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.

Working with Negative Numbers 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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