TEXAS
SAMPLE PAGES
SENIOR AUTHORS
James Burnett
Calvin Irons
PROGRAM CONSULTANTS
Diana Lambdin
Frank Lester, Jr.
Kit Norris
contributing authors
Debi DePaul
Beth Lewis
Peter Stowasser
Allan Turton
STUDENT JOURNAL
1
3.
Step In
Identifying Prime and Composite Numbers
Color an array to represent each of these numbers.
19
5
23
What do you notice?
A prime number is any whole number
greater than zero that has exactly two
unique factors – itself and 1.
PL
E
What are some other prime numbers that you know?
What are some composite numbers that you know?
M
How could you prove that a number is composite?
A composite number is a whole
number that has more than two
whole number factors.
SA
A composite number can be represented by an
array that has more than one equal row.
Step Up
13
1.Color all the composite numbers.
Then color a matching array to prove that each number is composite.
9
16
© ORIGO Education.
2
25
56
230915
ORIGO Stepping Stones Texas • Grade 5
3.
1
2. Look at this chart.
a.Loop the number 2. Draw a \ through all
the multiples of 2. What do you notice?
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
PL
E
b.Loop the number 3. Draw a / through all
the multiples of 3. What do you notice?
1
SA
M
c.Find the multiples of 6. What do you notice?
d.Loop the number 5.
Cross out all the multiples of 5.
e.Loop the number 7.
Cross out all the multiples of 7.
© ORIGO Education.
f.Choose three numbers that have not been
crossed out. What are their factors?
a
Step
Ahead
Write two prime numbers
greater than 120.
ORIGO Stepping Stones Texas • Grade 5
230915
57
3.
2
Step In
Reviewing Multiplication Strategies
Think about some of the different situations in which you use multiplication.
Multiplication is often used to
figure out the cost of purchases.
Imagine you have to buy carpet for this floor area.
Look at how these students figured out the
area to be covered.
PL
E
12 yd
Anna used partial products.
10 × 25 + 2 × 25
25 yd
Nancy used a
doubling-and-halving strategy.
M
12 × 25 is the same as 6 × 50
David used factors.
12 × 25 is the same as (3 × 4) × 25
and (3 × 4) × 25 is the same as 3 × (4 × 25)
Is there another way you could figure it out? Which way do you like best? Why?
SA
Use a strategy you like to calculate the area of a rectangle measuring 15 cm × 24 cm.
Step Up
Read these strategies for mentally calculating 36 × 50.
I multiplied 36 by 10. Then
I multiplied my answer by 5
because 50 is 5 x 10.
58
230915
© ORIGO Education.
I multiplied 36 by 100. Then
I halved my answer because
50 is one-half of 100.
ORIGO Stepping Stones Texas • Grade 5
3.
2
1. Use a method you like to calculate these.
a. 16 × 50 =
b. 24 × 50 =
c. 25 × 50 =
d. 27 × 50 =
e. 34 × 50 =
f.
PL
E
31 × 50 =
M
2. Write how you could use the double-and-halve method to figure out 32 × 25.
3. Use the double-and-halve method to mentally calculate these.
b. 16 × 25 =
c. 28 × 25 =
SA
a. 24 × 25 =
Step Ahead
Write the missing numbers in each machine.
a. IN
OUT
12
© ORIGO Education.
20
OUT
18
× 45
18
ORIGO Stepping Stones Texas • Grade 5
230915
b. IN
15
× 60
25
59
3.
3
Step In
Estimating to Solve Problems Involving Multiplication
A coach is buying 12 of these shirts for his team.
He has $400 to spend.
$29
Does he have enough money to buy the shirts?
How could you estimate the total cost?
I would round the price of
one shirt to 30 first to
make the estimation easier.
PL
E
Two friends shared their strategies.
Diana used her understanding
of place value.
Ashley used doubling and halving.
12 × 30
is the same as
6 × 60
12 × 3 is 36
so
12 × 30 is 360
M
Can you think of another way to make an estimate?
How could you estimate the total cost of 15 caps?
$11.98
SA
How did you round the amount to make your estimate?
What strategy did you use to carry out the calculation?
1.Estimate the total cost. Use rounding to make the calculation easier.
Show your thinking.
a. Buy 25.
