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Students calculate an exact square root and estimate approximate square roots by finding the length of the square flower bed of a given area, and give an explanation for their answers.

Students identify the different parts of algebraic expressions for the cost of repairing televisions.

Students identify significant figures in given numbers, and round numbers to a given number of significant figures.

Students perform calculations using whole numbers and negative numbers.

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.

Students describe algebraic expressions in words.

Students interpret a histogram showing the number of vehicles travelling at different speeds past a speed camera. Students need to calculate a percentage and the median to complete this task.

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 write and solve equations for story problems describing practical situations.

Students are required to use trigonometry to calculate the length of one side of a right-angled triangle in three problems based on a ski lift, a toy sail boat and a penguin on an iceberg.

Students study a box-and-whisker graph and answer questions on median, quartile and outliers.

Students use given information to solve a story problem about paper deliveries and identify the correct algebraic equation for the answer. They also write an algebraic equation for a similar story problem.

Students complete a bar graph from details about paua diving and answer questions interpreting the data, including finding an average.

Students are required to construct a composite bar graph based on Statistics New Zealand Time Use Survey data and are then required to make comparative statements based on gender.

For this practical task students construct a composite strip graph of the nutrient groups found in three different food products.

Students display data on a back-to-back stem-and-leaf graph to show the times taken to complete two walks. The longer of the two walks is then identified.

Students construct a back-to-back stem-and-leaf graph for heights of trees. They then answer a question on range and make a statement comparing the heights of akeake and kōhūhū.

Students demonstrate their understanding of standard form numbers by ordering given numbers from smallest to largest and by identifying the larger of two numbers.

Students explain who is most likely to win a game based on spinners, and how the game could be made fair.

Students interpret a back stem-and-leaf graph to answer questions about a measurement investigation.

Students consider three different sampling methods for a survey and decide if each is a fair sample, explaining their answer.

Students use rounding to estimate totals then discuss this as a method of estimation.

Students use a flowchart to find solutions and generate rules from them.

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 estimate and explain how they estimated their answer for two number problems: one involving multiplication; and the other division.