Active approaches to teaching numeracy

These maths games and exercises are specifically for people who have attended Pivotal Education’s Maths INSET days.  You will find many of the activities that you took part in on the day and many more.

We hope these are useful….

 

My Number

Time needed: 10 minutes

Group size: Full class

Suitable for: All ages

Curriculum Area(s): Numbers, Addition and Subtraction, Multiplication and Division, Fractions, Decimals, Angles

Resources needed: Large digit cards

Description: This is a great activity that gets the class moving whist being really easy to adapt to the age and level of your students.
Each student is given a laminated number or number on a postcard. Numbers should be large enough for others to see easily. They hold up the number in front of their chest so others can see the number too.
The teacher gives a command. E.g. “If your number is divisible by 4, run to the windows.” Students check the number, do the calculation and follow the instruction. Then repeat with another command. Differentiate by adapting your commands (and the numbers you give).
Younger children might be given numbers 1-10. Commands may be, “Sit down if you are an even number”, “Spin on the spot if your number is bigger than 5”.
Older or more able groups can be given fractions, decimals, negative numbers. Commands may be, “(With fractions), if you can be expressed in twelfths, kneel on the floor”. Or “If you get a negative number when you subtract 12 from your number, sing ‘happy birthday’.”

You can also try – Get into groups of people with the same remainder as you when you divide by a certain number. E.g. “Divide your number by 7. Get into groups with people who have the same remainder as you” Ask what students notice about others in their group. You can experiment with this set up more… Take two people from two different remainder groups – add them together and see what remainder group they end up in.

Also nominate students to give commands.

Use this game to reinforce properties of numbers you are looking at. This can also be played with times of the day or values of money if you are looking at time and money.

Differentiation/Extension: For Early Years: Give the children numbers on large pieces of card and ask them to line up in order.

 

 


 

Keep the Floor Alive

Time needed: 10 minutes

Group size: Full class

Suitable for: All ages

Curriculum Area(s): Numbers, Rounding, Shape

Resources needed: Space

Description: Pupils all move about the space individually. The teacher asks them to keep the floor alive. The floor needs people to run over it in every area to keep it well and alive. (This stops all pupils from walking/running around in an anti-clockwise circle, in which case they always tend to be near the same people). When the teacher calls out “Freeze”, pupils all freeze and are silent. The teacher will then call out an instruction and pupils follow that instruction. When each mini task has been completed, all pupils move around the space and keep the floor alive again. This should make sure that pupils keep getting into groups with different people.
1. Get into groups of 3, 4, 5, 6…
2. Number of points of contact with the floor
3. Bodies made into numbers. E.g. whole group makes ‘4′ with their bodies.
4. The smallest/largest number they can make as a group. Now round your number up to the nearest 10 or down to the nearest 10….

Differentiation/Extension:

1. “We are in groups of 5. We have 5 groups and 2 left over. How many people are here today?
2. “How many groups will we have if there are 4 in each group? What will the remainder be then?
3. “Can anyone think of a group size that will give us no remainders?”
Move from this extension activity into the activity called “Remainders”

 

 


 

Number Bonds

Time needed: 15 minutes

Group size: Small groups

Suitable for: KS1, KS2

Curriculum Area(s): Numbers, Addition and Subtraction

Resources needed: Giant Dice and Laminated A4 cards of numbers up to 12. Or Carpet tiles

Description: You can do this activity on a smaller scale, individually or in pairs at a desk. But for our purposes, we are using large numbers (laminated A4 numbers) and giant foam dice.
Lay the numbers 1 to 12 out in the space. Throw two dice. If the answer is 7, then you turn over all the numbers that are number bonds for that number – i.e. 7, 6 and 1, 5 and 2, 3 and 4. You are left with 8, 9, 10, 11, 12 face up. Your score is the total of the cards facing up. Number bonds for 8 would be 8, 1 and 7, 2 and 6, 3 and 5. But 4 would stay facing up with 9, 10, 11 and 12.
Play this for a bit. What is the worst number to throw to give the worst (highest) score? What is the best?
Extend this activity by using three dice and numbers to 18.
How else can we extend this?

 

 

 


 

Stepping Stones

Time needed: 10 minutes

Group size: Full class

Suitable for: All ages

Curriculum Area(s): Numbers, Addition and Subtraction, Multiplication and Division

Resources needed: Carpet tile stepping stones, Ribbons to suggest river banks

Description: Set up a river. Students move from one bank to the other, via two stepping stones. Each stepping stone has an operation on it. For example, lets use operations X2 and -1 on our stepping stones to begin with.

