Grade 5, Module 6
Core Focus
• Subtracting common fractions and mixed numbers (same, related, and different
denominators)
• Solving problems involving subtraction of common fractions and mixed numbers
• Measurement conversions involving inches, feet, yards, and miles
• Constructing and interpreting a line plot
Subtracting Common Fractions
• Students build on what they already know about equivalent fractions and strategies
for adding fractions to work with subtracting fractions and mixed numbers.
• Area models (e.g. rectangles) and length models (e.g. number lines) help students
make sense of fraction subtraction.
• When fractions have different denominators, visual models help students identify which
fraction needs to be rewritten so the denominators will be the same.
Subtracting Common Fractions (Unrelated Denominators)
6.3
Some parts of these pizzas have been eaten.
Seriously Supreme
Cheese and Cheese
Ideas for Home
• Continue to work with
your child on their basic
multiplication facts. They
use their multiplication
skills when converting
mixed numbers to improper
fractions and when rewriting
fractions using a common
denominator.
• Have your child solve
2
8
4 5 - 1 10 using one of the
strategies shown in this
letter. Ask them to describe
each step as they work.
Tasty Tomato
Which pizza has the least left over? Which pizza has the most left over? How do you know?
What are some subtraction stories you could make up about the pizzas?
What equations could you write to match your stories?
What do you notice about the denominators of the fractions you wrote?
What story problem could you write to match each of these equations?
3
4
− 1 =
2
3
3
− 1 =
4
5
4
Glossary
− 3 =
4
Subtract whole numbers
and fractions
How could you figure out each difference? Use the space below each sentence to show your thinking.
In this lesson, students use area models to subtract fractions with unrelated denominators.
Step Up
• Just as with addition, the
denominators
need to be c.made the same before students
a.
b.
9
can subtract. E.g. students could rewrite 2 34 − 1 121 as 2 12
− 1 121 .
1
5
1
4
1
5
1
3
4
5
© ORIGO Education.
• Students choose whether to subtract the whole numbers and the fractions separately,
or to change the mixed numbers to improper fractions before subtracting.
132
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ORIGO Stepping Stones 5 • 6.3
Subtracting Mixed Numbers (Related Denominators)
6.4
4
12
2 9 −1 1
1. Find the difference between the two fractions in each pair. Show your thinking.
2
3
2 3 −1 1
12
12
(2 − 1) + ( 9 − 1 )
=1
12
8
12
Subtract improper fractions
2 3 −1 1
4
12
2 9 −1 1
12
Jack bought these two strips of wood for a picture frame.
5
7
1
2
1
4
33
12
feet
12
12
− 13
12
= 20
12
feet
How could you figure out the difference in length?
© ORIGO Education.
Look at these students’ methods.
Teena subtracted using
improper fractions.
Jose subtracted the
whole numbers and then
subtracted the fractions.
Grace subtracted by
writing one mixed number
below the other.
1
15
2
− 21 =
1
2
7−5=
− 1 =
4
4
+
7 2
1
− 5 4
=
Before they subtract, what will they need to do with the fractions?
In this lesson,
students
describe
strategies
for subtracting mixed numbers.
What steps
will each student
follow to figure
out the difference?
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Step Up
1. Show how you could figure out each difference in two ways. One way should
use improper fractions. The second method should use mixed numbers.
1
Grade 5, Module 6
• Students encounter a new challenge in subtracting mixed numbers that they
did not experience with addition. Sometimes, students cannot subtract the whole
numbers and fractions separately because the first fraction is smaller than the
second.
• One strategy is to rewrite the first mixed number so its fraction part is larger
(by using 1 from the whole number and putting it in fraction form).
• Another strategy is to convert both mixed numbers to improper fractions.
Subtracting Mixed Numbers (Unrelated Denominators
and Decomposing Whole Numbers)
6.6
How could you figure out the difference between the amounts
in these two stockpots?
Why is it necessary to rewrite the fractions?
1
3
3
−1 1
2
= 3 2 −1 3
6
6
1
• Talk about which unit of
measure would be most
appropriate for different
situations ( e.g. measuring
a piece of paper, a length
of cloth, the length and width
of a room, or the distance
from home to school. )
Glossary
3 3 qt
1
1 2 qt
=
Ideas for Home
6 1 −2 2
Try to subtract the fractions first. What do you notice?
3
What could you do so you can subtract? How could you use this number line to help?
3
Rewriting a mixed number:
6 and 1
0
1
2
Felix wrote the mixed numbers as improper
fractions first to make it easier to subtract.
3
3
2
2
6
−1 3
6
6
3
(5 +
3 1 −1 1
3
6
−
(5 + 1) and 1
Emma worked with the mixed numbers.
3 1 −1 1
3
3
4
3
2
2
6
3
6
−1
5
6
=
a.
Same denominators
Customary Measurement
1
Now we can do the
subtraction:
6 1 −2 2 =5 4 –2 2
3
−1 2
−1
3
6
3
36 inches = 1 yard
1,760 yards = 1 mile
Converting Between Feet and Yards
Two friends play a game of golf. At the first hole, Carter’s ball stops 4 yards from the hole.
Emily’s ball stops 15 feet from the hole.
Whose ball is closer to the hole? How do you know?
I know there are
3 feet in 1 yard.
Carter misses his first putt.
1
3
3
3 feet = 1 yard
ORIGO Stepping Stones 5 • 6.6
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His ball is now 2
3
12 inches = 1 foot
• Students convert lengths that involve fractions. They find that 18 inches is the same
as 1 21 feet, or 138
that a length of 6 inches can also be described as being a half foot
long. This language matches how measurement is often used in real-life situations.
6.10
3
(5 − 2) + ( 4 − 2 ) or 3 2
3
© ORIGO Education.
4
3
which is
Show subtraction
• It is important that your child has a general sense of how big each customary unit of
Same denominators
Show subtraction
length is, as well asb. knowing
the formal
relationships (e.g.
how many inches in one foot).
3
5
2
3
4
3
6
What steps do you think she used?
What is the difference?
1. For each
of these,
rewrite the mixed
numbers soinvolving
the fractions have
the same
In this
lesson,
solve
subtraction
problems
mixed
numbers.
Step
Up students
denominators. Show how you subtract to find the difference.
2
) and 1
2 8 −1 3 =
What steps do you think he used?
Write the missing values in his equation.
3
3
3
yards from the hole.
12
quarts
1
6
quarts
1
2
ft
or
0.5
ft.
3
quart
1
4
ft
or
0.25
ft.
9
quarts
3
4
ft
or
0.75
ft.
ft.
How could you say this distance in feet?
© ORIGO Education.
You could write the equation Y Ö 3 = F to describe
the relationship between feet and yards.
What does the equation mean?
How could you use division to show the relationship?
In this
lesson, students
convert feet to yards, and yards to feet.
1. Convert yards to feet to complete these.
Step Up
a.
b.
6 yd =
ft
ft
1
5 3 yd =
ft
9 yd =
f.
e.
d.
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c.
15 yd =
18 yd =
ft
1
8 2 yd =
ft
ft
2