What is the sum of all the digits in all the integers from one to one million?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
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?
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?
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
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?
Who said that adding couldn't be fun?
Find the sum of all three-digit numbers each of whose digits is odd.
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Can you replace the letters with numbers? Is there only one solution in each case?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Replace each letter with a digit to make this addition correct.
A church hymn book contains 700 hymns. The numbers of the hymns 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.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
What happens when you round these three-digit numbers to the nearest 100?
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.
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?
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you substitute numbers for the letters in these sums?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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" .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
There are nasty versions of this dice game but we'll start with the nice ones...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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. . . .
The number 3723(in base 10) is written as 123 in another base. What is that base?
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.
Number problems for inquiring primary learners.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Can you work out some different ways to balance this equation?
Four strategy dice games to consolidate pupils' understanding of rounding.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
Have a go at balancing this equation. Can you find different ways of doing it?