Lesson 6.1
Enrich
Name
A Fraction Strip Above
the Rest
Use fraction strips to find the sum. Add the fractions and answer
the following questions.
1
1
3
1
3
1
1
4
1
4
1
4
1
2
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1.
What fraction represents each fraction
strip on the bottom row?
4.
What fraction represents each fraction
strip on the bottom row?
2.
Write the total amount shown by the
fraction strips on the bottom row.
5.
Write the total amount shown by the
fraction strips on the bottom row.
3.
Write the equation shown by the
fraction strips in the second row.
6.
Write the equation shown by the
fraction strips in the second row.
7.
If you add another 1_4 to the second row of the model
on the left, could you find the sum using the fraction strips in the second row?
8.
Stretch Your Thinking If you add another 1_8 to the second row of the model
on the right, how would your equation and answer change?
Enrich
© Houghton Mifflin Harcourt Publishing Company
E50
Grade 5
Lesson 6.2
Enrich
Name
Fraction Strip Subtraction
Find the difference between the fraction shown by the strips in
the first column and each of the three fractions shown by the
strips in the second column. Write each difference in simplest form
in the third column.
1.
–
1
4
1
4
1
4
1
3
2.
–
1
6
1
6
1
6
1
6
3.
–
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
4. Stretch Your Thinking
5
5
1
4
1
2
5
1
3
5
5
1
4
1
2
–
–
5
1
8
–
–
5
1
2
–
– 1
8
1
6
1
3
1
4
5
1
4
1
4
Label the fraction strips to complete the equation.
1
__
5 10
2
Enrich
© Houghton Mifflin Harcourt Publishing Company
5
E51
Grade 5
Lesson 6.3
Enrich
Name
Estimation Comes Full Circle
Estimate each sum or difference. Write your answers in the circle
connected to each expression.
2.
1.
11
___
12
5
__
6
1
2__
4
7
1__
8
3
1__
7
1
1__
6
8
2___
10
4.
3.
3
___
8
__
9
1
1__
7
5.
1
1__
5
5
2__
6
10
2
2__
5
2
2__
9
Think About It! Change the
6.
fractions in Exercise 2 so that all three
answers have the same estimate.
Enrich
© Houghton Mifflin Harcourt Publishing Company
3
1__
6
8
1__
9
Stretch Your Thinking Use two
fractions to write an expression with an
estimated sum of 2.
E52
Grade 5
Lesson 6.4
Enrich
Name
A Great Year
Find the number that is given as a product of its prime factors.
Write the letter that matches the number. The letters will spell
out the answer to the riddle
Why was the fifth grader looking forward to being eleven years old?
_
2323233
_
23337
_
3 3 13
_
33333
_
23535
_
23335
_
33335
_
2 3 23
_
23235
_
23232
_
232323232
_
2323333
_
33335
_
232323233
_
2 3 2 3 11
_
33335
_
23333
_
2323232
_
23337
_
33335
_
33335
_
23237
_
23335
_
23235
_
2323235
_
23237
a. 28
b. 18
d. 36
e. 45
h. 27
i. 20
k. 48
l. 8
m. 32
n. 44
o. 50
p. 39
r. 30
s. 24
t. 40
u. 46
w. 42
y. 16
Enrich
© Houghton Mifflin Harcourt Publishing Company
E53
Grade 5
Lesson 6.5
Enrich
Name
Find the Denominators
Find each pair of denominators.
1.
The least common denominator of
two fractions is 12. If you add the two
denominators, their sum is 7. What are
the denominators?
2.
The least common denominator of
two fractions is 24. If you add the two
denominators, their sum is 14. What are
the denominators?
3.
The least common denominator of
two fractions is 30. If you add the two
denominators, their sum is 17. What
are the denominators?
4.
The least common denominator of two
fractions is 20. If you subtract the two
denominators, their difference is 1. What
are the denominators?
5.
The least common denominator of two
fractions is 100. If you subtract the
two denominators, their difference is 5.
What are the denominators?
6.
The least common denominator of two
fractions is 28. If you subtract the two
denominators, their difference is 10.
What are the denominators?
7.
Explain in writing how you found the answer to Exercise 2.
Enrich
© Houghton Mifflin Harcourt Publishing Company
E54
Grade 5
Lesson 6.6
Enrich
Name
Let’s Make a Fraction
Use the conversion chart below to replace each letter with a fraction.
Find a common denominator and solve. Show your work. Write your
answer in simplest form. The first one is done for you.
Fraction Conversion Chart
a
_1_
b
_2_
c
_3_
d
_4_
e
_2_
f
_5_
g
_1_
h
_2_
i
_5_
j
_1_
k
_5_
l
_7_
m
_4_
n
_8_
o
2
6
8
3
6
8
4
7
9
a1c5
1.
2.
b1h5
5
7
9
5
8
3
10
113
_
_52
_13
_55
_ 5 11
_
2 4 4 4 4
4
3.
d2a5
4.
n2b5
5.
e1o5
6.
l2c5
7.
m1g5
8.
d2o5
9.
