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For this NEMP task students complete a table for a linear equation about fuel consumption.

Students describe a variable in a linear equation, solve the equation, and complete a second equation relating to weights.

Students complete a table showing times to boil different quantities of water. They identify the rule that relates the amount of water to boiling time and use it to answer questions.

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

Students use sticks to continue given patterns, and identify the number of sticks needed to make the new shapes in the pattern.

Students calculate the cost of hiring a search and rescue helicopter and compare this cost with another helicopter company's charges.

Students solve a number of mathematical problems involving money and distance, and compare the results to identify the cheapest taxi company.

Students calculate the repair charges for two different washing machine repair companies, and compare and explain their results.

Students calculate the repair charges of two different garages, graph them, and explain the results.

Students solve and write appropriate equations for story problems.

Given their intercepts and slopes, students are required to graph three different linear equations that have been written in a practical context.

Students find the unknown for a range of equations that require number property knowledge and understanding of relational thinking.

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.

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 complete subtraction and division linear equations with brackets by selecting from a range of numbers.

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

For this NEMP task students represent the number six in ten different ways using the four arithmetic operations.

Given a rule, students complete a table and answer questions about cycling distances for a cycling fitness programme, describe the rule for the pattern, and identify an expression for the rule.

Students complete a table showing the number of matchsticks used to build a series of pentagons. They identify the number of matchsticks required for a given pentagon and state the rule as an word equation.

Students complete a spatial pattern, record the sequence in a table, and complete a statement about the rule.

Students draw the next two patterns in a spatial pattern, complete a table and questions about the pattern, and write a rule to describe the pattern.

Students answer two questions about the number of seats available as more tables are added to a row, and state a rule for the pattern.

Students complete a table showing the number of counters used to make a series of L-shapes. They identify the number of counters needed for different situations, and describe the relationship as a rule.

Students identify the rule for continuing number patterns then develop their own pattern and write it as a rule.

Students complete a table showing the number of matchsticks used in a spatial pattern, identify the number of matchsticks required for a given shape, and describe the rule for the pattern.