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Problem Solving, Reasoning And Numeracy


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I'd be really interested to know anyone's experience of successful activities that have helped to engage children in aspects of problem solving, reasoning and numeracy. In particular, I'm looking for ideas of hands-on activities related to numbers, shapes, measuring and sums (the latter involving various types of calculation – addition, subtraction, multiplication, division, estimation etc). Activities that involve some type of physical or creative element would be ideal! Keen to bring some fun into mathematical learning, and to encourage children to explore for themselves.


Any ideas gratefully received. Thanks for your help!

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Welcome KDicker and congratulations on your first of hopefully many posts.


I'm unsure of the age you work in but I am in F2 and we used the outdoor area for many PSRN activities.

The children chose to play skittles and used addition, subtraction and estimation.


Hoops and bean bags were also successfullly used once more with addition. The children gave and marked each hoop with a number and then attempted to throw a specific amount of bean bags into the hoops. If they went in the hoop they were awarded the points. This worked particularly well for large number additions too.


Struggling now off the top of my head its way past my bedtime! I will give it some more thought, but I'm sure many other brilliant ideas will be here before then!





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Hi Vicky


Many thanks for your ideas, so promptly! It's really useful to know what works well. Skittles and throwing into targets sounds fun.


I'm looking at pre-school in particular. And keen to bring in aspects of problem solving wherever possible – to get the children thinking for themselves.


Thanks for your help.

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Welcome DKicker! What about using snack time for some PSRN. Try getting the children to count how many pieces of fruit they will need for their group and then provide one too many/too less pieces for them to problem solve. Outside try drawing a large carpark on the ground and then use a large foam +/- dice getting children to pretend to be cars and drive in or out of the carpark in response to the dice. My children love this game. :o



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we numbered our bikes and then made car parking spaces with chalk on the ground and encouraged the children to find the parking bay that corresponded with their bike number.


snack times ideas are good for simple problem solving, i sometimes dont put enough bowls out, so they have to work out how many more they need, or if too many out, how many more than we need.


addition and subtraction we do during singing with songs like- 5 green speckled frogs, men in a flying saucer etc...

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Number recognition and counting

• Use a pegged number line for counting, matching, missing number and jumbled up number games.

• Make a moveable number line using yoghurt pots. Label the pots with numbers. Children choose correct number of objects to put inside each pot and place in order.

• Make a vertical number line, using the children's handprints.

• Make a tactile number line using materials such as sandpaper, fur, cord, velvet etc. for a multi-sensory approach.

• Label attractive boxes with different numbers. Children place correct number of natural objects in each box e.g. shells, fir cones, conkers, feathers

• Place a few wooden/plastic numbers in a feely bag. Can children pull out a given number by feel only?

• Place wooden/plastic numbers in separate envelopes. Slowly pull them out one by one to reveal a small part of the number. How soon before the children can guess what the number is?

• Hang number cards on a mug tree. Can children hang the correct number of objects on each mug peg? Use scrunchies, rubber bands, bracelets, curtain rings

• Hang numbered pockets on the wall. Children place correct number of items in each pocket.

• Thread correct number of cotton reels/beads on to numbered laces.

• Hold a small number of marbles in your hand and slowly drop one by one into a covered container. Children listen carefully and tell you how many you dropped in.

• Show a number of objects on the floor. Cover them up. Can the children remember how many?

• Go for a number walk with a number card. See how many times the children can see that number e.g. on a bus, shop, menu, house, car

• Go for a number walk and take photos of numbers in the environment. Make a display of the photos.

• Collect examples of numbers on packaging, magazines, labels etc. from the environment and set up a display.

• Stick a number on each side of a box/tin. Children clip the correct number of pegs to each side of the container.

• Hide pieces from a number jigsaw around the room. Children have to go and find the pieces, bring them back to a central point and help put the jigsaw together.

• Label bikes and create numbered 'parking bays'. See if the children can park their bikes in the correct bays.


