problem solving unpacked jennie pennant jennie pennant growlearning [email protected] 07711...
TRANSCRIPT
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.
0.5 0.25 0.75 0.3
0.35 0.9 0.99 0.999
0.1 0.01 0.05 1.79
0.64 0.32 0.54 0.865
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-shirtsgenerate 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
https://nrich.maths.org/9623
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