WORD PROBLEMS AND GRID
These were used on the Year 5/6 training session. QCA reports that students have difficulty with word problems – knowing which operation to do and knowing whether to solve the problem mentally, on paper with pencil, or with a calculator.
- The sheet starting “Abbi had 53 storybooks…”
You need a sheet between two children. Cut up the problems.
You also need an A3 sheet with the grid “Work out / mentally …” per pair. (see end)
Students are to put the problems in the correct sections of the grid; then compare their placements with another pair and discuss.
There is not one right answer! Some may use pencil and paper to do 53 x 6, others may do it mentally.
*Each person in the group takes a cell on the grid and writes a problem to suit. These are then swapped with another group. etc.
- The sheet starting “I would love to swim 5 km …”
These are multi-task problems to cut up.
In pairs children:
cross out irrelevant phrases,
highlight important information,
decide what to do, in what order,
write down the calculations,
estimate the answer,
decide whether a mental / paper and pencil / calculator method is necessary,
perform the calculations,
relate the answers to the calculations back to the problem,
check that the answer is sensible.
- The sheet starting “What is 40 more than …”
These are problems for discussion – is there more than one way in which to do each question? How can we decide which is the easiest way? Does the order of operations matter – always / sometimes / never? Are diagrams useful / essential? Will it help to do the problem with easier numbers?
Abbi had 53 storybooks. She gave 8 of them to her younger brother.How many books did she have left? / Barney had 22 CDs.
His father boasted that he had five times as many.
How many CDs did his father have?
87 cows had to be slaughtered last year out of a farmer’s total stock of 234 cows.
How many cows survived? / A farmer planting cabbages knows that each cabbage plant has to have enough earth to grow fully. The farmer has enough space to plant 23 rows of cabbages, with 67 in each row. How many cabbage plants could he grow altogether?
36275 lottery prizes were not claimed last month out of 1256731 prizes altogether.
How many prizes were claimed?
[These figures were made up! Can you find out the real figures?] / A quantity surveyor calculated that a wall would need to be 458 bricks along and 37 bricks high.
How many bricks will he need?
A grandfather shared his bingo winnings of £472 equally between his 7 grandchildren.
How much did they each receive? / My friend is going to give me his whole stamp collection of 237 stamps. I have only just started saving stamps. I have 29.
How many stamps will I have altogether?
I decided to share my Smarties with my two friends. The tube had 36 Smarties in. How many did we each get? / I met 9 relations on Christmas Day and 14 different ones on Boxing Day.
How many relations did I meet altogether on those two days?
42574 people entered Tottenham Hotspur’s ground through 14 turnstiles.
If all were used equally, how many people entered through each one? / The area of southern Ireland is
68954km2. The area of northern Ireland is 13580 km2.
What is the total area?
What is 40 more than 30 less than 77?Is this the same as 30 less than 40 more than 77?
Explain your thinking. / What is the change from £10 after buying a shirt for £7.99?
In how many ways can you find the answer?
I want to double a number and then add 3.
Will this give the same answer as adding 3 first and then doubling the result?
Why does/doesn’t this work? / The answer is £2.50
Write a question to go with this answer and show at least two different ways of answering your question.
It is 39 paces from my front door to my best friend’s front door.
How many paces is it there and back?
Is this a multiplication sum or an addition?
Explain your answer. / Make up a story to go with each of these:
10 (2 + 3) and 10 2 + 3
I can check a subtraction sum by adding the answer to the smaller number. Show using numbers that this works.
How can you check the answer to a division sum? Show using numbers that your method works. / Natalie is prepared to share her conkers with her younger brother. She has 72 conkers. She wants to share them so that she ends up with twice as many conkers as her brother.
How many conkers will each have?
Choose a number. Increase it by 50%. Now decrease the answer by 50%.
Repeat this with 2 other starting numbers.
Explain what is happening. / From the product of 6 and 5 subtract the quotient of 10 and 2.
Make up a sum of your own using the words product and quotient.
My dad has painted three fifths of a fence. He has six metres left to paint.
How long is the whole fence? / Our kettle holds 3 litres of water. Our mugs hold a third of a pint.
About how many mugs of tea will our kettle make?
I would love to swim 5 kilometres.
How many lengths of the local pool would I have to swim, if the pool is 32 metres long? / I bought two CDs costing £14.99 and £12.50 each.
How much change did I get from three £10 notes?
Ridgebury Primary School has 69 Year 6 students. They are going on a trip, using minibuses, which carry twelve people in total. How many minibuses will they need if each minibus has to have an adult as well as the driver? / I fear that one of my fish is eating the others!
I now have 2 Angelfish, 5 Neon Tetras 4 guppies and 1 graveller.
I started with 17 fish.
How many have died?
I need to make 4 curtains. Each one is to be 1.3 metres long when finished. Each has to have 18cm allowed for hems at the top and the bottom.
How much material shall I buy? / A small theatre holds 256 people.
It has 4 boxes, which hold 4 people each, and it has 12 rows of seats.
How many seats are in each row?
I have to take two 5ml spoonfuls of medicine three times a day.
How long will the 175 ml bottle of medicine last? / Robert had 52 Amiga computer games. He sold 12 of the better ones, gave away 25 others and threw away one which the cat had chewed.
How many games has Robert got left?
In 1975 the English population was estimated at 46453700 out of a UK total of 55926100. The population of Wales at that time was 2769400.
What was the estimated population of Scotland and Ireland? / The oldest resident in Broxbourne was born in 1896. She wants to see her granddaughter reach 50 years of age in 2003.
How old will the grandmother be?
[Her life has spanned 3 centuries!]
I am twice as old as my son. He is 6 years older than his sister.
I am 48 years old now, how old is my daughter? / I need 150 grams of flour to make 12 fairy cakes.
How much flour would I need to make 30 of these fairy cakes for a party?
Work out /
Mentally
/ With paper and pencil / With a calculator+
_
x