Adding Integers With Manipulatives Lesson Plan

Manipulative options

For this lesson, it will be helpful to have at least one of the following options for students to help them add integers with manipulatives:

• Counters or algebra tiles that have different colored sides 
• Black and red colored pencils/pens/etc.

If neither of those options are available, have students draw “`+`” and “`–`” signs to represent positive and negative counters.

Warm Up

Read the warm up problem aloud with the class. Then give students a few minutes to try it on their own.

Given the context, most students should be able to identify that Matt is “in the red” because he owes more money than he earned. From there, students may recognize that the difference of the numbers is `2`, so their answer is `-2`. Some students may also count down, use number lines, or other visual representations. 

Using manipulatives

To help introduce the chip model, represent the warm up problem. Based off of the visual, most students will recognize that the black chips indicate the positive value while the red chips represent the negative value.

Although students may not know the vocabulary, “zero pair”, they will likely be able to explain that one black chip and one red chip cancel each other out. Make sure you also make connections between the chip model and the equation so that students can see how the model can become an equation. 

Solidifying zero pairs

Students should recognize there is no change when there is a red chip and a black chip added. Consider asking students to write the equation to represent this new model to help students practice adding integers with manipulatives.

Expanding on the warm up

With the warm up, Matt ended with `-$2`. In this problem, Matt earns money. Students should represent the scenario using their manipulatives to help them answer each question.

Words that indicate signs

Students may not be familiar or have experience with some of these words. It can help to give them these examples, although it may be helpful to have students think of other words that could potentially be used depending on context, like “increase” and “decrease”.

Representing a value with manipulatives

To make sure students understand how to represent values with their manipulatives, have them complete the two examples for representing values: one is positive, and one is negative.

After the second example, consider extending these examples by having students combine the examples so it requires them to add integers using the manipulatives. So if they had `$4` in their pocket and lost `$2` at the park, they should write `4 + (-2) = 2`. 

Adding integers practice

For the first example, students are given a description of what chips are used in a model to practice writing an equation to add integers with manipulatives. Allow students time to discuss how the completed example at the top “translated” the model into an equation.

Give students time to complete the example. Make sure students are writing the equations with addition! If students’ answers have the wrong sign, you may need to help clarify the model. 

Transitioning to equations

For the second example, the equation is given first, and the students must describe or draw their manipulatives and find the answer.

Because the problem they solve only includes negatives, some students may be confused and represent one of the values with black chips. Remind them that the color indicates the sign of the values. 

Manipulatives not required

At this point, some students may not need to add integers with manipulatives for every problem; however, continue encouraging students to use them if they are struggling.

Reflection

Ask students to identify what happened when they had all red chips, and what happened when they had red and black chips. The goal is for students to recognize that when the colors (or signs) are the same, they just find the total number of chips; however, when the colors (or signs) are different, they find the difference and keep the sign of the color that has leftover chips.

Next class recommendation

It is recommended that you use the Adding Integers lesson plan as a second day to reinforce what students learned in this lesson without manipulatives.