Download Introducing the Eights Multiplication Facts 6.1

6.1
Introducing the Eights Multiplication Facts
2. Write the products for these.
Look at this array. What do you see?
2×6=
=6×2
2×6=
=6×2
4×6=
=6×4
a.
b.
c.
d.
2×3=
2×7=
2×5=
2×8=
4×3=
4×7=
4×5=
4×8=
8×3=
8×7=
8×5=
8×8=
Look at the next array. What do you see?
What strategy can you use to figure out the product?
I used the double, double strategy.
Look at the next array. What do you see?
How can you use the fours fact to help you
figure out the product for the eights fact?
2×6=
=6×2
4×6=
=6×4
3. Use a doubling strategy to complete this table.
Number
8 sixes is the same as
double, double, double 6.
Double Double
(×4)
Double Double
Double (×8)
M
8×6=
7
20
=6×8
36
SA
What other eights facts could you solve using this strategy?
1. Look at these pictures. Write the products.
a.
b.
a.
double, double 9
8×9=
ORIGO Stepping Stones 3 • 6.1
© ORIGO Education.
4×9=
© ORIGO Education.
double, double, double 9
2×9=
Write numbers in the squares so that the numbers in each
row and column multiply to give the product in the circle.
Step Ahead
c.
double 9
128
Double
(×2)
6
Is this an easy strategy to use?
Step Up
PL
E
What strategy can you use to figure out the product?
8 2
4 5
32
10
ORIGO Stepping Stones 3 • 6.1
b.
c.
16
56
40
20
12
36
28
24
72
20
129
Reinforcing the Eights Multiplication Facts
6.2
2. Complete each picture.
a.
Amber bought 8 of these packs of pencils.
×2
×2
b.
×2
×2
5
How many pencils did she buy in total?
×2
×2
×2
×2
7
How could you figure it out?
×
What should you write in each of the boxes
below to show how many pencils she bought?
×2
d.
×2
×2
8
×
8
Jamal bought 8 different packs of pencils.
Each pack had 2 pencils. How many pencils did he buy?
How could you figure it out?
a.
SA
d. 24 =
is
double
is
double
is
double
is
double
is
ORIGO Stepping Stones 3 • 6.2
=
×
8×2=
×
×6
= 56
b.16 = 2 ×
c.
e.
f.40 =
× 8 = 64
h. 32 =
Use repeated doubling to
complete the missing numbers.
cards
c.
8×6=
=
×2
× 4 = 36
× 10
i. 3 × 8 =
×8
Step Ahead
© ORIGO Education.
double
stickers
g.7 ×
© ORIGO Education.
is
=
a. 4 × 7 =
b. Ramon bought 8 packs of trading
cards. There are 9 cards in each
pack. How many trading cards
did he buy in total?
double
b.
4. Think about the fours and eights facts. Write the missing number in each equation.
1. S
how how you could use the double, double, double strategy to
solve each word problem.
a. Zoe bought 6 packs of stickers.
There are 8 stickers in each pack.
How many stickers did she buy
in total?
8×3=
×
It is easier to think double 8 than double, double, double 2.
What other problems could you solve using these strategies?
×
3. Complete each fact. Then write the turnaround fact for each.
Double 3 is 6, double 6 is
12, and double 12 is 24.
So 8 packs of 3 is 24.
M
×
130
×2
4
×2
3
Step Up
×2
PL
E
×2
c.
×
×2
×2
×2
4
× 16
ORIGO Stepping Stones 3 • 6.2
131
6.3
Exploring Patterns with the Eights Multiplication Facts
Step Up
Look at this hundred chart.
Use the hundred chart on page 132 to answer these questions.
1. Look at the color pattern of numbers. Are the numbers odd or even?
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
40
41
42
43
44
46
47
48
49
51
52
53
54 55 56
57
58
59 60
61
62 63
64 65 66
67
68 69
70
71
72
73
74
76
77
78
80
81
82
83
84 85 86
87
88 89 90
91
92
93
94 95 96
97
98 99 100
75
4.a.Loop all the numbers in the chart that are products of the fours facts.
b. What pattern do you notice?
SA
Color all the numbers above that you know are
products of the eights facts.
79
50
3.
Look at the numbers that lie along a sloping line. What change happens
in the ones digit from one number to the next?
M
45
39
PL
E
1
2. Look at the numbers in a single column. What do you notice?
There are two numbers in the bottom two rows that
are the products of 8 × 11 and 8 × 12.
Is there a pattern you can see that could help you
figure out the numbers?
What strategy could you
use to check your answer?
132
© ORIGO Education.
ORIGO Stepping Stones 3 • 6.3
© ORIGO Education.
