Conjecturing and Generalising at KS2
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
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?
School Fair Necklaces
How many possible symmetrical necklaces can you find? How do you know you've found them all?
Diagonally Square
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Exploring Wild & Wonderful Number Patterns
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Take Three Numbers
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Always, Sometimes or Never? Number
Are these statements always true, sometimes true or never true?
Always, Sometimes or Never? Shape
Are these statements always true, sometimes true or never true?
Magic Vs
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Follow the Numbers
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.
Division Rules
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Make 37
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?
This Pied Piper of Hamelin
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Six Ten Total
This challenge combines addition, multiplication, perseverance and even proof.
Six Numbered Cubes
This task combines spatial awareness with addition and multiplication.
Neighbourly Addition
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Three Neighbours
Take three consecutive numbers and add them together. What do you notice?
Got It
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.
Factors and Multiples Game
This game can replace standard practice exercises on finding factors and multiples.