# Examining the CPA approach to primary maths

Explore the importance of the concrete, pictorial, abstract approach (CPA) in primary maths mastery classrooms

## Concrete, pictorial, abstract (CPA) approach resources to help pupils to develop a deep understanding of maths as part of mastery learning

CPA may be at the heart of teaching for mathematical mastery, but giving pupils objects and drawings to help them to understand key concepts isn’t anything new. So, what is it that makes this approach so valuable to the study of maths and particularly to the teaching for mastery?

As CPA is not about getting the answer quickly, concrete manipulatives are often used to help pupils to work through questions. They can also be used to encourage the transition to pictorial and abstract. After all, maths lessons aren't about teaching tricks; they are about giving pupils the tools to understand the problem in front of them.

CPA is for everyone; all abilities and all ages. Concrete manipulatives are a common feature of KS1 classrooms across the country, but they can be used just as effectively at KS2, and not just for pupils who are struggling. Mastery teaching encourages the use of concrete manipulatives in any lesson and suggests that there is value in KS2 pupils having a variety of equipment to aid their thinking.

In maths mastery, there doesn't have to be a linear progression from concrete to pictorial to abstract. Instead, teachers can apply a cyclical approach. For example, even when a pupil has worked out the answer using an abstract method, it is worth asking them to use concrete manipulatives to convince others that they are correct.

CPA is a way to deepen and clarify mathematical thinking. Learners are given the opportunity to discover new ideas and spot the patterns, which will help them reach the answer. From the start of KS1, it is a good idea to introduce CPA as three interchangeable approaches, with pictorial acting as the bridge between concrete and abstract. When teaching for mastery, the CPA approach helps learners to be more secure in their understanding, as they have to prove that they have fully grasped an idea. Ultimately, it gives pupils a firm foundation for future learning.

When using CPA in your classroom, almost anything can be used as a concrete manipulative, from lollipop sticks to cups and marbles. Feel free to be creative and make use of objects that are at hand in your classroom!

To get you started or give you a range of CPA lessons, activities and supportive visual aids to refresh your existing range, why not take a look at this hand-picked collection of innovative resources from the Tes community?

#### The importance of concrete - Professional development

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Select View more for an accompanying video. Fundamental to the powerful Concrete-Pictorial-Abstract (CPA) approach, concrete manipulatives are a key resource in developing a deep understanding of maths for pupils of all ages and abilities. Continuing the story of the remarkable Miss Rose ...

#### Area and volume

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Enabling teachers to continuously develop their practice is a key element of the [Mathematics Mastery Programme](http://www.mathematicsmastery.org/#utm_source=tes&utm_campaign=tes_mastery_corner&utm_medium=referral&utm_content=tes_cpd_videos). This CPD resource provides step-by-step...

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#### Numicon doubling butterflies to 10

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Numicon doubling butterflies to 10 with spaces for all numbers 1-10 and an extra couple of snail ones.

#### Subtraction with Numicon

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A series of worksheets using Numicon.

#### Recognising Unit Fractions - KS2

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A complete lesson for lower KS2 on recognising and describing unit fractions. The starter is based on using 'playdough' to give pupils a concrete reference for a 'whole' object and how dividing it into parts gives rise to fractions. If, however, you have access to other concrete manipulatives for te...

#### Ten frame template (CPA)

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This worksheet has a ten frame template, with a few questions for students to practice what two numbers makes up a ten. **CPA Approach ** *Concrete stage* - using counters on the ten frame template to develop counting and addition skills *Pictorial stage* - coloring the circles on the worksheet ...

#### Differentiated Worksheets - Doubling Numbers (using Base Ten, DIenes Cubes, Numicon)

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I made these worksheets for my year 2 class. It teaches them the skills of using partitioning with Dienes Cubes/ Base 10 in order to help them double numbers. It is very visual and they really understood it well. They drew the number that needed to be doubled twice and counted ones and tens to get...

#### Yr 3 Multiplication and Division as an array, repeated addition and on a number-line -CPA

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A printable template to encourage children to see calculations as arrays, on a number-line , as repeated addition and pictorially. Shrink them down and use them for starter activities too. I used it this week with my Year 3 class and they loved it.

#### Numicon Supporting Resources

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These are just some of the many Numicon resources I have created to support my students' learning. If you print them A3 then the images will be the same size as the real Numicon shapes. Enjoy and please leave a review!

#### Adding 10 Pictorially (Year 2) including Reasoning

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4 worksheets which supports adding 10's pictorially using the dienes cubes. Could be used as a sequence of lessons (3 days). All of the answers are below 100 - it does include a worksheet to support lower ability children as a stepping stone to this objective. Reasoning questions are built in tow...