Imagine the chart continued to 200.
What are some other numbers you would color to continue the pattern?
How do you know?
Complete these facts.
Then write about the pattern you notice.
Step Ahead
8×
= 32
4×
= 32
2×
= 32
ORIGO Stepping Stones 3 • 6.3
133
6.4
Introducing the Ones Multiplication Facts
2.Complete the number fact to match each picture.
a.
What do you see in this picture?
1 ball for each student
How many balls in total?
b.
1 line of ducks
How many ducks in total?
1×
×1=
=
What number sentence could you write to describe the row of vehicles?
3.In each story write a number greater than 1 but less than 10.
Then draw a matching picture and write the related number fact.
PL
E
What else might you see in one row? Draw a picture to match.
a.
7 birds sitting on a fence
How many birds in total?
×1=
134
b.
M
6 cookies in a jar
How many cookies in total?
×1=
ORIGO Stepping Stones 3 • 6.4
Step Ahead
×
=
muffins on a tray
How many muffins in total?
×
stamps in a row
How many stamps in total?
d.
=
flowers in a vase
How many flowers in total?
=
×
=
Write a rule you can use when you multiply by 1.
© ORIGO Education.
a.
c.
1.Complete the picture to match the problem.
Then complete the related number fact.
© ORIGO Education.
Step Up
×
SA
Write a number sentence to describe your picture.
bananas in a bunch
How many bananas in total?
b.
ORIGO Stepping Stones 3 • 6.4
135
6.5
Introducing the Zeros Multiplication Facts
2. Draw rows of 5 stars on the flag to match each multiplication fact.
a.
Describe what you see in each row.
b.
3 × 5 = 15
Row A
2 × 5 = 10
Row B
c.
Row C
PL
E
Row D
What number sentences could you write to describe each row?
d.
1×5=5
0×5=0
3. Draw jumps on the number line to show each fact. Then write the products.
Look at Row D. What happens when you multiply by 0?
a.
3 cookies in each jar
3×
c.
=
1 cookie in each jar
b.
0
M
a.
1.Draw the picture. Then write the multiplication fact.
2 cookies in each jar
3×
d.
1
2
8
4×2=
0
136
0 cookies in each jar
4×1=
6
7
8
9
10
4×0=
2
3
4
5
6
5×1=
7
8
9
10
5×2=
=
ORIGO Stepping Stones 3 • 6.5
5×0=
Write a rule you can use when you multiply by 0.
© ORIGO Education.
3×
5
=
© ORIGO Education.
=
4
1
Step Ahead
3×
3
b.
SA
Step Up
ORIGO Stepping Stones 3 • 6.5
137
Reinforcing the Ones and Zeros Multiplication Facts
6.6
2. Multiply the two numbers across each row and write the product in the
matching circle. Then multiply the two numbers down each column and write
the product in the matching circle.
Tyler planted seedlings in one row of 6.
a.
How many seedlings did he plant? How do you know?
How many stickers did Claire have left? How do you know?
1
4
c.
2
6
8
0
4
b.
5
10
M
d.
2
0
9
2
e.
10
0
1
2
1
18
4
2
0
5
2
c.
f.
10
0
0
4
4
1
7
0
5
1. Read the equation carefully. Then write the answer.
b.
9+1=
c.
8×0=
d.
1+7=
e.
0×4=
f.
5−0=
h. 97 + 0 =
i. 0 × 58 =
ORIGO Stepping Stones 3 • 6.6
Write a story problem to match this fact.
1×9=9
© ORIGO Education.
5×1=
Step Ahead
© ORIGO Education.
a.
g. 37 × 1 =
138
4
12
SA
Step Up
15
0
3.Figure out what numbers must be in each row and column to make
the product in the matching circle.
How many mushrooms did Gavin eat? How do you know?
What can you say about the math involved in each story?
5
3
15
How many pencils did Rita have in total? How do you know?
Gavin had 6 mushrooms on his plate.
He ate none of them.
3
2
b.
6 5
a.
Rita had 6 pencils on her desk.
Then her friend gave her another pencil.
1
PL
E
Claire had 6 packets of stickers. She gave stickers to each
of her friends until the packets were empty.
2
ORIGO Stepping Stones 3 • 6.6
139
6.7
Solving Word Problems Involving Multiplication
2. Figure out the solution to each problem. Show your thinking.
a. Isabelle had 4 pieces of ribbon. Each ribbon was 3 feet long. She needed
twice the total length that she had. How many feet of ribbon did Isabelle
need in total?
There are 6 plates on a picnic table.
Each plate has 4 strawberries.
There was also one banana on 2 of the plates.