$39
Estimate $
60
230915
b. Buy 15.
Baseball Ticket
$28
Estimate $
ORIGO Stepping Stones Texas • Grade 5
© ORIGO Education.
Step Up
3.
3
2. Estimate the total cost. Use rounding to make the calculation easier. Show your thinking.
a. Buy 20.
$11.95
b. Buy 16.
Estimate $
$25.12
Estimate $
PL
E
3. Use estimation to solve each problem. Show your thinking.
b.
A pet store has 25 fish tanks. 12 tanks
each hold 26 fish and 13 tanks each
hold 9 fish. About how many fish are
there in total?
SA
M
a. A farmer is planting a field of lettuce.
There are 45 rows which can each fit
68 plants. About how many seedlings
will the farmer need to buy?
seedlings
Step Ahead
fish
Awan has $20. Estimate the number of each item he could buy.
Popcorn
Soda
Meal Deal
Ice Cream
Popcorn
Soda
Meal Deal
$3.95
$4.98
$3.50
$6.95
© ORIGO Education.
Ice Cream
ORIGO Stepping Stones Texas • Grade 5
230915
61
3.
4
Step In
Using the Standard Algorithm to Multiply
Three- and Two-Digit Numbers
A ferry seats 132 people. It makes 24 trips each day.
100
Does the ferry carry more or less
than 2,500 people each day?
How could you figure out the exact number?
30
PL
E
Hugo drew this diagram to figure out the exact number.
How will it help him?
Write the partial products inside each part of the diagram.
2
Nicole used the standard multiplication algorithm to calculate the total.
How did she calculate the number in the first row?
What does the red digit in the hundreds place represent?
20
1
1
M
×
5
What numbers should she write in the second row?
Write numbers to show your thinking. Then write the total.
4
3
2
2
4
2
8
SA
What is the total number of passengers that could travel
on the ferry each day?
Step Up
1.Write the partial product inside each part
of the diagram below.
Then add these to calculate the area.
32 × 145 =
30
2
40
5
© ORIGO Education.
100
62
230915
ORIGO Stepping Stones Texas • Grade 5
3.
4
2.
Use the standard multiplication algorithm to calculate the exact product.
Then estimate the product to check that your answer makes sense.
1
×
d.
1
2
2
1
7
3
3
2
6
×
7
5
4
2
c.
2
×
e.
3
×
2
9
5
4
f.
2
×
1
4
4
2
0
8
7
3
SA
M
×
4
b.
PL
E
a.
1
1
×
1
2
4
6
1
4
1
5
8
4
1
4
6
7
3
0
© ORIGO Education.
Step Ahead
Look at this calculation.
Describe the mistake in words.
ORIGO Stepping Stones Texas • Grade 5
230915
63
3.
5
Step In
Extending the Standard Multiplication Algorithm
The local park is rectangular and measures 134 yd by 232 yd.
How could you figure out the area of the park?
Akeema drew this diagram of a rectangle split
into parts to make it easier to multiply.
100
Write the partial product inside
each part of her diagram.
30
Add the partial products and write
the area of the park below.
4
30
PL
E
200
yd2
Area is
1
2 6 8
1 4 0 2 0
2 6 8 0 0
1
M
Look carefully at the first and third row of his calculations.
What do you notice?
Why is the product in the third row 100 times greater than
the product in the first row?
3 1 0 8 8
1.Write the partial product inside each part of the diagram below.
Then add these to calculate the area.
SA
100
1
1 3 4
× 2 3 2
Toby used the standard multiplication algorithm to calculate
the area. What steps did he follow?
Step Up
2
153 × 328 =
50
3
20
8
© ORIGO Education.
300
64
230915
ORIGO Stepping Stones Texas • Grade 5
3.
5
2.
Use the standard multiplication algorithm to calculate the exact product.
Then estimate the product to check that your answer makes sense.
1
3
4
2
1
2
0
4
2
3
2
1
×
d.
1
×
5
8
7
4
2
0
c.
×
e.
×
4
2
7
2
0
5
f.
3
×
1
6
1
2
5
1
5
2
6
2
3
5
SA
M
×
b.
PL
E
a.
Step Ahead
© ORIGO Education.
a.
Color the
127 × 53
7,325 × 49
c.
