M AT H E M AT I C S Workt ext
3A
for learners 8 - 9 years old
Aligned to the US Common Core State Standards
Matholia Mathematics Matholia Mathematics is a series covering levels K-6 and is fully aligned to the United States Common Core State Standards (USCCSS). Each level consists of two books (Book A and Book B) and combines textbook-style presentation of concepts as well as workbook practice. Central to the USCCSS is the promotion of problem-solving skills and reasoning. Matholia Mathematics achieves this by teaching and presenting concepts through a problem-solving based pedagogy and using the concrete-pictorial-abstract (CPA) approach. Learners acquire knowledge and understanding of concepts through a guided progression beginning with concrete examples and experiences which then flow into pictorial representations and finally mastery at the abstract and symbolic level. This approach ensures that learners develop a fundamental understanding of concepts rather than answering questions by learned procedures and algorithms. Key features of the series include:
Anchor Task
1
Numbers to 10,000
Anchor Task
Open-ended activities serve as the starting point for understanding new concepts. Learners engage in activities and discussions to form concrete experiences before the concept is formalized.
3 2
Let’s Learn
Let’s Learn
Concepts are presented in a clear and colorful manner. Worked problems provide learners with guided step-by-step progression through examples. Series mascots provide guidance through helpful comments and observations when new concepts are introduced.
When we take a whole and divide it into equal parts, we get fractions. The whole orange is cut into 2 equal pieces. Each piece is a half which we write as 1 .
Let’s cut an apple
into 4 equal pieces
. Each piece is a quarte r.
2
2 halves make 1 whole.
1 2
1 whole
half
The numbers of a
1 2
1 2
half
fraction have specia l names.
1 2
1 4
1 whole
quarter
1 4
quarter
1 2
The top number is called the numerator.
The bottom numb er is called the denom inator. A half has a numerator of 1. ...and a denominator of 2!
1 4
1 4
1 4
1 4
1 4
quarter
1 4
quarter
4 quarters make 1 whole.
Ethan eats 3 pieces of the apple. We say he eats 3 quarte apple. We can write rs of the this as a fraction 3 . 4
1 4
1 4
1 4
I ate 3 quarters of the apple!
1 4
1 4
1 4
212
213
ii
Let’s Practice
and her baby A mother elephant of 4,670 kg. have a combined mass of 482 kg The baby has a mass is the mother? How much heavier
3.
Let’s Practice
drive 1,205 km A truck driver has to stops for a to deliver his load. He destination. rest 478 km from his d? How far has he travele
1.
Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.
Step 1 mother. Find the mass of the ?
478 km trip remaining
trip traveled
–
–
1,205 km
=
– The truck driver has 2.
mother
baby
=
–
km.
traveled
kg.
of
The mother has a mass
s carnival, At the school athletic 4,675 the red team scored scored points. The blue team more many How 3,858 points. score points did the red team than the blue team?
Step 2 . difference in masses Subtract to find the ? baby
–
mother red team blue team ?
–
=
–
kg heavier than her
The mother is
=
–
more points than the
The red team scored
baby. 139
blue team.
138
(b) Home At 1.
Count the number of different creatu re in the garden. Record your data on the next page.
At Home Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.
2.
Represent your data in the
bar graph below.
16
Number of Creatu res
14 12 10 8 6
4
2 0
272
Hands On
Hands On
do an activity.
1.
Tell your friends the time you
2.
One friends shows the time
3.
time on a clocks. The other friend shows the
4.
Switch roles.
273
using their arms.
Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.
Solve it! Riley spent her summe r vaction in Europe. Complete the division equations and match the letters to find the first city she visited. T
Solve It!
A
90
6÷2=
6÷3=
N
Activities that require learners to apply logical reasoning and problem-solving. Problems are often posed which do not have a routine strategy for solving them. Learners are encouraged to think creatively and apply a range of problem-solving heuristics.
H
8÷2=
6÷1=
S
E
14 ÷ 2 =
2
3
15 ÷ 3 =
1
5
4
7 279
Looking Back
3.
Looking Back Find the area of each figure in square (b) (a)
1.
Find the perimeter of the figure. 9m
12 m
units.
11 m 11 m
8m
11 m 10 m
Consolidated practice where learners demonstrate their understanding on a range of concepts taught within a unit.
Area =
Area =
square units.
17 m
square units. Perimeter =
(d)
(c)
4.
Find the area and perimeter of each
figure. 1 cm 1 cm
Area =
square units. Area =
2.
Find the area of the rectangles. (b) (a) 12 cm
square units.
10 m
4 cm 5m
Area =
Area =
Perimeter =
Perimeter =
Area = Area =
191
190
iii
Contents 1 Numbers to 10,000
2 4 12 20 32 43 52 56
2 Addition
66 66 77 86 94
Counting to 10,000 Numbers to 10,000 Place Value Comparing and Ordering Numbers Number Patterns Odd and Even Numbers Rounding Numbers
Addition Without Regrouping Addition With Regrouping Mental Addition Within 100 Word Problems
3 Subtraction
Subtracting 10s, 100s and 1,000s Subtraction Without Regrouping Subtraction With Regrouping Word Problems
iv
106 107 119 128 136
4 Multiplication
Repeated Addition Repeated Addition Word Problems Multiplying by 2 Multiplying by 3 Multiplying by 4 Multiplying by 5 Multiplying by 10 Multiplying by 6 Multiplying by 7 Multiplying by 8 Multiplying by 9 Multiplying by 6, 7, 8 and 9 Multiplication Word Problems
5 Division (1)
Sharing Equally Grouping Equally Dividing by 2 Dividing by 3 Dividing by 4 Dividing by 5 Dividing by 10
146 146 160 168 177 186 197 06206 218 226 234 242 253 260 272 272 282 289 294 299 304 309
v
1
Numbers to 10,000
Anchor Task
2
3
Counting to 10,000 Let’s Learn Count on in hundreds from 100. +100
100
+100
200
+100
300
+100
400
+100
500
+100
600
+100
700
+100
800
+100
900 1,000
100 more than 900 is 1,000. We read 1,000 as one thousand. Count on in thousands from 1,000. +1,000 +1,000 +1,000 +1,000 +1,000 +1,000 +1,000 1,000 +1,000 2,000 +1,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000
1,000 more than 9,000 is 10,000. We read 10,000 as ten thousand.
4
Count on in tens. (a)
+10
6,320 (b)
+10
6,330 +10
8,480
+10
6,340 +10
8,490
+10
6,350 +10
8,500
6,360 +10
8,510
8,520
Count on in hundreds. (a)
+100
7,720 (b)
+100
7,820
+100
6,955
+100
7,920 +100
7,055
+100
8,020 +100
7,155
8,120 +100
7,255
7,355
Count on in thousands. (a)
+1,000
5,999 (b)
+1,000
4,250
+1,000
6,999 +1,000
5,250
+1,000
7,999
+1,000
8,999
+1,000
6,250
9,999 +1,000
7,250
8,250 5
Let’s Practice 1. Count the jelly beans. (a) 100
100
10
10
10
10
10
210
(b) 100
100
100 10
100
10
10
10
10
10
(c) 10
100
10
6
10
10
10
10
100
100
100
2. Count the blocks.
3. Count on in 10s. (a)
425,
,
,
,
,
(b)
170,
,
,
,
,
(c)
680,
,
,
,
,
(d)
8,365,
,
,
,
,
(e)
7,050,
,
,
,
,
(f)
4,980,
,
,
,
, 7
4. Count on in 100s. (a)
1,200,
(b)
3,150,
(c)
4,700,
,
,
,
,
(d)
6,363,
,
,
,
,
(e)
7,790,
,
,
,
,
,
,
,
,
,
,
,
,
5. Count on in 1,000s. (a)
260,
(b)
1, 400,
,
,
,
,
(c)
3,210,
,
,
,
,
(d)
4,980,
,
,
,
,
(e)
5,000,
,
,
,
,
8
,
,
,
,
Hands On Form circles of 4 to 6 students. Each group receives a bean bag or ball. Your teacher will write a number on the whiteboard and say a count-on number. The student with the bean bag counts on from the number on the whiteboard and throws the bean bag to the next person in the group. They continue counting on and then pass the bean bag along. Continue until the teacher says 'Stop!' Count on in 50s!
4,600!
9
At Home 1. Count the lollipops. (a)
1,000 100
10
100
100
100
(b)
100
10
10
1,000
10
100
10
1,000
10
1,000
1,000
1,000
1,000
2. Count the blocks. (a)
(b)
3. Count on in 1000s. (a)
30,
(b)
1, 700,
,
,
,
,
(c)
2,803,
,
,
,
,
(d)
4,150,
,
,
,
,
,
,
,
, 11
Numbers to 10,000 Let’s Learn Find the number represented by the blocks. (a)
3 thousands
2 hundreds
8 tens
4 ones
We say: Three thousand, two hundred eighty-four. We write: 3,284. (b)
4 thousands
6 hundreds 1 ten
6 ones
We say: Four thousand, six hundred sixteen. We write: 4,616. (c)
9 thousands 4 tens
We say: Nine thousand, forty-seven. We write: 9,047. 12
7 ones
Find the number represented in the place value chart. (a)
Thousands
Hundreds
Tens
Ones
We say: Seven thousand, five hundred thirty-nine. We write: 7,539. (b)
Thousands
Hundreds
Tens
Ones
We say: Eight thousand, four hundred forty. We write: 8,440. (c)
Thousands
Hundreds
Tens
Ones
Tens
Ones
We say: Six thousand, nine. We write: 6,009. (d)
Thousands
Hundreds
We say: Five thousand, nine hundred. We write: 5,900.
13
Let’s Practice 1. How many jelly beans are there? (a) 100
10
100
100
100
10
(b)
100
10
100
10
10
100
10
10
100
10
(c)
10
14
100
100
100
100
100
100
100
100
10
10
10
100
2.
Match.
four thousand, six hundred twenty
7,201
five thousand, sixty
8,700
seven thousand, two hundred one
5,060
eight hundred seventy-three
4,620
eight thousand, seven hundred
873
15
3. Write as numerals and words. (a)
(b)
(c)
16
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
At Home 1. How many lollipops are there? (a)
1,000
10
1,000
10
10
10
100
10
100
100
10
(b)
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
100
100
100
100
100
100
100
100
100
17
2. Write as numerals and words. (a)
(b)
(c)
18
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
3. Write the number in words. (a)
(b)
(c)
(d)
(e)
19
Place Value Let’s Learn Find the value of each digit in the numbers shown. (a)
Thousands
Hundreds
Tens
Ones
1
4
6
3
The digit in the Thousands place is 1. It represents 1,000. The digit in the Hundreds place is 4. It represents 400. The digit in the Tens place is 6. It represents 60. The digit in the Ones place is 3. It represents 3.
1,000 + 400 + 60 + 3 = 1,463
1 is the smallest digit, but it represents the greatest value.
20
(b)
Th
H
T
O
The digit in the Thousands place is 8. It represents 8,000. The digit in the Hundreds place is 5. It represents 500. The digit in the Tens place is 9. It represents 90. 8,000 + 500 + 90 = 8,590
How does the number change if we add another bead to the Tens place?
21
Let's find the value of each digit in the number. (a)
5
6
9
8 8 9
0
6
0
0
5 0
0
0
The value of the digit 5 is 5,000. The value of the digit 6 is 600. The value of the digit 9 is 90. The value of the digit 8 is 8. 5,000 + 600 + 90 + 8 = 5,698
(b)
1
3
5
7 7
1
5
0
3
0
0
0
0
0
The value of the digit 1 is 1,000. The value of the digit 3 is 300. The value of the digit 5 is 50. The value of the digit 7 is 7. 1,000 + 300 + 50 + 7 = 1,357
22
Let’s Practice 1. Write the numbers shown in the place value charts. (a)
(b)
(c)
(d)
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
Thousands
Hundreds
Tens
Ones
23
2. Fill in the blanks. (a)
There are
thousand blocks. They represent
There are
hundred blocks. They represent
There are
ten blocks. They represent
There are
unit blocks. They represent
. . . .
(b)
There are
thousand blocks. They represent
There are
hundred blocks. They represent
There are
ten blocks. They represent
There are
unit blocks. They represent
24
. . . .
3. Write the value of the digit. (a)
(c)
(e)
(g)
1,234
7,260
8, 475
1,067
(b)
(d)
(f)
(h)
4,076
945
4, 431
5,032
25
4. Write the value of each digit. Then add the values. (a)
5
2
6
1
+
(b)
9
3
+
26
8
+
+
=
+
+
=
7
Hands On Work in pairs. Partner 1 uses base-ten blocks to make a 4-digit number. Partner 2 uses place value tiles to represent the same number. Write the number as numerals and in words. Switch roles and repeat.
Number
Words
27
At Home 1. Write the numbers shown in the place value abacus. (a)
(b)
Th
H
T
O
(c)
H
T
O
Th
H
T
O
Th
H
T
O
(d)
Th
H
T
O
(e)
(f)
Th
28
Th
H
T
O
2. Fill in the blanks. (a)
There are
thousand blocks. They represent
There are
hundred blocks. They represent
There are
ten blocks. They represent
There are
unit blocks. They represent
. . . .
(b)
There are
thousand blocks. They represent
There are
hundred blocks. They represent
There are
ten blocks. They represent
There are
unit blocks. They represent
. . . . 29
3. Write the value of each digit. Then add the values. (a)
1
9
2
8
+ (b)
3
7
4
+
30
+
+
=
+
+
=
6
Solve It! Match the numbers in two ways. Three thousand, ninety-two
5000 + 900 + 4
3000 + 90 + 2
6000 + 200 + 30 + 1
Six thousand, two hundred thirty-one
Five thousand, nine hundred four
31
Comparing and Ordering Numbers Let’s Learn Let's compare the numbers. (a) Compare the numbers 6,711 and 7,611. Which number is smaller? Thousands
Hundreds
Tens
Ones
6
7
1
1
7
6
1
1
First, compare the values in the thousands place. 6 thousands is less than 7 thousands. So, 6,711 is smaller than 7,611. (b) Compare the numbers 3,166 and 3,661. Which number is greater? Thousands
Hundreds
Tens
Ones
3
1
6
6
3
6
6
1
The values in the thousands place are the same. So, compare the values in the hundreds place. 1 hundred is smaller than 6 hundreds. So, 3,661 is greater than 3,166.
