Introduction to Negative Numbers
Lesson Plan

• 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.

• Describe how negative numbers are like and unlike positive numbers
• Find (by pointing) both negative numbers and positive numbers on a number line.
• Demonstrate competence at simple arithmetic operations using negative and positive numbers by solving problems.

• The teacher should have a master number line for demonstration to entire class. This can be drawn on the board or overhead.
• Each student needs a positive number line. This should be durable enough for repeated use. Printable number lines designed to be stored in a 3-ring binder can be found at http://www.lifeisastoryproblem.org/lesson/numberlinepersonal20inches.pdf.
• Each student will receive an extension to the number line for negative numbers.
• Each student will need scissors to trim the number line addition plus glue or tape to connect the two number lines.
• (Optional) A floor based number line durable enough to walk on helps students who learn best with concrete examples and students with kinesthetic learning styles to experience a number line with their whole body. A printable floor number line is found at http://www.lifeisastoryproblem.org/lesson/numberlinefloor17ftlong.pdf.

• Whole number
• Real number
• Magnitude.
• Positive
• Negative
• Opposite

None

1. Review
   1. Reintroduce the number line. Ask students to find various 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.
2. State the problem and objective
   1. Create cognitive dissonance by asking, "What is on the other size of zero on the number line?"
   2. State and write on the board that, at the end of the lesson, the student will be able to describe negative numbers and do addition with negative numbers.
3. Introduce 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 time to absorb this information then, pointing to the statement on the board, say "Forward" while pointing to the word forward. Say "is," pointing to the equal sign. Say "the opposite of", pointing to the negative sign. Say "backwards" pointing to backward.
4. Differentiate negative and minus signs.
   1. Differentiate between negative sign and minus sign. Point to negative sign and ask, "Is this a minus sign?" Lead discussion to conclusion that since backward is not being subtracted from anything it can not be a minus sign. State that it is a negative sign. Have students form groups and make a group statement of the difference between a minus sign and a negative sign.
5. Concrete guided practice
   1. Recall students attention to the statement "forward = -backward". Ask "What is the opposite of 1?" Elicit the answer "-1".
   2. Concrete guided practice: Have all students stand. Give a series of instructions such as "Take two steps forward," and "Take negative three steps backwards." If you are providing the students floor models of the number line, you can modify the words to match. 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.
6. 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.
7. Introduce the extension to the number line.
   1. Ask, "What do you think is on the opposite side of zero on the number line?" This can be class discussion or group work. Use inductive logic to analyze possibilities. If this activity is framed as a brainstorm, it may encourage students to propose ideas who might otherwise be afraid of being wrong.
   2. Extend the master number line. Have a class discussion on the nature of the number line. Include the concept of magnitude (-3 is just as far from zero as +3) and direction (left is negative, right is positive).
   3. Provide students with the personal number line extension, scissors and glue. Have them extend their personal number line.
8. Informal Assessment
   1. Say various positive and negative numbers on the number line and have students point to the number.
9. Reinforce the concepts of magnitude and direction
   1. Ask the students to point to a number with a magnitude of 3, then a different number with a magnitude of 3. Verify that all students are pointing to 3 or -3.
   2. State that there are two numbers on the number line with a magnitude of three. Ask students to leave a finger on the number they are pointing to and point with the other hand to the other number with a magnitude of three. Reinforce that magnitude means the distance from zero, but has no direction, so the direction can be positive or negative.
   3. Ask the students to point to a number with a negative direction. Students should be pointing to a number to the left of zero. Discuss why the students are pointing to that side of the number line. Then ask the students to point to a number with a positive direction. Discuss why, if needed. Then ask the students to point to a number with no direction that is neither positive nor negative. Verify that the students are pointing to zero. Discuss why zero has no magnitude and no direction. Introduce the concept that negative zero is the same as zero.
10. Formal Assessment - Group work
    1. Group work: Have each group come up with one to three sentences that describe 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.
11. Addition of negative numbers
    1. Write "4+ -2" on the board. Ask, "What might this mean?" Lead discussion.
    2. Take the students through the process of solving this statement on the number line. Ask, "If we are going to solve this statement, what would we do first?" Start at 4. "Next?" Add the opposite of two. Discuss what adding the opposite of two means.

• 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.

• 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 the nature of negative numbers as a formal assessment.
• 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.

Download rubric for student's descriptions of negative numbers.
Download this lesson plan in PDF format.