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. . . .
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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
Replace each letter with a digit to make this addition correct.
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 solutions can you find to this sum? Each of the different letters stands for a different number.
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. . . .
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
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
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.
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Find the sum of all three-digit numbers each of whose digits is
This activity involves rounding four-digit numbers to the nearest thousand.
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.
There are nasty versions of this dice game but we'll start with the nice ones...
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
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
How many six digit numbers are there which DO NOT contain a 5?
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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
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.
Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?
What happens when you round these three-digit numbers to the nearest 100?
The number 3723(in base 10) is written as 123 in another base. What
is that base?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you substitute numbers for the letters in these sums?
What happens when you round these numbers to the nearest whole number?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
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?
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?
Who said that adding, subtracting, multiplying and dividing
couldn't be fun?
Four strategy dice games to consolidate pupils' understanding of rounding.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Number problems at primary level that require careful consideration.
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?
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" .