2 Aims of the session This session is intended to help us to: Explore different types of mathematical activity:Classifying mathematical objects.Interpreting multiple representations.Evaluating mathematical statements.Creating problems.Analysing reasoning and solutions.
3 1. Classifying mathematical objects Learners examine and sort mathematical objects according to their different characteristics.They create and use categories to build definitionsThey learn to discriminate carefully and to recognise the properties of objects.They develop mathematical language.
4 Examples of classifying activities Find the odd one out tables activity (Maths Out Loud 4 – 13)Sorting shapes (Maths Out Loud 4 – 27)Resources required:Maths Out Loud Book 4 (BEAM)Maths Out Loud 6 (BEAM)Big Book of Word Problems Years ½String
5 2. Interpreting multiple representations Learners match cards showing different representations of the same mathematical idea.They draw links between different representations.They develop new mental images for concepts.
6 Examples of interpreting multiple representations Different representations of multiplicationSuggestionsDefinitions and images of shapesMatching sets of sumsShowing 100Definitions and images of shapes: activity devised for an MA publication forthcoming by Jenni Back and Liz WoodhamShow 100: ask children to ‘show me 100’ giving them lots of materials to make their own representation e.g. matchsticks, pasta, pulses, sticky paper, glue, scissors, sugar paper etc.
7 3. Evaluating mathematical statements Learners decide whether given statements are true or false (or possibly sometimes true.They are encouraged to develop mathematical arguments and justifications.They are encouraged to develop examples and counterexamples to defend their reasoning.
8 Examples of evaluating mathematical statements Sally’s Sweet Shop activityProperties of shapes: Stringy QuadsProperties of 2D shapes (Maths out Loud 6 – 27)Properties of shape activity from NRiCH website:
9 4. Creating and solving problems Learners devise their own mathematical problems for other learners to solve.Learners are creative and ‘own’ the problems.While others attempt to solve them, learners take on the role of teacher and explainer.The ‘doing’ and ‘undoing’ processes of mathematics are exemplified.
10 Examples of creating and solving problems Sum and product example (Maths Out Loud Book 4 – 15)Big Book of Word Problems (Year 1/2 Sleeping Ugly)Think of a number problemsFunction machines: The Number Crunching MachineHyperlink to NRICH problem:
11 5. Analysing reasoning and solutions Learners compare different methods for doing a problem.They organise solutions and/ or diagnose the causes of errors in solutions.They begin to recognise that there are different ways through a problem.They develop their own chains of reasoning.
12 Examples of analysing reasoning Using learner’s solutions both correct and incorrect especially from test papers.Collecting learner’s descriptions of their methods.Look at SATs paper results
13 Follow up taskPick one kind of activity from the suggestions and adapt it to meet the needs of your classTry it with your class and reflect on the quality of their responses to itCome to the session prepared to share your observations and some examples of children’s work