What numbers in the story helped you?
Which numbers would you use to
figure out how many pieces of fruit
there are in total?
I need to find the total
number of strawberries.
I can use the letter T
to represent the total
number of strawberries.
So T = 6 x 4.
b. A fruit store sells 3-kilogram bags of apples and oranges. Dad bought
2 bags of oranges and 6 bags of apples. What was the total weight of
all the fruit Dad bought?
1. W
rite an equation to match each story. You can use a letter for
the unknown amount. Then figure out the solution for each problem.
×
feet
c. Paige arranged a bookcase so
that each shelf had 9 books. There
are 4 shelves of books. 7 of the
books are about cats. How many
books are there in total?
×
=
cookies
laps
Step Ahead
Write a story that matches
this number sentence.
4 × 6, then add 3
d. Chairs in an auditorium were set
out in 6 rows. There were 8 chairs
in each row. Only 5 people sat in
each row. How many people are
there in total?
×
books
=
=
people
ORIGO Stepping Stones 3 • 6.7
© ORIGO Education.
=
M
×
b. Every day Mika and 2 of her
friends jog 3 laps around the
athletics track. How many laps
will Mika jog in 8 days?
© ORIGO Education.
a. The teacher has 5 rulers. Each
ruler is 1 foot long and 3 of them
are plastic. What is the total
length of the rulers if they are
laid end to end?
kg
c. Evan baked a tray of cookies. The tray held 4 rows of cookies with 7 cookies
in each row. He had some cookie dough left over so he baked another tray
that had only one row of 7 cookies on it. How many cookies did he bake?
SA
Step Up
140
feet
PL
E
How many strawberries are there in total?
How do you know?
ORIGO Stepping Stones 3 • 6.7
141
6.8
Exploring Related Partitions (Fraction Strips)
Janice had three strips of paper.
The picture shows how she folded two of them
into parts of equal size.
3.Write the fraction that matches the fraction words. Then write how many parts
are needed to fill the whole.
Fraction Word
1
one-third
The first strip is one whole.
What would you label each part of the other strips?
When you write
1
3
Fraction
Parts in One Whole
1
3
3
one-fourth
what does the 3 tell you?
The 3 tells me that three of the
parts are needed to fill the whole.
4.This strip is one whole.
a.Draw lines to split the strip into sixths. Then shade
Look at the folds that made sixths.
How are they related to the folds that made thirds?
2.Draw fold lines on the second strip
to show thirds. Draw fold lines
on the last strip to show ninths.
Then label each part of the strips.
Step Ahead
1
142
ORIGO Stepping Stones 3 • 6.8
Use paper strips to find a different fraction that belongs in each
of the 21 and 31 fraction families. Draw lines to show the folds
and label each part of the strips.
1
© ORIGO Education.
1
© ORIGO Education.
1
of the strip.
c.What does the 4 tell you?
SA
1.Draw a fold line on the second strip
to show halves. Draw fold lines
on the last strip to show fourths.
Then label each part of the strips.
M
The first strip in each of these is one whole.
4
6
b. What does the 6 tell you?
The paper strips belong to the
1
3 fraction family because you can
make sixths by first making thirds.
Step Up
PL
E
one-eighth
ORIGO Stepping Stones 3 • 6.8
143
Exploring the Additive Nature of Common Fractions
6.9
2.
For each number line, the distance from 0 to 1 is one whole. Write the answer
to each problem. Draw jumps on the number line to show your thinking.
a.
1
Mary has a bottle that holds 6
of a gallon of water. How many
bottles will she need to make
4
6 of a gallon of water?
Look at this number line.
The distance from 0 to 1 is one whole.
Show how you would mark
1
6
0
1
on the number line.
b.
Ella’s family bought a pizza cut
3
into eighths. Ella ate 8 of the
whole pizza. How many pieces
of pizza did she eat?
PL
E
I would split the line from 0 to 1 into 6 equal
parts. The distance from 0 to the first mark
1
will be 6 of the total distance from 0 to 1.
Wesley is making a cake.
3
He needs 4 cup of sugar
but only has a 41 measuring cup.
1
4
cup
+
1
4
+
What does this number line show?
1
4
Step Up
2
4
3
4
1
1
6
+
1
6
1
6
1
+
1
6
=
6
=
1
0
1
c.
=
0
1
b.
0
Step Ahead
1
ORIGO Stepping Stones 3 • 6.9
© ORIGO Education.
1
© ORIGO Education.
0
144
0
b.
1.Look at how each number line has been split up. The distance
from 0 to 1 is one whole. Write the fraction that each arrow is
pointing to.
a.
