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?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Can you work out some different ways to balance this equation?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Number problems at primary level that may require determination.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Follow the clues to find the mystery number.
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 is the sum of all the digits in all the integers from one to
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?
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.
Number problems at primary level that require careful consideration.
Replace each letter with a digit to make this addition correct.
Can you replace the letters with numbers? Is there only one
solution in each case?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by
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?
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" .
What happens when you round these three-digit numbers to the nearest 100?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit 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?
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 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
The number 3723(in base 10) is written as 123 in another base. What
is that base?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Four strategy dice games to consolidate pupils' understanding of rounding.
There are six numbers written in five different scripts. Can you sort out which is which?
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
What happens when you round these numbers to the nearest whole number?
Explore the relationship between simple linear functions and their
Who said that adding couldn't be fun?
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?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Number problems for inquiring primary learners.
Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. . . .
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)?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different 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.
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!