The Number Jumbler can always work out your chosen symbol. Can you work out how?
Where should you start, if you want to finish back where you started?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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. . . .
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. . . .
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. . . .
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.
Replace each letter with a digit to make this addition correct.
The number 3723(in base 10) is written as 123 in another base. What is that base?
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.
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.
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. . . .
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. . . .
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.
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.
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?
Try out some calculations. Are you surprised by the results?
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)?
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?
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 any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
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.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Find out about palindromic numbers by reading this article.
This feature aims to support you in developing children's early number sense and understanding of place value.
By selecting digits for an addition grid, what targets can you make?
Who said that adding couldn't be fun?
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!
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
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?
Use your knowledge of place value to try to win this game. How will you maximise your score?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many six digit numbers are there which DO NOT contain a 5?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Explore the relationship between simple linear functions and their graphs.
Can you work out some different ways to balance this equation?
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.
What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?