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] |