# Reasoning about numbers, with challenges and simplifications

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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.

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

24 gives students the opportunity to find different questions that give the answer 24.

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

Snakes explores what number patterns are created when you half and double numbers.

Consecutive sums explores the numbers you can make by adding consecutive numbers.

Magic squares asks students to explore magic squares given certain rules.

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

Different products explores the products students can make with given numbers.

Score Board explores the sums students can make with given numbers.

Sum to twelve explores the different ways students can make a sum of 12.

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

Ordering numbers ask students to create numbers using number cards and then order them.

Arithmagons is a structure for students to practice addition and subtraction.

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

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

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