Quick Check
Name
10-1A
1. Which fraction can be replaced with _12 when estimating with fractions?
2. Which fraction can be replaced with 0 when estimating with fractions?
A __
1 A __
15 8
__
B 2 9
C __
2 3
D ___
10 12
B __
3 4
C ___
8 20
D __
4 9
3. Which is the BEST estimate for 5
2
+ _ ?
the sum of __
5
12
4. Which is the BEST estimate for the difference of _ 78 − _ 49 ?
A 0 + 0 = 0
A 1 – 1 = 0
1 1 + 0 = __
B __
1 = 0
B __
1 – __
2
2
2
1 1 = __
C 1 – __
2
2
2
C 1 + 1 = 2
1 = 1
D __
1 + __
2
D 0 – 0 = 0
2
5. WritingtoExplain Keri says that you can replace a fraction with 0, _12 , or 1 by looking at the denominator first. If the numerator is half or close to half the value of the denominator, replace with _ 12 . If the numerator is closer to the value of the denominator, replace with 1. Is Keri correct? Use the number line and _ 58 as an example to help you explain your reasoning. 0
1
1
2
ART FILE:
1
10
1
6
TECH
44913_T07_049a
CUSTOMER: ScottForesman
CREATED BY:
lf
EDITED BY:
JOB NUMBER:
DATE:
created @ NETS
simple
blackline
10-8-08
DATE:
TIME:
REVISION:
11609
2 min
only altered @ NETS
Q 10•1A
mod.
greyscale
(place checkmark)
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
complex
v. complex
color
Par tner
Talk
Sh
Get Started
or
Choose a tile. Look at the fraction next to that tile number.
Decide if the fraction is less than 12 , equal to 12 , or greater than 12 .
Explain your thinking. Stack the tile in the space below your answer.
Display each 0–9 tile exactly once. If you have a partner, take turns.
0
3
5
1
4
8
2
7
12
3
5
10
4
2
3
5
7
16
6
5
11
7
8
15
8
3
6
9
5
12
The fraction The fraction The fraction is less is equal is greater than 1 .
2
If you have
more time
k.
are
wor
your t
hinking while you
to 1 .
2
than 1 .
2
Make up another fraction puzzle like this one.
Ask your partner to stack the number tiles for the fractions in your puzzle.
Center Activity H 10-1A
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
Par tner
Talk
Sh
Get Started
or
k.
are
wor
your t
hinking while you
Choose a tile. Read the addends next to that tile number.
Decide if each addend is closer to 0, 12 , or 1. Estimate.
Decide if the estimate is less than one, equal to one,
or greater than one. Stack the tile in the space below your answer.
Display each 0–9 tile exactly once. If you have a partner, take turns.
0
3
1
+
5 8
1
4
2
+
3 5
2
1
3
+
4 4
3
3
5
+ 6
8
4
3
4
+
8 7
5
1
2
+
12 5
6
5
3
+
8 8
7
9
6
+
10 7
8
2
4
+
3
5
9
3
4
+
7 9
The estimate is less than one.
If you have
more time
The estimate is equal to one.
The estimate is greater than one.
Make up another fraction puzzle like this one.
Ask a partner to stack the number tiles for the addends in your puzzle.
Center Activity HH 10-1A
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
Reteaching
Name
10-1A
Estimating Sums and
Differences of Fractions
To estimate the sum or difference of two fractions, replace each
fraction with the nearest half or whole. You can use a number line
to check whether each fraction is closest to 0, _12, or 1. Estimate
3
9
+ ___
.
the sum of __
8
16
Step 1: Find _38 on the number line. Is _38 closer to 0 or _12 ?
3
8
0
1
1
2
9
9
Step 2: Find __
on the number line. Is __
closer to _12 or to 1?
16
16
9
16
0
1
1
2
1 + __
1 = 1.
__
FILE: 44913_T07_050a
Step 3: Add to find theART
estimate.
1
10
2
2
ScottForesman
CUSTOMER:
JOB NUMBER:
lf
CREATED BY:
TECH
DATE:
11609
10-8-08
For 1 and 2, complete each
sentence to help DATE:
you replace each
EDITED BY:
fraction with the nearest half or whole. Use each
2 min line to help.
TIME:number
44913_T07_050b
ART
FILE:@ NETS
created
only altered @ NETSTECH
5
7 is between
___
and
but
2.
is between
and
1. __
1
11609
CUSTOMER: ScottForesman JOB NUMBER:
(place checkmark)
8
.
is closer to
lf
mod.
