Rich tasks
This is an open-ended activity that gives students an opportunity to create three questions from a set of statistics about a white heron called Koko. Students then compare their solutions to the problem with those of a partner. The task can be given at the start of a topic, done as the students gain enough knowledge to complete it, or given as a homework task.
Koko’s statistics
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1. Koko’s statistics
- When introducing this task, teachers may need to remind students that these are facts and not random numbers, so the questions they ask must be linked in some way to the context for the problems to make sense.
Finding what’s missing by jumping through a tens number page 56
- Develop ways to find the difference by jumping through a decade (tens number).
- Understand why this is an efficient strategy for mental calculations and explore how the strategy can be recorded on a number line.
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Teacher notes
- Expressions that have been used for tens numbers in the past such as “tidy numbers”, “tidy ten” or “decade” should be discouraged as the term “tens number” best describes these numbers.
- Using a number line supports students understanding about how a number can be partitioned in a way that jumps through a tens number. Initially some students may require number lines with appropriate scales, but as students’ number and basic fact knowledge improve, empty number lines should be encouraged as they allow students to calculate in a wider number range.
Adding by making a tens number page 59
- Solve addition problems by creating a tens number.
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Teacher notes
- This strategy is usually used when one of the numbers is close to a tens number. It is helpful to discuss with students how they would decide which number in an equation should become the tens number.
Adding and subtracting in parts page 61
- Develop efficient ways of partitioning numbers to add or subtract.
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Teacher notes
- Encourage students to look for efficient ways they can use tens numbers when deciding how to partition.
- Asking whether one strategy is ‘quicker’ or ‘easier’ in some way may help students to compare two or more strategies and decide which is more efficient.
- It is important that students practise explaining why they have chosen to partition in the way they have and are able to record their strategy using a number line or equations.
- Sometimes students may suggest an incorrect strategy or make a miscalculation that results in a wrong answer. This provides a valuable opportunity for teachers to explore with students why a strategy has been unsuccessful before investigating alternative strategies. It also encourages students to take risks because the focus is on the process of problem solving and the thinking involved rather than the answer.
Adding and subtracting using tens number strategies page 63
- Develop efficient ways of using tens number strategies to add or subtract.
- Suggest reasons why one strategy is more efficient than another and develop ways to explain and record strategies.
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Teacher notes
- The game in this section is a game to practice choosing an appropriate strategy to add or subtract.
