TABLE OF CONTENTS
Place value
Lesson 1
Place value . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Addition and subtraction
Add and subtract . . . . . . . . . . . . . . . . . . . . . .14
Multiplication
io
Multiplication concepts . . . . . . . . . . . . . . . . .24
at
Fact strategies . . . . . . . . . . . . . . . . . . . . . . . .34
More fact strategies . . . . . . . . . . . . . . . . . . . .44
uc
Lesson 3
Lesson 4
Lesson 5
Ed
Division
Division concepts . . . . . . . . . . . . . . . . . . . . . .54
Fact families . . . . . . . . . . . . . . . . . . . . . . . . . .64
nl
ow
Lesson 6
Lesson 7
n
Lesson 2
Fractions
aw
Plane geometry
ke
rB
ro
w
Lesson 8 Fraction concepts . . . . . . . . . . . . . . . . . . . . . .74
Lesson 9 Model equivalent fractions . . . . . . . . . . . . . .84
Lesson 10 Benchmark fractions . . . . . . . . . . . . . . . . . . .94
Lesson 11 Compare fractions . . . . . . . . . . . . . . . . . . . .104
Lesson 12 Fractions greater than 1 . . . . . . . . . . . . . . . 114
. . . . . . . . . . . . . . . . . . . . . . . .124
H
Lesson 13 Plane figures
©
Linear measurement and area
Lesson 14 Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
Lesson 15 Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . .144
Graphs
Lesson 16 Picture graphs and column graphs . . . . . .154
Additional lesson
Lesson 17 Understand area . . . . . . . . . . . . . . . . . . . . .166
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
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Lesson
1 PLACE VALUE
PART ONE: Learn about place value
?
How can you find the value of each digit in a number?
You know how to read whole numbers.
at
io
n
Explore
For example, you read 235 as two hundred and thirty-five.
nl
ow
Ed
uc
How can place value help you understand the value
of each digit in 235?
Tens
Ones
2
3
5
ro
w
Hundreds
Which digit is in the hundreds place?
Let’s
Talk
4
3
Which digit is in the ones place?
5
2
aw
Which digit is in the tens place?
H
The 2 has a value of 2 hundreds, or 200.
The 3 has a value of 3 tens, or 30.
©
Connect
ke
rB
Think
A place-value chart tells the value of each digit in a number.
The 5 has a value of 5 ones, or 5.
235 5 200 1 30 1 5
235 has 2 hundreds, 3 tens, 5 ones.
Think about showing the number 500 in a place-value chart.
What does each zero in the number mean?
CA12631 • 9781760010201 • © 2013 Hawker Brownlow Education
Place value
Think It Through
Fill in the blanks. Solve the problem.
These blocks show the number 1208.
uc
at
How can you write 1208 to show the value of each digit?
io
n
• One thousand
is the same as
10 hundreds.
Ed
■ How many thousands are shown?
What is the value of the thousands digit?
• One ten is the
same as
10 ones.
nl
ow
■ How many hundreds are shown?
• One hundred
is the same as
10 tens.
What is the value of the hundreds digit?
w
■ How many tens are shown?
ro
What is the value of the tens digit?
ke
rB
■ How many ones are shown?
What is the value of the ones digit?
©
H
aw
Solution: 1208 5 1000 1 200 1 0 1 8
Now, use what you know to solve this problem.
1. What is the value of the 6 in 2460?
Thousands
Hundreds
Tens
Ones
2
4
6
0
400
6
0
60
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
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PART TWO: Learn about writing numbers in different ways
How can you use place value to write numbers in
different ways?
You know how to find the values of the digits in a number.
Hundreds
Tens
Ones
7
3
4
734 5 7 hundreds 1 3 tens 1 4 ones
734 5 700 1 30 1 4
n
Explore
?
uc
at
io
How can you name the values in different ways?
nl
ow
What is the value of the 4?
4
hundreds
What is the value of the 7?
7
tens
What is the value of the 3?
3
4
hundreds 1
7
ke
rB
473 5
ro
w
Think
Ed
The blocks show 473.
473 5 400 1 70 1 3
ones
3
tens 1
ones
aw
H
©
Connect
You can regroup 1 hundred as 10 tens.
4 hundreds 5 3 hundreds and 10 tens
10 tens 1 7 tens 5 17 tens
473 5 300 1 170 1 3
Let’s
Talk
473 5 3 hundreds 1 17 tens 1 3 ones
6
How can you write 473 using only tens and ones?
Look at the base-ten blocks above to help you.
CA12631 • 9781760010201 • © 2013 Hawker Brownlow Education
Place value
Think It Through
Fill in the blanks. Solve the problem.
The place-value chart shows the number 3655.
Thousands
Hundreds
Tens
Ones
3
6
5
5
n
What is another way to write 3655 if you regroup
1 hundred as 10 tens?
io
at
■ How many hundreds are there in 3655?
hundreds 5
hundreds and
Ed
uc
hundreds
■ Regroup 1 hundred as 10 tens.
tens
nl
ow
■ How many tens are there after you regroup 1 hundred?
tens 1
tens 5
tens
w
thousands 1
Solution: 3655 5
tens 1
hundreds
ones
ke
rB
ro
1
There are many
ways to rewrite
numbers. You
can regroup:
• one or more
thousands as
hundreds
• one or more
hundreds as
tens
• one or more
tens as ones.
Now, use what you know to solve this problem.
©
H
aw
2. The place-value chart shows 8024.
Regroup 1 thousand as 10 hundreds.