• Play musical instruments behind a screen a certain number of times. Can children tell you how many bangs on the drum, shakes of the maracas etc?

• Play an instrument a certain number of times. Can the children play their instrument the same number of times?

• Sing and act out number rhymes and songs.

Sand, water and malleable materials

• Find foam numbers in water or sand

• Make numbers out of playdough

• Draw numbers with fingers in shaving foam/paint/gloop

• Catch given numbers of floating objects in nets.

• Fill and empty a variety of containers (tall, short, thin, wide, large, small etc.) with water, sand or materials such as lentils and rice.

Creative Area

• Make models with different sized, shaped, coloured and textured boxes and materials.

• Print with different shaped objects.

• Collage large numbers and shapes.

Cooking and snack time

• Make number shaped biscuits

• Stick certain number of currants/chocolate drops etc. on cakes/biscuits

• Make a recipe book using pictures and numbers of cupfuls/spoonfuls needed for each recipe.

• Make menus with prices, for the role-play cafe.

• Cut up fruit into segments and portions. Talk about halves, quarters and shapes.

• Encourage children to pour drinks for themselves.

• Share out biscuits/fruit together with the children.

• Count out fruit, biscuits, drinks


• Knock over numbered skittles

• Throw large dice and clap, jump, hop catch ball etc. correct number of times

• Throw correct number of beanbags into numbered containers

• Jump along numbered carpet tiles in order from 1-5/10

• Use large chalked shapes on the ground. Throw a shape dice, children run to correct shape. A harder version would be to add colours so children have to run to the red square, the green circle etc.

• Throw correct number of quoits over numbered cones.

Measuring and time

• Draw round hands and/or feet and cut out. Use for measuring activities and games.

• Give children a length of string, fabric or a ruler. How many things can they find that are longer/shorter?

• Place some pegs in a line on a pegboard. Can children add or take away pegs to make the line longer/shorter?

• Give children different sized containers. See how many conkers, cones, shells etc. they can fit inside them.

• Use role-play to encourage the children to find things to fit e.g. the right sized hat, belt, bag, container etc.

• Make a time line with photos of what the children do in the day e.g. register, snack, outdoor play ... encourage them to refer to it during the session.

• Use a sand timer at tidying up times in order to help children learn about the concept of time.


• Collect flat and 3D shaped items from the environment and make a display e.g. tins, food packets, money

• Stick a large favourite picture on to a piece of card. Cut into two or more shapes according to the ability of the child and see if they can put the picture together again.

• Carefully cut/break for example a toothpaste box, a flowerpot (watch edges) into pieces. Can the child put the item back together again?

• Play with flat shapes on the floor and find which are the same and which fit together.

• Cut sponges into different shapes and use to print shape pictures.

• Place shapes into a bag. Ask children to pull out a circle, a square, a curvy shape, a straight shape etc. by feel only.

• Go on a shape walk. Take a shape with you and look for that shape in the environment.

• Use shapes freely to make own pictures and patterns.

• Make shape biscuits.

• Make shapes with playdough.

• Mark out large shapes on the floor. Children run round to music and go and stand inside a given shape when the music stops.

• Children march/dance round to music. When the music stops, they make a shape with their body.

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Questions to ask to help develop mathematical understanding and problem solving

• How much/many?

• How do you know how much/many?

• Are there enough?

• What can you tell me about...?

• How do you think you could...?

• Is there another way you could...?

• What's different/what's the same?

• Why did you choose this?

• What can you say about...?

• What might happen if...?

• Which of these go together?

• What comes next?

• What comes before?

• How did you guess?

• Why do you think...?

• Suppose...what do you think might happen then?

• What do we do now?

• Can you find one the same?

• Do you think this will fit/be enough?

• Which/who has more/less?

Can you make it smaller/bigger/longer/shorter...?

• What/who is first/second/last...?

• What could we use to help us?

• Why doesn't this work?

• What have you done so far?

• What else could we do to...?

• How did you work that out?

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