32
(c) Compare the numbers 9,752 and 9,742. Which number is greater? Thousands
Hundreds
Tens
Ones
9
7
5
2
9
7
4
2
The values in the thousands place and the hundreds place are the same. So, compare the values in the tens place. 5 tens is greater than 4 tens. So, 9,752 is greater than 9,742. Let's compare and order the numbers. (a) Compare the numbers in the place value chart. Order the numbers from the greatest to the smallest. Thousands
Hundreds
Tens
Ones
7
1
9
2
7,192
7
2
0
2
7,202
6
9
7
9
6,979
First, compare the values in the thousands place. 7 thousands is greater than 6 thousands. So, 6,979 is the smallest number. Compare the values in the hundreds place. 2 hundreds is greater than 1 hundred. So, 7,202 is the greatest number. 7,202 greatest
7,192
6,979 smallest
33
(b) Compare the numbers in the place value chart. Order the numbers from the smallest to the greatest. Thousands
Hundreds
Tens
Ones
6
9
9
2
6,992
2
9
9
6
2,996
2
9
9
1
2,991
First, compare the values in the thousands place. 6 thousands is greater than 2 thousands. So, 6,992 is the greatest number. 2,996 and 2,991 have the same values in the hundreds and tens places. Compare the values in the ones place. 1 one is smaller than 6 ones. So, 2,991 is the smallest number. 2,991 smallest
34
2,996
6,992 greatest
Let’s Practice 1. Write the number represented by the blocks. Check the smaller number. (a)
(b)
35
2. Circle the greater number. (a)
1,067
2,067
(b)
3,479
3,299
(c)
4,880
3,909
(d)
5,512
5,507
(e)
3,141
4,314
(f)
8,906
900
36
3. Arrange the numbers from the smallest to the greatest. (a)
1,046
1,132
smallest
(b)
2, 467
greatest
3,908
smallest
(c)
5,905
7,634 smallest
1,772 greatest
5,899
smallest
(d)
887
6,001 greatest
7,620
7, 499 greatest
37
Solve It! Color the circles to show each number. Color a circle green to show 1. Color a circle red to show 10. Color a circle blue to show 100. Color a circle yellow to show 1,000. The first one has been done for you. (a)
3,241
(b)
one thousand, seven hundred thirty
38
(c)
four thousand, sixty-eight
(d)
six thousand, five hundred twelve.
39
At Home 1. Write the number represented by each abacus. Check the greater number. (a)
Th
H
T
O
Th
H
T
O
Th
H
T
O
Th
H
T
O
Th
H
T
O
Th
H
T
O
(b)
(c)
40
2. Circle the greatest number. Underline the smallest number. (a)
2,305
3,702
1,601
(b)
3,492
3,581
5,902
(c)
789
645
1,887
(d)
7,433
7,459
7,549
(e)
10,000
9,858
9,946
(f)
8,116
7,117
7,109
41
3. Arrange the numbers from the greatest to the smallest. (a)
4,569
10,000
greatest
(b)
3,500
smallest
3, 487
greatest
(c)
8,994
7,109 greatest
42
3,399 smallest
8,905
greatest
(d)
9,872
9,058 smallest
7,106
7,107 smallest
Number Patterns Let’s Learn What is the next number in the pattern? (a)
The numbers increase by 10.
+ 10
+ 10
+ 10 1,000
1,030 + 10 = 1,040
1,010
+ 10
?
1,030
1,020
The next number in the pattern is 1,040. (b)
The numbers increase by 25. + 25 3,450
3,525 + 25 = 3,550
+ 25 3,475
+ 25
+ 25
3,500
?
3,525
The next number in the pattern is 3,550. (c)
The numbers decrease by 200. – 200 – 200 8,200
– 200
7,600 – 200 = 7,400 – 200
8,000 7,800 7,600
?
The next number in the pattern is 7,400. 43
What is the missing number? (a)
The numbers decrease by 50. – 50 2,000
1,900 – 50 = 1,850
– 50
1,950
– 50
– 50 ?
1,900
1,800
The missing number in the pattern is 1,850. (b)
The numbers decrease by 1,000.
1,000 less than 8,709 is 7,709.
– 1,000 – 1,000 – 1,000 – 1,000 8,709
?
6,709
5,709
4,709
The missing number in the pattern is 7,709. (c)
The numbers increase by 200.
200 more than 7,600 is 7,800.
+ 200 + 200 7,400
7,600
+ 200 + 200 ?
8,000
8,200
The missing number in the pattern is 7,800. 44
What are the missing numbers? (a)
The numbers increase by 5. +5 9,010
9,010 + 5 = 9,015 9,020 + 5 = 9,025 +5
?
+5
+5 9,030
?
9,020
The missing numbers are 9,015 and 9,025. (b)
The numbers decrease by 50.
3,400
3,350 – 50 = 3,300 3,300 – 50 = 3,250
3,350
?
?
3,200
The missing numbers are 3,300 and 3,250. (c)
The numbers increase by 600.
6,000 6,600
6,600 + 600 = 7,200 7,800 + 600 = 8,400
?
7,800
?
The missing numbers are 7,200 and 8,400. 45
Let’s Practice 1. Fill in the missing numbers. (a)
Thousands
Hundreds
Tens
Ones
3
1
3
5
10 less
(b)
Thousands
Hundreds
Tens
Ones
5
7
6
4
20 less
(c)
Hundreds
Tens
Ones
8
9
2
2
50 more
Thousands
Hundreds
Tens
Ones
6
0
9
5
100 less
46
20 more
Thousands
50 less
(d)
10 more
100 more
(e)
Thousands
Hundreds
Tens
Ones
5
8
8
9
200 less
(f)
Thousands
Hundreds
Tens
Ones
4
0
0
7
10 less
(g)
10 more
Thousands
Hundreds
Tens
Ones
2
4
9
1
1,000 less
(h)
200 more
1,000 more
Thousands
Hundreds
Tens
Ones
8
4
1
0
1,000 less
1,000 more
47
2. Find the number that comes next in the pattern. (a)
428
438
448
458
(b)
1,680
1,780
1,880
1,980
(c)
2,002
1,902
1,802
1,702
(d)
3,325
4,325
5,325
6,325
(e)
8,400
8,300
8,200
8,100
(f)
9,641
8,641
7,641
6,641
(g)
5,705
5,805
5,905
6,005
(h)
6,600
6,700
6,800
6,900
(i)
4,049
3,049
2,049
1,049
(j)
2,468
3,468
4,468
5,468
48
3. Write the rule for the number pattern. (a)
9,311, 9,411, 9,511, 9,611 (b)
7,501, 7,511, 7,521, 7,531 (c)
5,936, 5,886, 5,836, 5,786 (d)
2,989, 2,939, 2,889, 2,839 (e)
8,951, 8,451, 7,951, 7,451
49
At Home 1. Fill in the missing numbers. (a) 10 more than 510 is
.
(b) 100 less than 576 is
.
(c) 1,000 more than 260 is (d) 10 less than 2,405 is
. .
(e) 100 more than 2,222 is
.
(f) 1,000 less than 3,400 is
.
(g) 100 more than 1,980 is
.
(h) 100 less than 4,000 is
.
(i) 1,000 more than 9,000 is
.
2. Find the missing numbers in the number pattern. (a) (b) 8,641,
, 8,238, 8,228, 8,218, 8,208, , 8,841, 8,941, 9,041,
(c) 5,220, 5,720, 6,220, (d) (e) 3,172, (f)
, 1,178, 1,278, 1,378, ,
, 1,578 , 3,247, 3,272, 3,297
, 2,035, 3,035, 4,035, 5,035,
(g) 5,990, 6,490, 6,990, 50
, 7,220,
,
, 8,490
3. Write the rule for the number pattern. (a)
420, 520, 620, 720 (b)
1,307, 2,307, 3,307, 4,307 (c)
6,600, 6,500, 6,400, 6,300 (d)
4,460, 3,460, 2,460, 1,460 (e)
5,260, 6,260, 7,260, 8,260
51
Odd and Even Numbers Let’s Learn The numbers below are even numbers.
2
4
6
+2
+2
8 +2
10 +2
In the hundred square, the even numbers are shaded.
52
1
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
Even numbers end in 0, 2, 4, 6 or 8.
The numbers below are odd numbers.
1
3
5
+2
+2
7
9
+2
+2
In the hundred square, the odd numbers are shaded. 1
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
Odd numbers end in 1, 3, 5, 7 or 9.
53
Let’s Practice 1. Circle the odd numbers.
4
15 1,201
126 339
3
8
1,000
592
27
2. Underline the even numbers.
10
121
768 900
36 4,267 292 55
3. Draw an odd number of flowers.
4. Draw an even number of houses.
54
1
1,334
At Home Help Sophie cross the river by coloring the odd numbers.
122
245
128
6
186
64
11
319
503
2
774
1,202
300
1997
14
2001
49
13
89
1,110
669
4,264
9,012
222
74
5307
732
1,306
2,468
800 55
Rounding Numbers Let’s Learn Round 4,514 to the nearest ten.
When rounding, remember 4 or less – round down!
4,514
4,510
4,515
4,520
4,514 is between 4,510 and 4,520. 4,514 is nearer to 4,510 than 4,520. 4,514 rounded off to the nearest ten is 4,510. Round off 5,998 to the nearest ten. When rounding to the nearest ten, we look at the digit in the ones place. The digit in the ones place is 8, so we round up.
5,998
5,990
5,995
When rounding, remember 5 or more – round up!
6,000
5,998 rounded off to the nearest ten is 6,000.
56
Round 8,742 to the nearest hundred. 8,742
8,750
8,700
8,800
When rounding to the nearest hundred, we look at the digit in the tens place. The digit in the tens place is 4, so we round down. 8,742 rounded off to the nearest hundred is 8,700. Round 2,390 to the nearest thousand. 2,390
2,000
2,500
3,000
hen rounding to the nearest thousand, we look at the digit W in the hundreds place. The digit in the hundreds place is 3, so we round down. 2,390 rounded off to the nearest thousand is 2,000. Round 5,780 to the nearest thousand. The digit in the hundreds place is 7. So we round up. 5,780 rounded off to the nearest thousand is 6,000.
57
Let’s Practice 1. Round each number to the nearest ten. (a) 678
(b) 444
(c) 1,006
(d) 2,311
(e) 805
(f) 5,495
(g) 2,207
(h) 1,863
2. Round each number to the nearest hundred. (a) 359
(b) 839
(c) 1,261
(d) 4,701
(e) 8,092
(f) 2,555
(g) 3,062
(h) 9,104
3. Round each number to the nearest thousand. (a) 967
(b) 1,285
(c) 4,500
(d) 3,814
(e) 9,518
(f) 7,397
(g) 2,345
(h) 5,439
58
4. Fill in the missing numbers. (a)
450
460
455 rounded off to the nearest ten is
.
(b)
1,400
1,450
1,500
rounded off to the nearest hundred is
.
(c)
6,000
6,500
7,000
rounded off to the nearest thousand is
.
(d)
1,000
1,500
2,000
rounded off to the nearest thousand is
. 59
At Home 1. Round each number to the nearest hundred. (a) 605 (c) 2,077
(b) 1,288
(d) 56
2. Round each number to the nearest thousand. (a) 2,299
(b) 5,502
(c) 7,659
(d) 1,504
3. Fill in the missing numbers. (a)
1,700
1,750
1,800
rounded off to the nearest hundred is
.
(b)
4,000
60
4,500
5,000
rounded off to the nearest thousand is
.
Solve It! Which child is correct? Explain your answer. (a) Round 4,624 to the nearest hundred. The digit in the tens place is 2. So, the answer is 4,600.
The digit in the hundreds place is 6. So, the answer is 4,700.
(b) Round 8,991 to the nearest ten. The digit in the tens place is 9. So, the answer is 9,000.
The digit in the ones place is 1. So, the answer is 8,990.
(c) Round 3,505 to the nearest thousand.
The digit in the hundreds place is 5. So, the answer is 4,000.
The digit in the hundreds place is 5. So, the answer is 3,000.
61
Looking Back 1. Count on in 100s. (a)
230,
(b)
1,850,
,
,
,
,
(c)
8,700,
,
,
,
,
,
,
,
,
2. Count on in 1000s. (a)
5,
(b)
2,209,
,
,
,
,
(c)
4,500,
,
,
,
,
,
,
,
,
3. Write as numerals and words. Thousands
62
Hundreds
Tens
Ones
4. Write the number in words. (a)
(b)
5. Write the value of each digit. Then add the values. (a)
1
2
7
+
4
+
+
=
63
(b)
9
1
6
+
5
+
+
=
6. Fill in the missing numbers. (a) 10 more than 220 is (b) 100 less than 1,057 is
. .
(c) 1,000 more than 860 is
.
7. Find the missing numbers in the number pattern. (a) (b) 650,
, 1,255, 2,255, 3,255, 4,255, , 550, 500, 450,
(c) 3,200, 3,100, 3,000,
64
, 2,800,
8. Circle the even numbers. Underline the odd numbers.
1 23
432 644 33
18
10
134 592
29
9. Round each number to the nearest thousand. (a) 2,309
(b) 1,488
(c) 7,087
(d) 9,502
10. Round each number to the nearest ten. (a) 78
(b) 278
(c) 1,046
(d) 1,164
11. Fill in the missing numbers.
460
465 rounded off to the nearest ten is
470 .
65
2
Addition
Addition Without Regrouping Anchor Task Thousands
66
Hundreds
Tens
Ones
Let’s Learn A clothes factory made 1,252 children’s shirts and 2,646 adult’s shirts. How many shirts did the factory make altogether? 1,252
2,646
children’s shirts
adult’s shirts ?
