Algebra: Odds and Evens

Australian curriculum number (ACMNA071; ACMNA083)

Students develop their understanding of the properties of odd and even numbers, by exploring the results of adding and subtracting odd and even numbers. They use these results to make generalisations, then use their generalisations to solve problems and explore patterns.

This sequence is for students who:

  • have an understanding of what makes a number even or odd.
  • see even numbers as numbers that are divisible by 2 with no remainder and odd numbers as those with a remainder of 1 when divided by 2.

Students will need to employ their mental computation skills.


Lesson 1: Number Maze

Students are presented with a number maze. As they move through the maze, students need to total the numbers on the path they follow. The challenge is to complete the maze with an odd total. By exploring possible solutions to the maze, students form generalisations about the results of adding odd and even numbers. They see that an odd number of odds in the sum is required to get an odd total.

Lesson 2: 10 to 1

This task challenges students to use addition, subtraction and the numbers 10 down to 1 to make a total of 27 and a total of 12. They will see that it is possible to create only an odd total with these numbers. Students look at the largest and smallest positive totals for the problem. They also look at the ways in which they can modify the task to create even totals.


Last updated June 14 2020.