List

Conjecturing and generalising at KS2 - primary teachers

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.

Take one example
article

Take one example

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.
Money Bags
problem
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Money bags

Age
5 to 11
Challenge level
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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?
Make 37 Poster
problem
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Make 37

Age
5 to 11
Challenge level
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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?

School fair necklaces
problem
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School fair necklaces

Age
5 to 11
Challenge level
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How many possible symmetrical necklaces can you find? How do you know you've found them all?
Neighbourly Addition
problem

Neighbourly addition

Age
7 to 14
Challenge level
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I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Factors and Multiples Game
game
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Factors and multiples game

A game in which players take it in turns to choose a number. Can you block your opponent?

Exploring Wild & Wonderful Number Patterns
problem

Exploring wild and wonderful number patterns

Age
7 to 11
Challenge level
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EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Diagonally Square
problem

Diagonally square

Age
7 to 11
Challenge level
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Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Magic Vs
problem
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Magic Vs

Age
7 to 11
Challenge level
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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Follow the numbers
problem
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Follow the numbers

Age
7 to 11
Challenge level
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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.

Take three numbers
problem
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Take three numbers

Age
7 to 11
Challenge level
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What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Division Rules
problem
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Division rules

Age
7 to 11
Challenge level
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This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Six Numbered Cubes
problem
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Six numbered cubes

Age
7 to 11
Challenge level
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This task combines spatial awareness with addition and multiplication.
Got It
problem
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Got it

Age
7 to 14
Challenge level
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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.

Three neighbours
problem
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Three neighbours

Age
7 to 14
Challenge level
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Take three consecutive numbers and add them together. What do you notice?
This Pied Piper of Hamelin
problem
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This Pied Piper of Hamelin

Age
7 to 11
Challenge level
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Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Six Ten Total
problem
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Six ten total

Age
7 to 11
Challenge level
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This challenge combines addition, multiplication, perseverance and even proof.