In the ever changing world of mathematics, schools are using different teaching strategies to help pupils achieve better. Many parents have asked for some more information on how to support their children so we hope this section of our website helps everyone.

AHPS Maths Calculation Policy 2020-2021

A Maths Mastery Curriculum

  • High expectations for every child
  • Few topics, greater depth
  • Number sense and place value come first
  • The use of objects and pictures before number and letters
  • Problem solving is central
  • Language and Communication lead to understanding
  • Challenge is provided through an increased depth, rather than acceleration of content

What does it mean to master something?

  • I know how to do it
  • It becomes automatic and I don’t need to think about it, e.g. driving a car
  • I’m really good at doing it
  • I can show someone else how to do it.

“In mathematics, you know you’ve matered something when you can apply it to a totally new problem in an unfamiliar situations.” Dr. Helen Drury, Director of Mathematics Mastery

Mastery of Mathematics is more…..

  • Achievable for all
  • Deep and sustainable learning
  • The ability to build on something that has already been sufficiently mastered
  • The ability to reason about a concept and make connections
  • Conceptual and procedural fluency

The Concrete – Pictorial – Abstract Approach

What are Manipulatives?

Manipulatives are physical objects that are used as teaching tools to engage children in the hands-on learning of mathematical concepts.  These are different resources such as cubes, counters, straws, bead strings, dienes, etc, which can be used to support the children to understand better. Below are some manipulatives that we use in school:

Teaching Strategies

Year 1 – Addition Calculations in Action


Year 1 – Subtraction Calculations in Action

The video below shows how using bar modelling and counters can be used to work out different types of subtraction calculations.

Year 1 – Multiplication Calculations in Action

Year 1 – Division Calculations in Action

Year 2 – Multiplication Calculations in Action

Year 2 – Division Calculations in Action

What is Bar Modelling?

The video below helps you to understand how bar modelling is used to represent problems so that children can then being to solve them.

How to teach Number Bonds?
The video below shows the strategies which can be used to teach all different types of number bonds. For example, each counter can represent 10 so you can work out number bonds to 100. The possibilities are endless!

Maths is all around us and problem solving is at the heart of the mastery approach. Look for maths problems you can solve together, making connections between what your child has been learning at school and the world around them.

Demonstrating these connections – and representing them in multiple ways – not only supports your child’s understanding and cements their knowledge; it reinforces the relevance of maths in our lives and makes it fun.

Some ideas:

  • Follow a recipe: work together to find out the quantities needed, ask your child to weigh the ingredients, discuss how you’d halve or double the recipe and discuss the ratio of ingredients.
  • Talk about the weather forecast: is today’s temperature higher or lower than yesterday’s? What do the numbers mean?
  • Going shopping: talk about the cost of items and how the cost changes if you buy two items instead of one. Let your child count out the coins when paying and discuss the change you get back. Use coins to explore addition, subtraction, multiplication and division.
  • Planning an outing: discuss how long it takes to get to the park, and so work out what time you need to leave the house. Encourage your child to work out the best solution based on the time and distances. Discuss what shapes you see when you get there
  • Telling the time, discussing the days of the week, talking about money or the coins needed to pay for items, how long things take to cook
  • GROWTH MINDSET – Everyone of us can master mathematics given the opportunity.

Ideas for Counting

  • Collections of objects – shells, buttons, pretty stones
  • Cars on a journey, e.g. how many red cars?
  • Animals in a field e.g. sheep, cows
  • Stairs up to bed, steps, etc.
  • Pages in a storybook
  • Counting buttons, shoes, socks as a child gets dressed
  • Tidy a cupboard or shelf and count the contents e.g. tins, shoes, etc.
  • Counting particular vehicles on a journey e.g. Eddie Stobart lorries, motorbikes, etc.

Other Tips

  • Keep maths practical and real life
  • Money – paying for things, playing shops, purses
  • Dishing up dinner – problem solving
  • Games (snakes and ladders, dice)

Think about a picture and see what questions you can derive from it to ask your child. For example, using this picture, look how many questions we can ask related to maths:

Mathematics language often uses common words in a new way. For example, ‘difference’, ‘right’, ‘product’, ‘table’.

To support your child’s understanding of mathematical words, ask them to explain the words they’ve been using and what they mean. Find out what new maths vocabulary your child’s teacher is introducing so you can use it at home to complement their learning.

Always encourage your child to explain how they have gone about solving a problem, and work with them to test, prove, explain, reflect and spot patterns. Questioning and prompts can be powerful tools to boost your child’s mathematical thinking: ‘What do you think…?’  ‘Why …?’ ‘What will happen if…?’ ‘What do you notice about…?’ ‘Can you see a pattern between…?’ ‘What if we try…?’

Communicating and discussing maths problems (in a way that others can understand) demonstrates depth of understanding – another fundamental aspect of mastering mathematics.


Please click on the links below to download some previous SATS papers:

Arithmetic 2018
Reasoning 2018
Arithmetic 2017
Reasoning 2017
Arithmetic 2016
Reasoning 2016

Below are some videos that go through some previous SATS questions with explanations to help you and your child understand better:

Year 2 Videos

Addition Workshop – Year 2 SATs preparation (KS1) for parents and children

Multiplication Workshop – Year 2 SATs preparation (KS1) for parents and children

Division Workshop – Year 2 SATs preparation (KS1) for parents and children

Subtraction Workshop – Year 2 SATs preparation (KS1) for parents and children

Useful Resources

The websites below have various games which would consolidate different aspects of children’s learning in maths: