Problem solving unpacked Jennie Pennant Jennie Pennant GrowLearning

Session 1 Rich tasks: promoting mathematical learning for all

National Curriculum The expectation is that the majority of children will move through the programmes of study at broadly the same pace. …Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding….

Problem solving unpacked ELAPS lesson versus investigations Naming and drawing attention to PS skills Structuring a PS Lesson Types of problem Objectives Recording Classroom culture

Five Steps to 50 (10586) This challenge is about counting on and back in steps of 1, 10 and 100. Roll a dice twice to establish your starting number - the first roll will give you the tens digit and the second roll will give you the units digit. You can then make five jumps to get as close to 50 as possible. You can jump forwards or backwards in jumps of 1 or 10 or 100.

Spiralling Decimals (10326) *

Maze 100 (91)

Bryony’s triangle (7392)

Problem-solving skills visualise work backwards reason logically conjecture work systematically look for a pattern trial and improvement

Session 2 The problem solving process under the microscope

The Problem-solving Process Stage 1: Getting started Stage 2: Working on the problem Stage 3: Going further Stage 4: Concluding

Problem-solving process 1.Getting started try a simpler case draw a diagram represent with model act it out 2. Working on the problem visualise work backwards reason logically conjecture work systematically look for a pattern trial and improvement 3. Going further generalise verify prove 4. Concluding communicate findings evaluate

Types of Task Finding all possibilities Visual problems Logic problems Rules and patterns Word problems

FAP Six beads (152)

Baravelle (6522)

Hundred Square (2397)

Number sequences: crosses, T-shirts generate and describe linear number sequences Colour sequences. What comes next? T-shirts Patterns from crosses Picture frames

Plenty of pens (1117)

Focus on recording

Reasons for recording to help me remember what I did so that I can repeat it to record what doesn’t work to keep a track of what I’ve tried it may enable me to see a pattern that helps me solve the problem it may help me see a short cut it helps me check I have all the solutions it helps me externalise my thinking it helps me confirm/agree my understanding with others it enables me to compare different ways of recording and learn to be elegant, efficient and succinct in the way I record my thinking.

Recording Recording in the moment Recording as thinking Recording for another person/time Recording mathematics

Problem solving unpacked ELAPS lesson versus investigations Naming and drawing attention to PS skills Structuring a PS Lesson Types of problem Objectives Recording Classroom culture