A student starts on one side of the river with a number, e.g. 20. Then they jump onto the first stepping stone and do the first operation… 20 x 2 = 40. Now they jump onto the second stepping stone and do the second operation… 40 – 1 = 39. So the number they end up with on the far bank is 39.
Another student repeats the activity with a different number. Record the numbers they start and end with.
Try negative numbers. Try fractions and decimals.
Possible extensions to this activity:

  • Plot the numbers that you start and end with on a graph. (X-axis shows starting numbers, Y-axis shows ending numbers). Look for a pattern.
  • Change the two operations round. So that you subtract 1 first then multiply by 2. Do you get the same answer? What is the relationship between the first answer and the second?
  • Alter the operations that you do. Get students to suggest different operations and you can differentiate according to ability.
  • Ask some students to go back across the river the other way. E.g. “If I end up with the number 43, what number did I start with?”
  • Play this game in teams of 4 or 5. Give each team a different set of stepping stones to travel across. Each individual within the team has a different number to start with. Team members take it in turn to cross the river. Once over the river, they each note down their final number, add all of the groups numbers up and race to take their ‘group number’ to the teacher.

 

 

 


 

Frogs and Robots

Time needed: 15 minutes

Group size: Full class

Suitable for: EY, KS1, KS2

Curriculum Area(s): Numbers, Addition and Subtraction, Multiplication and Division

Resources needed: 1-100 carpet tiles, Ribbon

Description: Set numbers 1-10 out in a number line. A child crouches on a number being a frog and then has to ‘add 1’ by jumping like a frog onto the next number.  What number is the frog on now?  The teacher can write the calculation (e.g. 4 + 1 = 5) on the board/large paper to show how it is notated.  Do the same with simple subtraction.

Differentiation/Extension:

  • The number line is extended to numbers greater than 10.  Children are programmable robots.  The robot is given a set of instructions, e.g. Add 10, subtract 3, add 5.  The robot moves like a robot through the instructions – moving up and down the number line as necessary.  What number do the end up on?
  • Extend previous point by working out what the final ‘answer’ number is relative to the original number?  E.g. If starting number is 7.  7 + 10 – 3 + 5 = 19.  Which is the same as saying 7 + 12 = 19.  Some robots will be able to simplify the operation mentally and move directly to the answer square.
  • Teach multiplication by addition and division by subtraction using the numberline.  So write a calculation on a large piece of paper (e.g. 5 x 4 = )  Then ask a child to start on 0 and count 5 as they walk 5 spaces on the number line (adding 5).  When they get to 5, the class counts the number of times they have moved forward 5 steps.  When the class gets to ‘4’, then the child should have moved 5 steps four times and should be standing on 20.  With division by subtraction pupils work out a calculation e.g. 21÷7, the child stands on 21 and then counts 7 steps repeatedly as they subtract numbers.  Each time the child counts 7 steps, the class counts how many groups of 7 steps have been counted.  When the child gets back to 0 the group should call out ‘3’ which is the answer.

 

 


 

Bingo

Time needed: 5 minutes

Group size: Full class

Suitable for: All ages

Curriculum Area(s): Numbers, Addition and Subtraction, Multiplication and Division

Resources needed: 1-100 carpet tiles

Description: Divide children into groups of 3.  Each group of 3 is given 8 random number tiles, which they lay out before them.  The teacher asks a question, which pupils work out the answer to.  If they have the answer on their tile, they can turn it over.  If a group turns all 8 of their tiles over they shout “Bingo” and have won the game.

Differentiation/Extension: For Yr 1 – the teacher could just call out the number. For Yr 2 – the teacher could say, for example, “1 more than 76”.  Or “84 minus 2”

 

 


 

Jumping Multiples

Time needed: 15 minutes

Group size: Small groups

Suitable for: KS1, KS2, KS3

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: Large numbers – 1-10

Description: Children sit in groups.  Each group is given a single digit.  The teacher counts upwards from 1 and when the teacher calls out a multiple of a groups number, the children in that group all jump. What numbers have the most groups jumping at the same time?  Then call out numbers at random and if your number is a factor of it then jump.

