# Adding and Subtracting Positive and Negative NumbersLesson Plan

1. Goal(s)/Standards
• From Utah State:
• Standard 1 - Students will acquire number sense and perform operations with real numbers.
• Objective 1.1 - Compute fluently and make reasonable estimates.
• Objective 1.2 - Represent real numbers in a variety of ways.
• Objective 1.3 - Identify relationships among real numbers and operations involving these numbers.
• Standard 3 - Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling.
• Objective 3.2 - Specify locations and describe spatial relationships using coordinate geometry.
2. Specific Objectives
At the end of the lesson the student will be able to:
• Describe with words adding and subtracting positive and negative numbers.
• Demonstrate mastery of simple arithmetic operations using negative and positive numbers by solving problems.
3. Materials/Preparation
4. Prerequisite Vocabulary
• Whole number means a counting number such as 1, 2, 3, etc.
• Real Number means a number that can be found on a real number line.
• Magnitude means the distance between a number and zero.
• Positive means in the positive direction from zero, in western culture typically to the right.
• Negative means in the negative direction from zero. In western culture typically to the left.
• Opposite means in the opposite direction. An example: Forward is the opposite of backwards.
5. Prerequisite Methodology
None
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 negative numberSubtracting a positive numberSubtracting a negative number
Image
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
• Blind students will need number line components with raised lines and Braille.
• Students that are limited in motion may need an alternate activity for parts of the lesson.
• Students with cognitive difficulties will need additional assistance bridging from the concrete to the abstract.
• Cognitively advanced students may do better skipping the concrete to abstract bridge.
• Some students may want to orally describe negative numbers rather than in writing.
• Student who learned reading in languages that are not left to right, top to bottom may require additional time to recognize right as positive and left as negative.
8. Assessments
• An informal assessment will be performed by watching students point to numbers on the number line.
• An informal assessment will be performed by watching students step out instructions in the whole-body part of the lesson.
• Students will describe adding and subtracting positive and negative numbers.
• Students will complete a worksheet as a formal assessment. The worksheet may be used as a substitute for a quiz.
• Students will complete a quiz as a formal assessment. A quiz may be used as a substitute for a worksheet.
9. Other Resources
Introduction to Negative Numbers by Purple Math http://www.purplemath.com/modules/negative.htm
Negative Numbers on Math Forum http://mathforum.org/library/drmath/sets/mid_negative.html
10. Materials Masters