Subtracting Integers

Summary

Students will add integers, solve application problems, and predict the effects of operating with integers as an increase or decrease of original value.

Materials

• Algeblocks and Basic Mats
• + and -- tiles
• Wall number line
• Graphing calculators
• Worksheets: Walking The Number Line To Subtract Integers (two-sided page), Subtracting Integers With Algeblocks, Walking The Number Line Integer Addition and Subtraction Practice

Background for Teachers

Enduring Understanding (Big Ideas):
Operations with integers

Essential Questions:

• How can a subtraction expression be re-written using an equivalent, related addition expression?
• How can the difference between two integers be found?

Skill Focus:
Subtracting integers

Vocabulary Focus:
Difference, opposite, related addition expression.

Ways to Gain/Maintain Attention (Primacy):
Technology, movement, music, drawing, cooperative activity.

Instructional Procedures

Starter:

1. What is the opposite of 3?
2. What is the additive inverse for -5?
3. What is the sum? -4 + 4
4. Find the sum for each:
   1. -3 + -3= n
   2. 3 + -3 = n
   3. -3 + 3 = n
   4. 3 + 3 = n

Lesson Segment 1: How can a subtraction expression be re-written using an equivalent, related addition expression? How can a difference between two integers be found.

Using + and -- to model:
You may want to use + and -- signs to model subtracting integers. You will need to teach 0 pairs for problems with unlike signs. Adding 0 to a problem gives you the identical problem. Thus, adding -3 and 3 is adding 0. You can form 0 pairs to produce either the + or -- signs needed to do the subtraction. Do in this order.

4 -- 3, + + + + subtract + + +
-4 - -3, - - - - subtract - - -
4 - -3, + + + + plus +-, +-, +- subtract - - -
-4 -- 3, - - - - plus +-, +-, +-, subtract + + +

Using Algeblocks to model:
Use the "Subtracting Integers With Algeblocks" worksheet with the class comparing the subtraction (taking away) and related addition sentences.

Using a number line to model
Model walking a number line for subtraction singing the Walking The Number Line song for subtraction. Model: 3 -- 5, 3 -- -5, -4 -- 8, -4 -- (-8)

Tell the students they will be using the graphing calculator to perform a little magic. Have them use the Numline Application to do each of the problems on side one of the Subtracting Integers Investigation worksheet (attached). They should set the range of the number line from -10 to 10 on the calculator. Work with them to do each of the problems asking:
Q. How are the two expressions the same? How are they different?
Q. How do the answers compare? Have them answer the question on the bottom of the worksheet page.

When the subtract sign has been changed to add AND the number being subtracted has been changed to the opposite of that number, we call the new expression a related addition expression.

Mix-Freeze-Pair: Have students mix around the room until you say, "Freeze". They find a partner closest to them. Anyone without a partner raises their hands high and looks for someone else whose hand is raised. Have them introduce themselves with each other and decide which of them will be partner #1 and partner #2. Put 5 -- 3 = 2 on the board. Ask them to THINK about how they would rewrite that as a related addition problem. You choose which partner will explain how and which will listen. partner. The listening partner then agrees, or disagrees and explains why. You show the correct way to rewrite the problem and have them either congratulate each other or say, "Nice try". Then have them mix again and repeat this for problems such as: -2 -3 = -5, 6 -- (-3) = 9, -5 -- (-1) = -4, -8 -- 1 = -9 etc.

Have students write the rule for subtracting integers under the foldable flap and show several example. Rule: When subtracting, write a related addition expression, then follow the addition rules.

Addition	Subtraction	Multiplication	Division
Rules and Example for Operations With Integers

Lesson Segment 2: Practice
Work with students on two addition and two subtraction problems on the attached worksheet. Then assign the remaining problems as practice for those who are ready to practice on their own. Students who are not yet ready to practice on their own may need to use the NumLine App to visualize the related sentences for subtraction problem and to practice addition.

Select application problems from a text such as:

Aaron dove 12 feet under the surface, while Amy dove 15 feet under the surface. How much further did Amy dive than Aaron?

Walking The Number Line (to A' Louetta)
On a number line, move from 0 to the first number in the expression. Face the positive direction. Sing the song and move as directed by the operation and the second number in the expression. A subtract sign tells you to turn around before beginning to walk.

To add a POSITIVE, we will just walk FORWARD
To add a POSITIVE, walk FORWARD just like this.
(Start at the first number and walk forward the distance of the second number.) Where do we end up?

To add a NEGATIVE, we will just walk BACKWARD
To add a NEGATIVE, walk BACKWARD just like this.
(Start at the first number and walk backward the distance of the second number.) Where do we end up?

Assessment Plan

Performance, questions.

Bibliography

This lesson plan was created by Linda Bolin.