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Puzzles and Problems
Objectives
To use inverse operations to create ‘Magic chains’ of numbers.
To use doubling and halving as part of a multi-step puzzle.
Resources
Abacus Workbook 2 | 📄 Magic chain | 📄 Working backwards
Vocabulary
problem | solve | add | subtract | less than | more than
Today's Lesson
What to Get Ready
Write the following instructions:
- Think of a 2-digit number less than 70.
- Add 30.
- Subtract 20.
- Add 10.
- Subtract 20.
- Add 3.
- Write down this final answer.
Introduction
Ask your student to follow the instructions, writing down the number they think of and answer as they go.
Ask them to tell you the number they first thought of. Quickly add 3 to this number and say, ‘Your answer is…’
Establish that you asked them to add 30 and 10, but subtract 20 and 20, before adding 3. So they added 40, then subtracted 40, which mean that you just had to add 3 to tell them their answer.
Explain that they are going to make their own ‘Magic chain’ like this.
Consolidate
Access the 📄 Magic chain sheet, if needed, to consolidate the task and to provide a template or example for the chain.
Main Activity
Ask your student to write their own instructions for a magic chain similar to that in the Introduction, where they ask someone to think of a 2-digit number, add and subtract the same total of numbers in different ways before performing a final addition or subtraction.
They should record these and then test them out with you or a willing participant.
Challenge them to make really long magic chains!
Extra Challenge
Ask your student to work through the 📄 Working backwards sheets – how do these link to magic chains?
Workbook
To help your student recap upon previous learning from this course, please ask them to complete the activities on page 40 of Abacus Workbook 2.