During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
This article for teachers suggests ideas for activities built around 10 and 2010.
Investigate the different distances of these car journeys and find out how long they take.
Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
Investigate what happens when you add house numbers along a street in different ways.
Number problems at primary level that require careful consideration.
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 draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
There are nasty versions of this dice game but we'll start with the nice ones...
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
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?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
Can you substitute numbers for the letters in these sums?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
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.
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Replace each letter with a digit to make this addition correct.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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 do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
If you have only four weights, where could you place them in order to balance this equaliser?
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.