Patterns and relationships resources

Students use rules to work out the number of shapes or matches in spatial patterns, and complete an algebraic rule from a word rule.

Students complete a table and a rule for a linear equation for a foreign currency exchange. The values are then plotted and interpreted.

This task requires students to interpret the relationship between noise level and time as illustrated by various points on a graph.

Students interpret a graph about getting to school, writing descriptions about each students journey and making statements comparing the journeys.

Students select the correct equation to describe a series of graphs.

Students complete number pairs, and write the equations for three 'number machines'.

Students draw in the next two shapes in a spatial pattern, complete a table and rules about the pattern, then calculate the number of triangles in the 8th shape.

Students answer two questions about exercise times for an incrementing fitness programme. They identify an expression relating time exercised to the number of weeks on the programme, and explain why this pattern couldn't continue indefinitely.

Students interpret graphs showing the different ways that four people run a race.

Students interpret a graph of the Hare's Progress to answer questions about rate, rest, and reading sections of the graph. They also identify the constant motion of the tortoise and explain the result of the race.

Students respond to questions about the relationship between diagonals, triangles and polygons; then write a rule to describe the pattern.

Students use cubes to construct part of a spatial pattern and answer questions on how to continue it.

In this task students build the next two models of a spatial sequential pattern and then use their results to predict subsequent patterns and give general rules for these in words and in equations.

Students construct a graph for each linear equation given.

Students identify the slope and intercepts of a linear equation, then plot a different function.

Students continue a spatial pattern of hexagons, then describe its rule.

Students complete a table showing the number of rungs for different sized ladders. They complete a sentence stating the rule to calculate the number of rungs given the length, and use the rule to identify if a ladder, at a lean, will reach a given height and show their working.

Task: interpret a graph of a car's journey and add to the graph to represent a further description of the journey. Assessment focus: graph interpretation.

The start of a spatial pattern of triangles is shown and described in a table. Students generate more of the pattern and describe the relationships algebraically.

A spatial pattern involving the area of a shape is represented by a table and a diagram. Students describe the rule in words and as an algebraic expression.

Students complete a table to describe a spatial pattern, and write an equation to express the rule.

Students use substitution into equations to evaluate the number of blocks and total surface areas in shapes of different heights. The stimulus can be used as a challenging task to try and derive the rules from the spatial pattern. This is classified as Patterns and Relationships.

Students continue two number patterns of diamonds in a sequential pattern, state the general rule for the number sequences and use the rule to find the pattern number with a given number of diamonds.

Students complete equations that give the rule for the general term for a number of spatial patterns.

This resource is about students continuing linear or quadratic spatial patterns, and giving rules for them.