7EDITED BY:
__
rounds to
blackline
8
10-8-08
DATE:
complex
is closer
DATE:
greyscale
1
2
to
2 min
TIME:
created @ NETS
0
but
16
REVISION:
CREATED
BY:
simple
10
5
. ___
rounds to
v. complex
16
color
only altered @ NETS
0
1
REVISION:
simple
mod.
1
1
(place checkmark)
2
v. complex
complex
For 3 through 10, estimate each sum or difference by replacing
blackline
greyscale
color
each fraction with 0, _12, or 1.
3
2 + __
3. __
5
7 – __
4
4. __
4
8
ART FILE:
6
7 + ___
7. ___
15
10
1
10
1 + __
4
5. __
7
2
9
7 – __
4
6. ___
12
44913_T07_050c
CUSTOMER: ScottForesman
CREATED
2 – __
4 BY:
8. __
lf
3 8BY:
EDITED
1
11609
10
CUSTOMER: ScottForesman
CREATED
5BY:
7 – __
10. __
greyscale
complex
JOB N
DATE:
DATE:
TIME:
(place checkmark)
R 10•1A
lf
8 BY:
6
EDITED
only altered @ NETS
mod.
44913_T07_050d
2 min
REVISION:
blackline
ART FILE:
DATE:
2 + __
4 10-8-08
9. __
5
9
DATE:
TIME:
simple
TECH
JOB NUMBER:
created @ NETS
9
v. complex
color
created @ NETS
only a
REVISION:
simple
mod.
blackline
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
greyscale
com
Practice
Name
10-1A
Estimating Sums and
Differences of Fractions
In 1 through 8, tell if each fraction is closest to 0, _12, or 1. You may
use a number line to help.
1
1. __
5
2. __
11
3. ___
6
4. ___
6
5. __
7
5
6. ___
3
7. __
12
8. ___
9
9
20
12
10
4
15
In 9 through 16, estimate each sum or difference by replacing
each fraction with 0, _12, or 1.
4
7 + __
9. ___
5
12
1 – __
1
13. __
6
8
1 + __
2
10. ___
4 – __
1
11. __
6
8
2 + __
12. __
3
2 – __
14. __
5 7
7 – __
7
15. __
5
2
16. ___
+ __
5
12
12
4
9
8
17. Which is the best estimate for the
9
– _49 ?
difference of __
16
A 1–1=0
1 = __
1
C 1 – __
1 – __
1=0
B __
2 2
D 0–0=0
2
6
9
9
18. Which fraction can NOT be
replaced with _12 when estimating?
10
A ___
2
12
__
B 2
6
4
C ___
10
___
D 13
24
19. Mia estimated _58 + _19 by replacing _58 with 1 and _19 with 0. Her
estimated sum was 1 + 0 = 1. Explain why Mia’s estimate is
NOT accurate.
P 10•1A
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Enrichment
Name
10-1A
Mentally Fit
Find the value for n that makes the equation true.
5
n  + __
1 = __
__
3
2
6
Hint: Use what you know about solving equations and renaming
fractions using a common denominator.
Step 1: Use properties of equality to get
the fraction with the variable alone.
1 __
5 __
n  + __
__
– 1 = __
–1
2 2
3
6 2
Step 2: Rename the known fractions using __
5 __
n  = __
–3
3
6
6
a common denominator.
Step 3: Simplify.
n  = __
2
__
3
6
Step 4: Use mental math to complete the
equivalent fraction and find the value of n.
1 = __
2 , so n = 1.
__
3
6
Step 5: Check your solution.
5
1 + __
1 = __
Does __
?
3
2
3
5
2 + __
__
__
=
6
6
6
6
So, n = 1 is correct.
Find the value for n that makes each equation true.
Show each step of your solution process.
5
1 + __
n  = __
1. __
5
1 + __
n  = ___
2. ___
5
10
10
3
1  + __
11
3. __
= ___
n
4 – __
n  = ___
2
4. __
5
5
n  – __
1 = __
5. ___
6
2 + __
1  = ___
6. __
n
8
12
3
7 – __
n  = __
7. __
8
n  – __
1 = __
1
8. ___
6 __
1
1
__
9. __
n  – =
3
n  + __
n  = __
10. __
8
4
4
16
8
8
12
4
6
3
3
8
12
3
8
13
n  – __
4 = ___
11. __
8
9
2
8
15
3
4
10
1 + ___
n  = ___
12. __
72
6
E 10•1A
12
12
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