Differentiation/Extension: Multiple Music. Children jump, tap, clap, click etc. as they count on certain numbers e.g. tap shoulders on multiples of 2, jump on multiples of 5, stamp on multiples of 10 etc. as you count on or back from 0 – 100.  In this extension, pupils have to concentrate on all multiples.  (This is like Fizz Buzz, see below)

 

 


 

Fizz Buzz

Time needed: 5 minutes

Group size: Full class

Suitable for: KS1, KS2, KS3, FS

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: None

Description: Children count round the class – each child says a number. Instead of numbers, they say ‘fizz’ on multiples of 3, and ‘buzz’ on multiples of 5, and ‘fizz buzz’ on multiples of 3 and 5 (15 etc.)

Differentiation/Extension: Add more noises for multiples of different numbers.

 

 


 

Hand Jive

Time needed: 10 minutes

Group size: Small groups

Suitable for: KS2, KS3

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: Numbers, Ribbon

Description: Hand Jive whilst counting. 5 actions:

1. open right hand palm up

2. open left hand palm up

3. touch left shoulder with right hand

4. touch right shoulder with left hand

5. both hands on head.

Practice to get the rhythm then ask questions such as, “Where will your hands be when we say 50?” “Where will your hands be when we say 38?” “Tell me about the numbers you say when you have your left hand on your right shoulder.” etc

Differentiation: 

  • Count in 2s instead of single whole numbers.  How does this change what action you do on different numbers?  What numbers have the same action as before?  Why?
  • Ask groups of students to create a sequence of movement for other times tables – i.e. a sequence of 8 moves for 8 times table.
  • For younger students, simplify.  Star Jumps: Children count in ones as they jump saying 1 as they put their arms up, and 2 as they put hands down and so on. Ask questions such as where will your hands be when you say 10, 5, etc.

Extension: count in 2s, 5s, 10s etc.

 

 


 

Numberlines

Time needed: 10 minutes

Group size: Full class

Suitable for: EY, KS1, KS2, KS3. KS4, FS

Curriculum Area(s): Numbers

Resources needed: Numbers, Ribbon

Description: For Foundation – put a string on ground. Child A given no 0 (or 1 if they can’t cope with Zero).  Child B given no 10. They stand near ends of string. Child C handed a suitably differentiated no and stands in appropriate place on line etc.  Repeat for other whole numbers between 0 and 10.  Teacher can ask “Is it in the right place?” and the class can help their classmates find the right place.

  • For foundation.  Using a complete number line, ask children to take up every other number and count the ones left to do odds and evens.
  • For years 1 and 2, the numberline can be extended to 30.
  • “Everyone that has a number less than 5 – jump”.  “Everyone that has a number more than 3 – sit down.”
  • Use larger whole numbers and/or negative numbers and/or simple fractions and decimals. Make one end of the line 0 and the other end of the line 1.  Use fractions and/or decimals.  You can give one pupil ¼ and another 2/8 and see if they know to stand at the same point on the line. Mix denominators of fractions e.g. pupils will have to work out what order the fractions come in and where they are positioned on the line in relation to other fractions.
  • Split the children into 3 ability groups. Give each child in each group a card from differentiated sets with metric measures on. Ask them to put themselves in order. Bring the groups together adding Group 2 to the Group 1 line and then adding Group 3.
  • Group 1 cards – 5cm, 1m, ½m, 10cm, ¼m , ¾ m, 90 cm etc.
  • Group 2 cards – 100cm, 0.5m, 0.1m, 0.3m, 0.8m, 0.75m, 0.25m etc.
  • Group 3 cards – 1/10m 3/10m 2/5m 0.8m, 50%m 25%m

Differentiation/Extension: 3 – digit numberline….

Human number line (ordering 3 digit numbers).  Children are given ‘post its’ with a 3 digit number and they have to work together to order themselves from smallest to largest number. Then ask them to describe their position in number line – why they are in a certain position using vocabulary – units, tens, hundreds, digit, larger, smaller etc.

 

 


 

Remainders

Time needed: 5 minutes

Group size: Full class

Suitable for: KS2, KS3. KS4, FS

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: 1-100 tiles

Description: Each child holds a card bearing a positive whole number.  They get into groups with same remainder when divided by (say) 4. Who will still be with you if you get into groups with same remainder when divided by 8?

Differentiation/Extension: Add 2 numbers in the group. Which group would the sum be in?… Choose 2 more nos in same group etc.

