Writing Addition Expressions

Introduction

The activities in this lesson plan will teach your learner about writing addition expressions. We will introduce the addition sign as a symbol for combining numbers and explore the commutative property of addition. By the end of this lesson, your learner will have a solid grasp of representing part-part-whole relationships through addition expressions and understanding the flexibility of addition.

Before beginning the activities, your learner should be familiar with part-part-whole cherry diagrams and bar models.

Key Concepts for Writing Addition Expressions

Here are a few concepts that are helpful to know for this lesson:

• Addition Expressions: In this lesson, we will focus on representing addition expressions within a part-part-whole context. Addition expressions show the combining or bringing together of quantities. For example, in a scenario where we have 3 apples in one basket and 2 apples in another basket, we can represent the total number of apples as 3 + 2.
• Addition Equations: Addition equations, on the other hand, use an equal sign to show the sum of the parts as equivalent to the whole for a part-part-whole context. For example, 3 + 2 = 5. We will work on writing equations in a separate lesson.
• Understanding the Commutative Property of Addition: The commutative property of addition states that changing the order of addends (the numbers being added) does not change the sum. This property allows us to write addition expressions in different ways. For instance, 3 + 2 can also be written as 2 + 3.

Teaching Plan

The following activities will help your learner become confident with writing addition expressions.

Examples and visuals to support the lesson:

1. Introducing the Addition Sign

This activity will use concrete objects and pictures to introduce your learner to the concept of the addition sign.

• Start by presenting your learner with concrete objects or pictures where the whole group is divided into two easily distinguishable parts.
• Organize the objects to draw your learner's attention to the parts (e.g., by moving the objects into two separate groups or drawing circles around the two parts).
• Show your learner that the two parts can be represented and combined using the addition symbol (plus sign).
• Emphasize writing the expression, rather than finding the sum at this stage. For example, demonstrate that four open umbrellas and five closed umbrellas can be written as 4 + 5.
• Rearrange the objects into different groups and have your learner practice writing expressions themselves using the addition sign.
• Continue to link the concrete and picture representations to the abstract symbols by describing the contexts and expressions in full sentences. For example: "There are four open umbrellas and five closed umbrellas. We can write it as 4 + 5. The 4 represents the number of open umbrellas and the 5 represents the number of closed umbrellas."
• Use stem sentences in the following format: "There are ___ and ___. We can write this as ___ plus ___. The ___ represents the ___ and the ___ represents the ___."

Skill Check
I can represent the parts of a group using an addition sign.

2. Writing Addition Expressions Two Ways

In this activity, we will explore the idea that the addends (numbers being added) can be written in either order, introducing your learner to the commutative property of addition.

• Discuss with your learner that the addends in addition expressions can be written in either order, such as 3 + 2 or 2 + 3. Use scaffolded examples that increase in difficulty.
• First, use examples such as empty and full glasses where the two parts are clearly grouped together. Rearrange the objects to scaffold the rearrangement of the expression, showing both arrangements. Ask your learner what's the same and what's different between the two arrangements.
• Next, use examples where the two parts are clearly grouped together, but the objects are not rearranged. Ask your learner to write both expressions from a single arrangement of objects.
• Now, present examples where the two parts are distinguishable but not clearly grouped together. Encourage your learner to recognize and identify quantities for the two groups, then write both expressions.
• Finally, use examples where the whole groups are not divided into two easily distinguishable parts. Encourage your learner to partition the group into two parts in different ways. For each partitioning, have them write both expressions.
• Throughout each example, encourage your learner to describe the contexts in full sentences, linking the concrete and picture representations to the abstract concept of the commutative property of addition.

Skill Check
I know that the numbers in an addition expression can be written in either order.

3. Modeling with Cubes and Counters

In this activity, we will use general representations, such as cubes and counters, to enhance your learner's understanding of addition expressions.

• Put a different quantity of cubes in each hand, ensuring they are visible. Have your learner write the expression to match the quantities in each hand. Cross over your hands and have them write the new expression based on the rearrangement of cubes.
• Next, place a different quantity of cubes in each of two containers. Have your learner write both expressions that represent the partitioning of the cubes in the containers.
• You can also use double-sided counters for examples where a given number can be partitioned in more than one way. For example, 3 counters that are red side up and 4 counters that are yellow side up can be expressed as 3 + 4 and 4 + 3.
• Throughout, make sure to include examples where one of the parts is zero. For example: "There are five counters red side up and no counters yellow side up. We can write this as 5 + 0 and as 0 + 5."
• Continuously encourage your learner to describe the contexts in full sentences, strengthening their understanding of the representations and corresponding addition expressions.

Skill Check
I can use different math tools to help me write addition expressions.

4. Challenge Activity

Provide your learner with a challenge activity to promote deeper understanding. For example, show your learner a group of bags that are different colors and sizes and ask them to partition the bags into two groups. This will encourage your learner to think about partitioning in more than one way. Encourage them to write different expressions that represent their partitions. By engaging in this challenge, your learner will strengthen their understanding of addition and its properties.

Summary

In this lesson plan, your learner explored writing addition expressions to represent part-part-whole relationships. They engaged with story problems that required combining quantities and used diagrams to visualize these relationships. They also learned to use the addition sign (+) to symbolize combining numbers and discovered the commutative property of addition, which allows for rearranging addends.

Teaching Plan adapted from NCETM under OGL license v3.