#883. Integer Subtraction

Mathematics, level: Middle
Posted Mon Mar 8 21:17:55 PST 1999 by Dave Kennedy (ckennedy@sprint.ca).
University of Toronto, preservice teaching program, Ontario, Canada
Materials Required: blackboard, die, and student volunteers
Activity Time: 40-60 minutes
Concepts Taught: explains why a negative number subtracted from another number changes the operation to addition

Grade 7/8 Math

Subtracting Integers

Objective: students will further demonstrate their understanding of integers by extending their knowledge of adding integers to subtracting integers. More importantly, students will understand why a negative number, subtracted from a negative number changes the operation to addition. [A - (-B)] = A+B. This knowledge will serve as a precursor into the following lesson, multiplying integers.

Set: Ask for a show of hands, how many students remember the Macarena. Tell the story of learning how to do it 3 years ago and how the dance is completed 4 times before you start off where you originally began. Call once around 1 MAC. The beginning of the dance is in the positive direction and 1/2 way through the dance, you are facing the negative direction. Talk about how this freakish annoying dance can be used to explain math concepts.

Input: Have a desk at the front of the room as zero. Place 4 students on each side of the desk: number line is formed. Each student must illustrate his/her number by fingers or different colours of paper. Select one student to begin at a number and move while considering turns.
Data Set: ·+3 - 2 --start facing to the positive on the number 3 and do 1/2 a MAC and go down 2 to 1
·-4 - 1--start facing to the positive on -4 and do 1/2 a MAC to face negative and go down 1 to -5
·1-(-3)--start facing to the positive on 1 and do a 1/2 MAC to face negative. The number is -3, so b/c of the negative, we have to do a 1/2 MAC again to face the positive and move to 4
·-3-(-1)--start facing positive on -3. Have to do a full MAC to go up one.
The point of this exercise is to have the students understand that (-)(-) = +. After check for understanding, this rule could be given. Based on the lesson, the class may need it now before check occurs.

Model: Done during student number line.

Check: After the demonstration is finished have students sit in their groups and number off 1-4. Give groups a letter from A-finish, depending on number of groups. Warn them that the roll of the die determines who answers the question. Same rules as before: 1-4 answers, 5 they choose and 6, I choose. Tell them that they will have time to think and discuss it in their groups but that everyone must be ready to have an answer in 1, maybe 2 minutes maximum. Ask, if I was a Martian and you had to explain why a number minus a negative number changes the operation to addition, how would I do it. Roll the die first and then pick a group from a bag or hat.
This might be a good time to tell them the rule that (-)( -) = + for every subtraction question. Write down all four possibilities:
A + (-B) = A-B
A - (+B) =A - B
A+ (+B) =A+B
A - (-B)=A+B

Practice: This area should contain assigned homework.

Closure: Rub off the rules on the board and randomly pick students to answer data set questions concentrating on the operation: e.g. 4+ (-4) = 4-4=0 etc. to reinforce a number subtracted from a negative number changes the operation.