Adding and Subtracting Integers: a Pre-algebra Activity

(Adapted from Radical Equation, by Robert P. Moses with Charles E. Cobb, Jr., Beacon Press, Boston)

· Brief description of students for whom activity is appropriate

Multi level (pre-GED through beginning GED) class of learners.

· Purpose of Activity (learning Objectives)

This activity is for strengthening an understanding of adding and subtracting signed numbers. The activity can be used to help students who learn best by moving around. The activity is aimed at helping students

v to distinguish between the positive/negative signs belonging to integers and the addition/subtraction that can be performed with integers

v to grasp the “directionality” (increase vs. decrease) yielded by adding or subtracting signed integers

v to reinforce their understanding of directionality, by moving correctly in response to the meaning of the signs and operations

Learners will be able to:

- Walk in the correct direction both forward and backward to demonstrate an understanding of addition and subtraction with integers.

- Use this understanding to explain addition and subtraction with integers written on a chalkboard, e.g.

2 + 2 = 4

2 – 2 = 0

(-2) + 2 = 0

(-2) – 2 = -4

2 + (-2) = 0

2 – (-2) = 4

(-2) + (-2) = -4

(-2) – (-2) = 0

· Strand addressed

Patterns, Functions and Algebra, Intermediate ABE and Pre-GED

· Materials needed

v A chalkboard (or whiteboard)

v An open area at least eight paces long

v 10 to 20 place-markers about a pace apart along a back and forth path. These could be things like duct tape strips on the floor or chairs in a row.

v Markers for each student that can be used to show her initial starting place and the direction she is originally facing, for example a sheet of paper with an arrow and the student’s name.

· Steps in activity

(1) Setup:

- Have the learners stand in a row in the middle of the path you laid out.

- Have them face the same direction.

- Have them mark the spot where they are standing with their paper arrows pointing in the direction they face.

- Tell the learners that in this activity they will walk both forward and backwards, sometimes without turning around.

- Explain that

“Plus” means keep facing the same direction,

“Minus” means face the opposite way (turn around in place)

“Positive” means walk forward (any number w/o a sign is positive, except zero)

“Negative” means walk backward (without turning around)

(2) Slowly read aloud an addition/subtraction problem, such as “(-2) – (+2) = ?”. For example, say “Negative two (pause) minus (pause) positive two (pause) equals ____”. Coach the learners to walk backwards two places, then turn around in place, and then walk two places forwards.

- Have them check their stopping place.

- Now ask them to see how many places they are from where they started (their arrow) and whether or not they are in front of or behind the direction their arrow is pointing.

- In this example, they will be four places behind their arrow, i.e. -2 – 2 = -4

(3) Caution: Allow plenty of space around each student, so that no one will be distracted by bumping into things or by running out of room.

· Assessment

- Have students point out and discuss any patterns they observe. For example, someone might see that the double negative “– (-2)” cancels itself to yield “+ 2”.

- Ask students to name real life uses for adding and subtracting integers. (Bank accounts, temperatures, sea level…). Discuss in enough detail to determine how firm a grasp each student has.

- Have students do a brief practice set adding and subtracting integers. Evaluate accordingly.

Concept for exploring further:

· Adaptation of activity

Use problems with integers of greater absolute value. Include decimals.