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
Replace each letter with a digit to make this addition correct.
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 activity involves rounding four-digit numbers to the nearest thousand.
Find the sum of all three-digit numbers each of whose digits is
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?
What is the sum of all the digits in all the integers from one to
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 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 values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
Use two dice to generate two numbers with one decimal place. 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?
There are six numbers written in five different scripts. Can you sort out which is which?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Number problems at primary level to work on with others.
Number problems for inquiring primary learners.
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?
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
A school song book contains 700 songs. The numbers of the songs are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
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.
What happens when you round these numbers to the nearest whole number?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The number 3723(in base 10) is written as 123 in another base. What
is that base?
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.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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)?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
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 '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.
Number problems at primary level that require careful consideration.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Four strategy dice games to consolidate pupils' understanding of rounding.
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