1. No category

Subtract Mixed Numbers
Le
Le
n n
sso sso
4
Students have performed addition and subtraction with fractions, and they
have added mixed numbers. They round out their experience with these
concepts by learning to subtract with mixed numbers. The number sense
that students build in these activities will serve them when they multiply
with fractions.
Common Core State Standard
5.NF.A.1 Add and subtract fractions
with unlike denominators (including mixed
numbers) by replacing given fractions with
equivalent fractions in such a way as to
produce an equivalent sum or difference
of fractions with like denominators. For
example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
(In general, a/b + c/d = (ad + bc)/bd.)
Vocabulary/ELL Support
Write the following problem on the board: Paula makes 2 peanut butter
sandwiches and cuts each one into fourths. She eats 3 pieces. How much
does Paula have left?
Give students two squares of construction paper.
■ Ask: How can you model this problem using the paper? [Sample: Cut
each square into fourths; remove __3 from one.]
4
5
1
■ Ask: How much does Paula have left? [ __, or 1__ ]
4
4
Elicit from students the two different ways of expressing the answer.
1 is a combination, or mix, of a whole number with a
Note that because 1__
4
fraction, the number is called a mixed number.
3
■ A mixed number (such as 2__ ) has a whole-number part (2) and a
4
3
fraction part ( __ ); it represents the sum of the parts.
4
The scale on this ship
indicates the ship’s draft,
the depth to which the
ship’s hull extends below
the water’s surface. How
would you compute a
change in the ship’s draft?
22
ETA hand2mind
Hands-On Standards, Common Core Fractions Grade 5
hand2mind.com
Add and Subtract Fractions
Set the Stage
Build Background
WHOLE CLASS
Distribute 11 x 17-inch paper and markers to groups of students.
Assign each group a different mixed number.
Ask students to write different ways of representing their mixed number
3
using number sentences. For example, for 2__
, the students could write
5
3
1
1
1
__
__
__
__
2 + 5 or 2 + 5 + 5 + 5 . Then, have students draw visual representations
of their number sentences, such as shading circles divided into fifths.
Have students locate their mixed number on a number line.
■ Ask: Why is it important to know different ways of representing mixed
numbers? [Sample: Knowing what mixed numbers represent helps us
add or subtract their parts to find sums or differences.]
Warm-Up Activity
Foundation Skill Practice
Use this short thinking exercise to jump-start
the instructional session.
Name
Use this VersaTiles activity to help students activate
their prior knowledge.
®
Can You Find a Difference?
Answer Key
4
Find the difference.
Suppose you have five cards with these numbers on them. Use four cards to
make the largest fraction of the form:
3
1
− 3__
8__
4
4
• If necessary, rename the first fraction so that
you can subtract fractional parts.
5
1
4
1
= 7 + __
+ __
= 7__
8__
4
4
4
4
• Subtract the fraction parts. Then subtract
the whole number parts.
5
3
− 3__
7__
4
4
• Simplify, if possible.
2
1
= 4__
4__
4
2
2
4__
4
3
1
1
So, 8__
− 3__
= 4__
.
4
4
2
1
2
3
4
5
Find the difference.
54
ANSWER: ___
1 15__23 − 4__13
2 9__57 − 3__47
3 8__56 − 2__46
4 10__14 − 3__24
5
9
− 3___
5 7___
10
10
6 13__89 − 8__29
7 21__18 − 14__58
8 19__25 − 12__45
10
12
− 8___
9 12___
15
15
10 22__49 − 15__79
11 85__34 − 49__14
12 40__56 − 29__26
12
COMMENTS & EXTENSIONS: The largest fraction, in general,
should have the biggest numerator and the smallest denominator.
Zero is not allowed as a denominator. Challenge students to
come up with the smallest fraction.
© ETA hand2mind™
Add and Subtract Fractions
■
Lesson 4
2
4__
5
1
36__
2
3
6__
4
1
11__
3
1
11__
2
3
6__
5
13
3___
15
1
6__
6
1
6__
2
2
6__
3
1
6__
7
2
5__
3
Objective: Find the difference between two mixed numbers with
like denominators.
Hands-On Standards®, Common Core Fractions
Online resource available at hand2mind.com/hosfractionsgr5
7
VersaTiles student book, page 7
®
23
ETA hand2mind
Hands-On Standards, Common Core Fractions Grade 5
hand2mind.com
Introduce the Concept
Model the Activity
WHOLE CLASS
Distribute Fraction Tower Equivalency Cubes, Fraction
Number Lines (Number 3, the blank line), and dry erase
markers. Have students work along with you in small
groups as you model the lesson.
