Student Probe What is Integer Subtraction At a Glance ? 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 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 teacher says or does… Expect students to say or do… If students do not, then the teacher says or does… 1. How have you modeled subtracting numbers? Separating cubes, with pictures, on a number line, counting up or counting down. The teacher says or does… Expect students to say or do… 2. Today we are going to extend our understanding of subtraction of numbers to integers. Show me using any strategy. 3. First, let’s solve the addition problem on a number line. 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 5. So we see that can be written as the addition statement . 6. Let’s solve on a number line. 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. If students do not, then the teacher says or does… Model. Let’s solve this problem: Sam had 2 marbles. He found some more and now has 6 marbles. How many did he find? 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. The teacher says or does… Expect students to say or do… 9. If we move to the right is positive it positive or negative? 10. What is the solution? Positive 4 (If students say 4, reinforce the notion of direction by having them explicitly share the positive sign.) 11. Write as an addition statement. 12. Let’s represent this statement on the number line. (See Teacher Notes.) 13. What is the difference Positive 6 between the two points? 14. Write as an addition statement. 15. How would we represent this statement on the number line? (See Teacher Notes.) 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 addition statement. If students do not, then the teacher says or does… When we are looking at direction to the right or up is given a positive sign. To the left or down is given a negative sign. Count with the students as you move from 2 to 6 on the number line. If students forget the sign prompt them about the direction of movement. left Remind the students that the start point was 3 and we want to end at . Prompt them about the direction of movement. Negative Negative 5 The teacher says or does… Expect students to say or do… 20. How would we represent this statement on the number line? (See Teacher Notes.) 21. What direction are we now moving to get to the second point? 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? right positive positive 1 If students do not, then the teacher says or does… 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 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: http://dww.ed.gov/practice/?T_ID=20&P_ID=48 Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide -­‐ Response to Intervention in Mathematics. Retrieved 2 25, 2011, from rti4sucess: http://www.rti4success.org/images/stories/webinar/rti_and_mathematics_webinar_presentati
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