Reasoning About Numbers, with Challenges and Simplifications

This booklet from the National Numeracy Strategy was written to help students:
* solve mathematical problems or puzzles, recognise and explain patterns and relationships, generalise and predict;
* explain methods and reasoning orally and in writing;
* suggest extensions by asking ‘What if …?’

All the activities give ideas for simplifications and challenges.

[b]Handshakes[/b] investigates the number of handshakes if everyone in a room shakes hands with everyone else.

[b]24[/b] gives students the opportunity to find different questions that give the answer 24.

[b]Decigame[/b] is a game for two players using division of numbers to give an answer between zero and one.

[b]Snakes[/b] explores what number patterns are created when you half and double numbers.

[b]Consecutive sums[/b] explores the numbers you can make by adding consecutive numbers.

[b]Magic squares[/b] asks students to explore magic squares given certain rules.

[b]Getting even[/b] is a two-player game based on sum of two numbers created by the players.

[b]Different products[/b] explores the products students can make with given numbers.

[b]Score Board[/b] explores the sums students can make with given numbers.

[b]Sum to twelve[/b] explores the different ways students can make a sum of 12.

[b]Changing money[/b] uses combinations of coins with different values to ask what amounts can be made.

[b]Ordering numbers[/b] ask students to create numbers using number cards and then order them.

[b]Arithmagons[/b] is a structure for students to practice addition and subtraction.

[b]Swapping places[/b] investigates the number of moves two colours of counters have to make to 'swap' sides.

[b]Bracelets[/b] asks students to create a 'bracelet' of numbers with appropriate number operations between the numbers.

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Age7-11, 7-11, 5-7
Published1990 - 1999

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This resource is part of National Strategies: Primary Mathematics



This was always a useful document and I'm really glad it's been brought to my attention. There's some good activities and I like the way they give the simplifications so that you can have all your children using the activities although pitched to their level of understanding. my year 3/4s liked the consecutive number investigation which was useful for mental arithmetic practise as well as encouraging methodical recording.