This activity involves rounding four-digit numbers to the nearest thousand.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
An investigation that gives you the opportunity to make and justify
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find the sum of all three-digit numbers each of whose digits is
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.
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.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge asks you to imagine a snake coiling on itself.
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?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
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.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Got It game for an adult and child. How can you play so that you know you will always win?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How many centimetres of rope will I need to make another mat just
like the one I have here?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Can you explain how this card trick works?
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?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
In how many ways can you arrange three dice side by side on a
surface so that the sum of the numbers on each of the four faces
(top, bottom, front and back) is equal?