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.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
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?
Investigate what happens when you add house numbers along a street
in different ways.
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
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
What is happening at each box in these machines?
There were 22 legs creeping across the web. How many flies? How many spiders?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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.
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.
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Use the number weights to find different ways of balancing the equaliser.
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you hang weights in the right place to make the equaliser
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal 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?
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?
Can you substitute numbers for the letters in these sums?
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 score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
If the answer's 2010, what could the question be?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.
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?