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# Using the Phases of Math Mastery to Plan for Small Groups

Written by: Krys Warstillo

If your class is anything like mine you know that kids come in at all ability levels with gaps in a hundred different places within math domains. You might have a kid rocking the number and operations domain but working below grade level in algebraic thinking sitting right next to a kid who is working above grade level everywhere except geometry. That’s why flexibility is so important when we’re creating small math groups. In this post, we'll go over simplifying how you plan small group math and differentiation by using the phases of math mastery.

## How do you create math groups?

I call students back to my teacher table based on their abilities within a specific skill. This way small math group instruction can be easily differentiated to meet my students exactly where they are.

## The Four Math Domains

First and second grade math is broken into four big domains. If you're not familiar with them here's a quick rundown of the skills generally included in each grade.

• Operations & Algebraic Thinking
• Number & Operations
• 1st Grade: read & write numerals to 120, understanding place value,
• 2nd Grade: read & write numberals to 1000, properties of addition & subtraction, mental math, +/- 10 & 100
• Measurement & Data
• 1st Grade: expressing length, ordering objects, time to hour & 1/2 hour, introducing graphs
• 2nd Grade: measurement & estimation with standard units, representing & interpreting data (graphs), time, money
• Geometry
• 1st Grade: 2D & 3D shapes and their attributes, partitioning shapes into equal parts
• 2nd Grade: 2D & 3D shapes and their attributes, partitioning using rows and columns & into equal parts

## What does small group math instruction look like?

We’re all about working smarter, not harder here at Lucky Little Learners. When you are creating or gathering the content for your small group math intervention, keep the requirements of your particular curriculum in mind. If your curriculum has ready-made interventions or supplemental materials, that’s a great place to begin. For example, if you’re using computer-mediated math instruction like Zearn, lean on the provided small group lessons.

If you find you need additional resources, our Small Group & Intervention Math Kit can fill in the gaps! Also, you can learn more about how to plan effective intervention lessons in this post. Last, create mini anchor chart stands with these easy step by step instructions!

An easy way to keep your small group instruction organized is by using the small group lesson plan tools in the . If you're still trying to figure out how to group your students use the math screener in the Intervention Math Kit. The screener has 30+ subtests to help you pinpoint learning gaps. Here's how to use math assessment tools to find gaps in student's understanding.

With an organization method in mind, it’s important that you’re aligning your small group math planning with the phases of mastery so your teaching is as effective as possible.

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## Use the Phases of Math Mastery to Simplify Planning and Differentiation for Small Groups

Second grade really begins that big shift from concrete to abstract math concepts so differentiating instruction from group to group is essential! If we can help them move through the phases of mastery we can set them up for success in upper elementary and beyond.

The phases of mastery are referred to by a few different names:

• CPA (concrete/pictorial/abstract)
• CSA (concrete/semi-concrete/abstract)
• CRA (concrete/representational/abstract)

In this post, I’m going to focus on CPA. Using the CPA approach has been shown to improve mathematical reasoning skills.

The CPA approach was developed in the 1960s by American psychologist Jerome Bruner. If you’re curious about its history this paper includes a short survey of its origins. It’s pretty interesting!

## Concrete Phase of Math Mastery

The concrete phase of mastery is when students are using physical objects to represent mathematical concepts. This is when students are using rekenreks, unifix cubes, clocks, shape blocks, beads, base ten blocks, ten frames, or double-sided counters. Math that can be held in their hands and physically manipulated.

If you find you have students who are struggling with a math standard like regrouping – backing up to concrete might be the first step. Having them physically compose and decompose numbers using base ten blocks is going to be really valuable. If you don’t have actual plastic base ten blocks or other manipulatives check out the printable manipulatives in the

Once students have mastered using manipulatives in any given skill then it’s time to move on to the next phase – pictorial.

## Pictorial Phase of Math Mastery

In this phase of mastery, students will be representing their math problems using drawings. This includes things like tally marks, number bonds, part-part-whole drawing, or just drawing a picture to represent their thinking. This is a great time to pull out the instructional mats in the Some teachers skip this step but it’s an important bridge between concrete and abstract. Your students are practicing the skill of visualizing a math problem.

In our regrouping example, students may be drawing base ten blocks on their paper to help them solve problems. Once students are confident and accurate, it’s time to move on to the abstract phase!

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## Abstract Phase of Math Mastery

Your kids have made it! The abstract phase of mastery is when students use abstract symbols to represent math problems- aka numbers and addition/subtraction/equal/inequality signs. During this phase your students may still need to revisit the concrete and pictorial phases, and that’s fine! The abstract phase is about putting it all together and touching base with the previous two stages to reinforce learning.

Going back to our regrouping example this phase would look like using the standard algorithm that we all know and love. This would be a great time to introduce your students to the Build a Robot math center. It’s a fun way for repeated practice that can be use independently or with a small group.

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## Teaching Small Group Math Virtually

Now, all of these phases of mastery are great, but can they be done virtually? We know this is something we need to keep in the back of our heads, just in case. How can your students move through the phases of mastery from home without the advantages of classroom supplies? The Lucky Little Toolkit has a collection of digital math manipulatives that you can use with virtual students during math intervention. Take a look at the video below for a closer look at those.

## Small Group Math Instruction

Planning effective small group math instruction can propel our students to new heights and set them up for success as they age into higher-level math with ever more abstract concepts. Using the CPA approach and flexible grouping to keep your little learners working towards mastery is a gift we can give our students that will pay dividends for years to come.