This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What two-digit numbers can you make with these two dice? What can't you make?
Can you work out some different ways to balance this equation?
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?
This activity focuses on rounding to the nearest 10.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
Number problems at primary level that require careful consideration.
Follow the clues to find the mystery number.
This article for primary teachers suggests ways in which to help children become better at working systematically.
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you replace the letters with numbers? Is there only one
solution in each case?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Have a go at balancing this equation. Can you find different ways of doing it?
Can you substitute numbers for the letters in these sums?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you find the chosen number from the grid using the clues?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
How many different triangles can you make on a circular pegboard that has nine pegs?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Find out about Magic Squares in this article written for students. Why are they magic?!
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An investigation that gives you the opportunity to make and justify
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you find all the different ways of lining up these Cuisenaire
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Find out what a "fault-free" rectangle is and try to make some of