the same size
and shape.
Try cutting and folding shapes
like these to check your work.
2