Think About It! Add the answer for Exercise 7 to the answer for
Exercise 8. What is the sum? Write your answer in simplest form.
10.
Stretch Your Thinking Find h 1 m. Subtract i from the sum. What is your answer?
Enrich
© Houghton Mifflin Harcourt Publishing Company
E55
Grade 5
Lesson 6.7
Enrich
Name
Mixed Number Sums and
Differences
Write equivalent fractions and then find the sum or difference. Write
the answer in simplest form. Write the letter of the exercise above its
sum or difference at the bottom of the page to answer the riddle. Two
have been done for you.
A.
15
1 1 2__
1__
3
4 ________________
E.
1
_
25
9 2 3__
2
5___
2
10
5 ________________
E.
15
5 2 7__
8__
8
2 ________________
N.
15
3 2 3__
4__
4
4 ________________
O.
75
3 1 1__
1__
4
8 ________________
R.
7 5
1 1 1___
2__
6
12 ________________
R.
1
_
4 5
9 1 1___
3
1___
6
10
15 ________________
S.
35
5 2 4__
6__
6
8 ________________
U.
45
5 2 6__
8__
6
9 ________________
V.
15
1 2 6__
7__
2
5 ________________
X.
85
1 1 1__
1__
6
9 ________________
What do you call a scared dinosaur?
7
3___
12
E
1
1__
2
__
21
2
R
__
33
4
Enrich
© Houghton Mifflin Harcourt Publishing Company
3
1___
10
__
35
8
7
2___
18
___
211
24
E56
__
31
6
__
11
8
1
3___
18
Grade 5
Lesson 6.8
Enrich
Name
Star Ray Differences
Start in the center of the star. Subtract the fraction or mixed number
along the arrows to find the five answers in simplest form.
1.
67
8
31
2
5.
2.
83
8
1
15
16
25
6
Start
24 3
4
43
5
4.
1.
6.
5
3. 9 1
3
3.
4.
Stretch Your Thinking Order the
7.
answers from least to greatest.
Enrich
© Houghton Mifflin Harcourt Publishing Company
2
3
7
9
1
10
2.
7
E57
5.
Explain how you found
the answer to Exercise 6.
Grade 5
Lesson 6.9
Enrich
Name
Fractions Rule
For each sequence, the first term and one more term are given.
Find a possible rule for the sequence.
1.
3
First term: 2_
2.
4
7
Sixth term: 3__
4
Eighth term: 5_
Possible rule:
Possible rule:
12
3.
5
1
First term: 3_
4.
9
12
Sixth term: 5_
Possible rule:
Possible rule:
1
3
3
First term: 2_
6.
4
1
First term: 7_
3
1
Eighth term: 12__
Seventh term: _
Possible rule:
Possible rule:
1
3
12
7.
7
First term: 6__
1
Seventh term: 7_
9
5.
First term: 10
Explain in writing how you found the answer to Exercise 1.
Enrich
© Houghton Mifflin Harcourt Publishing Company
E58
Grade 5
Lesson 6.10
Enrich
Name
The Path of Least Resistance
Always choose the path with the least value. Do not retrace
any parts of the path. What shapes are on this path?
2
7
11
⫹3
10
20
10
1
5
⫺6
3
9
12
1
7
⫺3
2
10
5
7
1
⫹3
8
4
3
Start
3
11
5
⫹4
12
6
1
2
⫹1
6
3
© Houghton Mifflin Harcourt Publishing Company
1
3
⫹1
4
8
2
7
⫺2
5
20
Which shape contains the greatest
value? What is that value?
Enrich
1
7
⫺2 8
2
4
3
⫹4
5
4
5
9
1.
1
1
⫹2
4
8
6
1
4
4 ⫹7
12
5
9
1
2.
Stretch Your Thinking Use the
second lowest value as your first choice.
Then use lowest values the rest of the
way. What shapes are on the new path?
E59
Grade 5
Lesson 6.11
Enrich
Name
Which Property?
Use the properties and mental math to solve. Find each
unknown number.
1.
__
5 13
_7__8 1 __43+ 1 ___
8
4
2.
____
3.
_34__5 1
____
+
5
1 5 115
__ 1 5__
__
6
5
6
4.
____
5.
4
3 5 1__
1 __
_5__8 1 ___
7+ 8
7
_
+
2
7 1 42
3 5 14__
___
__ 1 2___
10
3
10
3
____
1 1 9__
_52__3 1 8 ___
+ 31 5 23__61
6.
____
3 1 6___
7 1 10 ___
_8___
+ 125 5 25__43
12
____
7.
Tell how you can use the properties and mental
math to find the unknown number in Exercise 1.
8.
Stretch Your Thinking How does using properties help
you find unknown numbers mentally in these exercises?
Enrich
© Houghton Mifflin Harcourt Publishing Company
E60
Grade 5