We need to find the sum of 1,252 and 2,646. Step 1
Step 2
Add the ones.
Add the tens.
1
2 5 2
1
2 5 2
+ 2 6 4 6
+ 2 6 4 6
8
9 8
Step 3
Step 4
Add the hundreds.
Add the thousands.
1 2 5 2
1 2 5 2
+ 2 6 4 6
+ 2 6 4 6
8 9 8
3 8 9 8
1,252 + 2,646 = 3,898 The factory made 3,898 shirts altogether.
67
On Saturday, 4,515 people visited the Singapore Zoo. On Sunday, 5,220 people visited the Singapore Zoo. How many people visited the Singapore Zoo all weekend? 4,515
5,220
visitors on Saturday
visitors on Sunday ?
We need to find the sum of 4,515 and 5,220. Step 1
Step 2
Add the ones.
Add the tens.
4 5 1 5
4 5 1 5
+ 5 2 2 0
+ 5 2 2 0
5
3 5
Step 3
Step 4
Add the hundreds.
Add the thousands.
4 5 1 5
4 5 1 5
+ 5 2 2 0
+ 5 2 2 0
7 3 5
9 7 3 5
4,515 + 5,220 = 9,735 A total of 9,735 people visited the Singapore Zoo on the weekend.
68
Let’s Practice 1. Find the value represented by each set. Then add. (a)
+
(b)
+
69
2. Find the value represented by each set. Then add. (a) 100
10
100
1
1
100
10
10
1
1
1
100
10
10
1
1
100
10
10
10
10
100
10
1
10
1
+
(b) 1,000
100
10
1
1,000
100
10
1
1,000
10
10
1,000
10
10
1,000
10
+
70
1,000
3. Find the sum. (a) (b) 6 7 3 1 +
2
2
2
2
2
5
0
4
1
0
4
9
4
+
0
+
4 1 1 5 (i) (j) +
3
8
6
2
1
8
1
4
0
3
2
0
5
6
1
3
8
2
1
4
0
2
3
9
3
7
4
0
4
+
8 5 0 6 (g) (h) +
8
6
5 9 8 0 (e) (f) +
1
+
1 0 0 3 (c) (d) +
3
+
3
6
2
7
5
3
3
1
71
Solve It! Halle spent her vacation abroad with her parents. Match the letters to the sums to find out which country she visited. R
E 1 +
4
7
0
2
1
2
+
F 8
2
1
1
1
7
6
0
+
A
4
0
3
1
3
4
5
0
2
5
3
8
2
1
3
0
4
1
4
5
5
7
N 5 +
72
3
C +
9,971
2
0
7
3
6
1
2
1,682
+
5,685
7,598
8,846
5,474
(b) Home At 1. Find the value represented by each set. Then add. (a)
+
(b)
+
73
2. Find the value represented by each set. Then add. (a) 100
10
1
1
100
10
100
1
1
100
10
100
1
1
100
10
1
100
+
(b) 1,000
100
10
1
1,000
100
10
1
10 10 10
+
74
100
10
1
1,000
10
1
1,000
10
1
10
1
3. Find the sum. Add using the column method. (a) 2,040 + 417 =
+
(c) 6,122 + 320 =
+
(e) 5,382 + 4,500 =
+
(b) 4,305 + 132 =
+
(d) 1,025 + 4,270 =
+
(f) 7,766 + 2,233 =
+
75
(g) 1,113 + 6,330 =
+
(i) 6,234 + 1,742 =
+
(k) 3,702 + 4,077 =
+
76
(h) 4,332 + 5,504 =
+
(j) 225 + 7,760 =
+
(l) 5,633 + 3,205 =
+
Addition With Regrouping Let’s Learn In one week, a bookstore sold 5,543 math textbooks and 3,722 English textbooks. How many books were sold altogether? 5,543
3,722
math textbooks
English textbooks ?
Step 1
Step 2
Add the ones.
Add the tens.
5 5 4 3
5 5 4 3
+ 3 7 2 2
+ 3 7 2 2
5
6 5
We can regroup 12 hundreds into 1 thousand and 2 hundreds. Thousands
Hundreds
Tens
Ones
77
Step 3 Add the hundreds. 1
5 5 4 3
+ 3 7 2 2 2 6 5 Step 4 Add the thousands. 1
5 5 4 3
5 hundreds + 7 hundreds = 12 hundreds 12 hundreds = 1 thousand + 2 hundreds Write the 2 hundreds in the hundreds column and the 1 thousand in the thousands column.
5 thousands + 3 thousands + 1 thousand = 9 thousands
+ 3 7 2 2 9 2 6 5 5,543 + 3,722 = 9,265 In 1 week, the bookstore sold 9,265 books altogether.
Find the sum of 1,749 and 2,435. Step 1 Add the ones. 1
7 14 9
+ 2 4 3 5 4
78
9 ones + 5 ones = 14 ones 14 ones = 1 ten and 4 ones Write the 4 ones in the ones column and the 1 ten in the tens column.
Step 2 Add the tens. 1
4 tens + 3 tens + 1 ten = 8 tens
7 14 9
+ 2 4 3 5 8 4 Step 3 Add the hundreds. 1
1
7 14 9
7 hundreds + 4 hundreds = 11 hundreds 11 hundreds = 1 thousand + 1 hundred
+ 2 4 3 5 1 8 4 Step 4 Add the thousands. 1
1 7 14 9
1 thousand + 2 thousands + 1 thousand = 4 thousands
+ 2 4 3 5 4 1
8 4
The sum of 1,749 and 2,435 is 4,184. How can you check your answer?
79
Let’s Practice 1. Find the sum. 1 7 3 8 (a) (b) +
5
0
5
+
2 7 5 0 (c) (d) +
1
2
5
8
+
5 3 4 9 (e) (f) +
7
6
9
+
3 7 0 4 (g) (h) +
80
2
3
5
8
+
2
5
6
6
1
1
4
6
3
3
6
3
2
2
5
8
3
0
8
9
3
7
6
7
4
5
6
7
4
3
8
4
2. Find the sum. Add using the column method. (a) 1,863 + 681 =
+
(c) 4,477 + 1,287 =
+
(e) 5,382 + 1,998 =
+
(b) 1,307 + 965 =
+
(d) 3,590 + 2,645 =
+
(f) 6,364 + 2,767 =
+
81
Solve It! Use all of the numbers given so that the row and column each add up to the number the child is holding. (a) 200
166
31 166
200
397
110 87 (b) 267 150 241
241
500
124
124
109
(c) 234
234
305 450 120 191 82
875
120
(d) 298 297 122 381
298 801
206
(e) 400 333 124
857
400
188 269
(f) 441 566 98
898
234 359
83
(b) Home At 1. Find the sum. 2 3 7 5 (a) (b) +
1
4
5
+
4 3 2 2 (c) (d) +
1
2
7
8
+
6 2 1 8 (e) (f) +
1
7
8
9
+
7 8 8 3 (g) (h) +
84
1
8
8
7
+
2
6
5
8
1
3
5
2
5
5
0
5
1
6
7
9
4
5
8
6
3
5
0
6
2
9
3
6
2
4
7
4
2. Find the sum. Add using the column method. (a) 4,486 + 486 =
+
(c) 3,765 + 5,332 =
+
(e) 2,487 + 3,444 =
+
(b) 1,879 + 1,879 =
+
(d) 5,533 + 1,076 =
+
(f) 5,691 + 779 =
+
85
Mental Addition Within 100 Anchor Task
86
16¢
57¢
33¢
25¢
12¢
8¢
Let’s Learn Find the sum of 46 and 15 mentally. 46
+
First, add the tens. Then, add the ones.
15 10
5
46 + 10 = 56 56 + 5 = 61 46 + 15 = 61 The sum of 46 and 15 is 61. Find the sum of 37 and 58 37
+
Separate 58 into tens and ones, then add.
58 50
8
37 + 50 = 87 87 + 8 = 95 37 + 58 = 95 The sum of 37 and 58 is 95. Find the sum of 64 and 27 64
+
27 20
7
64 + 20 = 84 84 + 7 = 91 64 + 27 = 91 The sum of 64 and 27 is 91. 87
Find the sum of 48 and 24. 48 is close to 50. Let’s take 2 ones from 24 and make 50!
48
+
Make 10 first, then add.
24 2
Now, we can add more easily!
22
48 + 2 = 50 50 + 22 = 72 48 + 24 = 72 The sum of 48 and 24 is 72. Find the sum of 53 and 29. 53 52
+
29
1
29 + 1 = 30 52 + 30 = 82 53 + 29 = 82 The sum of 53 and 29 is 82. 88
29 is close to 30.
Let’s Practice 1. Add mentally. First, separate into tens and ones. (a) 20 + 35
20 +
+
=
20 + 35 = (b) 12 + 46
12 +
+
=
+
=
+
=
12 + 46 = (c) 31 + 63
31 + 31 + 63 = (d) 53 + 23
53 + 53 + 23 =
89
(e) 44 + 45
44 +
+
=
+
=
+
=
44 + 45 = (f) 65 + 13
65 + 65 + 13 = (g) 31 + 53
31 + 31 + 53 = (h) 18 + 27
18 + 18 + 27 =
90
+
=
2.
Add mentally. Make a ten first. (a)
29 + 21
(b)
18 + 25
29 +
= 30
18 +
30 +
=
20 +
29 + 21 = (c)
= 20 =
18 + 25 =
49 + 32
(d)
37 + 15
49 +
= 50
37 +
= 40
50 +
=
40 +
=
49 + 32 = (e)
37 + 15 =
78 + 16
(f)
57 + 13
78 +
= 80
57 +
= 60
80 +
=
60 +
=
78 + 16 =
57 + 13 = 91
Hands On Your teacher will call out 2 animals. Add the numbers mentally. When you know the answer, raise your hand!
45
17 15
23 26
42
47 7
9
50
92
12 36
39 19
22
At Home Add mentally. (a) 14 + 19 =
(b) 18 + 18 =
(c) 29 + 5 =
(d) 38 + 22 =
(e) 23 + 28 =
(f) 16 + 52 =
(g) 30 + 60 =
(h) 48 + 9 =
(i) 65 + 12 =
(j) 33 + 33 =
(k) 17 + 68 =
(l) 59 + 14 =
(m) 67 + 29 =
(n) 8 + 49 =
(o) 77 + 9 =
(p) 55 + 10 =
(q) 73 + 8 =
(r) 27 + 29 =
(s) 12 + 42 =
(t) 38 + 11 =
93
Word Problems Let’s Learn At Jackson’s Furniture Warehouse, the cost of a 3-seat sofa is $3,498. The cost of an armchair is $1,925. What is the total cost of the sofa and the armchair?
$3,498
$1,925
$3,498
$1,925
3-seat sofa
armchair
1
1
1
3 4 9 8
+
1
9 2 5
5 4 2 3
?
The total cost of the sofa and the armchair is $5,423. McDonald has 7,008 sheep and Mr. 2,803 cows on his farm. How many sheep and cows are on Mr. McDonald’s farm altogether? 7,008
2,803
sheep
cows ?
1
7 0 0 8 + 2 8 0 3 9 8
1
1
On Mr. McDonald’s farm, there are 9,811 sheep and cows altogether. 94
Mr. Spokes is saving money for a family vacation. In January, he saves $1,387. In February, he saves $156 more than in January. How much money did he save in total?
Step 1 Find the amount of money Mr. Spokes saves in February. $,1387
$156
January
1
1
1 3 8 7 +
February
1 5 6 1 5 4 3
?
1,387 + 156 = 1,543 Mr. Spokes saves $1,543 in February. Step 2 Add the amounts together to find the total. $1,387
$1,543
January
February ?
1
1
1 3 8 7 +
1 5 4 3 2 9 3 0
1,387 + 1,543 = 2,930 Mr. Spokes saves $2,930 in all. 95
Let’s Practice 1. Dominic’s smart watch records the number of steps he takes in a day. On Saturday, he walked 3,435 steps. On Sunday, he walked 5,380 steps. How many steps did he walk in total?
Saturday
Sunday ?
+
+
=
Dominic walked
steps in total.
2. Riley was playing a computer game. On Level 1, she scored 1,847 points. On Level 2, she scored 1,465 points. Find the total number of points she scored.
Level 1
Level 2 ?
+
Riley scored a total of
96
+
= points.
3. Class 3F are collecting rubbish to clean up a beach. They collect 959 plastic bottles. They collect 460 more plastic bags than bottles. How many bottles and bags did they collect in total? Step 1 Find the number of plastic bags collected.
plastic bottles plastic bags
+
?
+
=
They collected
plastic bags.
Step 2 Add the number of plastic bottles and bags together.
plastic bottles
plastic bags ?
A total of
+
+
= plastic bottles and bags were collected. 97
4. A ferry and a cruise ship arrive at a dock. There are 493 people waiting to board the ferry. There are 957 more people waiting to board the cruise ship than the ferry. How many people are waiting at the dock in total? Step 1
Step 2
98
people are waiting at the dock in total.
5. On Saturday, 2,369 people went to the beach. On Sunday, 188 more people went to the beach than on Saturday. How many people went to the beach on the weekend? Step 1
Step 2
people went to the beach on the weekend.
99
At Home 1. Mrs. Thakur bought some new equipment for her classroom. She bought a smart board for $2,338 and tablet for $855. How much money did she spend in all?
smart board
tablet ?
+
+
Mrs. Thakur spent $
100
= in all.
2. On vacation, Sophie traveled by train for 258 km. She then took a flight 1,958 km further than the train trip. What was the total distance that Sophie traveled? Step 1 Find the distance of the flight.
train
+
flight ?
+
=
The flight was
km.
Step 2 Add the distances together.
train
flight ?
+
+
=
Sophie traveled a total distance of
km.
1 01
3. A builder ordered a load of bricks for a job. She ordered 1,088 red bricks. She ordered 478 more yellow bricks than red bricks. How many bricks did she order in all? Step 1
Step 2
The builder ordered
1 02
bricks in all.