®
1 – 1__
1 =
Write 1__
2
• Fraction Tower Equivalency Cubes
®
common denominators.
• Fraction Number Lines (Number
3, the blank line)
■ Ask: What is a good common denominator? [6] Why?
3
How many sixths are in __
? [9]
2
9
__
Have students build a tower using teal fraction pieces
6
• dry erase markers
• squares of construction paper
• 11 x 17-inch paper, markers
and lay it on the blank Fraction Number Line to show
9
3
that __
equals __
. Have them trace the tower (using the dry
6
2
erase marker) and draw the sixths.
4
■ Say: Now let’s subtract __.
3
4
■ Ask: How many sixths are in __? [8]
3
Guided Practice
Lesson
Students can compare an 8-piece teal tower to the
4-piece orange tower to confirm. Have students cross out
8 of the sixths they drew on their number lines.
Answer Key
Name
Subtract Mixed Numbers
on the board.
■ Ask: How do you rename these mixed numbers as
fractions? [1__1 = __3, 1__1 = __4 ]
2 2 3 3
3
To model __
, build a tower using three pink fraction
2
4 , use four orange pieces.
pieces. To model __
3
3
Locate __
on the number line using the pink tower. Mark
2
3
1 , 1, and __
and label 0, __
.
2
2
3
4
■ Say: We need to subtract __ from __. It helps to have
3
2
Materials
4
3
Try This
■
Rename the mixed numbers as improper fractions.
■
Write the fractions and build models using Fraction Towers.
■
Find a common denominator. Use it to build a model of the first fraction.
■
Draw the model on the blank Fraction Number Line using a dry erase marker.
■
Subtract by crossing out fraction pieces on the drawing.
■
Sketch the drawing below and finish filling in the blanks.
1
■ Ask: What is the difference? [ __ ]
6
11
___
5 __
20 ___
2 __
12
1. 1__
– 3 = __
– 3 = ___
– 9 = _____
3 4
3 4
12 12
Guided Practice
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1
___
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
XXXXXXXXX
00
4
__
2.
8
__
1
__
3
__
22
1
__
6
1
__
6
1
__
6
5
__
®
1
1
__
__
X
X
X__16
6
6
1
__
6
0
0
4
__
3
1
1
8
__
3
__
16
___
15
___
2
2
3
3
2
2
3
3
15 2
___
8 2
33
1
___
3
1
5
2
10
10
10
– 1__
= _____
– _____
= _____
– _____
= _____
1__
5
2
XXXXXXXXXXXXXXX
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1
___
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
0
0
8
__
5
1
1
5
__
4
15
___
8
15
___
8
10
___
8
5
__
8
7
1
– 1__
= _____ – _____ = _____ – _____ = _____
4. 1__
4
8
1
__
8
1
__
8
1
__
8
1
__
8
1 __
1 __
1 __
1 __
1
__
X__18 X__18 X__18 X__18 X__18 X
8 X
8 X
8 X
8 X
8
00
11
Find the difference.
5
2___
2 __
12
6. 2__
– 1 = _____
3 4
1
__
5
1
8
5. 1__
– 1__
= _____
8
2
Add and Subtract Fractions
■
Lesson 4
© ETA hand2mind™
1
__
8
SMALL GROUPS
Prepare ahead Each small group will need two sets of
Fraction Tower Equivalency Cubes, a Fraction Number
Line (Number 3, the blank line), and a dry erase marker.
33
1 __
3
2
6
6
6
– 1 = _____
– _____
= _____
– _____
= _____
1__
3 2
1
__
6
3.
5
__
3
11
Students model subtraction with mixed numbers on the
blank Fraction Number Line. They rename the mixed
numbers as improper fractions and find a common
denominator. They model and draw the minuend
(renamed using the common denominator) on the
number line. Students find the difference by removing
(crossing out) the number of fraction pieces indicated
by the subtrahend.
1
__
1
1
1
6
7. 2__
– 1__
= _____
2
3
Hands-On Standards®, Common Core Fractions
Online resource available at hand2mind.com/hosfractionsgr5
24
ETA hand2mind
Hands-On Standards, Common Core Fractions Grade 5
hand2mind.com
Add and Subtract Fractions
Reinforce the Concept
Check for Understanding
WHOLE CLASS
Remediation
■ Ask: What if the number you’re subtracting is just a
fraction less than 1, not a mixed number? Does that
change the way you do the problem? If so, how?
