SAMPLE PAGES
SENIOR AUTHORS
PROGRAM CONSULTANTS
James Burnett
Diana Lambdin
Calvin Irons
Frank Lester, Jr.
Kit Norris
contributing authors
PROGRAM EDITORS
Peter Stowasser
James Burnett
Allan Turton
Beth Lewis
Donna Richards
Kevin Young
STUDENT JOURNAL
Exploring the Relative Position of Three-Digit Numbers
9.1
Where is 384 located on this number line? How do you know?
0
100
200
300
400
500
600
Which ten is closest? Which hundred is closest?
How do you know?
E
Where is 178 on the number line?
PL
How far away is 178 from the closest ten?
How far away is 178 from the closest hundred?
SA
M
Imagine you placed a ball on this special number line.
500
400
600
How could the ball help you decide which hundred is closest to 540?
Step Up
30
a.
b.
32
200
40
c.
36
50
d.
43
e.
47
49
ORIGO Stepping Stones 2 • 9.1
© ORIGO Education.
a.
1. For each number, write the ten that is closest.
2. For each number, write the hundred that is closest.
200
a.
300
b.
190
c.
240
400
d.
e.
320
360
380
3. Write how far away each number is from the nearest ten.
You can draw lines to help you.
60
64
E
b.
c.
68
80
d.
PL
a.
70
73
76
e.
79
SA
M
4. Write how far away each number is from the nearest hundred.
You can draw lines to help you.
600
a.
b.
615
Step Ahead
© ORIGO Education.
650
c.
630
655
700
d.
e.
680
690
Write two three-digit numbers that do not have a 0 or a 5.
Then complete the sentences. Use the number lines above to help.
a.
The distance to the nearest hundred is
.
b.
The distance to the nearest hundred is
.
ORIGO Stepping Stones 2 • 9.1
201
Estimating Answers (Adding within 100)
9.2
Imagine you had $80. Could you buy
both items? How do you know?
$4
How could you estimate the total cost?
$2
5
8
48 is close to 50 so I just think 50 + 25.
+5
10
20
30
40
50
60
75
70
PL
0
E
+20
80
What is another way you could estimate the total cost?
SA
M
You could add the digits in the tens place.
If it s close to $80, you then add the digits
in the ones place.
Which strategy do you prefer? Why?
How could you estimate the total cost
of these two items?
Step Up
$14
1. Write a number sentence to show how you could estimate
the total cost.
b.
$38
see
think
$
40
+
+ $
$26
26
$45
see
think
$
+
$19
+ $
ORIGO Stepping Stones 2 • 9.2
© ORIGO Education.
a.
202
$29
2. Estimate the cost of each purchase.
Then write an addition sentence to show your thinking.
a.
Blocks and Play house is about $
Toy Mania
Blocks
Play house
Tea set
Sports car
Sports car and Tea set is about $
E
b.
Bowl and Toy is about $
$35
$39
$18
$25
Puppy Palace
PL
Bed
B
ed
Toy
Bowl
Collar
SA
M
Bed and Collar is about $
$45
$18
$12
$29
3. Imagine
magine you had the amount in the wallet.
Color a
to show if you could buy both games.
$55
$138
9
Imagine you have $60 and buy two toys. Loop the two toys that
would give you the least amount of change.
Step Ahead
© ORIGO Education.
$$339
9
yes
no
$$3355
ORIGO Stepping Stones 2 • 9.2
$1385
$$2385
203
9.3
Estimating Answers (Subtracting within 100)
Imagine you cut off 39 cm from this piece of wood.
What is an easy way to estimate the length of the piece left over?
75 cm
PL
E
39 is close to 40 so I just think 75 Ð 40.
SA
M
How could you use the same
thinking to estimate 64 Ð 19?
Step Up
Write
rite a subtraction sentence to show how you could estimate
the amount left over.
b.
see
57
−
29
see
think
57
−
30
think
c.
−
48
−
d.
see
think
204
85
64
−
−
37
see
think
71
−
49
−
ORIGO Stepping Stones 2 • 9.3
© ORIGO Education.
a.
