This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in maths and get you ready for the exciting next step into Year 8!

It's not just about what the answer is, but why!

Some maths questions are called free response questions.

Free response means that you write the answer yourself, rather than selecting from a list of options. In other words, you won't just be asked to find an answer; you'll be asked to prove it!

Power through this guide, to find out:

• what a "reasoning" or "explain" question looks like

• how to explain your thinking clearly, using mathematical words

• how to use the word ‘because’ to justify your answer

• how to prove your answer is correct by showing your working

A reasoning question is your chance to show how your brain works. A great explanation has three key parts:

The answer: A clear "Yes" or "No", or "I agree with…"

The justification: This is where you use the word "because".

The proof: This is where you use numbers or a worked example to prove your point.

Top tip: the golden rule:

Always use the word "because" in your explanation.

"Yes, she is correct, because…"

"The answer is 12, because…"

"I disagree with Ben, because…"

This word forces you to stop and explain your thinking.

Let's look at a typical reasoning question you might see.

Example problem: ‘Laura says, "To multiply any number by 4, I can just double it, then double it again." Is she correct? Explain your reasoning.’

Model answer: "Yes, Laura is correct, because multiplying by 4 is the same as multiplying by 2 and then multiplying by 2 again (since 2 x 2 = 4).

Proof: If I want to solve 15 x 4:

Laura's method: 15 doubled is 30. 30 doubled is 60.

Standard method: 15 x 4 = 60. Both methods get the same answer."

Sometimes, a question will ask you to compare two different ways of thinking.

Example Problem: ‘A teacher asks, "Which of these fractions is NOT equivalent to 2/3?" The fractions are: 4/6, 6/9, 6/8, 8/12.

Michele says: "The answer is 6/8. I checked all the others by multiplying the top and bottom of 2/3 by the same number. 2/3 x 2 = 4/6. 2/3 x 3 = 6/9. 2/3 x 4 = 8/12. You can't multiply 2/3 by a whole number to get 6/8."

Gerard says: "The answer is 6/8. In all the other fractions, the denominator is 1.5 times the numerator (4 x 1.5 = 6, 6 x 1.5 = 9, 8 x 1.5 = 12). But in 6/8, the denominator is not 1.5 times the numerator."

Whose reasoning do you agree with? Explain why.

Model Answer: "I agree with both Michele and Gerard, because both of their methods are correct ways to identify the fraction that is not equivalent.

Michele’s reasoning is correct because she used the rule for equivalent fractions: you must multiply (or divide) the numerator and denominator by the same number. She proved 6/8 is the odd one out.

Gerard’s reasoning is also correct. He spotted a different pattern: the relationship between the numerator and denominator (that the denominator is 1.5 times the numerator, or 3/2). This is a more advanced way of thinking, but it also proves that 6/8 does not fit the pattern."

Brilliant reasoning! You now know that 'explain' questions are your chance to show how your brain works.

The keys are to show your working, use mathematical vocabulary and always justify your thinking with the word 'because'.

Think about these questions to stretch your thinking and sharpen your skills!

What is the difference between an 'answer' and an 'explanation'?

‘All square numbers are even numbers.’ Is this statement true or false? Explain your reasoning.

‘A rectangle can be a square, but a square can never be a rectangle.’ Is this true or false? Explain your reasoning.

Have a chat about your answers with a parent, teacher or your class.