[Sample: It doesn’t change the way I do the problem.
The only difference is I don’t need to rename the number
except to write it with a common denominator,
if necessary.]
Summarize
Use this page to give students additional
concrete-to-abstract practice.
Lesson
4
3
___
18 ___
4
1
9 __
10
– 1__
= __
– 3 = ___
– 15 = _______
1. 1__
5
5 2
2
10 10
1
__
5
1
__
5
1
__
5
1
__
5
1
__
5
1
__
5
1
__
5
1
__
5
1
WHOLE CLASS
1
__
5
1
__
5
1
__
5
1
__
5
1
__
5
1
__
2
1
■ Ask: How is subtracting with mixed numbers the same
1
__
2
as subtracting with fractions? [Sample: Both involve
subtracting fractional parts.]
Review with students what they did in the activity. Have
them describe in writing what they know about subtracting
with mixed numbers.
Answer Key
Name
Subtract Mixed Numbers
Use Fraction Towers and the blank Fraction Number Line
to build the model. Write the difference.
1
__
2
1
__
2
XXXXXXXXXXXXXXX
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1
___
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
0
9
__
5
1
2
3
Use Fraction Towers and the blank Fraction Number Line to
model the difference. Sketch the final step, when you subtract
using a common denominator. Fill in the blanks.
5
__
3
__
10
___
9
__
1
__
2
1
3
2
6
6
6
– 1__
= _______
– _______
= _______
– _______
= _______
2. 1__
3
2
1
__
6
0
3.
X X X X X X X X X
1
__
6
1
__
6
1
__
6
1
__
6
1
__
6
0
1
__
6
1
__
6
1
__
6
1
__
6
5
__
3
11
5
__
15
___
2
__
8
___
2 2
3
3
3
3
3
3
7
___
1 __
4
3
12
12
12
1__
– 2 = _______
– _______
= _______
– _______
= _______
4 3
XXXXXXXX
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1 ___
1
___
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
Independent Practice
0
4.
5
__
4
11
13
___
5
__
2 2
13
___
10
___
3
__
5
1
8
4
8
8
8
1__
– 1__
= _______
– _______
= _______
– _______
= _______
4
8
1
__
8
0
1
__
8
1
__
8
XXXXXXXXXX
1
__
8
1
__
8
1
__
8
1
__
8
0
1
__
8
1
__
8
1
__
8
1
__
8
1
__
8
1
__
8
13
___
8
11
2 2
© ETA hand2mind™
Use this VersaTiles activity to give students more
practice with the skills they learned in the lesson.
®
0
Find the difference.
Name Changes
1
__
1
___
2
1 __
12
6. 2__
– 1 = _______
3 4
3
1
8
5. 1__
– 1__
= _______
2
8
Add and Subtract Fractions
■
Lesson 4
5
__
1
2
6
7. 2__
– 1__
= _______
2
3
Hands-On Standards®, Common Core Fractions
Subtract.
6
1
− 1__
4__
2
8
• Write the fractions using the least common denominator.
6
4
− 1__
4__
8
8
• Regroup, as needed, to subtract the fractions.
4
12
= 3___
4__
8
8
• Subtract the fractions, then the whole numbers.
6
6
12
− 1__
= 2__
3___
8
8
8
• Simplify, if possible.
6
3
= 2__
2__
4
8
6
3
1
− 1__
= 2__
.
So, 4__
4
2
8
Online resource available at hand2mind.com/hosfractionsgr5
Enrichment
TM
Subtract.
1 9__25 − 6__35
2 7__13 − 2__23
3 12__15 − 7__23
4 11__38 − 8__56
5 9 − 5__67
6 13__19 − 10__23
7 8__18 − 7__34
8 16__29 − 7__13
9 12__25 − 9__18
10 6 − 2__56
11 5__14 − 4__23
12 7__16 − 1__14
This hands-on strategy
game combines
skill-building fractions
practice with tactical
game play.
13
2___
24
1
3__
6
8
4___
15
11
3___
40
11
5___
12
2
4__
3
3
__
8
4
2__
5
1
3__
7
7
___
12
4
2__
9
8
8__
9
Fractions Pack
Add and Subtract Unlike Fractions
Subtract Unlike Mixed Numbers
8
Objective: Find the difference between two mixed numbers with like and
unlike denominators.
hand2mind.com/versamate
VersaTiles student book, page 8
®
25
ETA hand2mind
Hands-On Standards, Common Core Fractions Grade 5
hand2mind.com