Number problems at primary level that may require resilience.
56 406 is the product of two consecutive numbers. What are these two numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Given the products of adjacent cells, can you complete this Sudoku?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
What is happening at each box in these machines?
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
This problem is based on the story of the 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!
Use the information to work out how many gifts there are in each pile.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Resources to support understanding of multiplication and division through playing with number.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.