7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School

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1 7 th Grade Integer Arithmetic 7-Day Unit Plan by Brian M. Fischer Lackawanna Middle/High School Page 1 of 20

2 Table of Contents Unit Objectives NCTM Standards NYS Standards....3 Resources and Materials.. 3 Overview of daily objectives.. 4 Day Day Day Day Day Day Day Page 2 of 20

3 Unit Objectives - Students will be able to add, subtract, multiply, and divide integers. use algebra tiles to model the addition and subtraction of integers. add and subtract integers using an interactive internet site that simulates algebra tiles. find the average of a set of integers. NCTM Standards for Grades 6-8 Number and Operations Standard Problem Solving Standard Reasoning and Proof Standard Communication Standard Connections Standard Representation Standard NYS Standards for Grades 7-8 Key Idea 1 Mathematical Reasoning Key Idea 3 Operations Key Idea 4 Modeling/Multiple Representations Key Idea 5 Measurement Key Idea 7 Patterns/Functions Resources & Materials Textbook: Middle School Math Course 2 by Foresman - Wesley, Supplemental worksheets from the Foresman Wesley textbook.. Algebra tiles minimum 10 yellow tile and 10 red tiles per student/pair. Computer lab with internet access. Students may work in pairs. Student worksheets. MATHO boards and MATHO problem cards. Scientific Calculator. Page 3 of 20

4 Overview of Daily Objectives Day 1 Students will understand the definition of additive inverse and the zero property of addition. be able to use algebra tiles to represent integer addition problems and determine their sums. develop rules for adding a pair of integers. Day 2 Students will be able to use an interactive internet site to represent integer addition problems with algebra tiles and determine their sums. be able to use an interactive internet site to represent integer subtraction problems with algebra tiles and determine their differences. Day 3 Students will be able to use algebra tiles to represent integer subtraction problems and determine their differences. rewrite integer subtraction problems as addition problems. Day 4 Students will be able understand the concept of a negative times a negative by using a visual aid. develop integer multiplication rules by developing patterns. Day 5 Students will be able to divide integers. Day 6 Students will be able to solve problems that involve finding the average of a set of integers. Day 7 Students will practice to integer arithmetic in a game format. Page 4 of 20

5 Day 1 Objective Students will be able to: Understand the definition of zero pairs and the Zero Property of Addition. Use algebra tiles to represent integer addition problems & determine their sums. Develop rules for adding a pair of integers. Materials algebra tiles, worksheets, overhead projector, algebra tiles for the overhead. Opening Activity Distribute worksheets. Have them copy the definitions of Additive Inverse and Zero Property of Addition. While they are doing this distribute the algebra tiles. Activity #1 Discuss the above definitions and zero pairs. Explain that a yellow tile represents +1 and a red tile represents -1. Demonstrate zero pairs using the tiles. Activity #2 Model worksheet problems 1 and 2 together and discuss question #3. Activity #3 Model worksheet problems 4 and 5 together and discuss. Activity #4 Have students model and solve problems 6 thru 9 on their own. Monitor their progress by observing. After they have completed the problems have them discuss their solutions with their group members. Students will then be selected to model and explain their solutions to the class using the overhead. Leave enough time to formalize the rules. Closing Activity Discuss the solution to question 10 and review the solution to question 3. Compare and contrast how to add integers with like and unlike signs. Collect the tiles. Homework page 453: 2, 6-18 even. Have them sketch algebra tiles. Page 5 of 20

6 Additive Inverse - Adding Integers The Zero Property of Addition - We will be using algebra tiles to model the addition of integers. Yellow tiles represent positive integers (unshaded squares in our diagrams). Red tiles represent negative integers (shaded squares in our diagrams). By the Zero Property of Addition, a yellow tile plus a red tile equals. 1. Use algebra tiles to model the addition problem (+5) + (+3). Sketch your model below. What is the sum of +5 and +3? 2. Use algebra tiles to model the addition problem (-2) + (-7). Sketch your model below. What is the sum of -2 and -7? 3. Describe how to find the sum of a pair of integers with like signs. 4. Write the addition problem for the model below. Circle the zero pairs, a positive and a negative tile paired up equals zero. What is the sum of the above model? Page 6 of 20

