Integer Subtraction. Preparation Prepare number line paper for each student. Each student will need blue and green markers.

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1 Integer Subtraction Student Probe What is? Answer: Students who do not understand integer subtraction might answer 5 or. Lesson Description This lesson is intended to help students develop an understanding of subtraction of integers. The lesson will focus on the number line model as a tool for students to develop the conceptual foundation. This lesson uses the definition of difference as a distance between two points. Rationale Integers are arguably the most important subset of the number system. The understanding of integers is essential for entry into higher- level mathematics. Students frequently over- generalize the negative sign as a subtraction operation as opposed to the description of the type of number when doing computations. Preparation Prepare number line paper for each student. Each student will need blue and green markers. Lesson At a Glance What: Subtraction of integers Common Core State Standard: CC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Matched Arkansas Standard: AR.7.NO.2.4 (NO.2.7.4) Understand Operations: Model and develop addition, subtraction, multiplication and division of integers Mathematical Practices: Model with mathematics Who: Students who have difficulty with subtracting integers Grade Level: 7 Prerequisite Vocabulary: positive, negative, difference, set, expression, equation, value Prerequisite Skills: integer addition Delivery Format: Individual, small group Lesson Length: 15 to 20 minutes Materials, Resources, Technology: Visual display, number line paper Student Worksheets: None The Expect students to say or do If students do not, then the 1. How have you modeled subtracting numbers? Separating cubes, with pictures, on a number line, counting up or counting down.

2 The Expect students to say or do If students do not, then the 2. Today we are going to extend our understanding of subtraction of numbers to integers. Show me strategy. 3. First, let s solve the addition problem using any on a We start at 2 and move 3 spaces to the right. What is the distance from 0 to our ending point? 4. How could you rewrite as an addition problem? Multiple strategies may be shared. 5 Model. Let s solve this problem: Sam had 2 marbles. He found some more and now has 6 marbles. How many did he find? 5. So we see that can be written as the addition statement. 6. Let s solve on a We will begin at 2. We want to end at 6. How far did I move and in what direction? Direction is of extreme importance here! 4 to the right. Write a number sentence to solve this problem. Refer to Translation of Word Problems SU. Place a point on 2 then a point on 6 then draw an arrow from 2 to 6. Make sure students share the number of moves and direction. You may need to reinforce the start position.

3 The Expect students to say or do If students do not, then the 9. If we move to the right is it positive or negative? positive When we are looking at direction to the right or up is given a positive sign. To the left or down is given a 10. What is the solution? (If students say 4, reinforce the notion of direction by having them explicitly share the positive sign.) 11. Write as an 12. Let s represent this statement on the 13. What is the difference between the two points? 14. Write as an 15. How would we represent this statement on the number line? 16. What direction are we now moving to get to the second point? 17. Is the direction of the distance to be traveled considered to be positive or negative? 18. What would be the difference between these two points? 19. Write as an Positive 4 Positive 6 left Negative Negative 5 negative sign. Count with the students as you move from 2 to 6 on the If students forget the sign prompt them about the direction of movement. Remind the students that the start point was 3 and we want to end at. Prompt them about the direction of movement.

4 The Expect students to say or do If students do not, then the 20. How would we represent this statement on the number line? 21. What direction are we now moving to get to the second point? right 22. Is the direction of the distance to be traveled considered to be positive or negative? 23. What would be the difference between these two points? positive positive 1 If students forget the sign give a hint about the direction of movement. Teacher Notes When subtracting numbers the difference will be represented on the number line as the distance between the two points and the sign indicates the direction moved from the start position which is positive or negative. 2 +? = 6 (- 1) +? = 5

5 3 +? = (- 2) (- 5) +? =- 4 Variations None Formative Assessment Solve these subtraction problems. Answers: References Mathematics Preparation for Algebra. (n.d.). Retrieved 12 10, 2010, from Doing What Works: Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide - Response to Intervention in Mathematics. Retrieved 2 25, 2011, from rti4sucess: on.pdf