308 × 426
d.
6,097 × 720
600
35,000
12,000
42,000
6,000
13,500
120,000
4,200,000
60,000
350,000
1,200
420,000
600,000
280,000
13,000
460,000
ORIGO Stepping Stones Texas • Grade 5
230915
b.
beside the estimate that you think is closest to the exact product.
65
6
3.
Step In
Solving Word Problems Involving Multiplication
(Large Numbers)
This table shows the payments that players received after each game
and the number of games that they played.
How much did Player A earn this season?
Player
Payment
Games Played
A
$4,350
4
B
$1,025
5
C
$895
11
D
$12,352
32
PL
E
What number sentence would you write to show the problem?
I would use the letter T
for the unknown total.
T = $4,350 � 4
How could you calculate the total amount?
Fatima used the standard
algorithm to multiply like this.
1
M
×
2
4 3 5 0
4
Jude used a doubling strategy.
1 7 4 0 0
Double 4,350 = 8,700
Double 8,700 = 17,400
SA
How would you figure out the total amount that Player B received?
1.Look at the table above. Using the letter T for the unknown amount, complete
a number sentence to show how to calculate the total amount paid to each of
these players. Then figure out the total. Show your thinking.
Player C
T=
T=
$
66
230915
Player D
$
ORIGO Stepping Stones Texas • Grade 5
© ORIGO Education.
Step Up
3.
6
2. Solve these word problems. Show your thinking.
$
b. It costs $7,320 to use the stadium for
each game. What is the total cost to
use the stadium for 41 games?
PL
E
a. It costs $795 to replace a backboard.
12 backboards were replaced in one season.
What is the total cost of replacing them?
$
d. Membership costs $245 for adults and
$125 for children. There are 4,043 adult
members. How much money has the club
made from adult membership?
SA
M
c. There are 28 seats in each row. There are
42 rows. 2 seats in each row are reserved.
What is the total number of seats available?
© ORIGO Education.
Step Ahead
$
Color the
beside the number sentence that shows how
to calculate the unknown total (T) in the following problem.
Player E is paid $12,499 for each game played and a bonus of $10,000 for a season win.
Player E participated in 42 games. His team won the season.
What is the total amount Player E received?
T = 42 × $12,499 − $10,000
ORIGO Stepping Stones Texas • Grade 5
230915
seats
T = $12,499 + $10,000 × 42
T = $12,499 × 42 + $10,000
67
7
3.
Step In
Exploring Volume
Place base-10 ones blocks on this base picture so it is six layers high.
How can you figure out how many ones blocks you used?
Complete this table to help you. What do you notice?
Number of Layers
Total Number
of Cubes
4
1
4
4
2
8
4
3
4
PL
E
Number of
Cubes in Base
The total number of
cubes tells you the
volume of the object.
4
M
4
How could you quickly figure out the total number
of cubes in any object?
Volume is the amount of space
that an object occupies.
SA
What do you need to know?
a.
68
230915
1. P
lace base-10 ones blocks on this base picture. Build up the number
of layers to match the data in the table. Then complete the table.
Number of
Cubes in Base
Number of Layers
Total Number
of Cubes
6
1
6
6
2
12
6
3
6
4
© ORIGO Education.
Step Up
ORIGO Stepping Stones Texas • Grade 5
3.
7
2. Complete these tables. You can use ones blocks to help.
a.
Number of
Cubes in Base
Number of Layers
5
1
Total Number
of Cubes
2
3
4
b.
Number of Layers
Total Number
of Cubes
PL
E
Number of
Cubes in Base
6
1
3
5
M
7
Number of
Cubes in Base
Number of Layers
7
2
SA
c.
Step Ahead
Total Number
of Cubes
4
6
8
1.Use 32 ones blocks to make an object that is the same on each layer.
Draw the base of your object.
2. Write the missing numbers.
© ORIGO Education.
a. Number of blocks in base
b. Number of layers
ORIGO Stepping Stones Texas • Grade 5
230915
69
3.
8
Step In
Analyzing Unit Cubes and Measuring Volume
Jerilene was storing these boxes in the garage.
How can she compare the amount of space
that each box will occupy?
Look at these objects.
Which object would you use to
measure the volume of each box?
How did you decide?
