In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Use the number weights to find different ways of balancing the equaliser.
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Can you substitute numbers for the letters in these sums?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
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.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
What is happening at each box in these machines?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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?
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.
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.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Investigate what happens when you add house numbers along a street in different ways.
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you hang weights in the right place to make the equaliser balance?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
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 ...
Number problems at primary level to work on with others.
Who said that adding couldn't be fun?
Number problems at primary level that may require resilience.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Investigate the different distances of these car journeys and find out how long they take.
This task combines spatial awareness with addition and multiplication.
Can you follow the rule to decode the messages?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?