Reasoning: Number and Calculation
Reasoning: Number and Calculation is where Year 5 pupils apply place value, the four operations, negative numbers and multiplication and division facts to multi-step word problems, rather than answering a bare sum.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the question twice: the first time for the story, the second time to identify exactly what number you need to find and which operations connect the pieces of information.
- Underline or note down every number given, along with what it represents, before starting any working - mixing up what a number means is the most common Year 5 reasoning mistake.
- Decide the order of steps needed. Many Year 5 reasoning questions are multi-step: work out one quantity first, then use that answer in a second calculation.
- Choose a formal written method (column addition or subtraction, short or long multiplication, or the bus stop method for division) for any calculation too large to do mentally, and set it out clearly so a mark can be awarded for method even if the final answer is wrong.
- If the question mentions negative numbers, picture or sketch a number line and count the jumps carefully, remembering numbers get smaller moving left of zero.
- Once you have an answer, check it against the story of the question: does the size of the number make sense, and have you answered the actual question asked, not just completed a calculation?
- Write the answer with its correct unit or context, such as '519 pencils' rather than just '519', since SATs mark schemes sometimes penalise a missing unit.
Worked example
A school is ordering pencils. Pencils come in boxes of 24. The school orders 18 boxes. They already have 87 pencils left over from last year. How many pencils does the school have in total now?
- Work out how many pencils are in 18 boxes of 24 by multiplying: 24 x 18.
- Using short or long multiplication, 24 x 18 = 24 x 10 + 24 x 8 = 240 + 192 = 432.
- Add the pencils left over from last year: 432 + 87.
- Using column addition, 432 + 87 = 519.
- Check the answer makes sense: 18 boxes of roughly 24 pencils is a bit over 400, plus about 90 more, is a bit over 500 - so 519 is sensible. The school has 519 pencils in total.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Zainab has 3.85 pounds saved. Her grandad gives her 2.60 pounds more. She then spends 90p on a magazine. How much money does Zainab have left?Show answer
Answer: 5.55 pounds (3.85 + 2.60 - 0.90)
Q2A minibus can carry 16 passengers. A school needs to transport 137 pupils on a trip. What is the smallest number of minibuses needed?Show answer
Answer: 9 minibuses (8 minibuses carry 128 pupils, leaving 9 pupils needing a 9th minibus)
Q3The temperature in a freezer is -18 degrees C. The temperature in a fridge is 22 degrees higher than the freezer. What is the temperature in the fridge?Show answer
Answer: 4 degrees C
Q4Ryan thinks of a number. He multiplies it by 6, then adds 15, and gets 87. What number did Ryan start with?Show answer
Answer: 12, since (87 - 15) divided by 6 = 12
Q5A charity raised 4,250 pounds in January and 3,875 pounds in February. Each month's total is rounded to the nearest 100 pounds for a poster. What is the rounded total shown on the poster for the two months combined?Show answer
Answer: 8,200 pounds (4,250 rounds to 4,300 and 3,875 rounds to 3,900)
Q6Ellie-Mae buys 4 packs of stickers costing 1.35 pounds each and a poster costing 2.50 pounds. She pays with a 10 pound note. How much change does she get?Show answer
Answer: 2.10 pounds
Q7Kwame has 156 marbles. He gives away a third of them to his brother, then buys 40 more. How many marbles does Kwame have now?Show answer
Answer: 144 marbles (156 - 52 + 40)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A cinema has 24 rows of seats. Each row has 18 seats. On Saturday, 187 seats were empty. How many seats were filled?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Arjun says that to find the answer to 3,400 divided by 100, you just remove two zeros, so the answer is 34. Use this method to work out 56,000 divided by 1,000, then explain in one sentence why the method works.
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Freddie is saving for a bike that costs 156 pounds. He has already saved 42 pounds. He earns 7.50 pounds a week from a paper round and saves all of it. What is the smallest number of full weeks Freddie will need to save for, before he has enough money for the bike?
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the reasoning: number and calculation worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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