k ick

o f f

Useful skills for this chapter:

Understanding place value of numbers to 1000.

The ability to pull apart numbers into their place-value components.

An understanding of the relative size of numbers and their placement on a number line.

1 Write the number that is 100 more than:

a 300 b 324 c 936 d 1013 e 19 079

2 Write the number that is 100 less than:

a 300 b 324 c 936 d 1013 e 19 079

3 Write the number that is 1000 more than:

a 5000 b 702 c 31 d 3058 e 19 892

4 Write the number that is 1000 less than:

a 8000 b 1003 c 11 035 d 10 403 e 20 202

Show what you know

1 Draw a number line from 0 to 1000. Mark in 25, 100, 400, 750 and 888.

2 Write the value of the 5 digit in these numbers.

a 57 903 b 957 c 1225 d 15 092 e 13 582

C h a p t e r 1 Preparation

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1Chap t e r

NumberandAlgebra

Positive and negative whole numbersThis chapter begins by looking at whole numbers; then we look at negative whole numbers.

The whole numbers are sometimes called the counting numbers. The whole numbers are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and so on. We can always add 1 to any whole number and get another whole number. That is why we say the list of whole numbers is infinite it never ends.

We use numbers to record countable quantities where we can ask how many?

For example:

How many buses are in the car park?

How many children are at school today?

How many salad rolls did you eat for lunch?

Australian Curriculum content descriptions ACMNA124

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We also use whole numbers for quantities that we measure, rather than count. When we are talking about quantities, we ask how much?

For example:

How much rice is needed for dinner?

How much money do you need to save for your holiday?

How much orange juice is in the jug?

negative whole numbers are used to describe numbers below zero, such as temperatures. For example, the temperature at the top of Mt kosciusko in winter can be as low as 18C.

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The digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 can be used to write:

a 5-digit number such as 89 371

a 6-digit number such as 450 672

a 1-digit number such as 2

any whole number.

We can use place-value cards to help break a number into its place-value parts.

These place-value cards show the value of each digit in the number 3461.

3 0 0 0

4 0 0

6 01

1643

Each place in a number has a special value.

For example, in the number 3 427 568:

the 3 means 3 millions

the 4 means 4 hundreds of thousands

the 2 means 2 tens of thousands

the 7 means 7 thousands

the 5 means 5 hundreds

the 6 means 6 tens

the 8 means 8 ones.

3 4 2 7 568

Thousands

Hundreds

Tens

Ones

Tens of thousands

Hundreds of thousands

Millions

1A Place value

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The value of a digit changes if it is in a different place. If we take the number 3 427 568 (on the previous page) and change the position of the digits to make 8 674 325:

the 8 means 8 millions

the 6 means 6 hundreds of thousands

the 7 means 7 tens of thousands

the 4 means 4 thousands

the 3 means 3 hundreds

the 2 means 2 tens

the 5 means 5 ones.

We can use base-ten materials to help us understand place value.

= 1 = 10 = 100 = 1000

This is the number 3461 shown with base-ten materials:

3461 means 3 thousands + 4 hundreds + 6 tens + 1 one.

8 6 7 4 325

Thousands

Hundreds

Tens

Ones

Tens of thousands

Hundreds of thousands

Millions

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knowing the value of the places in a number helps us to read it.

Millions

Hundreds of millions

Tens of millions

Millions

9 2 6

Thousands

Hundreds of

thousands

Tens of thousands

Thousands

7 1 4

H T O

5 3 8

We read 926 714 538 as nine hundred and twenty-six million, seven hundred and fourteen thousand, five hundred and thirty-eight.

Example1

Write the value of the 8 in each number.

a 28 774 b 289 c 18 693 002 d 781 721

Solution

a In 28 774, the 8 is in the thousands place, so it has the value of 8 thousands or 8000.

b In 289, the 8 digit is in the tens place, so it has the value of 8 tens or 80.

c In 18 693 002, the 8 digit is in the millions place, so it has the value of 8 millions or 8 000 000.d In 781 721, the 8 digit is in the tens of thousands place, so it has the value of 8 tens of thousands or 80 000.

SummaryThe value of a digit in a number depends on the place it is in.

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C onn e C t , a p p l y a n d b u i l d1A Whole class 1 Make the place-value cards from BLM 1 Place-value cards.

3 0 0 0

2 0 0

8 07

7823makes

Use your place-value cards to make these numbers.

a 8912 b4938 c389 d9072

2 a Use your place-value cards to make other numbers up to 9999.

b Match the numbers you make with your place-value cards to numbers shown on an abacus. Use a real abacus, or draw one.

c Match the numbers you make with your place-value cards to numbers made with base-ten blocks.

3 Write these numbers in words.

a 5038 b 28 445 c 46 102

d 298 577 e 1 305 084

4 Write the number:

a 85 tens and 2 ones

b 300 ones

c 23 hundreds, 5 tens and 3 ones

d 4 thousands, 5 hundreds and 18 ones

e 23 hundreds and 45 ones

f 128 thousands, 43 tens and 9 ones

g 34 ones, 18 hundreds

h 17 ones, 1 ten thousand, 23 hundreds

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1A Individual 1 Write each number.

a Eight thousand, two hundred and twenty-three

b one hundred and five thousand, two hundred and forty-nine

c Thirteen million, seven hundred and ninety-eight thousand, five hundred and sixty-two

2 Write each number in words.

a 91 b 48 c 392 d 6789

e 18 002 f 21 309 g 589 902 h 6 893 407

3 Write the value of each highlighted digit.

a 802 b 3196 c 54 795

d 83 2 4 89 e 1 904 684 f 589 444 239

g 60 3 54 0 0 02 h 347 862 919

4 Copy and complete this place-value chart.

Number Place-value parts

Tens of millions

Millions Hundreds of

thousands

Tens of thousands

Thousands Hundreds Tens Ones

9045

21 947

101 010

800 641

1 794 376

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A number line helps us make sense of numbers. To make a number line, draw a line on the page and mark 0 for zero. The arrow shows that the line continues in the same way forever.

0

Mark equally spaced points to the right side of the zero.

0

label the first marker to the right of the zero as 1.

10

label the next marker 2, then keep going.

6543210

You can make number lines out of string or tape, or draw them on paper. They can be used to show any number, from the very smallest number to the largest number you can think of.

Example2

Draw a number line from 0 to 10. Use large dots to mark the numbers 1, 3, 5 and 7.

Solution

109876543210

1B The number line

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A number ladder is like a vertical number line with equally spaced rungs. georgie has her left foot on 2, her right foot on 3 and her left hand on 7.

We usually mark 0 on the number line and then mark 1, 2, 3, evenly spaced as far as we need to go.

sometimes we mark the multiples of 10 or the multiples of 100, depending on what we need.

10

9

8

7

3

2

1

0

Example3

show where 150 would be on this number line.

10000

Solution

Mark in steps of 100. The number 150 is halfway between 100 and 200.

900 10008007006005004003002001000

150

We can also use number lines to compare numbers.

8000 100 200 300 400 500 600 700

200 500 700

numbers get larger as we go to the right on the number line. so 700 is larger than 200 because it lies further to the right.

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