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Students learn how to use written methods to order and calculate with negative numbers. Learning progress from performing arithmetic on a number line to multiplying and dividing with negatives.

This topic takes place in Term 2 of Year 9 and follows Properties of Numbers.

**Prerequisite Knowledge**

- count backwards through zero to include negative numbers
- interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
- use negative numbers in context, and calculate intervals across zero

**Success Criteria**

- order positive and negative integers
- apply the four operations, including formal written methods, to integers, both positive and negative

**Key Concepts**

- To order negative and positive numbers temperatures can be placed along a thermometer.
- Use a number line to demonstrate how negative number is less than its positive counterpart but of equal magnitude.
- Use a number line to demonstrate addition and subtraction involving negative and positive numbers.
- Adding a negative is equivalent to a subtraction. ( 4 + -2 = 4 – 2)
- Understanding why subtracting a negative results in an addition is vital to multiplying and dividing with negative numbers.

**Common Misconceptions**

- Students often incorrectly consider negative numbers with a larger magnitude than positives to have a greater value. For example, -3 < 2.
- Common incorrect answers to -4 + 6 are -2 (4 – 6) and -10 (-4 – 6)
- Trying to remember multiplication rules for when to leave the answer as a positive or negative often results in confusion when adding and subtracting. Use a number line to demonstrate -3 x 2 = -3 + -3 = 6.

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