Student Probe Integer Multiplication At a Glance What: Multiplication of integers Common Core Sate Standards: CC.7.NS.1 Apply and extend previous understandings Answer: 24 of operations with fractions to add, Students frequently over-­‐generalize their understanding subtract, multiply, and divide rational of multiplication of whole numbers and write . numbers. Apply and extend previous understandings of addition and subtraction Lesson Description to add and subtract rational numbers; This lesson is intended to help students develop an represent addition and subtraction on a understanding of multiplication of integers. The lesson horizontal or vertical number line diagram. focus is on using the array model on the coordinate plane Matched Arkansas Standard: AR.7.NO.2.4 as a tool for students to develop conceptual (NO.2.7.4) Understand Operations: Model understanding. and develop addition, subtraction, multiplication and division of integers Rationale Mathematical Practices: Model with mathematics Integers are arguably the most important subset of the Who: Students who have difficulty with number system. Understanding operations with integers multiplication of integers is essential for entry into higher level mathematics. Grade Level: 7 The main confusion when multiplying integers is which Prerequisite Vocabulary: positive, negative, sign (positive or negative) is placed on the product. product, set, expression, equation, value Prerequisite Skills: whole number addition Preparation Delivery Format: Individual, small group Prepare Coordinate Grid Paper, a set of two-­‐color Lesson Length: 15 to 20 minutes counters, and blue and red markers for each student. Materials, Resources, Technology: Visual display , two-­‐color counters, coordinate graph paper, use of an interactive white board with interactive integer multiplication coordinate grid (optional) Student Worksheets: Coordinate Grid Paper Lesson The teacher says or does… Expect students to say or If students do not, then do… the teacher says or does… 1. How have you modeled Arrays, skip counting, multiplication of numbers? repeated addition Today we are going to extend our understanding of multiplication of numbers to integers. What is ? The teacher says or does… 2.
3.
4.
5.
Expect students to say or do… (Distribute color counters to students and explain that yellow is the positive ********
side and red is the negative side.) ******** = 40 ********
Multiply using an array model. ******** (Distribute Coordinate Grid Paper to students.) Where is the positive part of the x-­‐
To the right of 0. axis located? What does the part of the x-­‐axis left Negative numbers of the origin represent? Show me the part of the y-­‐axis that Students should indicate represents negative numbers. a downward movement on the y-­‐axis below the x-­‐axis. What type of numbers are represented on the y-­‐axis above the Positive numbers x-­‐axis? Where would you find an ordered Quadrant I pair if the coordinates are ? 6. Any time you have a positive number multiplied by a positive number your answer will go in Quadrant I, which is a positive quadrant. 7. Demonstrate using 3 counters along the positive x-­‐axis, beginning at the origin, and using 4 counters along the positive y-­‐axis, beginning at the origin, and filling in a rectangular array. (See Teacher Notes.) 8. Now, build an array to represent . What is the product? 9. Is the product positive or negative? How do you know? If students do not, then the teacher says or does… Refer to Multiplying and Dividingf Whole Numbers. Refer to Graph Ordered Pairs on a Coordinate Plane. Refer to Graph Ordered Pairs on a Coordinate Plane. Students build the array of 30 counters. 30. Positive, because the array is in Quadrant I. Model. The teacher says or does… Expect students to say or If students do not, then do… the teacher says or does… 10. So we can see that when we multiply two positive integers, the product is positive. The teacher says or does… Expect students to say or If students do not, then do… the teacher says or does… 11. Where would we find an ordered pair Quadrant II Refer to Graph Ordered Pairs on a Coordinate if the coordinates are ? Plane. 12. Anytime we multiply a negative number by a positive number, the array (answer) will be in Quadrant II. Quadrant II is a negative quadrant. 13. Demonstrate using 3 counters along the negative x-­‐axis, beginning at the origin, and using 4 counters along the positive y-­‐axis, beginning at the origin, and filling in the array. (See Teacher Notes.) 14. So we can see that when we multiply a negative integer and a positive integer, the product is negative. 15. Now, build an array to represent Students build the array of 30 counters. . Negative 30. What is the product? There are 30 counters in How do you know? Quadrant II. Quadrant II is always negative. 16. Where would we find an ordered Quadrant III pair if the coordinates are ? 17. Any time we multiply a negative number by a negative number the array (answer) will be in Quadrant III. Quadrant III is a positive quadrant. Model. If the student answers 30, ask, “Is it positive or negative? Why” Refer to Graph Ordered Pairs on a Coordinate Plane. The teacher says or does… 18. Demonstrate using 3 Expect students to say or If students do not, then do… the teacher says or does… counters along the negative x-­‐axis, beginning at the origin, and using 4 counters along the negative y-­‐axis, beginning at the origin, and filling in the array. (See Teacher Notes.) 19. So we can see that when we multiply two negative integers, the product is positive. 20. Now, build an array to represent Students build the array of 30 counters. . Positive 30. What is the product? There are 30 counters in How do you know? Quadrant III. Quadrant III is always positive. 21. Where would we find an ordered pair Quadrant IV if the coordinates are ? 22. Any time we multiply a negative number by a negative number the array (answer) will be in Quadrant IV. Quadrant IV is a negative quadrant. 23. Demonstrate using 3 counters along the positive x-­‐axis, beginning at the origin, and using 4 counters along the negative y-­‐axis, beginning at the origin, and filling in the array. (See Teacher Notes.) 24. Any time you have a positive number multiplied by a negative number your answer will go in quadrant IV, which is a negative quadrant. Model. If the student answers 30, ask, “Is it positive or negative? Why” Refer to Graph Ordered Pairs on a Coordinate Plane. The teacher says or does… Expect students to say or do… 25. Now, build an array to represent Students build the array of 30 counters. . Negative 30. What is the product? There are 30 counters in How do you know? Quadrant IV. Quadrant IV is always negative. 26. So we can see that when we multiply a positive integer and a negative integer, the product is negative. If students do not, then the teacher says or does… Model. If the student answers 30, ask, “Is it positive or negative? Why” Teacher Notes Variations None Formative Assessment Find these products: Answers: References
Mathematics Preparation for Algebra. (n.d.). Retrieved 1 13, 2011, 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
on.pdf