Looking Back 1. Find the sum. Add using the column method. (a) 1,307 + 412 =
+
(c) 1,475 + 1,115 =
+
(e) 5,266 + 2,859 =
+
(b) 2,452 + 1,236 =
+
(d) 3,245 + 2,178 =
+
(f) 4,847 + 1,985 =
+
103
2. Add mentally. (a) 12 + 18 =
(b) 14 + 16 =
(c) 23 + 17 =
(d) 45 + 26 =
(e) 23 + 39 =
(f) 16 + 27 =
(g) 56 + 65 =
(h) 62 + 19 =
(i) 75 + 15 =
(j) 38 + 27 =
3. On holiday, Ethan took 1,309 photos. His brother, Timmy, took 728 photos. How many photos did they take in all?
Ethan’s photos
Timmy’s photos ?
+
=
Ethan and Timmy took 104
+
photos in all.
4. Mr. McIlroy is moving his business to a new office. He must pay 1 month rent and a security deposit. The rent is $2,465. The security deposit is $945 more than the rent. Find the total amount Mr. McIlroy must pay. Step 1 Find the cost of the security deposit.
rent
+
security deposit ?
+
=
The security deposit is $
.
Step 2 Add the rent and security deposit together.
rent
security deposit ?
+
+
=
Mr. McIlroy must pay $
in total.
105
3
Subtraction
Anchor Task
106
Subtracting 10s, 100s and 1,000s Let’s Learn Find 1,350 – 20. Cross out 2 tens and count the remaining blocks.
– 1,350 – 20 = 1,330
Th
H
T
O
1
3
1
3
5 2 3
0 0 0
Th
H
T
O
2
4 3 1
2 0 2
5 0 5
Find 2,425 – 300.
– 2,425 – 300 = 2,125
2
107
Find 5,473 – 4,000. 1,000
100
10
1,000
100
10
1,000
100
10
1,000
100
10
1,000
10 10
1 1
Cross out 4 thousands and count the remaining counters.
1
10
–
Th
H
T
O
5 4 1
4 0 4
7 0 7
3 0 3
5,473 – 4,000 = 1,473 Find 6,950 – 500 by counting back in 100s. 6,950
6,850
6,750
6,650
6,550
6,450
6,950 – 500 = 6,450 Find 8,030 – 6,000 by counting back in 1,000s. 8,030
7,030
8,030 – 6,000 = 2,030
108
6,030
5,030
4,030
3,030
2,030
Let’s Practice 1. Cross out the base-10 blocks and count the remaining blocks. Fill in the blanks. (a) Find 1,710 – 200.
–
(b) Find 2,245 – 30.
–
109
(c) Find 4,316 – 4,000.
–
(d)
– 600 =
–
110
2. Cross out place value disks and find the value of the remaining disks. Fill in the blanks. (a) Find 5,680 – 500. 1,000 100
100
10
10
1,000 100
10
10
1,000 100
10
10
1,000 100
10
1,000 100
10
–
(b) Find 7,085 – 6,000. 1,000 1,000
10
10
1
1,000 1,000
10
10
1
1,000
10
10
1
1,000
10
1
1,000
10
1
–
111
3. Subtract by counting back. Fill in the blanks. (a)
– 10
– 10
–
=
– 10
– 10
– 100
– 100
– 1,000
– 1,000
– 1,000
– 1,000
6,380
(b)
– 100
– 100
2,525 – (c)
– 1,000
= – 1,000
7,190 – (d)
– 1,000
= – 1,000
8,007 –
112
=
4. Subtract using the column method. Fill in the blanks. (a) 1,280 – 50 =
–
(c) 6,122 – 4,000 =
–
(e) 9,500 – 6,000 =
–
(b) 2,415 – 400 =
–
(d) 7,797 – 20 =
–
(f) 8,602 – 300 =
–
113
Hands On Mental Subtraction Races! Stand up in pairs.
114
(b) Home At 1. Cross out place value disks and find the value of the remaining disks. Fill in the blanks. (a)
– 3,000 = 1,000 100
100
10
1
1,000 100
100
1
1,000 100
100
1
1,000 100
100
–
100
(b)
– 800 = 1,000 1,000 100
100
10
1,000 1,000 100
100
10
1,000 1,000 100
100
10
1,000 1,000 100
10
1,000
10
100
–
115
(c)
– 5,000 = 1,000 100
(d)
116
10
1
1
1,000 100
1
1
1,000 100
1
1,000 100
1
1,000 100
1
–
– 70 = 1,000 100
100
10
10
1
1,000 100
100
10
10
1
1,000 100
10
1,000 100
10
100
10
–
2. Subtract by counting back. Fill in the blanks. (a)
– 10
– 10
–
=
– 10
– 10
– 10
– 100
– 100
– 100
– 1,000
– 1,000
– 1,000
– 1,000
– 1,000
– 1,000
1,062
(b)
– 100
– 100
3,809 – (c)
– 1,000
= – 1,000
8,335 – (d)
– 1,000
= – 1,000
9,112 –
=
117
3. Subtract using the column method. Fill in the blanks. (a)
4,466 – 10 =
(b)
–
(c)
5,043 – 3,000 =
–
(d)
–
(e)
9,370 – 200 =
–
118
3,757 – 40 =
8,591 – 500 =
–
(f)
4,728 – 4,000 =
–
Subtraction Without Regrouping Let’s Learn 1,395 students attend Brookwater Primary School. 1,182 students attend Mountain Creek Primary School. How many more students attend Brookwater than Mountain Creek? 1,395 Brookwater Primary School ? Mountain Creek Primary School
more
1,182
?
Cross out counters to subtract.
Thousands
Hundreds
Tens
Ones
Step 1
Step 2
Subtract the ones.
Subtract the tens.
1 – 1
3 9 5
1
3 9 5
8 2
– 1
1 8 2
1
3
1 3
119
Step 3
Step 4
Subtract the hundreds.
Subtract the thousands.
1 3 9 5 – 1
1 8 2
1 3 9 5 – 1
2 1 3
1
8 2
2
1 3
1,395 - 1,182 = 213. 213 more students attend Brookwater than Mountain Creek. Subtract 2,415 from 7,895. Step 1
Step 2
Subtract the ones.
Subtract the tens.
7 8 9 5
7 8 9 5
5
– 2 4 1 5
0
8 0
– 2 4
1
Step 3
Step 4
Subtract the hundreds.
Subtract the thousands.
7 8 9 5 – 2 4 1 5 4 8 0 7,895 – 2,415 = 5,480.
120
7 8 9 5 – 2 4
1 5
5 4 8 0
Let’s Practice 1. Find the number represented by the counters. Note how many have been crossed off and write a subtraction sentence. (a)
1,000
100
100
10
1
1
1,000
100
100
10
1
1
1,000
100
100
10
1
1,000
100
10
1
1,000
100
1
– (b)
=
1,000 1,000
100
100
10
10
1
1
1,000 1,000
100
100
10
10
1
1
1,000 1,000
100
100
10
10
1
1
1,000 1,000
100
100
10
10
1
1
–
=
121
2. Subtract. (a) (b) 1 5 5 8 –
4
2
3
–
4 3 7 0 (c) (d) –
2
3
4
0
–
2 4 8 6 (e) (f) –
4
5
3
–
9 8 3 5 (g) (h) –
2
4
3
5
–
6 3 7 4 (i) (j) –
1 22
3
2
5
0
–
2
2
6
7
1
0
1
6
3
5
9
6
3
1
5
4
5
3
8
7
4
1
0
6
7
6
6
4
4
6
5
1
8
1
5
6
1
1
1
1
(k) (l) 8 5 7 7 –
3
0
1
3
–
9 9 7 6 (m) (n) –
2
1
3
4
–
4 7 5 4 (o) (p) –
1
1
0
0
–
7 8 8 8 (q) (r) –
1
3
4
5
–
4 7 5 5 (s) (t) –
1
5
1
0
–
5
3
6
3
4
1
4
1
6
8
3
8
5
6
1
1
5
3
8
7
4
1
0
6
3
6
5
2
2
0
1
2
6
8
9
9
2
6
1
4
123
Solve It! What is Riley’s favorite breakfast? Subtract and match the letters to the numbers below to find out. M
S –
6 6
3
7
4 3
2
1
–
I
9
6
9
9
5
2
1
8
8
6
4
2
4
0
1
9
8
8
2
2
3
7
1
L –
4
7
9
5
2
4
8
4
–
U
E –
2,316 124
9 5
2
8
1
0
7
2
8,321
–
7,511
4,481
8,241
2,311
(b) Home At 1. Find the number represented by the counters. Note how many have been crossed off and write a subtraction sentence. (a)
10
1
1
1,000 1,000
10
1
1
1,000 1,000
10
1
1
1,000
10
1
1
1,000
10
1
1,000 1,000
100
– (b)
=
1,000 1,000
100
100
10
1
1,000 1,000
100
100
10
1
1,000
100
1,000
100
1,000
100
–
= 125
2. Subtract using the column method. (a) 3,757 – 342 =
–
(c) 8,865 – 7,041 =
–
(e) 5,355 – 1,224 =
–
126
(b) 8,496 – 155 =
–
(d) 4,368 – 1,127 =
–
(f) 9,889 – 7,030 =
–
(g) 7,889 – 3,330 =
–
(i) 4,965 – 2,634 =
–
(k) 7,999 – 2,356 =
–
(h) 1,597 – 451 =
–
(j) 9,187 – 3,014 =
–
(l) 4,566 – 1,050 =
–
127
Subtraction With Regrouping Let’s Learn A watermelon has a mass of 2,254 grams. A coconut has a mass of 1,527 grams. How much heavier is the watermelon than the coconut? Let’s subtract 1,527 from 2,254 to find the difference.
Thousands
Hundreds
Tens
Th
Ones
–
2 1
H
2 5
T 4
5 2
O 14
4 7 7
Subtract the ones. Regroup 1 ten into 10 ones. 14 ones – 7 ones = 7 ones.
Regroup 1 ten into 10 ones.
1 28
Now we can cross out 7 ones.
Thousands
Hundreds
Tens
Th
Ones
2 1
–
H
2 5
T 4
5 2 2
O 14
4 7 7
Subtract the tens. 4 tens – 2 tens = 2 tens Thousands
Hundreds
Tens
Th
Ones
1
–
2 1
H 12
2 5 7
T 4
5 2 2
O 14
4 7 7
Subtract the hundreds. Regroup 1 thousand into 10 hundreds. 12 hundreds – 5 hundreds = 7 hundreds
Thousands
Hundreds
Tens
Th
Ones
1
–
2 1
H 12
2 5 7
T 4
5 2 2
O 14
4 7 7
Subtract the thousands. 1 thousand – 1 thousand = 0 thousands 2,254 – 1,527 = 727 So, the watermelon is 727 grams heavier than the coconut.
129
Find 7,304 – 3,658. Step 1 Subtract the ones.
7 2 3 9 0 144 – 3 6 5 8 6 Step 2 Subtract the tens.
We cannot subtract 8 ones from 4 ones. There are no tens to regroup. Regroup 1 hundred into 9 tens and 10 ones. 14 ones – 8 ones = 6 ones 9 tens – 5 tens = 4 tens
7 2 3 90 144 – 3 6 5 8 4 6 Step 3 Subtract the hundreds. 6
7 123 9 0 144
– 3 6 5 8 6 4 6 Step 4 Subtract the thousands. 6
7 123 9 0 144
– 3 6 5 8 3 6 4 6 7,304 – 3,658 = 3,646 130
We cannot subtract 6 hundreds from 2 hundreds. Regroup 1 thousand into 10 hundreds. 12 hundreds – 6 hundreds = 6 hundreds
6 thousands – 3 thousands = 3 thousands
Let’s Practice 1. Subtract. 1 2 5 0 (a) (b) –
1
4
3
–
4 8 8 3 (c) (d) –
1
9
9
3
–
6 0 3 4 (e) (f) –
8
7
6
–
9 5 3 2 (g) (h) –
3
7
2
9
–
6 3 (j) 0 4 (i) –
2
4
1
6
–
5
1
6
4
1
0
8
3
7
3
7
4
3
6
5
5
2
4
2
1
1
7
1
4
8
0
6
0
1
3
3
1
8
0
3
0
5
5
3
2
131
2. Subtract using the column method. (a) 2,244 – 346 =
–
(c) 1,080 – 555 =
–
(e) 9,870 – 4,146 =
–
1 32
(b) 3,303 – 779 =
–
(d) 4,412 – 1,731 =
–
(f) 8,477 – 3,887 =
–
Solve It! Forgetful Ethan left his mathematics notebook outside again. Rain has washed away some of the numbers. Write the missing numbers. (a)
7
5
3
0
5
2
7
0
5
(b)
3
2
5
1
8
– 1
3
0
1
0
2
1
9
5
0
0
9
0
5
8
3
0
– 2
7
0
1
– 1
6
5
2
2
3
8
9
4
1
7
8
4
3
5
0
7
2
7
2
– 1
2
4
1
– 1
7
2
3
3
1
0
9
5
3
9
9
2
6
4
4
5
6
9
1
9
0
2
– 3
7
3
3
7
4
2
1
9
5
8
–
(c)
(e)
(g) –
1
(d)
(f)
(h)
133
(b) Home At Subtract using the column method. (a) 1,540 – 322 =
–
(c) 3,174 – 1,882 =
(b) 2,276 – 635 =
–
(d) 5,293 – 2,433 =
–
–
(e) 7,538 – 1,665 =
(f) 8,954 – 4,335 =
–
–
1 34
(g) 6,510 – 1,652 =
(h) 2,061 – 1,234 =
–
–
(i) 6,104 – 5,305 =
(j) 7,131 – 4,433 =
–
–
(k) 6,221 – 4,353 =
–
(l) 8,804 – 5,855 =
–
135
Word Problems Let’s Learn A plane was flying at a height of 2,853 m. It had to descend 577 m due to stormy weather. At what height is the plane flying now?
2,853 m 7
14
13
2 8 5 3
original height new height
descent
?
