Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Delight your friends with this cunning trick! Can you explain how
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This challenge asks you to imagine a snake coiling on itself.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Can you explain how this card trick works?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Got It game for an adult and child. How can you play so that you know you will always win?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Find out what a "fault-free" rectangle is and try to make some of
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
This activity involves rounding four-digit numbers to the nearest thousand.
Can you find the values at the vertices when you know the values on
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?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Find the sum of all three-digit numbers each of whose digits is
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?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
A package contains a set of resources designed to develop
pupils’ mathematical thinking. This package places a
particular emphasis on “generalising” and is designed
to meet the. . . .
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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.
It would be nice to have a strategy for disentangling any tangled
What would you get if you continued this sequence of fraction sums?
1/2 + 2/1 =
2/3 + 3/2 =
3/4 + 4/3 =
A collection of games on the NIM theme