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3. Integers
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Stage 3

3.01 Integers

Lesson
Practice
Lesson

Are you ready?

Can you represent worded statements using numbers or number sentences? Try this question before continuing.

Examples

Example 1

Ray has 10 comic books. Danielle has 3 less comic books than Ray.

Write a number sentence to find the number of comic books that Danielle has.

Worked Solution
Create a strategy

If Danielle has less books we need to subtract.

Apply the idea

We subtract 3 from the number of comic books Ray has. \text{Danielle's comic books}=10-3

Idea summary

Some words that we may find in a story could be:

AdditionSubtraction
MoreLess
AddSubtract
Give toTake away
PlusMinus

Integers

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Examples

Example 2

A man drove 10 km East, then 24 km West, then 8 km East.

a

Is he now East or West of his original position?

A
Back to his original position
B
West
C
East
Worked Solution
Create a strategy

Use a number line to represent the information where East is the right direction and West is the left direction.

Apply the idea

We can let the point 0 be his original position.

To show 10 km East, start from 0 and move 10 places East (right).

-15-10-5051015

To show 24 km West, move 24 places West (left).

-15-10-5051015

To show 8 km East, move 8 places East (right).

-15-10-5051015

The point ended to the left side of the 0, which means he is West of his original position. So the correct answer is B.

b

How far West is he from his original position?

Worked Solution
Create a strategy

Count the number of spaces he ended up from 0.

Apply the idea

The man ended up at the following point:

-15-10-5051015

This is 6 spaces to the left of 0. So he is 6 km West of his original position.

Idea summary

When we express numbers as directed numbers, our number indicates a value and direction.

PositiveNegative
ProfitLoss
AscendingDescending
UpDown
ForwardBackward

Outcomes

MA3-4NA

orders, reads and represents integers of any size and describes properties of whole numbers

MA3-5NA

selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

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