Adding and Subtracting Positive and Negative Numbers
Lesson Plan

Developed byDavid McAdams
Last update11/22/2006
Grade Level7
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CopyrightUnpublished copyright work © 2005-2006, David McAdams, Orem Utah. This document may be reproduced for non-commercial educational use only.
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ModelThink, Pair, Shair
  1. Goal(s)/Standards
  2. Specific Objectives
    At the end of the lesson the student will be able to:
  3. Materials/Preparation
  4. Prerequisite Vocabulary
  5. Prerequisite Methodology
  6. Instructional Procedure
    1. Quick Review
      Some 10th grade students need just a reminder about this material. A quick review sheet can be used to give them the opportunity to oil their mental cogs.
    2. Pretest
      If this unit is being used as a review for advanced grades, a pretest may be appropriate.
    3. Review
      1. Reintroduce the number line. Ask students to find various positive and negative numbers on the number line.
      2. Activate prior knowledge of addition and subtraction using the number line. Ask students to show by pointing various addition and subtraction problems involving positive numbers. Emphasize that we are moving in a positive direction or a negative direction.
      3. Frame the concept of magnitude. Ask the students, "How is 3 different from 5?" Accept all answers and emphasize that the number 3 on the number line is 3 units from zero, and the number 5 is 5 units from zero.
    4. State the problem and objective
      1. Create cognitive dissonance by asking, "How could we add and subtract negative numbers?"
      2. State and write on the board that, at the end of the lesson, the student will be able to describe addition and subtraction of positive and negative numbers in their own words.
      3. State and write on the board that, at the end of the lesson, the student will be able to add and subtract negative and positive numbers.
    5. Reintroduce the concept of negative as the opposite of positive.
      1. Ask, "What is the opposite of forward?" (Backwards).
      2. Write on the board "forward = - backward". Give the students some time to process this visual information.
      3. Translate between visual and auditory forms, and between mathematical and English languages.
        • Say "Forward," while pointing to the word forward.
        • Say "is," while pointing to the equals sign.
        • Say "the opposite of," while pointing to the negative sign.
        • Say "backwards," while pointing to the word backwards.
    6. Differentiate negative and minus signs.
      1. Think-Pair-Share The purpose of this Think-Pair-Share section is to come up with a statement describing the difference between a negative sign and a minus sign, not deciding what that difference is.
        • Point to negative sign and ask, "Does this symbol mean subtract?"
        • Lead discussion to the conclusion that, since the word "backward" is not being subtracted from anything, it can not be a minus sign.
        • State that it is a negative sign. Put four math phrases on the board with different combinations of plus and minus, positive and negative. Help the students sort out the negative signs from the minus signs.
        • Have students come up with a statement consisting of full sentences describing the difference between a minus sign and a negative sign. After a reasonable time, have the students pair up and revise their descriptions. Then form groups of four. Have each group of four present their description.
    7. Relate math concept to kinesthetic activity.
      In this exercise students will use their bodies to represent addition and subtraction of positive and negative numbers. Facing in the positive direction represents addition. Facing in the negative direction represents subtraction. Stepping forward represents a positive number. Stepping backwards represents a negative number.
      Adding a positive number
      Adding a negative numberSubtracting a positive numberSubtracting a negative number
      Image Person walking forward, faced in the positive direction (to the right) representing adding a positive number. Person walking backwards, faced in the positive direction (to the right) representing adding a negative number. Person walking forward, faced in the negative direction (to the left) representing subtracing a positive number. Person walking backward, faced in the positive direction (to the left) representing subtracting a negative number.
      Facing direction Addition (to the right) Addition (to the right) Subtraction (to the left) Subtraction (to the left)
      Walking direction Positive (forwards) Negative (backwards) Positive (forwards) Negative (backwards)
      Effect Result is more positive Result is more negative Result is more negative Result is more positive
    8. Concrete guided practice
      1. Recall students attention to the statement "forward = -backward". Ask "What is the opposite of 1?" Elicit the answer "-1".
      2. Have a student come forward to demonstrate use of the number line for negative numbers. Go through various combinations of addition, subtraction, positive, and negative.
      3. Have all students stand. If there are sufficient large floor number lines, assign one to four students to a number line. Give a series of instructions such as "Take two steps forward," and "Take negative three steps backwards." Observe students and reinforce the concept that the word negative means the opposite of. When all or nearly all of the students are consistently following the instructions, move on.
      4. Now give instructions in math terms, saying things such as "Start at -2. Add negative 3. Subtract 2." When all students are consistently following instructions, continue with the lesson.
    9. Extend concept of negative as a unary operator
      1. Write "- - forward" on the board. Ask students what it means (the opposite of the opposite of forward or forward). This can involve group work with a report to the class.
    10. Formal Assessment - Group work
      Group work: Have each group come up with a few sentences that describe adding and subtracting positive and negative numbers, plus a real-world application as an example. This can be an opportunity to introduce competition in the class. See the "Describing Negative Numbers Rubric" for suggestions on scoring the competition. Note: If you will be having students do poster work later in this lesson, make sure to tell them to hang on to their descriptions. Use Rubric A for grading this assignment.
    11. Formal Assessment - Poster (optional)
      Have the students create a poster describing the addition and subtraction of positive and negative numbers. Use Rubric D for grading this assignment.
    12. Formal Assessment for Learning - Quiz (optional)
  7. Differentiation for Diverse Student Needs
  8. Assessments
  9. Other Resources
    Introduction to Negative Numbers by Purple Math
    Negative Numbers on Math Forum
  10. Materials Masters
    Download 17 foot long floor number line template. Requires assembly.
    Download 20 inch personal number line for 3-ring binder. Requires assembly.
    Download Rubric A
    Download Rubric D
    Download worksheet
    Download this lesson plan in PDF format