577 m
–
5 7 7 2 2 7 6
2,853 – 577 = 2,276 The plane is flying at a height of 2,276 m. A farmer planted 7,428 apple seeds and 4,355 peach seeds. How many more apple seeds were planted than peach seeds? 7,428 3
+ 4 3 5 5
peach seeds 4,355
12
7 4 2 8
apple seeds
?
3 0 7 3
The farmer planted 3,073 more apple seeds than peach seeds. 136
Mr. Robbins spent $5,625 on flights and accommodation for his family vacation. If the accommodation cost $1,850, how much more did the flights cost?
Step 1 Find the cost of the flights.
4
15
12
5 6 2 5
$5,625 accommodation
flights
$1,850
?
– 1
8 5 0
3 7 7 5
5,625 – 1,850 = 3,775 The flights cost $3,775. Step 2 Subtract to find the difference in cost. $3,755 2
flights accommodation $1,850
?
17
3 7 5 5
– 1
8 5 0
1
9 0 5
3,755 – 1,850 = 1,905 The flights cost $1,905 more than the accommodation. 137
Let’s Practice 1. A truck driver has to drive 1,205 km to deliver his load. He stops for a rest 478 km from his destination. How far has he traveled? 478 km trip traveled
trip remaining
1,205 km
–
–
=
The truck driver has traveled
km.
2. At the school athletics carnival, the red team scored 4,675 points. The blue team scored 3,858 points. How many more points did the red team score than the blue team?
red team blue team ?
–
=
The red team scored 138
–
more points than the blue team.
3. A mother elephant and her baby have a combined mass of 4,670 kg. The baby has a mass of 482 kg. How much heavier is the mother? Step 1 Find the mass of the mother. ? baby
mother
–
–
=
The mother has a mass of
kg.
Step 2 Subtract to find the difference in masses. ? baby mother
–
The mother is
–
= kg heavier than her baby. 139
4. A factory produces 8,544 cars and motorcycles in 1 year. A total of 3,470 motorcycles were produced. How many more cars than motorcycles were produced? Step 1
Step 2
The factory produced 140
more cars than motorcycles.
(b) Home At 1. A television and speaker set are sold for $1,790. If the television costs $1,385. How much cheaper are the speakers than the television? Step 1 Find the cost of the speakers. ? television
speakers
–
–
=
The cost of the speakers is $
.
Step 2 Subtract to find the difference in masses.
television speakers
– ?
–
The speakers are $
= cheaper than the television. 1 41
2. At a baseball game, 3,277 hot dogs and burgers are sold. 1,410 hot dogs are sold. How many more burgers than hot dogs are sold? Step 1
Step 2
142
more burgers than hot dogs are sold.
Looking Back 1. Subtract by counting back. Fill in the blanks. (a)
– 10
– 10
–
=
– 10
– 10
–
=
– 10
– 10
– 10
1,776
(b)
– 10
4,030
(c)
– 100
– 100
– 100
– 100
– 1,000
– 1,000
6,428 – (d)
– 1,000
= – 1,000
– 1,000
7,666 –
=
143
2. Subtract using the column method. (a) 2,374 – 1,252 =
–
(c) 7,522 – 3,011 =
–
(e) 8,434– 2,527 =
–
144
(b) 8,859 – 2,435 =
–
(d) 6,575 – 5,837 =
–
(f) 6,641 – 988 =
–
3. On the weekend, a total of 5,325 people visited the museum. On Saturday 2,588 people visited the museum. How many more people visited the museum on Sunday than on Saturday? Step 1
Step 2
more people visited the museum on Sunday than
on Saturday. 145
4
Multiplcation
Repeated Addition Anchor Task
146
Let’s Learn How many cherries are there in all?
There are 3 groups of cherries.
There are 3 groups of 2. 2+2+2=6 3x2=6 There are 6 cherries in all.
There are 2 cherries in each group.
There are 6 cherries in all.
The symbol ‘x’ means multiply. 3 x 2 is a multiplication equation.
147
How many bananas are there in all?
There are 4 groups of 4. 4 + 4 + 4 + 4 = 16 4 x 4 = 16 There are 16 bananas in all. How many fingers are there in all?
There are 6 groups of 3. 3 + 3 + 3 + 3 + 3 + 3 = 18 6 x 3 = 18 There are 18 fingers in all. How many fingers are there in all?
There are 3 groups of 5. 5 + 5 + 5 = 15 3 x 5 = 15 There are 15 fingers in all. 1 48
Let’s Practice 1. Match. 2 groups of 4
2x8
6 groups of 3
3x4
8 groups of 2
6x3
5 groups of 5
4x4
2 groups of 8
8x2
3 groups of 4
2x4
4 groups of 4
5x5
149
2. Fill in the blanks. How many cubes in all? (a)
There are
+
groups of +
There are
+
. =
cubes in all.
(b)
There are
+
groups of +
There are
.
= cubes in all.
(c)
There are
+
There are
150
groups of +
+ cubes in all.
. +
=
(d)
There are
+
groups of +
There are
+
. +
=
cubes in all.
(e)
There are
+
There are
groups of +
.
= cubes in all.
1 51
(b) Home At 1. Match.
152
6 twos
5x3
7 twos
3x3
5 fours
3x6
3 threes
6x2
5 threes
5x4
8 fours
7x2
3 sixes
8x4
2. Fill in the blanks. How many objects in all? (a)
+
twos =
x
+
+
+
=
+
+
=
There are
keys in all.
(b)
+
threes =
x
There are
+
+
=
= kittens in all. 1 53
(c)
+
fours =
x
+
=
=
There are
books in all.
(d)
+
fives =
x
There are
154
+
+
+
=
= ice cream scoops in all.
3. Fill in the blanks. How many objects in all? (a)
twos =
x
=
There are
shoes in all.
(b)
sixes =
x
There are
= eggs in all.
155
(c)
threes =
x
=
There are
birds in all.
(d)
threes =
x
There are 156
= cherries in all.
4. Complete the equations. (a)
threes =
x
=
(b)
= x
=
(c)
= x
= 1 57
(d)
= x
=
(e)
158
= x
=
Solve It! Add the numbers. Match the letters to find Riley’s favorite soup.
K
P
N
I
U
M
12
16
24
12
9
18
20 159
Repeated Addition Word Problems Let’s Learn There are 5 snakes. Each snake has 3 eggs. How many eggs are there in all? 3
?
3 + 3 + 3 + 3 + 3 = 15 5 x 3 = 15 There are 15 eggs in all. There are 4 beetles on a branch. Each beetle has 6 legs. How many legs are there in all? 6
?
6 + 6 + 6 + 6 = 24 6 x 4 = 24 There are 24 legs in all.
160
There are 4 cars. Each car has 4 wheels. How many wheels are there in all? 4
?
There are 4 fours. 4 x 4 = 16 There are 16 wheels in all. There are 8 plants. Each plant has 3 flowers. How many flowers are there in all? 3
?
There are 8 threes. 8 x 3 = 24 There are 24 flowers in all.
Instead of drawing 8 rectangles, we can use the dotted lines like this.
161
Let’s Practice 1. There are 5 lilies in a pond. On each lily there are 3 frogs. How many frogs are in the pond in all?
There are
+
groups of +
There are
+
. +
=
frogs in the pond in all.
2. There are 6 birthday cakes. On each cake there are 4 candles. How many candles are there in all?
There are
+
There are 1 62
groups of +
+
. +
candles in all.
+
=
3. There are 3 fruit bowls. In each bowl there are 6 pieces of fruit. How many pieces of fruit are there in all?
threes =
x
=
There are
pieces of fruit in all.
4. 4 children visited the library. Each child borrowed 6 books. How many books did the children borrow in all?
sixes =
x
=
The children borrowed
books in all.
163
(b) Home At 1. There are 3 spiders. Each spider has 8 legs. How many legs are there in all?
There are
+
groups of +
There are
.
= legs in all.
2. A bakery sells donuts in boxes of 6 donuts. How many donuts are in 4 such boxes?
There are
+
There are 164
groups of +
+
. =
donuts in 4 boxes.
3. There are 5 shirts. Each shirt has 7 buttons. How many buttons are there in all?
sevens =
x
=
There are
buttons in all.
4. There are 10 bicycles at a rack. Each bicycle has 2 wheels. How many wheels are there in total?
twos =
x
There are
= wheels in total.
165
5. Mr. Hopkins bakes a tray of 8 cookies. Each cookie has 6 chocolate chips. How many chocolate chips did he use in baking the cookies?
sixes =
x
=
He used
chocolate chips.
6. 3 mini buses are used to take students to a sports carnival. Each bus has 10 seats. How many seats are there in total?
tens =
x
There are 166
= seats in total.
Solve It! An automotive company makes motorcycles and cars. In 1 day, they produce 12 cars and 8 motorcycles. How many wheels will they need in total? Use the space below to find the answer.
The automotive company will need
wheels in total. 1 67
Multiplying by 2 Let’s Learn There are 8 pairs of socks. How many socks are there in all?
There are 8 groups of 2.
I need to find 8 x 2.
Skip count in 2s.
2 1 1 2 3 4 5 6 7 8
168
4
6
8
10
12
2
Multiply using dot paper. 8 x 2 = 16 There are 16 socks in all.
14
16
There are 10 plates. There are 2 apples on each plate.
1
2
1 2 3 4 5 6 7 8 9 10
10 groups of 2. 10 x 2 = 20 Let’s learn the 2 times table. 1x2=2 2x2=4 3x2=6 4x2=8 5 x 2 = 10 6 x 2 = 12 7 x 2 = 14 8 x 2 = 16 9 x 2 = 18 10 x 2 = 20 169
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
chillies in all.
(b)
x
=
There are
almonds in all.
(c)
x
There are 170
= cubes in all.
2. Fill in the blanks. (a) 4
6
8
8
10
12
4
6
16
(b)
(c) 12
3. Color the 2 times table. 1
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
171
(b) Home At 1. Color the balloons that give the same number. Use a different color for each pair of balloons.
2 twos
2x2
6x2
9 twos
10 twos
4 twos
10 x 2
9x2
172
6 twos
4x2
2. Fill in the blanks. (a)
twos =
x
=
twos =
x
=
twos =
x
=
(b)
(c)
173
3. Draw groups of dots to show the multiplication sentence. Complete the equation. (a) 6 x 2
6 x 2 = (b) 5 x 2
5 x 2 = (c) 7 x 2
7 x 2 = (d) 10 x 2
10 x 2 = 174
4. Use the dot paper to make a multiplication equation. 1 2 (a) (b)
1
1
2
1
2
2
3
3
4
x
=
1 2 (c) (d)
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
x
=
x
=
2
9
x
=
5. Complete the equations. (a) 2 x 5 =
(b) 7 x 2 =
(c) 2 x 9 =
(d) 3 x 2 =
(e) 6 x 2 =
(f) 2 x 8 =
(g) (i) 2 x (k)
x 2 = 2 (h)
x 2 = 20
= 18 (j)
x 7 = 14
x 2 = 16 (l)
x 2 = 12
175
Hands On Play Multi-Bingo! in pairs. Fill each board with the numbers shown on the balls. Roll a 10-sided dice and multiply the number by 2. Cross out the matching number in Board 1. Switch roles with your partner. The first person to get 3 in a row is the winner. Play the game again using Board 2.
8
24 12
14
Multi-Bingo! Board 1
176
10
20
18
4
6
Board 2
Multiplying by 3 Let’s Learn There are 9 bunches of cherries. There are 3 cherries in each bunch. How many cherries are there in all?
There are 9 groups of 3.
I need to find 9 x 3.
Skip count in 3s.
3
6 1
1 2 3 4
2
9
12
15
18
21
24
27
3
Multiply using dot paper.
5 6 7 8 9
9 x 3 = 27 There are 27 cherries in all. 177
There are 7 tubes of tennis balls. There are 3 tennis balls in each tube. How many tennis balls are there in all? 1
2
3
1 2 3 4 5 6 7
7 groups of 3. 7 x 3 = 21 Let’s learn the 3 times table. 1x3=3 2x3=6 3x3=9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18 7 x 3 = 21 8 x 3 = 24 9 x 3 = 27 10 x 3 = 30 178
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
balloons in all.
(b)
x
=
There are
pebbles in all.
(c)
x
There are
= cubes in all. 179
2. Fill in the blanks. (a) 3
6
9
9
12
15
15
18
21
(b) 18
(c) 30
3. Color the 3 times table.
180
1
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
Hands On Play Multi-Bingo! in pairs. Fill each board with the numbers shown on the balls. Roll a 10-sided dice and multiply the number by 3. Cross out the matching number in Board 1. Switch roles with your partner. The first person to get 3 in a row is the winner. Play the game again using Board 2.
21
27
24
12
9
18
15 6
30
Multi-Bingo! Board 1
Board 2
181
(b) Home At 1. Color the balloons that give the same number. Use a different color for each pair of balloons.
5 threes
7x3
9 threes
3 threes
10 threes
10 x 3
9x3
7 threes 3x3
182
5x3
2. Fill in the blanks. (a)
threes =
x
=
threes =
x
=
threes =
x
=
(b)
(c)
183
3. Draw groups of dots to show the multiplication sentence. Complete the equation. (a) 5 x 3
5 x 3 = (b) 9 x 3
9 x 3 = (c) 7 x 3
7 x 3 = (d) 6 x 3
6 x 3 = 184
4. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 1 2 3
1 2 3 1 2 3 4
x
=
x
(c) (d) 1 2 3 1 2 3 4 5 6 7 8
=
1 2 3 1 2 3 4 5 6 7 8 9
x
=
x
=
5. Complete the equations. (a) 3 x 5 =
(b) 7 x 3 =
(c) 3 x 6 =
(d) 3 x 8 =
(e) 10 x 3 =
(f) 3 x 2 =
(g) (i) 3 x (k)
x 3 = 12 (h)
x3=3
= 12 (j)
x 7 = 21
x 3 = 27 (l)
x3=9 185
Multiplying by 4 Let’s Learn There are 7 stacks of books. There are 4 books in each stack. How many books are there in all?
There are 7 groups of 4.
I need to find 7 x 4.
Skip count in 4s.
