# Working with Negative Numbers

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.

##### Problem Solving and Revision Lessons

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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