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.

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.

Show health and safety information

Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.


You might also like

Resource collection
Resource collection
Resource collection

Published by


Share this resource


This resource is part of National Strategies: Primary Mathematics

Lists that tag this content



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.