PL
E
To measure the space, she decides to fill each box with objects that are the same shape.
How will this help?
Jerilene chose to use centimeter cubes to find the volume of the jewelery box.
M
Does she need to fill the whole box with cubes?
What is an easier way to figure out the volume?
SA
Just find the number of cubes in one layer. Then find the number of layers.
70
230915
1.Use base-10 ones blocks to cover the area of this rectangle.
Then complete the table.
Dimensions of the Base
of the Prism (cm)
Number
of Layers
×
1
×
2
×
3
×
4
Total Number of
Centimeter Cubes
© ORIGO Education.
Step Up
ORIGO Stepping Stones Texas • Grade 5
3.
8
2. Use base-10 ones blocks to cover the area of this rectangle. Then complete the table.
Dimensions of the Base
of the Prism (cm)
Number
of Layers
×
1
×
2
×
3
×
5
Total Number of
Centimeter Cubes
3.
Complete each table to show the total number of centimeter cubes in each prism.
1
4×5
2
4×5
3
4×5
M
4×5
Dimensions of Number Total Number of
the Base (cm) of Layers Centimeter Cubes
PL
E
Dimensions of Number Total Number of
the Base (cm) of Layers Centimeter Cubes
5
8×3
1
8×3
2
8×3
4
8×3
5
SA
Write a rule to figure out the total number of cubes in a prism when you know the dimensions
4.
of the base and the number of layers. Use your answers in Question 3 to help.
Archie pours cubes into this container to figure out the volume. He counts
58 cubes. Do you think his calculation is accurate? Explain your thinking.
© ORIGO Education.
Step Ahead
ORIGO Stepping Stones Texas • Grade 5
230915
71
3.9
Step In
Developing a Formula to Calculate Volume
How can you figure out the volume of this prism without
counting each individual cube?
I know there are 8 cubes in the base.
There are 4 layers. 8 + 8 + 8 + 8 = 32.
Antonio multiplied the height of the prism
by the number of cubes in the base.
Height
4 layers
8 × 4 = 32 cubes
Volume is 32 cubes.
How are their methods similar?
Length
4 cubes
Height
4 cubes
4 × 2 × 4 = 32 cubes
Volume is 32 cubes.
What rule could you write to match each method?
Volume is usually measured in
cubic units. The abbreviation
for cubic centimeters is cm³.
M
Look at Kuma's method.
Does it matter in what order she multiplies the dimensions?
How do you know?
1.Imagine you built this prism with base-10 ones blocks.
SA
Step Up
Width
2 cubes
PL
E
Base
8 cubes
Kuma multiplied the dimensions.
a. Complete this table.
Length
(Blocks)
Width
(Blocks)
b. Write the volume of the prism.
Height
(Blocks)
Total Number
of Blocks
cm3
2. Here are the dimensions of another prism.
Length 8 cm
Height 5 cm
Write how you can calculate the volume without counting blocks.
© ORIGO Education.
Width 3 cm
72
230915
ORIGO Stepping Stones Texas • Grade 5
3.9
3. Use your rule from Question 2 to calculate the volume of these prisms.
Length (cm)
Width (cm)
Height (cm)
a.
5
4
3
b.
9
6
4
c.
7
5
5
d.
7
6
3
Volume (cm3)
4.Calculate the volume of each prism.
Then write an equation to show the order that you multiplied the dimensions.
b.
c.
M
PL
E
a.
SA
cm3
Step Ahead
cm3
cm3
This square-based pyramid has been built with base-10 ones blocks.
cm3
© ORIGO Education.
Calculate the volume of the pyramid.
ORIGO Stepping Stones Texas • Grade 5
230915
73
10
3.
Finding the Dimensions of Prisms
with a Given Volume
Step In
The volume of a box is 60 in³. Write some possible dimensions for the box.
×
×
= 60 in3
×
×
= 60 in3
×
×
= 60 in3
How did you figure out the dimensions?
What do you notice about each of the dimensions?
Each dimension is a factor of 60.
60 has a lot of factors.
How do you know?
Step Up
1.For each of these, draw and label the dimensions of a prism to match.
Then write the volume.
just less than 80 in3
b.
just more than 80 in3
in3
just less than 55 in3
d.
in3
74
230915
in3
just more than 55 in3
in3
ORIGO Stepping Stones Texas • Grade 5
© ORIGO Education.
c.