 

 


 

Play Your Cards Right

Time needed: 5 minutes

Group size: Full class

Suitable for: KS1, KS2, KS3. KS4, FS

Curriculum Area(s): Probability, Estimating

Resources needed: Carpet tiles 1-100

Description: Set out 8 markers in a line on the floor (these can be carpet tiles number side down).  Then randomly select 8 further tiles from the ‘pack’ of numbers.  The teacher turns one number over.  As a group, the class must decide where the number should be placed.  The aim is to place the 8 tiles in the right order (smallest to largest) on the markers, but as the class are unaware what numbers are coming, they have to make judgements about where to place the number.  Continue turning over tiles and placing them by markers.  If a tile cannot be placed, then it is put on a separate pile to the side.  How many tiles cannot be placed?  Repeat.  Did we do any better?

Differentiation/Extension: What happens if we only use numbers 1-50 but still have 8 places?  What happens if we have 10 places?  What if we have 8 positions and only 16 cards?  Are we more likely to be successful? Do we have fewer cards on the discarded pile?

 

 


 

1 to 100

Time needed: 5 minutes

Group size: Small groups

Suitable for: EY, KS1, KS2

Curriculum Area(s): Numbers, Estimating

Resources needed: Numbers 1-100 (playing card size)

Description: Use playing card size numbers 0 – 100. Throw randomly in heap on floor .Get a group to place them in a line on hall floor. Before starting put 0 in place and ask them to estimate where 100 will be. Y2/3, for example, find it difficult to work as a team. You need to stop them and discuss how they can help the whole group to achieve result.

Differentiation/Extension: Estimate how many cards/numbers would we need to get all the way to the other side of the hall?  What number do you think we would be at by the other side of the playground? How can we make a good estimate?  You will need to measure.

 

 


 

Constructing a 100 Square

Time needed: 5 minutes

Group size: Small groups

Suitable for: KS1, KS2, KS3

Curriculum Area(s): Numbers

Resources needed: Carpet tiles 1-100

Description: Children lay out the tiles in a 100 square. This can be an interesting activity in itself and can take a considerable amount of time.  It is useful to have some of the class organising the number square and the others watching.  The teacher can ask those watching questions and they can think about other ways that the task could be organised.

Differentiation/Extension: Teacher/LSA can give instructions, directions to students.  Put one child in charge of planning and leading the rest in this operation. Split the numbers into groups of 10 (i.e. 1-10, 11-20…) and give to different groups to order within set and then lay out within 100 square.

 

 


 

Finding Patterns

Time needed: 10 minutes

Group size: Full class

Suitable for: EY, KS1, KS2, KS3, KS4, FS

Curriculum Area(s): Numbers

Resources needed: Carpet tiles 1-100

Description: Stand on a number in the 2 x table.  Teacher changes the language. “Now stand on a number that is a multiple of 2” or “Now stand on an even number”.  Stand on a number that has 4 as a factor. Even number…Multiple of 10…Stand on a prime number…Stand on a square number.

Differentiation/Extension:

  • With KS1 you can generate the tables by counting out the numbers between each multiple.  So for the three times table, one pupil stands on 3.  Then the class counts and puts a different child on each multiple.
  • You can do division by subtraction in this way also.
  • Stand on a square where the sum of the digits is 11. WHY are you standing in a straight line? Would this be the case if the digit sum were 12?

 

 


 

3s and 9s Experiment

Time needed: 5 minutes

Group size: Full class

Suitable for: KS2, KS3, KS4, FS

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: 100 Square

Description: Lay out 100 square

  1. Stand on a number in the 3 x table. (up to 9 x 10)
  2. Pupils shut their eyes. “What number is in front of you?  To the left?  Diagonally 1 place away?”
  3. Move, if necessary, (from your multiple of 3)  to a multiple of 9
  4. Add the digits in the number you are standing on. Move to the square which is the sum of the digits (everyone on one square so a bit of a squash!).
Why did that happen?  Would we get the same result with any other times table?

Differentiation/Extension: 4 people needed – the rest watch and think. Stand at the 4 corners of a rectangle whose sides are parallel to the sides of the 100 square. Add the numbers at the opposite ends of the diagonals. What do you notice about the 2 answers? Why?

 


 

Jumping Number Bonds

Time needed: 5 minutes

Time needed:  5 minutes

Group size:  Full class

Suitable for:  EY, KS1

Curriculum Area(s):  Numbers

Resources needed: Carpet tiles or numberline

Description: In pairs “make 10”. 1st child choose a number less than ten and jumps that number. The partner must jump the appropriate number to “make 10”.

