Or search by topic
There are 145 NRICH Mathematical resources connected to Conjecturing and generalising, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Conjecturing and generalisingThere are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This activity focuses on similarities and differences between shapes.
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
This task requires learners to explain and help others, asking and answering questions.
This task requires learners to explain and help others, asking and answering questions.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
There are nasty versions of this dice game but we'll start with the nice ones...
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Play this game and see if you can figure out the computer's chosen number.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
A game in which players take it in turns to choose a number. Can you block your opponent?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
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?
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.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
What do you notice about these squares of numbers? What is the same? What is different?
There are six numbers written in five different scripts. Can you sort out which is which?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.