1.
2. Estimate the difference between these lengths.
Then write a number sentence to show your thinking.
a.
29 cm
54 cm
cm.
The difference is about
b.
96 cm
38 cm
cm.
E
The difference is about
c.
85 cm
The difference is about
cm..
cm
SA
M
d.
PL
48 cm
52 cm
19 cm
cm.
cm
The difference is about
e.
26 cm
The difference is about
Step Ahead
cm.
Estimate the length of the piece of wood that will be left over
after all of these lengths have been cut off.
1 length of 26 cm
© ORIGO Education.
72 cm
95 cm
1 length of 18 cm
1 length of 34 cm
ORIGO Stepping Stones 2 • 9.3
Left over length of wood is about
cm.
205
9.4
Using the Associative Property of Addition with Three
One- and Two-Digit Numbers
Imagine you threw three small beanbags onto this target.
If each beanbag lands in the red circle,
what total scores might you record?
24
How could you figure out the totals?
32
7
5
9
3
18
E
I chose 7, 9, and 3.
Then I added in this order
7 + 3 + 9 because 7 + 3
makes 10 which is easy.
46
PL
Imagine two beanbags land in blue and one beanbag lands in red.
How could you figure out the total scores you could record?
SA
M
I could add friendly pairs of numbers like 18 and 32 first.
Why are 18 and 32 called friendly pairs?
What other numbers make friendly pairs?
Step Up
a. Imagine
Imagine three beanbags land in different pink parts of this target.
Write addition sentences to show all the scores you might record.
6+4+8=
15
8
4
6
2
45
© ORIGO Education.
10
40
206
ORIGO Stepping Stones 2 • 9.4
b. Imagine two beanbags land in purple and one beanbag lands in yellow.
Write addition sentences to show four possible total scores.
40
25
7
2
8
3
35
20
PL
E
magine two beanbags land in orange and one beanbag lands in pink.
c. Imagine
Write addition sentences to show four possible total scores.
SA
M
45
Step Ahead
5
6
4
26
15
35
10
40
© ORIGO Education.
5
Jordan threw three beanbags onto
this target and scored a total of 55.
Where did the beanbags land?
Write addition sentences to show three different
possible solutions.
ORIGO Stepping Stones 2 • 9.4
14
5
1
9
6
15
207
9.5
Using the Associative Property of Addition with Four
One- and Two-Digit Numbers
Imagine you had to build a fence around this garden.
How many meters of fencing would you need?
2m
9m
How could you figure out the total?
7m
8m
8m
SA
M
PL
How could you use the same thinking
to add these numbers?
E
I added 8 + 2 first because that s 10.
Then 9 + 7 is 16 and 10 + 16 is 26.
Step Up
a.
4m
6m
7m
1. Figure
igure the total length of all the sides without measuring.
Write an addition sentence to show your thinking.
7m
4m
6m
9m
b.
5m
12 m
8m
208
ORIGO Stepping Stones 2 • 9.5
© ORIGO Education.
6m
2. Write an addition sentence to show how you find the total length of all the sides.
a.
17 m
7m
b.
18 m
5m
13 m
9m
12 m
21 m
c.
E
31 m
d.
PL
22 m
23 m
8m
19 m
25 m
SA
M
17 m
26 m
Step Ahead
Amelia figured out that she would need 90 meters of fencing
to fence this whole property.
Write the missing lengths.
There is more than one possible answer.
20 m
25 m
© ORIGO Education.
m
m
ORIGO Stepping Stones 2 • 9.5
Working Space
209
Solving Word Problems
9.6
What does this clipboard show?
What is a standing jump?
Standing Jumps
What are some different word problems
you can make using these numbers?
82 cm
Elena
75 cm
Connor
68 cm
Sophie
65 cm
E
How much farther did
Owen jump than Connor?
Owen
PL
Who jumped 10 cm less than Elena?
Think about each word problem.
What information do you know?
SA
M
What information do you need to find out?
How would you solve each problem?
