Once a basic number sense has developed for numbers up to ten, a
strong 'sense of ten' needs to be developed as a foundation for
both place value and mental calculations.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Marion Bond recommends that children should be allowed to use
'apparatus', so that they can physically handle the numbers
involved in their calculations, for longer, or across a wider
ability band,. . . .
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Lee was writing all the counting numbers from 1 to 20. She stopped
for a rest after writing seventeen digits. What was the last number
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
Number problems for inquiring primary learners.
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
Number problems at primary level that require careful consideration.
There are nasty versions of this dice game but we'll start with the nice ones...
Nowadays the calculator is very familiar to many of us. What did
people do to save time working out more difficult problems before
the calculator existed?
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the sum of all three-digit numbers each of whose digits is
This activity involves rounding four-digit numbers to the nearest thousand.
This activity focuses on rounding to the nearest 10.
Four strategy dice games to consolidate pupils' understanding of rounding.
Follow the clues to find the mystery number.
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
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?
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.
Who said that adding couldn't be fun?
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?
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Number problems at primary level that may require determination.