Then
rewrite the
number. Tens
Thousands
Hundreds
8
0
8024 5
thousands 1
1
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
tens 1
2
Ones
4
hundreds
ones
7
PART THREE: Choose the right answer
Solve the problem. Then read why each answer choice is correct
or not correct.
io
at
What is the value of the hundreds digit?
Ed
2000
100
ro
w
800
nl
ow
1000
uc
Solve
n
The blocks show 2185.
ke
rB
Check to see if you chose the correct answer.
In the number 2185 the hundreds digit is the 1.
aw
So, the correct answer is .
H
Why are the other answer choices not correct?
2000
©
Check
The block shows 1 hundred. The value of 1 is 100.
8
1000
800
This is the value of the thousands digit.
This is the value for 1 thousand, not 1 hundred.
8 is the tens digit, not the hundreds digit.
CA12631 • 9781760010201 • © 2013 Hawker Brownlow Education
Place value
Solve each problem. Use the hints to avoid mistakes.
• Find the correct place of the digit. Then
figure out the value of the digit.
• Remember that there are 10 ones in 1 ten,
10 tens in 1 hundred and 10 hundreds in 1
thousand.
Ones
9
5
4
io
2
Tens
at
Thousands Hundreds
5. What number do the blocks show?
n
3. What is the value of the 9 in 2495?
uc
9000
900
90
2005
9
2051
nl
ow
Ed
2510
ke
rB
ro
w
4. What is the value of the 2 in 1241?
2501
6. What is another way to write 348?
Hundreds
Tens
Ones
3
4
8
2
20
2 hundreds 1 4 tens 1 18 ones
200
3 hundreds 1 3 tens 1 8 ones
H
aw
3 hundreds 1 4 tens 1 18 ones
©
2000
2 hundreds 1 14 tens 1 8 ones
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
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PART FOUR: Write the best answer
Study the model. It is a good example of a written answer.
Student model
Hundreds
Tens
Ones
5
4
1
7
io
Thousands
n
What is another way to write 5417 if you regroup
1 thousand as 10 hundreds?
at
Show
The place-value chart shows 5417.
uc
Use pictures, words or numbers to show your work.
nl
ow
Ed
5 thousands 5 4 thousands 1 10 hundreds
10 hundreds 1 4 hundreds 5 14 hundreds
thousands 1
7
ro
1
ten 1
hundreds
ones
ke
rB
1
14
w
4
Solution:
The student
shows each
step.
The student
correctly
answers the
question
asked.
aw
I started with 5 thousands. I regrouped 1 thousand and
then had 4 thousands and 10 hundreds. I added the
The student
gives
important
details about
how to write
the number.
H
Explain
Explain how you got your answer.
©
10 hundreds to the 4 hundreds I already had: 10
hundreds
1
4 hundreds
5
14 hundreds. The tens place
and the ones place did not change.
10
The student
uses the
maths words
regroup,,
regroup
thousands,,
thousands
hundreds,,
hundreds
tens place
and ones
place.
place
CA12631 • 9781760010201 • © 2013 Hawker Brownlow Education
Place value
Solve the problem. Use what you learned from the model.
CHECKLIST
7. What is another way to write 2960 if you regroup
1 hundred as 10 tens?
Did you . . .
show each step?
Thousands
Hundreds
Tens
Ones
2
9
6
0
answer the question
asked?
Use pictures, words or numbers to show your work.
n
give important details?
Solution:
ke
rB
ro
w
nl
ow
Ed
uc
at
io
use maths words?
thousands 1
tens
ones
aw
1
hundreds 1
©
H
Explain how you got your answer.
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
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PART FIVE: Prepare for a test
As you solve place-value problems, you may want to:
• think about the value of each digit.
• make a place-value chart to help you.
Solve each problem.
io
n
10. Germaine has a roll of tape that is
14 hundred centimetres long. How
long is the tape?
at
8. What is the value of the digit in the
tens place in 1076?
uc
14 centimetres
140 centimetres
Ed
1400 centimetres
7
70
700
w
nl
ow
14 000 centimetres
ke
rB
ro
7000
11. Which place-value chart shows
8 thousands 1 4 hundreds 1 7
tens 1 9 ones?
Thousands Hundreds
9. What is another way to write 3592?
2 thousands 1 5 hundreds
1 19 tens 1 2 ones
aw
2 thousands 1 15 hundreds
1 9 tens 1 2 ones
©
H
3 thousands 1 5 hundreds
1 19 tens 1 2 ones
3 thousands 1 15 hundreds
1 9 tens 1 2 ones
4
8
Ones
7
9
Tens
Ones
9
7
Tens
Ones
7
9
Tens
Ones
8
9
Thousands Hundreds
8
4
Thousands Hundreds
8
4
Thousands Hundreds
7
12
Tens
4
CA12631 • 9781760010201 • © 2013 Hawker Brownlow Education
Place value
14. The place-value chart shows 7013.
How can you write this number by
regrouping 1 thousand?
12. A school building has 18 hundred
students. How many students are
there?
18
180
800
Thousands Hundreds
7
ten 1
io
84
ones
at
hundreds
uc
80
3
n
13. What is the value of the hundreds
digit in 3084?
1
0
1
0
Ones
thousands 1
1800
Tens
nl
ow
Ed
3000
ro
w
15. What is another way to write 3681 if you regroup 1 thousand
as 10 hundreds?
ke
rB
Thousands Hundreds
3
Tens
Ones
8
1
6
aw
Use pictures, words or numbers to show your work.
thousands 1
hundreds 1
tens 1
one
©
H
Solution:
Explain how you found your answer.
© 2013 Hawker Brownlow Education • 9781760010201 • CA12631
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