4
8 1
1 2 3 4 5 6 7
186
2
3
12
16
20
24
28
4
Multiply using dot paper. 7 x 4 = 28 There are 28 books in all.
There are 8 bunches of bananas. There are 4 bananas in each bunch. How many bananas are there in all?
1
2
3
4
1 2 3 4 5 6 7 8
8 groups of 4. 8 x 4 = 32 Let’s learn the 4 times table. 1x4=4 2x4=8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24 7 x 4 = 28 8 x 4 = 32 9 x 4 = 36 10 x 4 = 40 1 87
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
pieces of chocolate in all.
(b)
x
=
There are
balloons in all.
(c)
x
There are 1 88
= cubes in all.
2. Fill in the blanks. (a) 4
8
12
12
16
20
20
24
28
(b) 24
(c) 40
3. Color the 4 times table. 1
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
189
Hands On Play Multi-Bingo! in pairs. Fill each board with the numbers shown on the balls. Roll a 10-sided dice and multiply the number by 4. Cross out the matching number in Board 1. Switch roles with your partner. The first person to get 3 in a row is the winner. Play the game again using Board 2.
8
24 40
20
Multi-Bingo! Board 1
190
28
16
36
12
32
Board 2
(b) Home At 1. Color the balloons that give the same number. Use a different color for each pair of balloons.
8 fours
8x4
3x4
9 fours
7 fours
9x4
10 fours
3 fours 7x4
10 x 4
191
2. Fill in the blanks. (a)
fours =
x
=
fours =
x
=
fours =
x
=
(b)
(c)
192
3. Draw groups of dots to show the multiplication sentence. Complete the equation. (a) 6 x 4
6 x 4 = (b) 2 x 4
2 x 4 = (c) 7 x 4
7 x 4 = (d) 9 x 4
9 x 4 = 193
4. Use the dot paper to make a multiplication equation. 1 2 3 4 (a) (b)
1
1
1
2
2
2
3
4
3 4
x
=
x
1 2 3 4 (c) (d)
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
2
= 3
4
8 9
x
=
x
=
5. Complete the equations. (a) 3 x 4 =
(b) 5 x 4 =
(c) 4 x 6 =
(d) 9 x 4 =
(e) 10 x 4 =
(f) 7 x 4 =
(g) (i) 8 x (k)
194
x 4 = 16 (h)
x 4 = 24
= 32 (j)
x4=0
x 4 = 28 (l)
x4=8
Solve It! 1. There are 10 children at East Coast Park. Some children are riding bicycles. Some children are riding tricycles. This tricycle has 3 wheels.
My bicycle has 2 wheels.
There are 24 wheels in all. How many children are riding bicycles? How many children are riding tricycles? Complete the table below to help you find the answers. Number of bicycles
Number of wheels
Number of tricycles
Number of wheels
Total number of wheels
3
3x2=6
7
7 x 3 = 21
27
4
4x2=8
6
6 x 3 = 18
26
7 x 2 = 14
3
3x3=9
23
5 6 7
children are riding bicycles.
children are riding tricycles. 195
2. Mr. McDonald has chickens and sheep on his farm.
He counts his animals. There are 14 animals and 42 legs. How many chickens does Mr. McDonald have? How many sheep does he have? Complete the table below to help you find the answers. Number of Number of chickens chicken legs
Number of sheep legs
Total number of legs
9 x 4 = 36
46
5 x 4 = 20
38
5
5 x 2 = 10
9
6
6 x 2 = 12
8
7
7
8
6
9
9 x 2 = 18
Mr. McDonald has 196
Number of sheep
5 chickens and
sheep.
Multiplying by 5 Let’s Learn There are 4 stacks of pizza boxes. There are 5 pizza boxes in each stack. How many pizza boxes are there in all?
There are 4 groups of 5.
I need to find 4 x 5.
Skip count in 5s.
5
1 1 2
2
3
4
5
10
15
20
Multiply using dot paper.
3 4
4 x 5 = 20 There are 20 boxes in all. 197
There are 8 stacks of donuts. There are 5 donuts in each stack. 1
2
3
4
5
1 2 3 4 5 6 7 8
8 groups of 5. 8 x 5 = 40 Let’s learn the 5 times table. 1x5=5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30 7 x 5 = 35 8 x 5 = 40 9 x 5 = 45 10 x 5 = 50 1 98
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
tomatoes in all.
(b)
x
=
There are
flowers in all.
(c)
x
There are
= cubes in all. 199
2. Fill in the blanks. (a) 5
10
15
35
20
25
30
50
(b)
(c) 15
25
35
3. Color the 5 times table.
2 00
1
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
Hands On Play Multi-Bingo! in pairs. Fill each board with the numbers shown on the balls. Roll a 10-sided dice and multiply the number by 5. Cross out the matching number in Board 1. Switch roles with your partner. The first person to get 3 in a row is the winner. Play the game again using Board 2.
25
35
15
45
10
50
40 30
20
Multi-Bingo! Board 1
Board 2
2 01
(b) Home At 1. Color the balloons that give the same number. Use a different color for each pair of balloons.
5 fives
9x5
10 x 5
7 fives
5x5
1x5 10 fives
7x5
202
9 fives
1 five
2. Fill in the blanks. (a)
fives =
x
=
fives =
x
=
(b)
203
3. Draw groups of dots to show the multiplication sentence. Complete the equation. (a) 7 x 5
7 x 5 = (b) 6 x 5
6 x 5 = (c) 4 x 5
4 x 5 = (d) 9 x 5
9 x 5 = 2 04
4. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5
1
1
1
2
2
3
3
2
3
4
5
4
x
=
1 2 3 4 5 (c) (d)
x 1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
2
= 3
4
5
9
x
=
x
=
5. Complete the equations. (a) 5 x 5 =
(b) 5 x 8 =
(c) 4 x 5 =
(d) 9 x 5 =
(e) 10 x 5 =
(f) 5 x 6 =
(g) (i) 5 x (k)
x 5 = 10 (h)
x 5 = 35
= 5 (j)
x 5 = 40
x 5 = 15 (l)
x 5 = 50
205
Multiplying by 10 Let’s Learn There are 8 egg cartons. There are 10 eggs in each carton. How many eggs are there in all?
There are 8 groups of 10.
I need to find 8 x 10.
Skip count in 10s.
10 1
20 2
3
30 4
5
6
40 7
8
50
60
70
80
9 10
1 2 3 4
Multiply using dot paper.
5 6 7 8
206
8 x 10 = 80 There are 80 eggs in all.
There are 7 bundles of sticks. There are 10 sticks in each bundle. 1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7
7 groups of 10. 7 x 10 = 70 Let’s learn the 10 times table. 1 x 10 = 10 2 x 10 = 20 3 x 10 = 30 4 x 10 = 40 5 x 10 = 50 6 x 10 = 60 7 x 10 = 70 8 x 10 = 80 9 x 10 = 90 10 x 10 = 100 207
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
candles in all.
(b)
x
=
There are
grapes in all.
(c)
x
There are 208
= boxes in all.
2. Fill in the blanks. (a) 10
20
30
70
20
30
40
80
(b)
(c) 50
70
90
3. Color the 10 times table. 1
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
99 100 209
Hands On Play Multi-Bingo! in pairs. Fill each board with the numbers shown on the balls. Roll a 10-sided dice and multiply the number by 10. Cross out the matching number in Board 1. Switch roles with your partner. The first person to get 3 in a row is the winner. Play the game again using Board 2.
80
50 40
70
Multi-Bingo! Board 1
21 0
100
20
60
30
10
Board 2
(b) Home At 1. Color the balloons that give the same number. Use a different color for each pair of balloons.
10 tens
7 tens
5 x 10
2 tens
9 x 10
2 x 10
5 tens
7 x 10
9 tens
10 x 10
211
2. Fill in the blanks. (a)
tens =
x
=
tens =
x
=
(b)
212
3. Draw groups of dots to show the multiplication sentence. Complete the equation. (a) 7 x 10
7 x 10 = (b) 3 x 10
3 x 10 = (c) 8 x 10
8 x 10 = (d) 4 x 10
4 x 10 = 213
4. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5 6 7 8 9 10 1
1
2
3
4
5
6
7
8
9 10
6
7
8
9 10
1
2
2
3
3 4 5 6
x
=
x
1 2 3 4 5 6 7 8 9 10 (c) (d)
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
2
= 3
4
5
10
x
=
x
=
5. Complete the equations. (a) 10 x 1 =
(b) 5 x 10 =
(c) 2 x 10 =
(d) 9 x 10 =
(e) 10 x 4 =
(f) 10 x 8 =
(g) (i) 6 x (k) 21 4
x 5 = 50 (h)
x 10 = 70
= 60 (j)
x 3 = 30
x 10 = 100 (l)
x 10 = 0
Hands On Work in pairs. Think of a multiplication equation. Use blocks to model the equation. Your partner says the equation and writes it in the space below. Switch roles and repeat 4 times.
(a)
x
=
(b)
x
=
(c)
x
=
(d)
x
=
215
Solve It! Fill in the missing numbers. (a)
3
1
3
10
2
9
10
10
15
4
8
(c)
4
3
(b)
3
27
5
20
(d)
2 12
21 6
(f)
4
5 6
32 50
36 (e)
5
40
40
10
8
100
24
14
Hands On Work with your partner to color the 2, 3, 4, 5 and 10 times tables. Use a different color for each times table. Do you notice any patterns? Are any numbers colored more than once? Why? 1
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
We have learned the 4 times table to 40. Can you continue the pattern to 100?
217
Multiplying by 6 Let’s Learn How many cubes are there altogether? Count in sixes.
6
12
18
24
30
36
There are 10 groups of 6. 10 x 6 = 60 There are 60 cubes altogether.
42
48
54
10 x 6 is the same as 6 x 10.
There are 7 bunches of bananas. There are 6 bananas in each bunch. How many bananas are there altogether?
There are 7 groups of 6. 7 x 6 = 42 There are 42 bananas altogether.
6, 12, 18, ...
1 1 2 3 4 5 6 7
218
60
2
3
4
5
6
There are 5 beetles. Each beetle has 6 legs. How many legs are there altogether?
1
2
3
4
5
6
1 2 3 4 5
6 x 5 = 30 There are 30 legs altogether. Let’s learn the 6 times table. 1x6=6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36 7 x 6 = 42 8 x 6 = 48 9 x 6 = 54 10 x 6 = 60
219
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
eggs altogether.
(b)
x
=
There are
donuts altogether.
(c)
x
There are
22 0
= crayons altogether.
2. Fill in the blanks. (a)
sixes =
x
=
sixes =
x
=
sixes =
x
=
sixes =
x
=
(b)
(c)
(d)
221
3. Fill in the blanks. (a) 6
12
18
24
30
42
(b) 48
(c) 30
42
48
60
4. Color the 6 times table.
22 2
1
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
(b) Home At 1. Fill in the blanks. (a)
sixes =
x
=
sixes =
x
=
sixes =
x
=
(b)
(c)
223
2. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5 6
1
1
2
3
4
5
6
1
2
2
3
3 4
x
=
5 6
x 1 2 3 4 5 6 (c) (d)
1
1
1
2
2
3
3
4
4
2
= 3
4
5
6
5
x
6 7
=
8 9 10
x
=
1 2 3 4 5 6 (e) (f)
1
1
1
2
2
2
3
4
5
6
3
x
=
4 5 6 7 8 9
x 224
=
3. Write two multiplication equations to show the number of squares in each grid. (a)
x
=
x
=
x
=
x
=
(b)
4. Complete the equations. (a) 10 x 6 =
(b) 5 x 6 =
(c) 6 x 10 =
(d) 9 x 6 =
(e) 6 x 4 =
(f) 6 x 8 =
(g) (i) 6 x (k)
x 6 = 18 (h) = 54 (j) x 2 = 12 (l)
x6=0 x6=6 x 7 = 42
225
Multiplying by 7 Let’s Learn How many cubes are there altogether? Count in sevens.
7
14
21
28
35
There are 10 groups of 7. 10 x 7 = 70 There are 70 cubes altogether.
42
49
56
63
70
10 x 7 is the same as 7 x 10.
There are 5 stacks of boxes. There are 7 boxes in each stack. How many boxes are there altogether?
7, 14, 21, ...
There are 5 groups of 7. 5 x 7 = 35 There are 35 boxes altogether.
1 1 2 3 4 5
22 6
2
3
4
5
6
7
There are 7 branches. There are 7 leaves on each branch. How many leaves are there altogether?
1
2
3
4
5
6
7
1 2 3 4 5 6 7
7 x 7 = 49 There are 49 leaves altogether. Let’s learn the 7 times table. 1x7=7 2 x 7 = 14 3 x 7 = 21 4 x 7 = 28 5 x 7 = 35 6 x 7 = 42 7 x 7 = 49 8 x 7 = 56 9 x 7 = 63 10 x 7 = 70 227
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
balloons altogether.
(b)
x
There are 228
= pancakes altogether.
2. Fill in the blanks. (a)
sevens =
x
=
sevens =
x
=
sevens =
x
=
(b)
(c)
229
3. Fill in the blanks. (a) 7
14
21
28
35
49
(b) 56
(c) 56
35
63
4. Color the 7 times table.
230
1
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
(b) Home At 1. Fill in the blanks. (a)
sevens =
x
=
sevens =
x
=
sevens =
x
=
(b)
(c)
231
2. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5 6 7
1
1
1
2
2
3
3
4
4
5
5
2
3
4
5
6
7
6
7
6
x
7
=
8
x 1 2 3 4 5 6 7 (c) (d)
1
1
1
2
2
3
3
4
4
2
= 3
4
5
5
x
=
6 7
x 1 2 3 4 5 6 7 (e) (f)
1
1
1
2
2
3
3
4
4
5
5
6
6
2
= 3
4
5
6
7 8
x
9
x
232
=
=
7
3. Write two multiplication equations to show the number of squares in each grid. (a)
x
=
x
=
x
=
x
=
(b)
4. Complete the equations. (a) 7 x 6 =
(b) 5 x 7 =
(c) 7 x 10 =
(d) 7 x 7 =
(e) 4 x 7 =
(f) 9 x 7 =
(g) (i) 6 x (k)
x 7 = 21 (h)
x7=7
= 42 (j)
x 7 = 28
x 7 = 14 (l)
x 7 = 56
233
Multiplying by 8 Let’s Learn How many cubes are there altogether? Count in eights.
