Number problems at primary level that require careful consideration.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
What is the sum of all the three digit whole numbers?
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?
An old game but lots of arithmetic!
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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?
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
What is happening at each box in these machines?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
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!
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Number problems at primary level that may require resilience.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Can you work out what a ziffle is on the planet Zargon?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Use your logical reasoning to work out how many cows and how many sheep there are in each field.