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Solving The Problem of Problem Solving Q’s in SATs

Updated: Sep 1, 2023

Picture this…

Your child is confident with numbers and maths operations. They can divide a fraction by an integer, are able to find the perimeter and area of a shape with no probs and have no trouble with place value. Then they come across a question that is in words, has minimal numbers, but is asking for a mathematical answer! What is this nonsense!? Is it a joke? Is it a riddle? No my friends, this is a reasoning problem. Most of these types of test questions ask that we take loads of info, combine different kinds of maths and perform multi-step calculations.

You’re thinking yeah, but, HOW DO WE DO IT?! Well never fear, hold your horses, make a cuppa and I’ll help you out.

Get Creative

We know now that the 2 + 2 = 4 approach won’t work here, and getting creative doesn’t mean 2 + 2 = 22. We need to work out what the question is asking us, break it down and work out what answer it wants from us. In other words, we need to be flexible in our thinking and adventurous in trying things out. Coming up next is a ‘tried and tested’ Sammie Allen tutor’s ‘Step-by-Step’ to come at these questions with an open mind.

Step-by-Step, we’ll get there…

Read your question as many times as it takes to sort it out in your head. Do you understand the question? Take your time and read 2-3 times to get to grips with it.

Underline or circle what it is asking for, eg. ‘How many metres have they travelled?’ or ‘How many eggs has Josie got left?’ or ‘What is the perimeter of Reagan’s rectangle?’

Hint: This bit is the main goal!

Find out what information is not there yet, but needed to reach your main goal. In other words, the stepping stones to the final answer. These are your mini-goals!

What information is the question giving you? Note down what you need to know separated out from the wording to get it clear in your head.

Decide how we need to use the information to get to your mini-goals first. What bits of info go together to get the answer you need?

Try it out! Don’t be afraid to experiment with these maths problems. You can do it! Execute and solve the problem.

Here, Let’s do one together!

Step 1

Do you understand the question? No? Well read, read, and read again to help you unpick and get it in your noggin!

Step 2

Underline what it’s asking for, in this case it’s, ‘How much change does he get from £5?’

Now we know the answer must be in pounds and pence! This is the MAIN GOAL.

Step 3

What info do we need?

We need to know what weight carrots and potatoes Jack has bought!

Then how much altogether these cost.

Step 4

Now we’re searching for the information. And here we have it:

  • Jack is buying 1 ½ kg of potatoes and ½ kg of carrots

  • Potatoes are £1.50 per kilogram

  • Carrots are £1.80 per kilogram

Step 5

Now in this section I realise that there is some tricky maths!

Here it is a short version so we can focus on the very serious business of problem solving. If you need help with this kind of thing, why not get in touch with Sammie Allen Tutoring and we can tell you aalllllll about it!

Now we need to decide what to do first, we can multiply or divide, it’s up to you!

We need to take the price of the veg and use it to work out how much each type costs.

Potatoes first (mmmm my favourite!)

£1.50 1 ½ = £2.25

Then, our Carrots

£1.80 ½ = £0.90

Now add those together!

£2.25 + £0.90 = £3.15

Step 6

Mini-goals achieved! Now we can just put £3.15 in the answer box, right? NO!

We need to know what change Jack will get, not how much it costs to complete our main goal. To do this we need one final operation, which is of course, subtraction!

Simply take the total of the carrots and potatoes and subtract from the £5.

£5.00 - £3.15 = £1.85

Woo hoo! Well done, and good luck! Just follow these 6 easy steps when sitting your SATs and you should be able to tackle reasoning, no problem!


This list will break down some of the words we find in reasoning and what they mean in maths terms!


  • Add

  • Plus

  • More

  • Sum

  • Total

  • Altogether


How many altogether?

What is the total of ______ and _______?

What is ______ doubled?


  • Subtract

  • Minus

  • Leave

  • Left

  • Take away

  • Difference between


How many are left over?

How much less is _____ than ______?

How many fewer is _____?


  • Lots of

  • Times

  • Multiply

  • Groups of

  • Product

  • Multiple of

  • Repeated addition

  • Array


Use repeated addition to…

______ lots of _____…

What is the product of _____ and ______?


  • Divide

  • Divided by

  • Divided into

  • Share

  • Shared equally

  • Equal groups of


_______ is shared equally into_____ groups of_____.

_____ divided by _____ is ____.


  • Makes

  • Total

  • Same as

  • Equivalent

  • Balances


What is the total number of _____?

How many ____ does ____ make?

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