Number problems at primary level that may require determination.
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
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.
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?
Replace each letter with a digit to make this addition correct.
Find the sum of all three-digit numbers each of whose digits is
Can you substitute numbers for the letters in these sums?
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
A church hymn book contains 700 hymns. The numbers of the hymns are
displayed by combining special small single-digit boards. What is
the minimum number of small boards that is needed?
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?
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
This activity involves rounding four-digit numbers to the nearest thousand.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Who said that adding couldn't be fun?
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
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?
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?
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 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?
There are six numbers written in five different scripts. Can you sort out which is which?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
There are nasty versions of this dice game but we'll start with the nice ones...
Number problems for inquiring primary learners.
Can you replace the letters with numbers? Is there only one
solution in each case?
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. . . .
Using balancing scales what is the least number of weights needed
to weigh all integer masses from 1 to 1000? Placing some of the
weights in the same pan as the object how many are needed?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do 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?
Can you work out some different ways to balance this equation?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
What is the sum of all the digits in all the integers from one to
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?
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.
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.
Investigate the different ways these aliens count in this
challenge. You could start by thinking about how each of them would
write our number 7.
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?