8
16
24
32
40
48
56
64
72
80
10 x 8 is the same as 8 x 10.
There are 10 groups of 8. 10 x 8 = 80 There are 80 cubes altogether. There are 7 stacks of cookies. There are 8 cookies in each stack. How many cookies are there altogether?
8, 16, 24, ...
1 1 2 3 4 5 6 7
There are 7 groups of 8. 7 x 8 = 56 There are 56 cookies altogether. 23 4
2
3
4
5
6
7
8
There are 3 stacks of books. There are 8 books in each stack. How many books are there altogether?
1
2
3
4
5
6
7
8
1 2 3
3 x 8 = 24 There are 24 books altogether. Let’s learn the 8 times table. 1x8=8 2 x 8 = 16 3 x 8 = 24 4 x 8 = 32 5 x 8 = 40 6 x 8 = 48 7 x 8 = 56 8 x 8 = 64 9 x 8 = 72 10 x 8 = 80 235
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
balloons altogether.
(b)
x
There are
236
= legs altogether.
2. Fill in the blanks. (a)
eights =
x
=
eights =
x
=
eights =
x
=
(b)
(c)
237
3. Fill in the blanks. (a) 8
16
32
56
(b) 32
40
56
(c) 32
48
72
4. Color the 8 times table.
23 8
1
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
80
(b) Home At 1. Fill in the blanks. (a)
eights =
x
=
eights =
x
=
eights =
x
=
(b)
(c)
239
2. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5 6 7 8
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
2
3
4
5
6
7
8
6
7
8
6
7
8
9
x
10
x
=
=
1 2 3 4 5 6 7 8 (c) (d)
1
1
1
2
2
3
3
2
3
4
5
4
x
=
5
x 1 2 3 4 5 6 7 8 (e) (f)
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
2
= 3
4
5
8 9
x x
240
=
=
3. Write two multiplication equations to show the number of squares in each grid. (a)
x
=
x
=
(b)
x
=
x
=
4. Complete the equations. (a) 8 x 8 =
(b) 1 x 8 =
(c) 7 x 8 =
(d) 3 x 8 =
(e) 4 x 8 =
(f) 9 x 8 =
(g) (i) 6 x (k)
x 8 = 40 (h) = 48 (j) x 8 = 0 (l)
x 8 = 64 x 8 = 80 x1=8 2 41
Multiplying by 9 Let’s Learn How many cubes are there altogether? Count in nines.
9
18
27
36
45
54
63
There are 10 groups of 9. 10 x 9 = 90 There are 90 cubes altogether.
72
81
90
10 x 9 is the same as 9 x 10.
There are 4 cakes. There are 9 candles on each cake. How many candles are there altogether? 9, 18, 27, ...
1 1 2 3 4
There are 4 groups of 9. 4 x 9 = 36 There are 36 candles altogether. 2 42
2
3
4
5
6
7
8
9
There are 9 loaves of bread. There are 9 slices of bread in each loaf. How many slices of bread are there altogether? 1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8
9 x 9 = 81 There are 81 slices of bread altogether.
9
Let’s learn the 9 times table. 1x9=9 2 x 9 = 18 3 x 9 = 27 4 x 9 = 36 5 x 9 = 45 6 x 9 = 54 7 x 9 = 63 8 x 9 = 72 9 x 9 = 81 10 x 9 = 90 243
Let’s Practice 1. Fill in the blanks. (a)
x
=
There are
balloons altogether.
(b)
x
There are 2 44
= logs altogether.
2. Fill in the blanks. (a)
nines =
x
=
nines =
x
=
nines =
x
=
(b)
(c)
245
3. Fill in the blanks. (a) 9
18
36
54
(b) 45
54
81
(c) 27
36
72
4. Color the 9 times table.
2 46
1
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
90
(b) Home At 1. Fill in the blanks. (a)
nines =
x
=
nines =
x
=
nines =
x
=
(b)
(c)
247
2. Use the dot paper to make a multiplication equation. (a) (b) 1 2 3 4 5 6 7 8 9
1
1
1
2
2
3
3
4
4
5
5
6
6
7
7
2
3
4
5
6
7
8
9
6
7
8
9
6
7
8
9
8
x
=
9 10
x 1 2 3 4 5 6 7 8 9 (c) (d)
1
1
1
2
2
3
3
2
= 3
4
5
4
x
=
5
x 1 2 3 4 5 6 7 8 9 (e) (f)
1
1
1
2
2
3
3
4
4
5
5
6
6
2
= 3
4
5
7
x
=
8
x
2 48
=
3. Write two multiplication equations to show the number of squares in each grid. (a)
x
=
x
=
x
=
x
=
(b)
4. Complete the equations. (a) 2 x 9 =
(b) 4 x 9 =
(c) 9 x 0 =
(d) 3 x 9 =
(e) 9 x 8 =
(f) 9 x 7 =
(g) (i) 6 x (k)
x 9 = 45 (h) = 54 (j) 9 x x 9 = 18 (l)
x 9 = 81 = 27 x1=9 249
Solve It! Complete the multiplication grids. What number does each shape represent? (a)
4 12 8 =
=
=
(b)
50 25 =
25 0
60 =
=
(c)
30 =
24 =
=
(d)
36 21 27 =
=
=
=
2 51
Hands On Work with your partner to color the 6, 7, 8, and 9 times tables. Use a different color for each times table. Do you notice any patterns? Are any numbers colored more than once? Why? 1
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
We have learned the 6 times table to 60. Can you continue the pattern to 100? 252
Multiplying by 6, 7, 8 and 9 Let’s Learn Multiply.
4 x 6 = 24 6 x 4 = 24
4 groups of 6
6 groups of 4
6x4 4x6 So, 4 x 6 = 6 x 4.
253
Let’s Practice Multiply. (a)
x
=
x
=
x
=
x
=
x
=
x
=
(b)
(c)
254
(d)
x
=
x
=
x
=
x
=
x
=
x
=
x
=
x
=
(e)
(f)
(g)
2 55
(b) Home At 1. Multiply. (a)
x
(b)
1
2
= 3
4
5
6
7
x
=
8
1 2 3 4 5 6 7 8 9
x
=
x
=
x
=
x
=
(c)
2 56
(d)
x
=
x
=
x
=
x
=
(e)
2. Complete the equations. (a) 7 x 3 =
(b) 9 x 5 =
(c) 8 x 0 =
(d) 3 x 8 =
(e) 4 x 7 =
(f) 9 x 4 =
(g) (i) 6 x (k)
x 9 = 54 (h) = 42 (j) 9 x x 7 = 49 (l)
x 8 = 72 = 36 x 7 = 63 2 57
Solve It! Fill in the blanks. What is the rule? The first one has been done for you. (a)
2
6
4
4
12
3
8
6
15
27
The rule is x 2 . (b)
2
6
6 The rule is 258
5
18 .
(c)
3
7
15 The rule is
(d)
6
35
40
.
4
7
16 The rule is
30
6
28
9
24
.
259
Multiplication Word Problems Let’s Learn 1. Riley baked 8 muffins. Chelsea baked 4 times as many muffins as Riley. How many muffins did Chelsea bake? 8
? 8 x 4 = 32 Chelsea baked 32 muffins. 2. Halle saves $6 every week. How much money does Halle save in 7 weeks? $6
? 6 x 7 = 42 Halle saves $42 in 7 weeks. 3. Mrs. Brown bought 9 cartons of eggs. Each carton contained 10 eggs. How many eggs did Mrs. Brown buy in all? 10
?
10 x 9 = 90 Mrs. Brown bought 90 eggs in all. 26 0
Let’s Practice 1. Blake has 8 boxes. He packs 8 donuts into each box. How many donuts does Blake pack altogether?
x
=
Blake packs
donuts altogether.
2. Mrs. Thakur buys 7 packets of pasta. A packet of pasta costs $9. How much does Mrs. Thakur spend in all? $
x
=
Mrs. Thakur spent $
in all.
261
3. Wyatt and his brother sold 5 cups of lemonade on Saturday. They sold 5 times as many cups of lemonade on Sunday. How many cups of lemonade did they sell on Sunday?
x
=
Wyatt and his brother sold
cups of lemonade on Sunday.
4. Jordan has 6 marbles. Ethan has 8 times as many marbles as Jordan. How many marbles does Ethan have?
x
Ethan has 2 62
= marbles.
(b) Home At 1. Wyatt buys 4 chocolate bars. Each chocolate bar costs $2. How much did Wyatt spend in all? $
x
=
Wyatt spent $
in all.
2. A carton of milk has a mass of 2 kg. A crate of milk cartons hold 8 such cartons. Find the total mass of milk cartons in a crate. kg
x
=
8 cartons of milk has a mass of
kg.
263
3. Color pencils come in a pack of 10. Mrs. Choi buys 10 such packs for her class. How many color pencils did she buy in total?
x
=
Mrs. Choi bought
color pencils in total.
4. There are 9 strawberries on a chocolate cake. How many strawberries are there on 9 identical cakes?
x
There are 264
= strawberries on 9 cakes.
Solve It! Each shape represents a number. Fill in the blanks. (a)
x
=4
x
x
(b)
x2=
=9 =
+
=6
has a value of
(c)
x
= 15
x
=
has a value of
.
+4 .
265
(d)
x
=
x
= 27
x7=
has a value of
(e)
x4=
x
=6
+
=6
has a value of
(f) 3 x
.
=
x
=
x
= 15
has a value of
2 66
.
+2
.
Looking Back 1. Complete the following. (a)
+
sixes =
x
+
+
+
=
+
+
=
There are
cubes in all.
(b)
+
nines =
x
+
+
=
=
There are
dots in all.
(c)
sevens =
x
There are
= dots in all. 2 67
2. Fill in the blanks. (a) 3
6
9
21
15
20
25
24
30
(b) 35
(c) 36
(d) 7
14
36
45
16
24
42
49
(e) 63
72
(f) 48
56
80
90
(g)
26 8
100
3. Write two multiplication equations to show the number of dots. (a)
1
2
3
4
5
6
7
8
1 2 3 4 5 6
(b)
1
2
3
4
x
=
x
=
5
1 2 3 4 5 6 7 8 9
(c)
1
2
3
4
5
6
x
=
x
=
7
1 2 3 4 5 6 7 8
(d)
1
2
3
4
5
6
7
8
x
=
x
=
9 10
1 2 3 4 5 6 7 8 9 10
x
=
x
= 269
4. Color the 4 times table blue and the 9 times table red. 1
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
5. Complete the equations. (a) 7 x 3 =
(b) 9 x 5 =
(c) 8 x 0 =
(d) 3 x 8 =
(e)
x 9 = 54 (f)
(g) 6 x (i)
x 8 = 72
= 42 (h) 9 x x 7 = 49 (j)
= 36 x 7 = 63
(k) 7 x 3 =
(l) 9 x 5 =
(m) 8 x 8 =
(n) 10 x 8 =
(o) 270
x 9 = 90 (p)
x 10 = 100
6. A train carriage has 10 seats. How many seats are there in 4 such carriages?
x
=
There are
seats in 4 train carriages.
7. A block of chocolate is divided into 9 pieces. How many pieces are there in 8 such blocks?
x
There are
= pieces of chocolate in 8 blocks.
271
5
Division (1)
Sharing Equally Anchor Task
27 2
Let’s Learn There are 6 cookies. There are 2 children. Share the cookies so that each child gets the same number of cookies.
The 6 cookies are divided into 2 equal groups. There are 3 cookies in each group. Each child gets 3 cookies. We write: 6 ÷ 2 = 3 We say: Six divide two is three. The symbol ‘÷’ means divide. 6 ÷ 2 = 3 is a division equation. 273
There are 9 carrots. There are 3 rabbits. Share the carrots equally among the rabbits. How many carrots will each rabbit get?
The carrots have been shared equally. Each rabbit gets 3 carrots. We can write this as: 9 ÷ 3 = 3
2 74
There are 24 cubes.
Let’s share the cubes equally in different ways. (a) There are 3 groups. There are 8 cubes in each group.
24 divide 3 is 8. 24 ÷ 3 = 8 (b) There are 4 groups. There are 6 cubes in each group.
24 divide 4 is 6. 24 ÷ 4 = 6
275
(c) There are 2 groups. There are 12 cubes in each group.
24 divide 2 is 12. 24 ÷ 2 = 12 (d) There are 12 groups. There are 2 cubes in each group.
24 divide 12 is 2. 24 ÷ 12 = 2 276
Let’s Practice 1. Share the chocolates equally. Draw 1 chocolate on each plate and cross them off until no more remain. Fill in the blanks.
There are
chocolates in total.
On each plate there are
chocolates.
2. Share the raisins equally among the cookies. Fill in the blanks.
Each cookie gets
divide
÷
raisins. is
.
= 277
3. The counters have been shared equally. Write the division equation. (a)
10 ÷ 2 = (b)
9÷
=
(c)
÷
278
=
Solve It! Riley spent her summer vacation in Europe. Complete the division equations and match the letters to find the first city she visited. T
A
6÷2=
6÷3=
N
H
8÷2=
6÷1=
S
E
14 ÷ 2 =
2
3
15 ÷ 3 =
6
5
4
7 279
At Home 1. Share the worms equally among the birds. Fill in the blanks.
Each bird gets
divide
÷
worms. is
.
=
2. Share the flowers equally among the children. Fill in the blanks.
Each girl gets
divide
÷
280
flowers. is =
.
3. The counters have been shared equally. Write the division equation. (a)
÷
=
÷
=
(b)
281
Grouping Equally Let’s Learn Halle packs 12 soft toys into boxes. 6 soft toys fit into each box. How many boxes does she use?
