It's often difficult for students to understand how to add or subtract negative numbers because the concept is intangible. This lesson plan uses manipulatives to concretize the concept of negative numbers in an innovative way.

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### Background

This lesson assumes that you have already shown students where negative numbers lie on a number line. At the same time, students often struggle with using a number line to understand addition and subtraction of negative integers. After all, if you ask students to subtract -3 from a number, how do they know which way to move on the number line? This lesson will help them conceptualize what you are doing when you add and subtract negative integers.

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### Addition of Negative Integers

- Explain to students that each of the green magnets symbolizes +1. Write the following problem on the board: 4 + 3 = __. Count out four magnets and place them on the board. Then explain that you are adding three positive magnets. Ask students how many magnets are on the board (7). Explain that when we add 3 + 4, we do this process without thinking, but that we might have to think more when adding negative integers.
- Explain to students that each of the red magnets symbolizes -1. Write the following problem on the board: 4 + -3 = ?. Count out four green magnets and place them on the board. Then explain that you are adding three negative magnets, and add three red magnets to the board. Tell students that positives and negatives will pair up because each negative cancels out a positive. Move three of the green magnets so that they are paired up with the three red magnets, and then move them to the far side of the board. Ask students how many are magnets are left (1). Explain that therefore, 4 + -3 = 1.
- To approach this problem from different angles, ask students to show how they could represent this number on a number line. As they do so, prompt them to see if they understand that 4 + -3 is the same thing as 4 – 3. If they do not, point it out to them.
- Model another problem or two for students, perhaps calling volunteers to the board to model the technique you have taught. Then encourage students to make their own manipulatives cut out of paper and colored with markers. Provide additional problems for students to solve using their manipulatives.

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### Subtraction of Negative Integers

Challenge students with the following problem: 4 – -3 = ?

- To start, put four green magnets on the board. Then ask students what you should do next. Guide them to understand that you will need to add negative magnets to the board, but that in order to do so, you will need to add the same number of positive magnets to the board. Add three pairs of magnets to the board. Then remove three negative magnets and ask students how many magnets remain (+7).
- To approach this problem from different angles, ask students to show how they could represent this number on a number line. As they do so, prompt them to see if they understand that 4 – -3 is the same thing as 4 + 3. If they do not, point it out to them. Give students additional problems for practice.

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### Generalization of Concepts

Make a two-column chart on the board, and write “+ -“ and “- -“ in the left column. Ask students to generalize what they have learned in the lesson so far. They should respond that “+ -“ equals “-“ and that “- -“ equals “+." To make this clearer for auditory learners, ask for a volunteer to summarize the chart, and write the summary on the board to be read aloud. The summary should be similar to the following: “plus a negative is the same thing as minus, and minus a negative is the same thing as plus." Have students use this summary to solve additional problems without their manipulatives.