DATE
NAME
Parts and Wholes
1.
P
In a tangram …
M
• 2 small triangles (S) cover a medium triangle (M)
L
What fraction of each shape is covered by a single small triangle?
S
• 2 small triangles (S) cover a square (SQ)
SQ
• 2 small triangles (S) cover a parallelogram (P)
S
L
• 4 small triangles (S) cover a large triangle (L)
a)
d) b)
c)
e)
f )
2. What fraction of the shape is shaded? Explain how you know.
a)
b)
c)
d)
3. What fraction of the trapezoid is covered by a single small triangle?
Show your work.
4. If
a)
F-76
= red and
= blue, approximately what fraction of each flag is shaded red? Explain.
b)
c)
d)
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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NAME
DATE
Fraction Strips
2
3
4
6
1
2
3
6
3
4
6
8
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3
5
6
10
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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DATE
NAME
Investigating Mixed Numbers and Improper Fractions (1)
NOTE: The blocks shown here are not actual size! hexagon
triangle
rhombus
trapezoid
Euclid’s bakery sells hexagonal pies. They sell pieces shaped like triangles,
rhombuses, and trapezoids.
1. a) Shade 2 5 pies. 6
b) How many pieces did you shade? c) Write an improper fraction from the amount of pie shade.
2. M
ake a model of the pies below with pattern blocks. (Place the smaller shapes on
top of the hexagons). Then write a mixed number and improper fraction for each
group of pies.
a)
b)
c)
Mixed Number: Mixed Number:
Mixed Number:
Improper Fraction: Improper Fraction:
Improper Fraction:
3. U
se the hexagon as the whole pie. Use the triangles, rhombuses, and trapezoids as
the pieces. Make a pattern block model of the fractions below. Then sketch your
models on the grid.
a) 2 1 b) 1 1 1
6
d) 1 2 c) 2
2
3
e) 3 f )11 g) 5 h)10 2
3
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6
3
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2
DATE
NAME
Investigating Mixed Numbers and Improper Fractions (2)
4.
Using the trapezoid as the whole pie, and triangles as the pieces, make a pattern
block model of the fractions. Sketch your models on the grid. The first one is done for
you.
a) 5 b) 7 c) 1 2 d) 2 1 3
3
3
3
Draw sketches (using the hexagon as the whole) to answer the questions.
5. Which fraction is greater: 1 5 or 9 ?
6
6
6. Which fraction is greater: 2 1 or 14 ?
6
6
9. How much larger than a whole is 4 ?
10. Crystal ate 2 of a pie each day for 4 days in a 3
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6
8. How much larger than a whole pie is 7 of a pie?
7. Draw a picture to show 3 − 1 .
6
11.Ahmed ate 1 1 pies during the week.
12.Alice ate 3 2 pies in January.
3
Jill ate 1 of a pie each day for a week.
Who ate more pie?
3
row. How much did she eat altogether?
3
6
How many third-sized pieces did she eat?
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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DATE
NAME
Pattern Blocks
Triangles
Squares
Rhombuses
Trapezoids
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Hexagons
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DATE
NAME
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Equivalent Fractions Memory (1)
1
2
3
5
1
3
2
4
6
10
3
9
1
4
3
7
2
5
3
12
6
14
6
15
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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DATE
NAME
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2
3
3
4
3
8
8
12
9
12
6
16
5
8
7
8
4
5
10
16
21
32
16
20
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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Equivalent Fractions Memory (2)
DATE
NAME
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Equivalent Fractions Memory (3)
7
9
5
6
6
7
56
72
45
54
36
42
4
9
5
11
7
12
28
63
55
121
63
108
Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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DATE
NAME
Organized Lists
Many problems in mathematics and science have more than one solution.
Some problems involve two quantities. To make sure you don’t miss any possible
solutions, list the values of one of the quantities in increasing order.
1. Fill in the number of pennies, nickels, dimes, or quarters you need to make each amount.
a) Make 17¢
b) Make 45¢
c) Make 23¢
dimes
pennies nickels
0
0
0
1
1
1
2
2
2
3
3
3
4
4
d) Make 32¢
pennies nickels
dimes
e) Make 65¢
quarters
pennies 0
0
1
1
2
2
pennies
f ) Make 85¢
pennies quarters
pennies
3
2.
Ben wants to find all the ways he can make 60¢ using quarters
and nickels. He lists the number of quarters in increasing order.
Why did he stop at 2 quarters?
quarters
nickels
0
1
2
a) 90¢ using dimes and nickels
b) 25¢ using quarters and dimes
4.
Alicia wants to find all the ways she can make 70¢ using quarters
and dimes. Which entry in her chart won’t work? Put an “ ” in the
“dimes” column for that row.
quarters
dimes
0
1
2
5.
Make a chart to show all the ways to make 85¢ using quarters and dimes.
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Blackline Master — Number and Operations—Fractions — Teacher’s Guide for AP Book 5.1
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3.
Make a chart to show all the ways you can make the given amount.
DATE
NAME
Always, Sometimes, or Never True (Numbers)
A
B
If you multiply a three-digit number
by a one-digit number, the answer
will be a three-digit number.
If you subtract a three-digit
number from 999 you will not
have to regroup.
The product of two numbers
is greater than the sum.
D
E
F
If you divide a number by itself
the answer will be 1.
The product of 0 and
a number is 0.
Mixed numbers are larger
than improper fractions.
G
H
I
The product of two even
numbers is an even number
The product of two odd numbers
is an odd number.
When you divide an even number
by 4, the remainder is 0.
J
K
L
When you round to the nearest
thousands place, only the
thousands digit changes.
When you divide, the remainder
is less than the number you
are dividing by.
To multiply a fraction by a whole
number, you multiply the numerator
and denominator by the number.
M
N
Five times a number
is even.
Improper fractions are
greater than 1.
C
O
If you have two fractions, the one
with the smaller denominator is
the larger fraction.
1. C
hoose a statement from the chart above and say whether it is always true,
sometimes true, or never true. Give reasons for your answer.
What statement did you choose? Statement Letter
This statement is…
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Always True
Sometimes True
Never True
Explain:
2. Choose a statement that is sometimes true, and reword it so that it is always true.
What statement did you choose? Statement Letter
Your reworded statement:
3. Repeat Questions 1 and 2 with different statements.
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