SA
M
a.
PL
E
How many different prisms can you make from a number that is prime?
3.
10
2. Complete each table to show the dimensions of four different prisms that have the same volume.
a.
Length
c.
b.
Volume is 36 in3
Width
Height
d.
Volume is 100 in3
Height
Length
Height
Volume is 72 in3
Width
PL
E
Width
Width
Height
M
Length
Length
Volume is 64 in3
SA
3. Write the dimensions for another prism that has the same volume as 4 cm × 8 cm × 10 cm.
cm
Length
Step Ahead
Width
cm
Height
cm
Prism A is made with inch cubes. It is 4 cubes long, 5 cubes wide, and
2 cubes high. Prism B is made with centimeter cubes. It is 10 cubes long,
2 cubes wide, and 2 cubes high.
© ORIGO Education.
Which prism has the greater volume? Explain your thinking.
ORIGO Stepping Stones Texas • Grade 5
230915
75
11
3.
Step In
Working with Volume
The base of this prism has 6 sides.
It is called a hexagonal-based prism.
How could you calculate the volume of this prism?
PL
E
Andrea split the prism into two rectangular-based prisms.
How will breaking the prism into parts help her figure out the volume?
What number sentences would you write to match?
SA
M
Paul used a different strategy. He added more blocks to change
the hexagonal-based prism into a rectangular-based prism.
How could Paul's strategy help him figure out the volume of the prism?
What number sentences would you write to match?
1.Each of these small cubes is 1 cm³. Figure out the volume of the prism.
Write number sentences to show your thinking.
cm3
76
230915
ORIGO Stepping Stones Texas • Grade 5
© ORIGO Education.
Step Up
3.
11
2.These prisms are made with centimeter cubes. Figure out the volume of each prism.
Show your thinking.
a.
a.
a.
b.
a.
cm3
PL
E
c.
cm3
a.
e.
3 cm
SA
5 cm
M
d.
3 cm
cm3
9 cm
2 cm
5 cm
4 cm
3 cm
8 cm
cm3
cm3
ORIGO Stepping Stones Texas • Grade 5
230915
cm3
Some centimeter cubes have been removed from the middle of this prism.
Figure out the volume of the new object.
© ORIGO Education.
Step Ahead
3 cm
77
12
3.
Step In
Solving Word Problems Involving Volume
Emily is moving some household items into storage.
She decides to pack the items into boxes.
Boxes are sold in these three sizes.
What is the volume
of each box?
How do you know?
4 ft
3 ft
2 ft
Write the volume
on each box.
3 ft
2 ft
1 ft
1 ft
2 ft
Medium
Large
PL
E
Small
3 ft
Emily rents some storage space with the dimensions 10 ft × 10 ft × 8 ft.
What is the volume of the storage space?
She buys and fills 5 large boxes and 5 medium boxes.
How much space do the boxes occupy in storage?
M
How much storage space does she have left?
Think about the dimensions of the boxes and the dimensions of the storage space.
What size box would you use to fill the storage space? Why?
SA
The height of the storage space is 8 feet so there would
be some space left over if I used the medium boxes.
a.
1.Use the box sizes above. Figure out the total volume that each group of boxes
would occupy. Show your thinking.
b.
2 large boxes and 3 medium boxes
ft3
78
230915
3 large boxes, 2 medium boxes
and 6 small boxes
ft3
ORIGO Stepping Stones Texas • Grade 5
© ORIGO Education.
Step Up
3.
12
2. Use the box sizes shown on page 78 to solve these word problems. Show your thinking.
a. Helen buys and fills 4 boxes of each size.
What is the total volume of the boxes?
b. Jadyn has 5 medium boxes in the attic and
2 large boxes in the basement. Which
group of boxes has the greater volume?
PL
E
ft3
SA
M
c. Ricardo has a storage space that measures 9 ft × 9 ft × 9 ft. What is the greatest number
of medium boxes he can pack into this space?
Look at Question 2c above. After Ricardo packs the medium boxes into
storage, how much space will be left over?
© ORIGO Education.
Step Ahead
ft3
ORIGO Stepping Stones Texas • Grade 5
230915
medium boxes
79