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Different starts can meet the same result

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Number Play · Explore the Kaprekar routine · 3:48

You'll learn: Compare selected trajectories and recognise a fixed result

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Different starts can meet the same result

3:48

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Different starts can meet the same result

You'll learn: Compare selected trajectories and recognise a fixed result

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Same topic

Explore the Kaprekar routine

1

Rearrange subtract and repeat
3:35
Rearrange subtract and repeat
You'll learn: Follow the four-digit routine with valid starting digits

Next topic

Find number patterns in clocks and calendars

1

Clock and calendar digit puzzles
3:30
Clock and calendar digit puzzles
You'll learn: Find patterns within the chosen display convention

Next topic

Use mental arithmetic and spot patterns

3

Regroup to make a friendly calculation
3:34
Regroup to make a friendly calculation
You'll learn: Explain mental addition and multiplication
An operation changes more than the digits
3:38
An operation changes more than the digits
You'll learn: Reason about possible result sizes
Always sometimes or never
3:40
Always sometimes or never
You'll learn: Support a claim or find a counterexample

Next topic

Explore the Collatz process

2

Two rules create a number journey
3:28
Two rules create a number journey
You'll learn: Apply half for even numbers and three times plus one for odd numbers
Examples leave a bigger question
3:42
Examples leave a bigger question
You'll learn: Understand what an unproved conjecture means

Next topic

Estimate quantities sensibly

2

Estimate using a small count
3:37
Estimate using a small count
You'll learn: Use representative groups to estimate a larger quantity
Choose a sensible scale for an estimate
3:33
Choose a sensible scale for an estimate
You'll learn: Check whether a result is plausible

Next topic

Explore games and winning strategies

2

Work backwards in a counting game
3:32
Work backwards in a counting game
You'll learn: Find useful target totals for adding one two or three
Change the rules and rethink the strategy
3:40
Change the rules and rethink the strategy
You'll learn: Adapt reasoning when the target or allowed move changes

Next topic

Turn a question into a small data collection

2

What do we need to find out
3:30
What do we need to find out
You'll learn: Turn a practical question into collectable responses
Collect data consistently
3:44
Collect data consistently
You'll learn: Record each response once in useful categories

Next topic

Organise observations with tally marks

2

Tallies help us keep count
3:30
Tallies help us keep count
You'll learn: Record observations in groups of five
Turn tallies into a frequency table
3:48
Turn tallies into a frequency table
You'll learn: Read category counts and verify totals