There are 2 groups of 6 soft toys. Halle uses 2 boxes. 12 divide 6 is 2. 12 ÷ 6 = 2
2 82
How can you check the answer?
Dominic has 24 pieces of candy. He gives each of his friends 6 candies. How many friends does Dominic give his candies to?
There are 4 groups of 6 candies. Dominic gives his candies to 4 friends. 24 divide 6 is 4. 24 ÷ 6 = 4. There are 40 cubes. (a) Divide the cubes into groups of 10. How many groups of cubes are there?
There are 4 groups of 10 cubes. 40 ÷ 10 = 4 283
(b) Divide the cubes into groups of 8. How many groups of cubes are there?
There are 5 groups of 8 cubes. 40 ÷ 8 = 5 (c) Divide the cubes into groups of 2. How many groups of cubes are there?
There are 20 groups of 2 cubes. 40 ÷ 2 = 20
2 84
Let’s Practice 1. Circle groups of 2 butterflies.
(a) How many butterflies are there in total? (b) How many groups did you make? (c) Complete the sentence.
divide
is
.
(d) Complete the division equation.
÷
=
(e) Now circle groups of 5 butterflies. How many groups did you make? (f) Complete the sentence.
divide
is
.
(g) Complete the division equation. 285
2. Circle groups of 6 flowers.
(a) How many flowers are there in total? (b) How many groups did you make? (c) Complete the sentence.
divide
is
.
(d) Complete the division equation. (e) Now circle groups of 3 flowers. How many groups did you make? (f) Write a division sentence. (g) Write a division equation. 286
At Home 1. Circle groups of 3 buttons.
(a) How many buttons are there in total? (b) How many groups did you make? (c) Complete the sentence.
divide
is
.
(d) Complete the division equation. (e) Now circle groups of 5 flowers. How many groups did you make? (f) Write a division sentence. (g) Write a division equation.
2 87
2. Circle groups of 4 blocks.
(a) Write a division sentence. (b) Write a division equation. (c) Circle groups of 9 blocks and write a division equation. 3. Complete the division equations. (a) 4 ÷ 2 =
(b) 6 ÷ 2 =
(c) 9 ÷ 3 =
(d) 10 ÷ 2 =
(e) 10 ÷ 5 =
(f) 14 ÷ 7 =
(g) 16 ÷ 4 =
(h) 12 ÷ 6 =
(i) 20 ÷ 5 =
(j) 24 ÷ 4 =
288
Dividing by 2 Let’s Learn Sophie has 10 soccer balls. She puts an equal number of balls into 2 boxes. How many balls are in each box? ?
10
2 x 5 = 10
10 ÷ 2 = 5 There are 5 soccer balls in each box. Michelle has 18 candies. She puts an equal number of candies into 2 bags. How many candies are in each bag?
18 ÷ 2 = 9 There are 9 candies in each bag. 289
Let’s Practice 1. The buttons are grouped in 2s. Fill in the blanks.
(a) There are
groups of
buttons.
(b) Complete the division equation.
÷
=
2. Circle groups of 2 blocks and complete the division equation. (a)
÷2=
(b)
290
÷2=
3. Circle groups of 2 dots and write a division equation. (a)
(b)
4. Complete the division. (a) 2 ÷ 2 =
(b) 4 ÷ 2 =
(c) 6 ÷ 2 =
(d) 8 ÷ 2 =
(e) 10 ÷ 2 =
(f) 12 ÷ 2 =
5. Fill in the missing numbers. (a) 14 ÷ (c) 6 ÷ 2 =
= 7 (b)
÷ 2 = 10
(d)
÷ 2 = 16
291
At Home 1. The coins are grouped in 2s. Fill in the blanks.
(a) There are
groups of
coins.
(b) Complete the division equation.
÷
=
2. Circle groups of 2 blocks and complete the division equation. (a)
÷2=
(b)
2 92
÷2=
3. Circle groups of 2 dots and write a division equation. (a)
(b)
4. Complete the division. (a) 2 ÷ 2 =
(b) 6 ÷ 2 =
(c) 10 ÷ 2 =
(d) 14 ÷ 2 =
(e) 18 ÷ 2 =
(f) 22 ÷ 2 =
5. Fill in the missing numbers. (a) 16 ÷ (c) 4 ÷ 2 =
= 8 (b)
÷ 2 = 12
(d)
÷ 2 = 14
293
Dividing by 3 Let’s Learn 15 cookies are shared equally among 3 friends. How many cookies does each friend get? ?
15
3 x 5 = 15
15 ÷ 3 = 5 Each friend gets 5 cookies. 24 cans of spaghetti are packed equally into 3 boxes. How many cans of spaghetti are in each box?
24 ÷ 3 = 8 There are 8 cans of spaghetti in each box. 2 94
Let’s Practice 1. The crayons are grouped in 3s. Fill in the blanks.
(a) There are
groups of
crayons.
(b) Complete the division equation.
÷
=
2. Circle groups of 3 blocks and complete the division equation. (a)
÷3=
(b)
÷3= 295
3. Circle groups of 3 triangles and write a division equation. (a)
(b)
4. Complete the division. (a) 3 ÷ 3 =
(b) 6 ÷ 3 =
(c) 9 ÷ 3 =
(d) 12 ÷ 3 =
(e) 15 ÷ 3 =
(f) 18 ÷ 3 =
5. Fill in the missing numbers. (a) 15 ÷ (c) 6 ÷ 3 =
2 96
= 5 (b)
÷ 3 = 18
(d)
÷ 3 = 24
At Home 1. The ducks are grouped in 3s. Fill in the blanks.
(a) There are
groups of
ducks.
(b) Complete the division equation.
÷
=
2. Circle groups of 3 blocks and complete the division equation. (a)
÷3=
(b)
÷3= 297
3. Circle groups of 3 stars and write a division equation. (a)
(b)
4. Complete the division. (a) 9 ÷ 3 =
(b) 12 ÷ 3 =
(c) 21 ÷ 3 =
(d) 24 ÷ 3 =
(e) 27 ÷ 3 =
(f) 30 ÷ 3 =
5. Fill in the missing numbers. (a) 18 ÷ (c) 9 ÷ 3 =
2 98
= 6
(b)
÷ 3 = 15
(d)
÷ 3 = 21
Dividing by 4 Let’s Learn There are 16 cupcakes. 4 cupcakes are placed into each box. How many boxes are needed?
4
16
4 x 4 = 16
16 ÷ 4 = 4 There are 4 cupcakes in each box. 24 balloons are shared equally among 4 children. How many balloons does each child get?
24 ÷ 4 = 6 Each child gets 6 balloons. 299
Let’s Practice 1. The leaves are grouped in 4s. Fill in the blanks.
(a) There are
groups of
leaves.
(b) Complete the division equation.
÷
=
2. Circle groups of 4 blocks and complete the division equation. (a)
÷4=
(b)
300
÷4=
3. Circle groups of 4 dots and write a division equation. (a)
(b)
4. Complete the division. (a) 4 ÷ 4 =
(b) 24 ÷ 4 =
(c) 8 ÷ 4 =
(d) 28 ÷ 4 =
(e) 12 ÷ 4 =
(f) 32 ÷ 4 =
5. Fill in the missing numbers. (a) 28 ÷ (c) 24 ÷ 4 =
= 7 (b) (d)
÷ 4 = 10 ÷4=9
3 01
At Home 1. The nuts are grouped in 4s. Fill in the blanks.
(a) There are
groups of
nuts.
(b) Complete the division equation.
÷
=
2. Circle groups of 4 cubes and complete the division equation. (a)
÷4=
(b)
302
÷4=
3. Circle groups of 4 hearts and write a division equation. (a)
(b)
4. Complete the division. (a) 16 ÷ 4 =
(b) 36 ÷ 4 =
(c) 8 ÷ 4 =
(d) 20 ÷ 4 =
(e) 40 ÷ 4 =
(f) 12 ÷ 4 =
5. Fill in the missing numbers. (a) 24 ÷ (c) 36 ÷ 4 =
= 6 (b)
÷4=8
(d)
÷4=7
303
Dividing by 5 Let’s Learn There are 15 bottles of ketchup. 5 bottles of ketchup are packed into each box. How many boxes are needed?
5
15
5 x 3 = 15
15 ÷ 3 = 5 3 boxes are needed. 45 strawberries are shared equally among 5 children. How many strawberries does each child get?
45 ÷ 5 = 9 Each child gets 9 strawberries. 304
Let’s Practice 1. The sweets are grouped in 5s. Fill in the blanks.
(a) There are
groups of
sweets.
(b) Complete the division equation.
÷
=
2. Circle groups of 5 blocks and complete the division equation. (a)
÷5=
(b)
÷5= 305
3. Circle groups of 5 dots and write a division equation. (a)
(b)
4. Complete the division. (a) 5 ÷ 5 =
(b) 10 ÷ 5 =
(c) 15 ÷ 5 =
(d) 20 ÷ 5 =
(e) 25 ÷ 5 =
(f) 30 ÷ 5 =
5. Fill in the missing numbers. (a) 40 ÷ (c) 50 ÷ 5 =
306
= 8 (b)
÷5=3
(d)
÷5=5
At Home 1. The clips are grouped in 5s. Fill in the blanks.
(a) There are
groups of
clips.
(b) Complete the division equation.
÷
=
2. Circle groups of 5 blocks and complete the division equation. (a)
÷5=
(b)
÷5= 307
3. Circle groups of 5 moons and write a division equation. (a)
(b)
4. Complete the division. (a) 35 ÷ 5 =
(b) 45 ÷ 5 =
(c) 25 ÷ 5 =
(d) 50 ÷ 5 =
(e) 15 ÷ 5 =
(f) 40 ÷ 5 =
5. Fill in the missing numbers. (a) 45 ÷ (c) 35 ÷ 5 =
308
= 9 (b)
÷5=4
(d)
÷5=6
Dividing by 10 Let’s Learn There are 60 eggs. 10 eggs are packed into each carton. How many cartons of eggs are there?
10
60
10 x 6 = 60
60 ÷ 10 = 6 There are 6 cartons of eggs. A florist has 100 flowers. She places an equal number of flowers into 10 vases. How many flowers are in each vase?
100 ÷ 10 = 10 There are 10 flowers in each vase. 309
Let’s Practice 1. The marbles are grouped in 10s. Fill in the blanks.
(a) There are
groups of
marbles.
(b) Complete the division equation.
÷
=
2. Circle groups of 10 blocks and complete the division equation.
31 0
÷ 10 =
3. Circle groups of 10 dots and write a division equation. (a)
(b)
4. Complete the division. (a) 40 ÷ 10 =
(b) 10 ÷ 10 =
(c) 20 ÷ 10 =
(d) 70 ÷ 10 =
(e) 90 ÷ 10 =
(f) 30 ÷ 10 =
5. Fill in the missing numbers. (a) 70 ÷ (c) 50 ÷ 10 =
= 7 (b)
÷ 10 = 9
(d)
÷ 10 = 4
311
At Home 1. The shells are grouped in 10s. Fill in the blanks.
(a) There are
groups of
shells.
(b) Complete the division equation.
÷
=
2. Circle groups of 10 blocks and complete the division equation.
312
÷ 10 =
3. Circle groups of 10 stars and write a division equation. (a)
(b)
4. Complete the division. (a) 50 ÷ 10 =
(b) 10 ÷ 10 =
(c) 20 ÷ 10 =
(d) 40 ÷ 10 =
(e) 80 ÷ 10 =
(f) 60 ÷ 10 =
5. Fill in the missing numbers. (a) 50 ÷ (c) 100 ÷ 10 =
= 5 (b)
÷ 10 = 8
(d)
÷ 10 = 7
313
Looking Back 1. Share the raisins equally among the cookies. Fill in the blanks.
Each cookie gets
divide
÷
raisins. is
.
=
2. Share the fruits equally among the bowls. Fill in the blanks.
Each bowl gets
divide
÷
314
fruits. is
=
.
3. Circle groups of 6 buttons.
(a) How many buttons are there in total? (b) How many groups did you make? (c) Complete the division equation. 4. Divide by 2. Complete the equations. (a) 2 ÷ 2 =
(b) 10 ÷ 2 =
(c) 6 ÷ 2 =
(d) 16 ÷ 2 =
(e) 20 ÷ 2 =
(f) 4 ÷ 2 =
(g) 8 ÷ 2 =
(h) 12 ÷ 2 =
(i) 14 ÷ 2 =
(j) 18 ÷ 2 =
5. Divide by 3. Complete the equations. (a) 9 ÷ 3 =
(b) 3 ÷ 3 =
(c) 15 ÷ 3 =
(d) 24 ÷ 3 =
(e) 21 ÷ 3 =
(f) 6 ÷ 3 =
(g) 12 ÷ 3 =
(h) 18 ÷ 3 =
(i) 30 ÷ 3 =
(j) 27 ÷ 3 = 315
6. Divide by 4. Complete the equations. (a) 36 ÷ 4 =
(b) 28 ÷ 4 =
(c) 32 ÷ 4 =
(d) 8 ÷ 4 =
(e) 12 ÷ 4 =
(f) 4 ÷ 4 =
(g) 40 ÷ 4 =
(h) 24 ÷ 4 =
(i) 16 ÷ 4 =
(j) 20 ÷ 4 =
7. Divide by 5. Complete the equations. (a) 5 ÷ 5 =
(b) 15 ÷ 5 =
(c) 10 ÷ 5 =
(d) 30 ÷ 5 =
(e) 35 ÷ 5 =
(f) 20 ÷ 5 =
(g) 45 ÷ 5 =
(h) 25 ÷ 5 =
(i) 50 ÷ 5 =
(j) 40 ÷ 5 =
8. Divide by 10. Complete the equations. (a) 40 ÷ 10 =
(b) 10 ÷ 10 =
(c) 20 ÷ 10 =
(d) 70 ÷ 10 =
(e) 90 ÷ 10 =
(f) 30 ÷ 10 =
(g) 50 ÷ 10 =
(h) 100 ÷ 10 =
(i) 80 ÷ 10 =
(j) 60 ÷ 10 =
316