7 5. Write the addition problem for the model below. Circle the zero pairs, a positive and a negative chip paired up equals zero. What is the sum of the above model? 6. Use algebra tiles to find the sum of (+3) and (-8). Show your model below. 7. Use algebra tiles to find the sum of (+5) and (-2). Show your model below. 8. Use algebra tiles to find the sum of (-6) and (-3). Show your model below. 9. Use algebra tiles to find the sum of (-6) and (+8). Show your model below. 10. Describe how to find the sum of a pair of integers with different signs. Page 7 of 20

8 Day 2 Objective Students will be able to: Use algebra tiles to represent integer addition/subtraction problems & determine their sums/differences. Materials computers connected to the internet and a video display so that the students can observe the teacher s interaction with the computer. Opening Activity Have the students seated at a computer in pairs and have them observe the teacher work with the algebra tiles on the computer. Go to the web site and go through 2 demonstration problems. Have this web site written on the chalkboard and/or stored in favorite places. Always check a web site prior to using it. Activity #1 Have the students access this website and solve some integer addition problems. Have them write these problems and their solutions on a sheet of paper. Let each student solve about 3 problems. Activity #2 Review the rules for adding integers. Activity #3 Go to the web site and go through 2 demonstration problems. Have this web site written on the chalkboard and/or stored in favorite places. Activity #4 Have the students access this website and solve some integer subtraction problems. Have them write these problems and their solutions on a sheet of paper. Let each student solve about 3 problems. Closing Activity Discuss integer subtraction. See if they made a connection to addition. Homework page 453: 2, even, 33, and 36. Page 8 of 20

9 Day 3 Objective Students will be able to: Use algebra tiles to represent integer subtraction & determine differences. Develop rules for subtracting a pair of integers. Materials algebra tiles, worksheets, overhead projector, algebra tiles for the overhead. Opening Activity Distribute worksheets and algebra tiles. Activity #1 Have students demonstrate problems 1 and 2 on the overhead. This should be extremely simple and take virtually no time. Activity #2 Model problem 3 on the overhead. Ask the students questions to recall the information they acquired yesterday. Activity #3 Have students do problems 4 and 5 by themselves. After a few minutes, have them check their answers and discuss their solutions with their partners. Select students to demonstrate their solutions on the overhead. Activity #4 Have students complete the chart in problem 6 and review their answers. Activity #4 Discuss question 7 and relate subtraction to addition. Closing Activity Have rewrite the subtraction problems (8-11) and review their answers. Collect the tiles and review the subtraction to addition rule. Homework page : 8-20 even, 32. Page 9 of 20

10 Subtracting Integers 1. Use algebra tiles to model the subtraction problem (+5) - (+3). Sketch your model below. Cross out the tiles that you are removing to represent the tiles being subtracted. What is the difference of +5 and +3? 2. Use algebra tiles to model the addition problem (-5) - (-2). Sketch your model below. What is the difference of -5 and -2? 3. Use algebra tiles to model the addition problem (+1) - (+3). Sketch your model below. What is the difference of +1 and +3? 4. Use algebra tiles to model the addition problem (-3) - (-5). Sketch your model below. What is the difference of -3 and -5? Page 10 of 20

11 5. Use algebra tiles to model the addition problem (+2) - (-3). Sketch your model below. What is the difference of +2 and -3? 6. Use algebra tiles to find the sums and difference in the table below. (+1) + (-6) = (-4) + (-1) = (-1) + (+1) = (+2) + (+2) = (-3) + (-7) = (+1) - (+6) = (-4) - (+1) = (-1) - (-1) = (+2) - (-2) = (-3) - (+7) = 7. Describe how to rewrite an integer subtraction problem as an integer addition problem. Rewrite each subtraction problem as an addition problem and evaluate (-18) = (+18) = (-18) = (+18) = Page 11 of 20

