Challenge Level

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Challenge Level

Where should you start, if you want to finish back where you started?

Challenge Level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Challenge Level

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. . . .

Challenge Level

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. . . .

Challenge Level

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. . . .

Challenge Level

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.

Challenge Level

The number 3723(in base 10) is written as 123 in another base. What is that base?

Challenge Level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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.

Challenge Level

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

More upper primary number sense and place value tasks.

Challenge Level

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. . . .

Challenge Level

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

Challenge Level

What happens when you add a three digit number to its reverse?

This article develops the idea of 'ten-ness' as an important element of place value.

Challenge Level

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.

Challenge Level

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?

Challenge Level

Try out some calculations. Are you surprised by the results?

Challenge Level

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)?

Challenge Level

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?

Challenge Level

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.

Challenge Level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Challenge Level

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.

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.

Challenge Level

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Challenge Level

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?

Challenge Level

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Challenge Level

Find the values of the nine letters in the sum: FOOT + BALL = GAME

This feature aims to support you in developing children's early number sense and understanding of place value.

Challenge Level

By selecting digits for an addition grid, what targets can you make?

Challenge Level

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

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!

Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Challenge Level

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

Challenge Level

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Challenge Level

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?

Challenge Level

Use your knowledge of place value to try to win this game. How will you maximise your score?

Challenge Level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Challenge Level

How many six digit numbers are there which DO NOT contain a 5?

Challenge Level

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Challenge Level

Explore the relationship between simple linear functions and their graphs.

Challenge Level

Can you work out some different ways to balance this equation?

Challenge Level

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the 1000th digit you would write down.

Challenge Level

What happens when you round these numbers to the nearest whole number?

Challenge Level

What happens when you round these three-digit numbers to the nearest 100?