Explains positive and negative whole numbers using the number line, then sets out the rules for adding, subtracting, multiplying and dividing integers with worked examples. Finishes with a BODMAS example and a self-check so students can confirm they have the sign rules right.
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Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Integers Explained: Working with Negative Numbers
Year 7 students (typically ages 12–13) working on integers. It is pitched at level 2 · standard.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try Year 7 Integers (Directed Numbers) Worksheet — Level 2.
Year 7 · Mathematics · Integers
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Integers are the whole numbers and their opposites: … −3, −2, −1, 0, 1, 2, 3 … Negative numbers sit to the left of zero on the number line, so the further left a number is, the smaller it is. −5 is smaller than −2, even though 5 is bigger than 2. Think of temperatures: −5 °C is colder than −2 °C.
Ordering from smallest to largest: −5 < −2 < 0 < 3. The opposite of a number is the same distance from zero on the other side: the opposite of 4 is −4.
Work out −5 + (−3) and 6 − (−2)
Multiplying and dividing. Multiply or divide the numbers as usual, then decide the sign: same signs give a positive, different signs give a negative.
| Signs | Result | Example |
|---|---|---|
| positive × positive | positive | 4 × 6 = 24 |
| negative × negative | positive | −3 × −7 = 21 |
| positive × negative | negative | 5 × −4 = −20 |
| negative ÷ positive | negative | −18 ÷ 3 = −6 |
| negative ÷ negative | positive | −20 ÷ −4 = 5 |
Order of operations (BODMAS). BODMAS still applies with negative numbers: Brackets, Orders (powers), Division and Multiplication, then Addition and Subtraction. Be especially careful with the signs.
2 − 3 × (−4)
Answers: 1. 3 2. −13 3. 8 4. 40 5. −4 6. −13 (2 × (−5) = −10, then −3 + (−10) = −13)
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Adding, subtracting, multiplying and dividing positive and negative numbers. Expected-level practice for this year group. This Year 7…
Adding, subtracting, multiplying and dividing positive and negative numbers. Expected-level practice for this year group. This Year 7…
Adding, subtracting, multiplying and dividing positive and negative numbers. A challenge set for students ready to stretch further. This…
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