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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Conjecturing and Generalising at KS2 - Primary Teachers

### Take One Example

### Money Bags

### School Fair Necklaces

### Diagonally Square

### Exploring Wild & Wonderful Number Patterns

### Take Three Numbers

### Always, Sometimes or Never? Number

### Always, Sometimes or Never? Shape

### Magic Vs

### Follow the Numbers

### Division Rules

### Make 37

### This Pied Piper of Hamelin

### Six Ten Total

### Six Numbered Cubes

### Neighbourly Addition

### Three Neighbours

### Got It

### Factors and Multiples Game

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

The "What if..?" questions are such an important part of mathematical thinking. Knowing what to ask means that you understand something about the structure of the problem, and being able to see similarities and differences means you're starting to generalise.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

Age 5 to 11

Challenge Level

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

Age 5 to 11

Challenge Level

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Age 7 to 11

Challenge Level

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Age 7 to 11

Challenge Level

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Age 7 to 11

Challenge Level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Age 7 to 11

Challenge Level

Are these statements always true, sometimes true or never true?

Age 7 to 11

Challenge Level

Are these statements always true, sometimes true or never true?

Age 7 to 11

Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Age 7 to 11

Challenge Level

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Age 7 to 11

Challenge Level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Age 7 to 11

Challenge Level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Age 7 to 11

Challenge Level

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Age 7 to 11

Challenge Level

This challenge combines addition, multiplication, perseverance and even proof.

Age 7 to 11

Challenge Level

This task combines spatial awareness with addition and multiplication.

Age 7 to 14

Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Age 7 to 14

Challenge Level

Take three consecutive numbers and add them together. What do you notice?

Age 7 to 14

Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Age 7 to 16

Challenge Level

This game can replace standard practice exercises on finding factors and multiples.