Introducing Equations and the Equal Sign

Introduction

This lesson plan will familiarize your learner with the concept of equivalence and writing equations with equal signs. We will focus on using the equal sign to write an equation in the form addend + addend = sum and emphasize that the "=" symbol represents "is equal to". Your learner will also explore the commutative property of addition.

Before beginning the lesson, your learner should be comfortable writing addition expressions.

Key Concepts for Equations and the Equal Sign

Here are a few concepts that are important to understand as you introduce your learner to equations and the equal sign.

• Equations: Equations are mathematical statements that use symbols (like "=") to show that two expressions have the same value. Introducing equations involves helping learners grasp the concept of balance and equivalence between quantities.
• Part-Part-Whole Models: Part-part-whole models demonstrate the relationship between a whole quantity and its parts. Whether the objects are grouped together as a whole or split into parts, the total quantity remains the same.
• Addition Vocabulary: In this lesson, we will focus on writing addition equations. The numbers in the equation are called the addends and the sum. The addends are the values added together and the sum is the total. In the context of part-part-whole problems, the addends represent the parts and the sum represents the whole.
• Commutative Property: The commutative property of addition states that we an add numbers in any order. For example, we can show the sum of three and two as 3 + 2 or 2 + 3. While your learner does not need to know the name of the property at this stage, they should understand the concept.
• Structure of Equations: Since both sides of an equation are equal, the equation can be written more than one way. For example, the equation 3 + 2 = 5 has the addends on the left and the sum on the right side. We can also write the same equation as 5 = 3 + 2 with the sum on the left and the addends on the right.

Teaching Plan

The following activities will help your learner become confident in writing equations and using equal signs.

Examples and visuals to support the lesson:

1. Equations and Equal Signs

This activity will introduce your learner to the concept of equivalence and the different ways addition equations can be written.

• Explain to your learner the concept of equations and the equal sign as a representation of equivalence. Highlight that the equal sign shows that the combined parts are equal to the whole.
• Use concrete objects or pictures where the whole group is divided into two easily distinguishable parts. Begin by referring to the whole and model how it can be split into two parts, for example, 5 = 2 + 3.
• Show how four different equations can be written for each example:
  • 5 = 2 + 3
  • 5 = 3 + 2
  • 2 + 3 = 5
  • 3 + 2 = 5
• Throughout the examples, have your learner explain in full sentences what each number and symbol in the equation represents. Use the words "addend" and "sum" to refer to the different parts of the equation.

Skill Check
I can identify the addends and sum in an equation and describe what they mean.

2. Part-Part-Whole Models and Equations

In this activity, we will build on your learner's previous experience of part-part-whole models, using either cherry diagrams or bar models to represent picture contexts.

• Provide an example of a cherry diagram or bar model representing a specific context, such as cupcakes with and without cherries. Have your learner describe how the numbers in the diagram or model relate to the context.
• For example, explain that the 5 represents the whole group of cupcakes, the 3 represents the cupcakes with no cherries, and the 2 represents the cupcakes with cherries. Then have them explain which numbers represent parts and which number represents the whole.
• Write the equation for the context in all four ways, emphasizing the commutative property of addition. Have your learner describe the equations using the words addend and sum and relating them to the context of the picture.
• If you find that your learner mistakenly interprets the equations, for example, 5 = 3 + 2 to mean five plus three plus two, give them more time using concrete resources before moving on.

Skill Check
I understand how the parts of an equation relate to diagrams and picture stories.

3. Writing Equations

In this activity, your learner will practice writing their own equations to represent different contexts.

• Provide your learner with contexts where the whole group is a number of identical objects that can be partitioned in different ways.
• For each example, have your learner draw a part-part-whole model to represent each of the different outcomes and describe how the model represents the outcome.
• Next, have your learner write all four equations to represent each of the different outcomes and describe how the equations represent the outcome.
• Encourage your learner to use complete sentences to describe the equations. For example: Five is equal to four plus one. Four plus one is equal to five. Four and one are the addends. Five is the sum."

Skill Check
I write equations to represent a group of objects that I split into parts.

4. Writing Stories and Equations

In this activity, you can use generalized representations such as double-sided counters, without a story context.

• Have your learner explore different partitioning arrangements and equations, then create their own stories to go with each of them. Have them explain how the manipulatives, part-part-whole model, and equations represent their story.
• Use a story to encourage them to consider zero as an added. For example, "Dan has ten pennies and two pockets. What are the most pennies he can have in one pocket? How many pennies would be in the other pocket?"

Skill Check
I can write stories and draw models to represent equations.

Summary

In this lesson, your learner explored the world of equations and equal signs. They translated story problems into addition equations, and applied the concept of part-part-whole models to represent the equations. Through hands-on activities and discussions, your learner developed an understanding of the commutative property and applied it to writing equations in different ways.

Teaching Plan adapted from NCETM under OGL license v3.