# Questions for deepening

We’ve all read about the vision for ‘mastery’ learning in maths; I’d figured that what teachers want is to see actual examples that they might be able to use with their class. So once we got back from our residential, I decided to post pictures of questions that I use with my year 6 class (and the odd example from around the school) to deepen their learning. The reaction on social media has been very positive, so I’ve dumped them all on this blog.

At the start of the year I used one of my favourite questions:

Which two numbers have a sum of 9 and a difference of 4?

This one’s more complex than it may initially seem as the solution involves halves. An easier version is shown below:

Sara and John spent a total of 40p at the school council shop. Sara spent 10p more than John. How much did John spend?

Then came deepening within rounding:

A question exploring the difference between negatives & decimals:
How many time do you have to halve 128 until you get a negative number?

And drawing together rounding and negative numbers:

Note that for question 3, one of the numbers is negative.

Two fractions questions with multiple solutions:

A year 4 question looking at deepening vertical addition:

And finally reasoning in multiplication:

I’m hoping to keep these posts coming (Twitter @gareth_metcalfe or FB Gareth Metcalfe Primary Maths) and, in the fullness of time, to make freely available a set of deep reasoning questions for all year-groups. If you’ve found it useful, or you know someone who might be interested, please share this blog post!

My maths resources, published by Alan Peat ltd, have also been designed to deepen children’s experience of maths.

First Class Maths provides deep, extremely challenging and quirky tasks: https://garethmetcalfe.wordpress.com/2015/02/01/first-class-maths-curious-and-challenging/

The Maths Apprenticeship gives extended challenges for deepening mathematical and personal competence skills: https://garethmetcalfe.wordpress.com/2014/05/22/tma-the-how-to-guide/

And Logic Squares is all about getting children playing with numbers: https://garethmetcalfe.wordpress.com/2015/10/03/the-learning-in-logic-squares/