The Number Jumbler can always work out your chosen symbol. Can you work out how?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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. . . .
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)?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Replace each letter with a digit to make this addition correct.
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.
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
Use your knowledge of place value to try to win this game. How will you maximise your score?
More upper primary number sense and place value tasks.
Who said that adding couldn't be fun?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.
This article develops the idea of 'ten-ness' as an important element of place value.
This set of activities focuses on ordering, an important aspect of place value.
One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.
This feature aims to support you in developing children's early number sense and understanding of place value.
Try out some calculations. Are you surprised by the results?
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?
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.
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.
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
The number 3723(in base 10) is written as 123 in another base. What is that base?
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 happens when you round these three-digit numbers to the nearest 100?
Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.
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!
Find the sum of all three-digit numbers each of whose digits is odd.
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 positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
How many six digit numbers are there which DO NOT contain a 5?
Number problems at primary level that may require resilience.
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" .