CAMBRIDGE PRIMARY MATHEMATICS 2: TEACHER’S RESOURCE
Developing mental strategies
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Teachers cannot see what is going on inside a learner’s head, but they can hear it and see the results. Learners can describe, show and explain their thinking using counting objects, shapes, patterns, measuring tools or something else. To find out what learners are thinking, you may need to listen in when learners talk to or show their work or ideas to a partner or a group, ask learners questions or simply ask learners to explain. See below for some suggested questions. As Stage 2 progresses, learners will be increasingly able to explain their thinking. Encourage the use of spoken and written words, diagrams, symbols and other written work, often alongside practical resources.
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Teachers need to introduce and model the relevant vocabulary so that learners have the words they need to talk about their strategies. Class teachers should value learner’s intuitive methods as well as introducing methods and approaches for learners to practise. Learners then have the opportunity to choose which strategy to use and develop their own. Any method that works is a correct method. It is important that you provide regular opportunities for learners to explain and discuss their methods, so they share ideas with one another and acquire a range of mental strategies. Not all learners will carry out a mental calculation in the same way, but some methods are more efficient and reliable than others. If you allow time for learners to discuss, explain and compare different methods you can support them to choose and use efficient methods. Learners will see the need for methods that can be applied generally, and this eventually leads towards using standard written methods. This helps to raise learners’ awareness of other strategies and develop their confidence and fluency. This could be through mini plenaries within the session or during a closing plenary. Mental strategies are not restricted to calculations. Visualising patterns, shapes and quantities is a key skill which supports learners to develop their mental imagery and strategies across all areas of mathematics. As learners manipulate objects, they are internalising their actions and making sense of the mathematics.
SA
There are many patterns in our counting sequence. Learners need to recognise and internalise these so that they can use them to develop their understanding of how our number system works and how it all fits together. Learners will then use this information to predict the next number when counting in ones, twos, fives and tens. Counting in multiples of 2, 5 and 10 will support learners as they develop their understanding of multiplication and division. As learners begin to learn about place value in numbers, they will develop a sense of the size of numbers so that they can compare and order them. Learners need to experience quantities of objects and measures to support estimating. Learners will have already experienced estimating measurements using non-standard measures such as their own foot or hand span. With some experience of standard units of measure such as centimetres, grams and litres, learners will begin to estimate measurements. The same is true of numbers. As learners extend their counting range to 100, they also need to experience collections of 10, 20, 50 and 100 objects before they can estimate amounts. With some experience of a number line, they will begin to estimate the position of a number when only a few key positions are marked. In Stage 2, learners begin to calculate with numbers up to a total of 100. Learners add and subtract 2-digit numbers, without regrouping ones or tens. This gives learners lots of opportunities to practise and begin to recall number facts for all numbers up to 9, since this is the maximum number
22 Original material © Cambridge University Press 2020. This material is not final and is subject to further changes prior to publication.