Differentiation/Extension: “Make 20”.

 

 


 

Factor Pairs

Time needed: 5 minutes

Group size: Full class

Suitable for: KS2, KS3, KS4, FS

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: Carpet tiles 1-100

Description: Using 12 children.  Each child stands on a factor of 96 (1,2,3,4,6,8,12,16,24,32,48,96), no 2 people on same tile. Teacher chooses one of these numbers and the person standing on that number finds the “factor pair” making 96. Children move off the tiles in these factor pairs

 

 


 

Sieve of Eratosthenes

Time needed: 5 minutes

Group size: Full class

Suitable for: KS2, KS3, KS4, FS

Curriculum Area(s): Numbers

Resources needed: ???

Description: Clearing up procedure (Sieve of Eratosthenes). Remove 1 from the boeard.

  • Teacher stands on no 2, children pick up all other multiples of 2.
  • Teacher stands on no 3, children pick up all other multiples of 3.
  • Teacher stands on no 5, children pick up all other multiples of 5.
  • Teacher stands on no 7, children pick up all other multiples of 7. Etc…

What numbers are we left with?  What is special about these numbers?

 

 

 


 

Number Rectangles

Time needed: 10 minutes

Group size: Full class

Suitable for: KS2, KS3, KS4, FS

Curriculum Area(s): Numbers, Multiplication and Division

Resources needed: Carpet tiles 1-100

Description: Pupils stand on multiples of 10 on the 100 square.  Now stand on numbers that have a remainder of 1 when divided by 10.  Remainders of 2.  What do we notice about all of these?  Now stand on multiples of 9.  Why are we in a line when we are standing on multiples of 10?  Make a rectangle to show the 9 X table.  i.e. 1-9 across the top row, 10-18 across row 2 and so on up to 90.  Now what happens when we stand on multiples of 9?  Are we in a straight line?  What about remainders of 3 when we divide by 9?  Where will we stand?  Now lets make a rectangle that will help us with the 7 times table.  Repeat exercises.

What patterns can we find in the different times tables?

 

 

 


 

Number Police

Time needed: 20 minutes

Group size: Full class

Suitable for: EY, KS1, KS2, KS3, KS4, FS

Curriculum Area(s): Numbers, Addition and Subtraction, Moltiplication and Division

Resources needed: 100 square, 2 telephones, large paper and pens

Description: Half the class are policemen, half are informants.  The police are looking for a number who is suspected of committing a crime.  As a group, informants decide what number is guilty.  Police have all the numbers from 0 to 100 lined up on a ‘suspect board’ (or on the floor).  Informants call up the police station on a telephone (two telephones and a telephone sound effect are perfect here, but not necessary).  Informants must provide clues to help the police eliminate some of the numbers from their suspect lists.  E.g. ‘The number you are looking for is even’ or ‘The number you are looking for is a multiple of 4’ or ‘The number you are looking for has a 2 in it” or “The number you are looking for is three more than a prime number” or “The number you are looking for is three more than a triangle number”.  As the police eliminate suspect numbers they turn them over.  They are left with the number that caused the crime.

Differentiation/Extension: Use a smaller range of numbers for lower year groups. Foundation can just use 10 numbers. Use more complicated clues for older children – encourage them to use more complex mathematical language. For older children – limit the number of clues the informants are allowed to give and specify the language they must use in clues e.g. factor, greater than, divisible by…. Try switching it around so that the police are interviewing the informants and asking specific questions – but are only allowed to ask a certain number of questions.

 

 


 

Blind Numbers

Time needed: 15 minutes

Group size: Full class

Suitable for: EY, KS1, KS2, KS3, KS4, FS

Curriculum Area(s): Numbers, Addition and Subtraction

Resources needed: Carpet tiles 1-100, Card with series of calculations on, 100 square printed in pack

Description: With the number tiles in a 100 square, turn all the tiles over so that you can’t see any of the numbers.  Individually, give children a number to go and stand on the right square.  When the child thinks they are on the right place, ask the rest of the children if they agree.  The child can adjust their positioning if they want to.  Reveal the number they are standing on and see if they are right.

  • Give easier numbers to find in the blind square to the less able (e.g. single digits, or 21, 31…).  Or begin by having some numbers revealed to give clues on the square.  The less able pupils can start the game and then gradually, you can
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