Problem-solving in mathematics

Some of the problems below are based on ideas from NNS training materials, the excellent DfEE publication Mathematical challenges for able pupils in Key Stages 1 and 2, and the Nrich web site. Most are original problems developed by myself.

They are all in Word format and may be freely downloaded, adapted and copied. Aimed at able Years 5 and 6, they can be modified for older or younger pupils or differentiated for a range of abilities. Just change numbers or text, print or save the file onto your PC and it's done. Enjoy!

Mike Kite, 2003

Badminton battles - how many games are played in a round-robin + knockout competition?
Heads and tails - coin combinations tossing 3 coins & 4 coins
Handball heroes - how many games are played in an inter-school tournament?
World Championships - how did England fare in the World Handball Championships?
Holiday gear - what combinations of polo shirts and shorts can Laurence wear?
Lots of little legs - how many ladybirds and spiders did Key Stage 1 collect?
Lots and lots of legs - variation on above
Wheels, wheels, wheels - how many vehicles is Mr Spanner repairing?
Wheels all around - slightly easier version of above
Car colours - a fractions problem using quarters and eighths
Car colours 2 - a harder fractions problem using fifths and tenths
Fruitful thoughts - Harry, James and George buy packs of 4 apples and 5 oranges
Ladybirds 1 - how many 4-spotted and 7-spotted ladybirds are there?
Ladybirds 2 - how many 4-spotted and 9-spotted ladybirds are there?
Ladybirds 3 - how many 3-spotted and 7-spotted ladybirds are there?
One pound - coin combinations of 50p, 20p & 10p
Two pounds - coin combinations of £1, 50p, 20p & 10p
Seven coins - coin combinations of £2, £1, 50p, 20p, 10p & 5p
Weighty matters - measuring with combinations of weights
Silver coins - what change was received from £2 and £5?
Snooker break - which colours did Typhoon Tom pot?
Double top - ways of scoring 35 with 2 darts
Double trouble - ways of scoring 58 and finishing on a double
Albert's cafe (harder) - what do his burgers, ice-creams and cans of coke cost?
Albert's cafe (easier) - simplified version of above
Albert's cafe 2 (harder) - what do cakes, ice-creams and cups of tea cost?
Albert's cafe 2 (easier) - simplified version of above
The choc shop - how much do the different chocolate bars cost?
The choc shop (easier) - simplified version of above
The choc shop 2 - how many chocolate bars did Billy and George buy?
The fruit shop - what do apples, bananas and oranges cost?
The fruit shop (easier) - simplified version of above
The fruit shop 2 - how many apples and bananas did Janet buy?
The fruit shop 2 - (harder) how many bananas and oranges did James buy?
Lunchbox goodies - what did Dad pay for the food in Sarah's lunchbox?
Lunchbox goodies (easier) - simplified version of above
Fruit basket - find the percentage of different fruits
Garden visitors - find percentages and numbers of birds visiting Brian's garden
Late breakfast - how much are the cereals and sandwiches in Joe's cafe?
Coffee break - how many people went to Joe's for coffee and cake?
Coffee break - (alternative version)
Birds of a feather - a question of blue or green budgerigars
At the May fair - what did Katie sell on the cake stall?
In the refreshment tent - how many teas and coffees were made?
Pineapple and peaches - decisions in the fruit aisle at Safeway
Curious conserves - what do the jars of marmalade and jam weigh?
Fruitful thoughts - how many grapefruits and pineapples can you buy?
Counting carbohydrates - how many baguettes and croissants can you buy?
The bike shop - how many bikes and scooters were sold?
Getting round - how many children have bikes or scooters?
Round and about - how many children have skateboards or bikes?
Cribbage - making a total of 15 points with playing cards
Birdwise - a little matter of owls, parrots and toucans
Birdwise 2 - another little matter of ducks, swans and penguins
A dose of medicine - capacity problems based around a 300ml bottle of medicine
Soup for supper - capacity problems based around a 400ml soup can
Problems with pompoms - combinations of coloured pompoms on a clown's hat
Duck ponds 1 - adapted from Mathematical challenges
Duck ponds 2 - placing 15 ducks in specified groups
Fast food - how many cokes and burgers were bought?
Fast food (harder) - variation on above
Tea time - how many cakes and cups of tea were bought?
Tea time (harder) - variation on above
The witch's spell - making up a recipe from the witch's larder
A bowl of fruit - adaptation of a fractions problem from the Nrich website
Fine feathers - a fractions problem using fifths and tenths
Safari sums - a fractions problem using quarters and eighths
Farmyard figures - a difficult fractions problem using thirds and quarters
Popular pets - a difficult fractions problem using thirds and fifths
Plenty of pens - a shopping problem adapted from the Nrich site
Lovely grub - a shopping problem
Zios and Zepts - a combination problem adapted from the Nrich site
Put out the flags - a percentage problem adapted from the Nrich site
Furry pets - adapted from Mathematical challenges
Furry pets 2 - a simpler version
Final score - deducing possible half-time scores from the final result
Santa's selection - which reindeer will he choose to pull his sleigh? [Answer]