+
0
1
4
SA
0
M
+
1
4
1
3. Write an addition equation to match the jumps on the number line.
a.
What can he do to measure the correct amount of sugar?
0
1
1
Complete each equation.
1
a. 3 + 3 + 3 =
ORIGO Stepping Stones 3 • 6.9
3
b. 1 + 1 + 1 + 1 + 1 =
8
8
8
8
8
8
c. 1 + 1 =
2
2
2
145
Exploring Improper Fractions (Number Line Model)
6.10
One batch of 12 muffins needs
On each number line, the distance from 0 to 1 is one whole.
Write the fraction that should be in each box. Draw jumps to help you.
2
3
cup of mashed banana.
1
Logan wants to make 2 batches but he only has a 3 measuring cup.
2.
What can he do to measure the correct amount of banana
for 2 batches of muffins?
0
PL
E
0
How could you show your thinking on a number line?
What fraction could you write to show the total amount of banana?
+
+
1
3
+
1
3
+
a.
b.
4
3
1
What do you notice about the fraction
4
3?
b.
4
146
4
c.
2
d.
4
a.
1
2
c.
1
b.
d.
3
c.
2
d.
4
ORIGO Stepping Stones 3 • 6.10
Complete each equation.
1
1
1
1
1
+ 4 + 4 + 4 + 4 =
4
b.
4
c.
© ORIGO Education.
a.
1
a.
Step Ahead
© ORIGO Education.
0
2
5. Use the fractions you wrote on the number lines above.
b.List the fractions that are greater
a. List the fractions that are less than 1.
than 1 but less than 2.
1.
On this number line, the distance from 0 to 1 is one whole. Write the
fraction that should be in each box. Draw jumps to help you.
Step Up
d.
2
SA
The numerator is greater than the denominator.
4
I can see on the number line that 3 is greater than 1.
5
3
M
0
2
3
c.
4.
1
3
0
1
3
1
b.
3.
1
Logan can use the 3 measuring cup two times for one
batch, so he can use it four times for two batches.
1
3
a.
1
1
1
1
1
1
1
+
+
+
+
+
+
=
6
6
6
6
6
6
6
ORIGO Stepping Stones 3 • 6.10
d.
6
1
1
1
1
+ 3 + 3 + 3 =
3
1
1
1
1
1
+
+
+
+
=
2
2
2
2
2
3
2
147
Exploring Improper Fractions (Area Model)
6.11
2. Each large shape is one whole. Color the shapes to show each fraction.
a.
On this number line, the distance from 0 to 1 is one whole.
b.
6
4
0
1
2
5
2
c.
d.
What fraction is the arrow pointing to?
Fractions greater than 1 can also be shown with shapes.
PL
E
9
8
How do you know?
e.
Each large square on the right is one whole.
Each whole is split into four parts of equal size.
M
What fraction is shown?
g.
8
3
h.
6
3
13
8
1. Each large shape is one whole. Write the fraction that is shaded.
SA
a.
f.
9
6
How many fourths are shaded in total?
Step Up
10
4
b.
Step Ahead
Each square is one whole. Draw lines to split the squares into
parts of equal size. Then color parts to show 94 .
148
ORIGO Stepping Stones 3 • 6.11
© ORIGO Education.
© ORIGO Education.
c.
ORIGO Stepping Stones 3 • 6.11
149
Identifying Fractions
6.12
For these number lines, the distance from 0 to 1 is one whole.
Draw a line to connect each fraction to its position on the number line.
3.
Eight friends shared a pizza.
Each friend had one-eighth of the whole pizza.
0
1
2
3
What fraction can you write to show how many eighths were eaten?
a.
What is another way of describing how much pizza was eaten?
is the same as one whole. ýOne wholeý is the same as 1.
0
Step Up
e.
f.
g.
2
3
3
3
4
3
5
3
6
3
e.
9
4
b.
3
6
1
8
6
2
c.
6
6
d.
3
12
6
e.
15
6
b.List the fractions
that equal 2.
a.List the fractions
that equal 1.
c. What are three other fractions that would equal 2?
Step Ahead
Draw shapes to show
looks like.
7
2.
Be sure to explain what one whole
7
3
2. Loop the fractions above that are equal to 1 or 2.
150
12
4
ORIGO Stepping Stones 3 • 6.12
© ORIGO Education.
d.
d.
8
4
5. Use the fractions above to answer these questions.
M
c.
1
3
© ORIGO Education.
b.
a.
1. Each red shape is one whole. Color parts to show each fraction.
SA
a.
c.
4
4
4.
PL
E
8
8
b.
5
4
ORIGO Stepping Stones 3 • 6.12
151