Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Number problems at primary level that may require resilience.
What is the sum of all the digits in all the integers from one to one million?
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
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.
Who said that adding couldn't be fun?
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?
Number problems at primary level to work on with others.
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
Can you replace the letters with numbers? Is there only one solution in each case?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Follow the clues to find the mystery number.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Find the sum of all three-digit numbers each of whose digits is odd.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Have a go at balancing this equation. Can you find different ways of doing it?
Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Number problems for inquiring primary learners.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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?
Number problems at primary level that require careful consideration.
Explore the relationship between simple linear functions and their graphs.
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?
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
The number 3723(in base 10) is written as 123 in another base. What is that base?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Can you substitute numbers for the letters in these sums?
Replace each letter with a digit to make this addition correct.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
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. . . .
How many six digit numbers are there which DO NOT contain a 5?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.
Carry out cyclic permutations of nine digit numbers containing the digits from 1 to 9 (until you get back to the first number). Prove that whatever number you choose, they will add to the same total.