### Have you ever been in the middle of teaching a math lesson and noticed your students look like this?

Math can be stressful for students *and *teachers...but it doesn't have to be!

Use the **Concrete, Pictorial, Abstract (CPA) **approach to help students build a deep understanding of **math concepts** and develop problem-solving skills.

## Concrete Stage

**What is it? **

the

**"doing" stage**students model math problems using

**concrete objects**

**Example:**

**laying out**two mittens and adding three more mittens to find the sum**cutting**a watermelon into twelve pieces to model twelfths

### Concrete representations are bestfor:

when students are learning a

**new concept**

## Pictorial Stage

**What is it? **

the

**"seeing" stage**students model math problems by

**drawing**

**Example:**

**drawing**two mittens and drawing out three more mittens to find the sum**drawing**a picture of a watermelon and dividing it into twelve pieces to model twelfths

### Pictorial representations are bestfor:

concepts that

**don't have a concrete representation**(like negative numbers)when students show

**mastery of concrete representations**

## Abstract Stage

**What is it? **

the

**"symbolic" stage**students model math problems using

**symbols**like +, -, x, ÷, =

**Examples:**

writing the

**equation**:2 + 3 = 5using the

**equation**:1 ÷ 2 = 1/2

### Abstract models are bestfor:

concepts that

**don't have a concrete representation**(like negative numbers)when students show

**mastery of concrete and pictorial representations**

## Why use the CPA Approach?

### The CPA approach is beneficial because:

students achieve a

**deeper understanding**of math concepts instead of using memorizationteachers can

**scaffold**abstract math concepts to make them more accessiblestudents and teachers can

**go between stages**as neededit can be used with students in

**both****primary and secondary school**you can use any of the models alongside each other to provide

**multiple representations**of class material or to**double-check student knowledge**

#### Quiz

Mrs. Ramirez just began a multiplication unit with her class. Her students have minimal experience with multiplication. She wants to show her students how to solve 3 x 10. Which of the following methods would be most useful in introducing this concept?

## Take Action

### Are you ready to use the CPA approach in your classroom?

## Your feedback matters to us.

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