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Reasoning and Problem Solving
Step 5: Multi-Step Problems
National Curriculum Objectives:
Mathematics Year 5: (5C4) Solve addition and subtraction multi-step problems in contexts,
deciding which operations and methods to use and why
Differentiation:
Questions 1, 4 and 7 (Problem Solving)
DevelopingSolve a multi-step word problem involving numbers up to 3 digits. Limited
exchange and use of visual representations.
ExpectedSolve a multi-step word problem involving numbers up to 4 digits. Includes
exchange and some visual representations/word problems in context.
Greater Depth Solve a multi-step word problem involving numbers up to 4 digits. Word
problems in context and some numbers to be retrieved from tables.
Questions 2, 5 and 8 (Reasoning)
DevelopingExplain the answer to a multi-step word problem involving numbers up to 3-
digits. Limited exchange and use of visual representations.
ExpectedExplain the answer to a multi-step word problem involving numbers up to 4-
digits. Includes exchange and some visual representation.
Greater Depth Explain the answer to a multi-step word problem involving numbers up to 4-
digits. Includes exchange, knowledge of doubling and halving, and word problems in
context.
Questions 3, 6 and 9 (Problem Solving)
DevelopingWrite and solve a word problem for a given context based on a multi-step
calculation involving numbers up to 3-digits. Limited exchange and use of visual
representation.
ExpectedWrite and solve a word problem for a given context based on a multi-step
calculation involving numbers up to 4-digits.
Greater Depth Write and solve a word problem for a given context based on a multi-step
calculation involving numbers up to 4-digits. Information to be retrieved from charts and
graphs in context.
More Year 5 Addition and Subtraction resources.
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Reasoning and Problem Solving – Multi-Step Problems – Teaching Information
Multi-Step Problems Multi-Step Problems
1a. Tree A is 378m tall. 1b. A school orders 455 maths books.
Tree B is 253m shorter than tree A. They order 258 fewer English books than
maths books, and 86 more art books than
Tree C is 73m taller than tree A. English books.
378m A – 253m A + 73m
Maths English Art
Tree A Tree B Tree C 455 Maths – 258 English + 86
What is the total height of the trees? How many books are ordered in total?
D PS D PS
2a. There are 500 marbles in a pack. 2b. Eric has 723 stamps in his collection
100 100 100 100 100 100 100 100 100 100 100 100 10 10 1 1 1
Box A has 141 marbles. Box C has 152 Book A has 423 stamps in. Book B has 225
more than box A. fewer than book A.
H T O H T O H T O H T O
+
? – ?
Box A Box B Box C Book A Book B Book C
How many marbles are in box B? How many stamps are in book C?
Convince me. Convince me.
D R D R
3a. Write a word problem to go with the 3b. Write a word problem to go with the
following calculation. following calculation.
225g + 334g – = 414g 512cm – + 123cm = 317cm
100 10 100 10 100 100 100 10 100 10 100 10
100 10 100 10 100 10 100 1 1 10 100 1
1 1 100 10 100 100 1 1 1 100 1
1 1 1 1 1 1 100 1 1
1 1 1 1 1 100 1 1
Solve your word problem. Solve your word problem. 1
D PS D PS
© Classroom Secrets Limited 2018 classroomsecrets.co.uk
Reasoning and Problem Solving – Multi-Step Problems – Year 5 Developing
Multi-Step Problems Multi-Step Problems
4a. A charity want to raise £9,559. 4b. A warehouse is receiving a bulk
shipment of pet food.
They raise £4,522 in the first month.
6,016 of the tins are dog food.
They raise two thousand, six hundred and
twenty-five pounds less in the second They receive 4,634 fewer tins of cat food
month. than dog food.
In the third month, they raise £1,540 more They receive 1,020 more tins of fish food
than what they raised in the second than cat food.
month.
How many tins of pet food do they
Does the charity reach their goal? receive in total?
E PS E PS
5a. Jack is organising his sticker 5b. There are 4,498 counters in one bulk
collection. He has 9,292 stickers in total. bag.
Box A has 4,906 stickers. Box C has 1,208 Box A holds 1,197 counters. Box B holds
fewer stickers than box A. 586 more counters than box A.
A B C A B C
4,906 1,197
How many stickers are in box B? How many counters are in box C?
Convince me. Convince me.
E R E R
6a. Write a word problem to go with the 6b. Write a word problem to go with the
following calculation. following calculation.
7,886ml–4,392ml+ ml =6,399ml £6,688 + £2,501 – £ = £7,626
Solve your word problem. Solve your word problem.
E PS E PS
© Classroom Secrets Limited 2018 classroomsecrets.co.uk
Reasoning and Problem Solving – Multi-Step Problems – Year 5 Expected
Multi-Step Problems Multi-Step Problems
7a. A printing company are recording 7b. Jet Air are tracking the number of
their quarterly sales. They want to print bookings made year on year to measure
8,500 flyers in this quarter. the company’s growth.
In January, they printed 2,264 flyers. Year Number of bookings
In February, they printed half the amount 2016 2,267
printed in January. 2017 Up 2,796
In March, they printed 234 more than 2018 Down 2,978
January and February combined.
Have they met their goal for this quarter? How many bookings were made in each
year and in total?
GD PS GD PS
8a. 4,432 buttons are made in three hours. 8b. Three boxes hold 9,567 elastic bands
It takes six hours to make enough buttons altogether. When box C has been filled
to fill three boxes. there are 6,909 elastic bands left.
When Box B has been filled, there are Box A has twice as many elastic bands as
3,363 buttons remaining. Box C holds half box B.
the amount of buttons as Box A.
A B C A B C
How many more are there in box A than How many more are there in Box C than
box C? Box B?
GD R GD R
9a. These are the items in a school 9b. These are the results of a traffic survey.
stationery cupboard. Write a word Use the information to write a word
problem using the information from the problem. It must have at least two steps
table. It must have at least two steps and and the answer must be a 4-digit number.
the answer must be a 4-digit number.
Item Number
Pens 2,764
Pencils
Rulers 2,009
Total 8,672
Solve your word problem. Solve your word problem.
GD PS GD PS
© Classroom Secrets Limited 2018 classroomsecrets.co.uk
Reasoning and Problem Solving – Multi-Step Problems – Year 5 Greater Depth
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