Grade 4, Module 7
Core Focus
• Using partial products to multiply two-, three-, and four-digit numbers
• Solving multistep word problems involving multiplication
• Subtracting common fractions, including mixed numbers and solving word problems
involving mixed numbers
Multiplication
• Students work with multiplying a single-digit number by multi-digit numbers using
the partial products strategy. Multi-digit numbers are decomposed into place-value
parts so the multiplication is easy to do using an array model. Each part is multiplied
(as in area) and then added together, resulting in the total product.
Using the Partial-Products Strategy to Multiply
(Two-Digit Numbers)
7.1
Emma is painting the concrete floor of a playground.
She needs to know the area of the playground
to figure out how much paint to buy. The dimensions
are shown to the right.
Length is 24 yards
Width is 6 yards
How could you figure out the exact area?
Mary drew this grid to help. She split 24 into tens and ones
then multipled 6 × 20 and 6 × 4.
You can split a rectangle
into parts to find the
partial products.
6
20
Glossary
4
How could you use this strategy to figure out 3 × 28?
In Lesson 1, students partition rectangular arrays into sections to determine
the total of squares
inside
array.around the grid. Color the tens part blue
1. Write
thethe
dimensions
Step Up
and the ones part yellow. Write the product for each part then add
the products to figure out the area of the grid.
• The partial products
strategy works
a.
4 × 17 for numbers with two, three, and four digits.
4 × 10 =
• The partial products array model represents multiplication
for two two-digit numbers,
4×
7 =
as well. In the example below, students find the area of each rectangle and then
Area
sq units
add the products together. Here is an array showing 15 × 16.
6 × 24
6×
10
100
60
5
50
30
10
6
=
10 × 10 = 100
6 × 10 × 6 ==60
5 × 10 = 50
Area
sq units
5 × 6 = 30
152
090115
© ORIGO Education.
b.
• To help your child with
partial product multiplication,
practice facts involving
multiples of ten. E.g. 4 × 40
(4 × 4 × 10= 160), 4 × 400
(4× 4 × 100 = 1600), 40 × 40
(4 × 4 × 10 × 10 = 1600), etc.
• Use the array model
together when multiplying
multi-digit numbers and
discuss how it works.
sq yards
Area is
Estimate the area of the playground.
Would it be more or less than 100 sq yards?
Ideas for Home
ORIGO Stepping Stones 4 • 7.1
100 + 60 + 50 + 30 = 240
The partial products strategy
uses the distributive property,
multiplying each place value
separately to get a partial
product and then adding the
products together, resulting in
one product.
© ORIGO Education.
• This visual approach to multiplying multi-digit numbers prepares students for later
lessons on the standard multiplication algorithm. Students master the multiplication
algorithm more easily if they first have opportunities to work with multiplication using
their understanding of place value and area found in the partial products strategy.
The standard multiplication
algorithm – the familiar paperand-pencil procedure for
multiplying multi-digit numbers
that most adults were taught
in school. Students will learn
and master the algorithm in
Grade 5.
1
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Grade 4, Module 7
Fractions
• Building on the addition of fractions work from Module 6, students will now focus
on subtracting common fractions and mixed numbers using a number line. There
are 2 ways to subtract using a number line. Below is an example of each using the
problem 13
− 84 .
4
8
4
−
1
4
0
2
4
3
4
5
4
1
6
4
7
4
9
4
2
10
4
11
4
13
4
3
14
4
15
4
4
Start with the total and take part away (count-back). This is take away. The
answer is where the arrow lands ( 5 ).
4
5
4
+
0
1
4
2
4
3
4
4
4
5
4
6
4
7
4
8
4
9
4
10
4
11
4
12
4
13
4
14
4
4
• Number lines visually represent subtraction. The model is flexible and reinforces
that fractions are numbers. When subtracting mixed numbers, a number line
is a convenient way to find the difference. Here, the problem is 5 34 − 3 24 .
The difference is the jumps in between, which is 1 54 or 2 41 .
3
3
2
4
4
2
4
+
+1
5
• Encourage your child to
explain the number line
representations to you, and
also to think about and draw
number lines or other pictures
whenever they are working
with fractions.
• Practice subtracting mixed
numbers that require
regrouping. E.g. 7 25 − 4 54 .
Decompose 7 25 into 6 + 55
+ 25 , which equals 6 57 . Then
subtract 6 57 − 4 54 , which
results in 2 53 .
15
4
Start with the part and the total and count what is in-between (count-on). This is
comparison. The answer is in the jumps ( 5 ).
+
Ideas for Home
3
4
Glossary
A mixed number is a whole
number and a common
fraction added together and
written as a single number
without the addition symbol.
2+
5
6
3
4
1
2
2
1
2
• One additional challenge with subtraction is when the fraction being subtracted is too
big. One way students learn to handle this situation is to decompose the whole number
and regroup the fraction, similar to what is done when regrouping whole numbers.
Calculating the Difference Between Mixed Numbers
(Decomposing Whole Numbers)
7.11
Amos has two pet lizards. One is 3 84 inches long and the other is 1
How could you figure out the difference in their lengths?
3
Maka figured it out like this.
What did she do to make the subtraction easier?
How could you use addition to help you calculate
the difference?
−1
7
8
12
8
− 1
7
8
2 − 1 = 1
12
8
Look at the number lines below.
What is the same about the two methods shown?
What is different?
−
7
8
=
The difference is 1
1
© ORIGO Education.
inches long.
is the same as
2
5
8
5
8
inches.
4
+ 8
+ 8
+1
In Lesson 11, students decompose whole
numbers
into
equivalent fractions
in order to subtract mixed numbers.
1
2
3
4
7
8
4
8
3
• In the above problem, 87 cannot1 be subtracted from 84 . So
the 3 is decomposed into
8 8
4
2 + 1, which can be rewritten 2 ++ 8 ( 8 = 1)+ 1+ 8 , which+ equals 2 12
. Now the problem
8
7
has become 2 12
−
1
,
which
is
easier
to
subtract.
The
answer
is
1 58 inches.
8
8
1
1
4
8
8
2
1
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8
7
8
7
8
3
4
3
4
8
2