12 Objective Students will be able to: Day 4 Develop rules for multiplying a pair of integers. Materials worksheets, overhead projector, worksheet transparency. Opening Activity Distribute worksheet and have them complete quadrant of the times table. Activity #1 Answer questions 1 and 2 from the worksheet. Activity #2 Complete the 4 th quadrant of the times table together (transparency). Activity #3 Have students complete the 2 nd quadrant of the times table by themselves. Check on their work. Review their answers by asking each students a times problem in that quadrant and simultaneously place the correct answers on the transparency. Activity #4 Start the students on the 3 rd quadrant and let them finish it. Review their answers in a similar fashion and put answers on the transparency. Activity #5 Discuss and answer question 3. Closing Activity Create multiplication problems to reinforce the rules. Do a problem that involves the multiplication of three integers. Review the rules. Homework page 464: 4-16 even,24, and 26. Page 12 of 20

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14 Objective Students will be able to: Divide integers. Day 5 Materials none Opening Activity Have the students evaluate ( 2) 2, ( 2) 3, ( 2) 4, and ( 2 ) 5 about the definition of exponents.. Remind them Activity #1 Review their answers and discuss the pattern. Ask them what they think the signs would be for other powers of base -2. Activity #2 Review the rules of integer multiplication and tell them that these same rules apply to division. Activity #3 Have the students work problems odd on page 469. Have them check their answers with their group members. Review the answers in class. Activity #4 Have the students work on (-8) + (+3) and (-8) (-3). Discuss their solutions and review the rules for addition and how to rewrite subtraction problems. Closing Activity Solve the problem -12/-3 and -24/+8. Review the rules for dividing. Homework page 469: even. Page 14 of 20

15 Day 6 Objective Students will be able to: Find the average of a set of integers. Solve word problems with integers Materials worksheets, overhead projector, worksheet transparency. Opening Activity Have the students do these problems: , 30-(-29), (-4)(-8), and 64/(-4). Activity #1 Have students display their work on the overhead and explain. Activity #2 Discuss the term mean/average. Find the average of a sample set of grades such as 82, 70, 94, and 98. Activity #3 Distribute the worksheet, Guided Problem solving 9-7. Select a student to read the problem. Answer questions 1 through 3 together. Activity #4 Have the students answer questions 4 through 7 by themselves. Monitor their progress. After a few minutes, let them discuss their solutions with their group members. Have a student display their work on the overhead and explain. Activity #5 Discuss question 8. Closing Activity Review the rules integer operations. Homework Solve another problem (located at the bottom of the worksheet). Page 15 of 20

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17 Objective Students will be able to: Day 7 Add, subtract, multiply, and divide integers. Materials MATHO cards and corresponding integer problems. Teacher Note - Following this page are 2 blank MATHO cards that can be copied and customized by any teacher. My cards range from -25 to +25. Each series of numbers is placed under a certain letter, just as in BINGO. Problems that correspond to your cards have to be created and put in a jug. Also attached are 2 of my cards. Opening Activity Have the students do these problems: -20+(-20), 10-19, (-3)(-7), and 42/(-3). Activity #1 Review their answers and the rules Activity #2 Distribute each student a MATHO card. Explain the rules to the students. Color in the free space. A student will be selected by the teacher to draw a problem from the jug. He/she must then solve it on the chalkboard and explain their work. If a student has that integer on his/her board, then it is colored in. Another student is then selected to draw and solve a problem. The first student to get 5 numbers in a row wins. Activity #3 Check the winners card and play another game. Closing Activity Review the rules integer operations. Homework Study for the test. Page 17 of 20

18 M A T H O FREE SPACE Page 18 of 20

19 M A T H O FREE SPACE Page 19 of 20

20 FREE SPACE FREE SPACE FREE SPACE FREE SPACE Page 20 of 20

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