Grade 5, Module 4
Core Focus
• Adding common fractions and mixed numbers (same, related, and different
denominators)
• Solving problems involving addition of common fractions and mixed numbers
• Order of operations (focus on use of parentheses)
Adding Common Fractions
• Students make sense of fraction addition through visualization using area models
(rectangles) and length models (number lines). These help students identify which
fractions should be rewritten to make the denominators the same, so the fractions
can easily be added.
Adding Common Fractions (Related Denominators)
4.2
These pizzas were left over after a party.
Very Veggie
Mostly Meat
Super Supreme
Choose two types of pizza to take home. What are the possible combinations you could choose?
What number sentence could you write to show how to figure out the total for each combination?
Ideas for Home
• Finding common
denominators is a key skill
when working with fractions.
Say two numbers less than
12 (e.g. 3 and 5) and ask
your child to find a common
multiple. E.g. the multiples for
3 are 3, 6, 9, 12, 15, and the
multiples for 5 are 5, 10, 15. A
common multiple for
3 and 5 is 15.
Which combinations of leftover pizzas match these equations?
1
3
1
6
+
5
12
=
+
1
6
1
3
=
+
5
12
• Ask your child which method
they prefer when adding
mixed numbers — changing
to improper fractions, or
adding the whole numbers
and fractions separately.
Be sure to ask why.
=
What do you notice about the denominators in each pair?
How would you figure out the total?
I can see that the denominator 12
is a multiple of the denominator 3.
1. For each of these, rewrite the equation so the denominators are the same.
In this
students
use area models to help add fractions with
Steplesson,
Up
Use the number line to help. Then write the total.
different but related denominators.
a.
b.
2
5
1
10
+
c.
3
20
=
+
3
5
3
10
=
+
5
5
=
1
20
0
1
10
1
5
1
Adding Mixed Numbers (Related Denominators)
ORIGO Stepping Stones 5 • 4.2
824.4
250914
Manuel bought these two strips of wood for a picture frame.
5
7
1
2
1
4
feet
feet
How would you figure out the total length of both strips?
© ORIGO Education.
15
2
+
21
4
=
Brady added the
whole numbers and
then the fractions.
Claire added by writing
one mixed number below
the other.
1
7 2
1
1
7+5+ 2 + 4
1
+ 5 4
Add improper fractions
1
3
5
4 +2 8
7
5
4 +2 8
14
21
8 + 8
35
= 8
Add whole numbers
and fractions
1
1
3
4
6
8
+2
+2
(1 + 2) + (
=3
6
8
11
8
5
8
5
8
+
5
8
)
Before they add, what will they need to do with the fractions?
How do you think they will figure out the total?
In this lesson, students use area models to help add fractions with
1. Show how you would figure out each total in two ways. One way should use
Step Up
different
but related
denominators.
improper
fractions. The second method should use mixed numbers.
060815
• Help your child to develop
flexibility in thinking about
fractions by talking about
equivalent fractions in
everyday activities. If a pizza
is cut into eight equal slices
and your child eats two
slices, ask them to describe
2
how much they ate (i.e. 8 or
1
4 of the pizza).
Glossary
Look at these students’ methods.
Nadie thought it would be
easier to add the lengths
using improper fractions.
This is what she wrote.
© ORIGO Education.
• When adding fractions that have different, unrelated denominators, such
as 31 + 41 , students think of multiples for each denominator to figure out a common
denominator. In this case, each fraction could be rewritten with 12ths as the common
4
3
7
denominator (i.e. 12
+ 12
= 12
).
1
Grade 5, Module 4
• Students think about strategies for adding fractions that are greater than 1
2
(improper fractions such as 12
5 , ormixed numbers such as 2 5 ).
• Students choose whether to add the whole numbers and fractions separately,
or to change the mixed numbers to improper fractions before adding.
• Depending on the strategy students use to add mixed numbers, the answer will
be a mixed number or an improper fraction. Students see that both methods result
in equivalent answers.
4.8
Solving Multi-Step Word Problems Involving
Mixed Numbers
Look at the timesheet.
Chang’s Timesheet
How could you figure out the total number of hours
Chang worked in this week?
Monday
1
Tuesday
1
Emma changed all the fractions to a common denominator.
Then she added the fractions and the whole hours.
Wednesday
1
Describe the steps you think Emma used.
Friday
Thursday
1
What total would she get?
Cole added pairs of times that made whole hours first.
Then he added the times that were left.
He recorded his thinking like this.
Describe the steps Cole followed.
1
1
4
+1 3 =3
1
1
2
+1
1
4
1
2
3
4
3
4
1
2
hours
hours
hours
hour
hours
4
3+3+
What is another way you could add the times?
1
2
=3
3
4
=6
3
4
In this
students
situations
that
involve
1.
Solve each solve
problem. everyday
Show your thinking.
You can draw
a picture
to help. adding
Steplesson,
Up
fractions and mixed numbers.
a. Mrs. Waters bought 3 lengths of fabric that measured 2
How many yards of fabric did she buy in total?
1
2
yd, 3
2
3
yd, and 1
1
4
yd.
Order of Operations
• Students learn to write and evaluate mathematical expressions written horizontally,
such as 5 × 3 + 2 (= 17). Students connect the expressions to real-world
situations
yd
b. Mr.fi
such as, “We bought
vebought
sandwiches
fora $3
and some
that cost $2.
ft.
Reed
a strip of wood to make
pictureeach,
frame that measured
3 ft by 1 chips
What was the total length of the strip of wood he bought?
How much did we spend in all?”
3
4
© ORIGO Education.
94
4.10
ORIGO Stepping Stones 5 • 4.8
Investigating Order with Two Operations
• Remove the picture cards
from a deck of cards, give
your child three of the
remaining cards and ask
them to write an expression
that is as close to 25 as
possible (over or under).
E.g. with the numbers 3, 5,
and 7, a possible expression
is 3 × 5 + 7 (= 22). They can
use any combination of the
four operations: addition,
subtraction, multiplication,
and division.
• Create different stories
with your child that can
be represented with an
expression. An expression to
match the story, “I read for
25 minutes three times this
week, then I read for
40 minutes one day” is
3 × 25 + 40.
1
2
• Students learn that parentheses (brackets) can be used to clarify which operation to
do first, and that sometimes this can make a big difference.
ft
250914
Ideas for Home
Glossary
If there is one type of
operation in a sentence, work
left to right. If there are two or
more types of operation, work
left to right in this order:
How could you figure out the number of cubes in this prism?
This prism is 4 layers high. Each
layer has 6 rows and 3 cubes in each
row. So I would multiply 4 x 6 x 3.
What would you write to show your thinking?
Which part is easier to multiply? Why?
How many cubes are in the prism?
Here is another example where parentheses
are used to help.
4
6
3
You don«t need parentheses
for multiplication but they
do tell which two factors to
multiply first.
5
How would you figure out the total number
of squares in this array?
23
The rows can be split into parts to make it easier
to figure out. How have these rows been split? 5
© ORIGO Education.
20 + 3
5 × 23 = 5 × (20 + 3)
Look at these equations. What do you notice?
1. perform any operation
inside parentheses
2. multiply or divide pairs
of numbers
3. add or subtract pairs
of numbers.
An expression is a combination
of numbers and operations
that do not show a relationship,
e.g. 5 × 8, or 40 + 3.
5 × (20 + 3) = (5 × 20) + (5 × 3)
1. Write an equation with parentheses to show how to figure out the total number
Steplesson,
Up
In this
students
learn about the need for parentheses to
of cubes in each prism. Make sure you write the total.
indicate the order in which the operations are to be completed.
a.
b.
2
060815