Year level: 7

Strand: Algebra / Number / Space

Lesson length: 60 mins

In this lesson, students play games and learn about space and location, the Cartesian plane, pattern recognition and reductive reasoning by playing games and thinking. Students create algebraic equations to describe their strategy. Follow this lesson with Graphs: formulas and variables, though both lessons can be taught in isolation.

A game of Battleship also called the sea battle board game.

Achievement standard

Students create tables of values related to algebraic expressions and formulas and describe the effect of variation.

Students represent objects two-dimensionally in different ways, describing the usefulness of these representations. 

Students use coordinates to describe transformations of points in the plane.

Content descriptions

Students generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane. AC9M7A05

Students represent objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations.AC9M7SP01

Students describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point.AC9M7SP03

Students recognise, represent and solve problems involving ratios. AC9M7N08

General capabilities


  • Number patterns and algebraic thinking (Level 7)
  • Positioning and locating (Level 5)

Critical and Creative Thinking:

  • Draw conclusions and provide reasons (Level 5)
  • Consider alternatives (Level 5)

Digital Literacy:

Related content

Digital Technologies: AC9TDI9P02

The following formative assessment is suggested.

Use slide 11 from the teacher's slides as a prompt to instruct students to graph their linear rules on GeoGebra or other dynamic graphing software and submit at least one screenshot. Students may hand draw their graphs. Students could submit a paper copy, if preferred.

Some students may:

  • confuse or mix up the x and y axes; write the y-coordinate instead of the x-coordinate: (y, x) instead of (x, y)
  • unable to connect the negative parts of the axes compared with the positive parts of the axes
  • unable to connect how the coordinates represent real-world data and what that means
  • not connect the purpose of algebra and why letters and symbols are used to represent a relationship to investigate
  • think of ‘n’ as a placeholder for only one number, and not any number
  • confusing the order of operations and think that the ‘=’ sign symbolises equivalence and not an instruction to work out, like an operation
  • hold misconceptions around equations without understanding the equation is describing a relationship (y=mx+c) and when that equation varies (for example, c is missing) are unable to apply this thinking or describe it
  • have challenges maintaining a consistent sense of scale or have difficulty visualising and manipulating shapes and patterns either in a grid, a plane, or in their minds.


  • create algebraic expressions to represent relationships involving one or more operation
  • use words or symbols to express relationships involving unknown values
  • evaluate an algebraic expression or equation by substitution
  • collect and access data using a range of digital tools and methods in response to a defined question or problem
  • analyse and visualise multidimensional data by selecting and using a range of interactive tools to draw conclusions and make predictions
  • use maps and grid references to find locations, describe routes using directional language, and interpret keys, scales and compass directions as a precursor to working on the Cartesian plane.

Definitions for linear function, linear equation, linear expression, growing patterns and the Cartesian plane can be found at Version 9 mathematics glossary.

What you need:

  • Lesson Plan (Word)

  • Teacher's slides (PowerPoint)

  • Grid paper, rulers, pencils, erasers for each student

  • Dynamic graphic software e.g. GeoGebra or Wolfram (optional)