Introducing the Subtraction Sign

Introduction

This lesson plan will introduce your learner to subtraction signs and subtraction equations. We will explore story problems that require finding a missing part in a part-part-whole relationship. This will prepare your learner for writing and solving subtraction equations later on.

Before beginning the lesson, your learner should be familiar with finding missing parts of part-part-whole models.

Key Concepts for Introducing the Subtraction Sign

Here are a few things to keep in mind as you introduce your learner to subtraction signs and subtraction equations.

• Partitioning: Breaking a whole group into two or more parts is called partitioning. Partitioning can be represented as addition or subtraction depending on the arrangement of the values in the equation.
• Subtraction Equations for Partitioning: When representing partitioning as a subtraction equation, it can follow the format whole - part = part. For example, a group of 5 apples partitioned into a part with 3 apples and a part with 2 apples can be written as 5 - 3 = 2.
• Subtraction Vocabulary: The three values in a subtraction equation are the minuend, subtrahend, and difference. The minuend is the first value (the whole), the subtrahend is the value that is subtracted, and the difference is the remaining value. They can be represented as minuend - subtrahend = difference.

Types of Subtraction Problems

There are three main types of subtraction problems. This lesson focuses on part-part-whole problems, but it is helpful to know about the others as you continue working with your learner.

• Part-Part-Whole Problems: Part-part-whole problems present scenarios where the learner is asked to find the value of a missing part of a known whole quantity. The problem provides information about some parts and the whole, requiring the learner to calculate the unknown part. For example: If there are 12 marbles in total and 8 marbles are blue, how many marbles are red?
• Separating Problems: Separating problems involve situations that begin with a quantity, and the learner needs to determine how much remains after some of the quantity is taken away. This type of problem is often framed with phrases like "take away" or "how many left." For example: If there are 8 apples and 3 are eaten, how many apples are left?
• Comparison Problems: Comparison problems involve comparing quantities to determine the difference between them. Learners are asked to find out how much more one quantity is compared to another, how much longer one length is compared to another, etc. For example: John has 15 baseball cards, and Sarah has 9 baseball cards. How many more baseball cards does John have compared to Sarah?

Teaching Plan

The following activities will help your learner understand how missing part problems can be represented with subtraction signs and subtraction equations.

Examples and visuals to support the lesson:

1. Story Problems with a Missing Part

Begin by providing your learner with story problems that require finding a missing part. Encourage them to represent the stories using concrete objects or by drawing pictures.

Story problem examples:

• There are six children. Two have put their coats on. How many have not put their coats on?
• There are eight pencils. Five have been sharpened. How many have not been sharpened?
• There are five windows. Three are open. How many are closed?
• There are seven children. Six are eating a snack. How many are not eating a snack?

Skill Check
I can find the missing part of a part-part-whole story problem.

2. Subtraction Equations

This activity will gradually introduce your learner to using the subtraction symbol.

• Revisit one of the story problems from the previous activity. Provide your learner with a picture to represent the story. For this example, we will use the context of the six children where two have put their coats on.
• Have your learner circle the children who have put their coats on. Then ask them, "How many children have not put their coats on?" Encourage your learner to discuss and justify their answer.
• Next, demonstrate how the story can be written as a subtraction equation in the form minuend - subtrahend = difference. For this example, it would be 6 - 2 = 4, or six minus two is equal to 4.
• Ask your learner what they notice about the equation and draw attention to the subtraction symbol which in this case means "separate, split, or partition." Be careful not to use "take away" which represents a different type of subtraction problem.
• Then ask your learner to describe, in full sentences, what each number and symbol in the equation represents. For example: The six represents all of the children. The minus 2 represents the children who have put their coats on. The 4 represents the children who have not put their coats on.

Skill Check
I can describe what each part of a subtraction equation represents.

3. Diagrams with Missing Parts

In this activity, your learner will create part-part-whole models that have a missing part.

• Provide your learner with a story problem along with a blank cherry diagram or bar model. Ask them to interpret the story problem and identify where each number fits in the diagram.
• Encourage them to write a question mark to represent the unknown part. At this stage, it is not essential for your learner to find the solution. This task serves as an interim step before writing the equation and solving the problem.

Skill Check
I can draw part-part-whole diagrams that show the unknown part as a question mark.

4. Relating Addition and Subtraction

Use this activity to bring together the structures of addition and subtraction explored during the lesson.

• Give your learner a set of multilink cubes or connecting blocks. Demonstrate moving them together and apart while saying the words "putting together...taking apart" and "addition...subtraction." Have your learner follow along while repeating the words.
• Next, ask your learner to think of a story for each structure (addition and subtraction). Remind them of the types of stories explored previously such as putting parts together to make a whole or finding a part that has been separated from the whole.
• For further exploration, encourage your learner to look through picture books or explore their surroundings to find a variety of addition and subtraction contexts.

Skill Check
I know that putting together is addition and taking apart is subtraction.

Summary

The activities in this lesson plan introduced your learner to representing "missing part" problems as subtraction. They practiced describing the parts of subtraction equations and representing unknown values on diagrams. Learning to recognize scenarios that can be modeled with subtraction signs and equations will prepare them for writing and solving subtraction problems on their own.

Teaching Plan adapted from NCETM under OGL license v3.