What number sentence would you write?
1. Color the
beside the number sentences that show the thinking
you could use to solve each problem. There is more than one
possible way of thinking.
a. Cooper jumped 77 cm.
Emilia jumped 59 cm.
What is the difference?
77 − 59 =
87 + 20 =
77 + 59 =
78 − 20 =
95 − 77 =
20 +
59 +
210
b. Hannah jumped 87 cm.
This was 20 cm more than Amos.
How far did Amos jump?
= 77
= 87
© ORIGO Education.
Step Up
87 − 20 =
ORIGO Stepping Stones 2 • 9.6
2. Write a number sentence to show how you solve each problem.
You can use the number line to help.
40
c.
80
Justin jumped 75 cm.
Maria jumped 17 cm less than Justin.
How far did Maria jump?
Deven jumped 58 cm.
This was 15 cm less than Wendell.
How far did Wendell jump?
Anton jumped 75 cm.
This was 17 cm more than Hailey.
How far did Hailey jump?
Michael
ichael jumped 23 cm farther
than Claire. Claire jumped 49 cm.
How far did Michael jump?
SA
M
d.
70
E
b.
60
PL
a.
50
e.
Hernando
ernando jumped 19 cm less than
Carmen. Carmen jumped 56 cm.
How far did Hernando jump?
Step Ahead
Lucas jumped 82 cm. This was 15 cm more than Luke but 7 cm
less than Vanessa. Use the number line to figure out the length
of each jump.
© ORIGO Education.
Luke
40
ORIGO Stepping Stones 2 • 9.6
50
60
70
cm
80
Vanessa
90
cm
100
211
9.7
Identifying One-Half, One-Fourth,
and One-Third of a Collection
These sheets of paper have been folded into parts that are the same size,
then opened out again.
How many parts do you see on each sheet of paper?
E
What is one part on each sheet called?
PL
Imagine these 12 blocks are shared equally
between the parts on the green paper.
How many blocks will be in each part? How do you know?
How could you describe the number of blocks in each part?
SA
M
One-half of 12 is 6.
How many blocks will be in each part on the blue and the orange paper?
How could you describe the number of blocks in each part?
Step Up
1. Loop
oop fruit to show two equal groups. Then complete the sentence.
b.
One-half of 20 is
212
.
One-half of 32 is
.
ORIGO Stepping Stones 2 • 9.7
© ORIGO Education.
a.
2. Loop fruit to show four equal groups. Then complete the sentence.
a.
b.
One-fourth of 28 is
One-fourth of 24 is
.
.
3. Loop fruit to show three equal groups. Then complete the sentence.
b.
One-third of 15 is
PL
E
a.
One-third of 21 is
.
.
SA
M
4. Complete each sentence.
a. One-half of 50 is
.
b. One-fourth
O
of 60 is
.
c. One-third
ne-third of 30 is
.
d.
.
Step Ahead
One-half of 70 is
Is one-third of 24 more or less than 6? Explain your thinking.
one-half of 24 is 12
© ORIGO Education.
one-fourth of 24 is 6
ORIGO Stepping Stones 2 • 9.7
213
9.8
Identifying One-Half, One-Fourth,
and One-Third of a Region
These sheets of paper have been folded into parts that are the same size,
then opened out again.
Some parts have been shaded orange.
How many parts of each sheet are orange?
E
On each sheet, how would you describe the total amount that is orange?
PL
How could you prove that each sheet shows one-half?
SA
M
You could rearrange the
orange parts to look the same
as those in the first sheet.
What are some other ways you could show one-half?
1. Col
Color
or parts to show one-half in three different ways.
© ORIGO Education.
Step Up
214
ORIGO Stepping Stones 2 • 9.8
2. Color parts to show one-fourth in three different ways.
PL
E
3. Color parts to show one-third in three different ways.
SA
M
4. Loop the pictures that show one-fourth red.
red.
Step Ahead
b.
© ORIGO Education.
a.
Draw lines on each picture.
Then color each picture to show one-third.
