Directed Number Lesson 2: Roller Coaster

Australian curriculum number (ACMNA124)

Lesson abstract

Students throw dice to construct a “roller coaster” that goes above ground level (positive numbers) and below ground level (negative numbers). Directed numbers are modelled by height above and below the ground and movements up and down are recorded as addition or subtraction statements. Additionally, the elevation of the roller coaster can be estimated at any point along the track.

Mathematical purpose (for students)

Movements up and down a number line relate to adding and subtracting numbers.

Mathematical purpose (for teachers)

This lesson aims to extend students’ mental model of directed number and give meaning to a limited range of addition and subtraction statements.  In particular students work with additions such as -4 + 3 interpreted as starting at position -4 and moving up 3 units, and a subtraction such as 4 – 2 as starting at position -4 and moving down 2 units.  There is potential to extend beyond integers.  

At the end of this lesson, students will be able to:

  • Position positive and negative integers on a vertical number line.
  • Understand that adding and subtracting involves moving in a particular direction on the number line.
  • Move above and below zero on the number line and express this using symbolic notation.