B. Ditectif Digid

Introduction
An activity on combining inverse arithmetic operations with place value. The aim is to develop the sense of number size, related to reasonableness of answers.
Children investigate their mental intuitive methods in simple addition problems and share these methods. Then they handle problems where there are multiple solutions or no solutions, and progress onto problems with a number of steps and with alternative routes, including multiplication.
This activity has four episodes. Each episode consists of an introduction, paired or group work and whole class sharing. The session must finish with a whole class reflection phase, regardless of how far the class has got.
Episode 1: : Making intuitive methods explicit
Children first distinguish between digits and numbers. They use intuitive methods for solving a single missing digit problem, describing various methods. They progress to questions with two missing digits.
In the sharing phase, they recognise alternative methods, and the fact that they all combine place value with inverse operations.
Episode 2: : Impossible and multiple solutions
Children identify cases where no solution is possible or where there is more than one solution and discuss the range of possible values.

Episode 3: Three-digit sums

Children handle more complex problems combining inverse operations, place value, and decomposition.

Episode 4
Children find maximum and minimum sums and products for two-digit numbers with different digits. This extends the strategies they have been using.
Reflection: Sharing of mental methods
Children comment on the advantages of making their intuitions explicit. Comparison and sharing of methods gives children a wider range of strategies.
BEFORE YOU TEACH
Tell children that the lesson starts with simple calculations to allow them to talk about their ways of thinking through the problem.

License

Gwersi PCAME a Dewch i Feddwl Mathemateg (9 i 11 oed) Copyright © by Ann Longfield, David Johnson, Jean Hindshaw, Linda Harvey, Jeremy Hodgen, Michael Shayer, Mundher Adhami, Rosemary Hafeez, Matt Davidson, Sally Dubben, Lynda Maple, and Sarah Seleznyov. All Rights Reserved.

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