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.
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?
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?
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
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
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 for inquiring primary learners.
Who said that adding couldn't be fun?
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?
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
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.
Four strategy dice games to consolidate pupils' understanding of rounding.
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Have a go at balancing this equation. Can you find different ways of doing it?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
What happens when you round these numbers to the nearest whole number?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Number problems at primary level to work on with others.
Can you work out some different ways to balance this equation?
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
There are nasty versions of this dice game but we'll start with the nice ones...
This activity involves rounding four-digit numbers to the nearest thousand.
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?
What two-digit numbers can you make with these two dice? What can't you make?
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?
Can you substitute numbers for the letters in these sums?
This article, written for teachers, looks at the different kinds of
recordings encountered in Primary Mathematics lessons and the
importance of not jumping to conclusions!
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?
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.
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?
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
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?
Follow the clues to find the mystery number.
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?
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 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.
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?
Number problems at primary level that may require determination.