ORIGO Stepping Stones 2 • 9.8
215
9.9
Exploring Fractions
Look at these pictures. What fractions have been shaded purple?
E
What do you notice about each fraction?
What is the same? What is different?
PL
Each shape shows the same fraction.
The shape of the parts is different.
SA
M
What is another way you could show the same fraction?
Step Up
1. Draw
raw lines to join each fraction picture with a matching name.
one-half
one-fourth
© ORIGO Education.
one-third
216
ORIGO Stepping Stones 2 • 9.9
2. Color parts of each picture to show the same fraction two different ways.
a.
one-half is shaded
PL
E
b.
one-fourth is shaded
SA
M
c.
one-third is shaded
Step Ahead
b.
© ORIGO Education.
a.
Draw more lines to divide each of these into parts of equal size.
ORIGO Stepping Stones 2 • 9.9
217
9.10
Analyzing Fractions
Imagine you cut each sandwich in half to share with a friend.
Compare the halves of each sandwich.
What is the same? What is different?
E
Each sandwich shows two parts the same size.
PL
One-half of one sandwich is less
than one-half of the other sandwich.
SA
M
Imagine Peta had 12 marbles in a bag and gave one-half to Emily.
Isaac had 18 marbles in a bag and gave one-half to Ryan.
Now Emily and Ryan both have one-half of a bag of marbles.
Do they have the same number of marbles? How do you know?
Does one-half always show the same quantity or amount?
Step Up
b.
© ORIGO Education.
a.
1. Color one-half of each picture.
218
ORIGO Stepping Stones 2 • 9.10
2. Color one-half of each picture.
a.
b.
3. Color one-fourth of each picture.
b.
PL
E
a.
4. Color one-third of each picture.
b.
SA
M
a.
Color parts in the last picture to continue the pattern.
© ORIGO Education.
Step Ahead
ORIGO Stepping Stones 2 • 9.10
219
9.11
Working with Parts of a Whole (Equal Size)
PL
How many parts are in each whole?
E
Look at how each picture has been divided. Are the parts the same size?
Compare each picture.
What do you notice about the size of the parts?
SA
M
As the number of parts increases
the size of each part decreases.
1. LLoop
oop the pictures that have been divided into parts of equal size.
© ORIGO Education.
Step Up
220
ORIGO Stepping Stones 2 • 9.11
2. Color blue one part in each picture. Then write the numbers.
a.
b.
Number of blue parts
Number of blue parts
Total number of parts
Total number of parts
d.
E
c.
Number of blue parts
PL
Number of blue parts
Total number of parts
f.
SA
M
e.
Total number of parts
Number of blue parts
Number of blue parts
Total number of parts
Total number of parts
Step Ahead
Fold a sheet of paper in half three times.
a. After each fold, write the
number of parts of equal size.
b. What pattern do you see?
© ORIGO Education.
1 fold = 2 parts
2 folds =
parts
3 folds =
parts
ORIGO Stepping Stones 2 • 9.11
221
9.12
Exploring Area
Look at this handprint. How many whole squares are inside?
How many part squares are inside?
About how many squares are inside? How do you know?
PL
E
Brady drew the outline of his pencil case.
Write how many squares are inside.
About
squares
SA
M
Imagine you had to figure out how much carpet is needed to cover the floor of a room.
How could you figure it out?
Step Up
1. Write
rite the number of squares that each picture covers.
B
A
© ORIGO Education.
squares
squares
222
ORIGO Stepping Stones 2 • 9.12
2. Look at the number of whole squares and part squares inside each picture.
Write the total number of squares for each.
C
D
squares
squares
PL
E
E
squares
SA
M
3. Look
ook at all the pictures in Questions 1 and 2.
Which
hich picture covers the greatest number of squares?
Step Ahead
1. This
This letter C has an area of 11 squares. Shade squares to show
the first letter of your first name and last name.
© ORIGO Education.
2. Write how many squares are in each letter.
a. first name
ORIGO Stepping Stones 2 • 9.12
squares
b. last name
squares
223