# Title: Integers: Quick, Fun and Easy To Learn

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1 Title: Integers: Quick, Fun and Easy To Learn Brief Overview Students will identify and understand positive and negative integers. Using this understanding, the students will use the number line, study guides, worksheets, manipulatives and computer technology to perform addition and subtraction of integers. This will give the students the knowledge to extend the whole number system in both directions as well as magnitude. NCTM Content Standard/National Science Education Standard: 6.0 Knowledge of Number Relationships or Computation Apply knowledge of rational numbers and place values. Read, write and represent integers from 100 to 100. Grade/Level: 6th Duration/Length: Outcomes: 3 days, 45 minute class periods Students will: Understand the vocabulary as it relates to each activity. Understand the number line concept using positive and negative integers with and without counters. Order integers using words and symbols to indicate order relations between particular pairs of integers. Create real world integer models. Be able to perform addition and subtraction of integers using the addition and subtraction of integer rules. Materials and Resources: Teacher Resource Sheets Student Resource Sheets Manipulatives Worksheets

5 Teacher will now model subtraction problems on the overhead or board using counters to show the additive inverse. Example: 7 3 Place 7 negative counters on the table. Remove 3 positive counters. (There are none to remove) Add 3 zero pairs to the set. Now you can remove 3 positive counters. How many are left? (4). Now practice subtracting integers on the number line Labeling the negative and positive directions. Student Application: Teacher will hand out the worksheet for subtraction of integers (Student Worksheet #3 and counters. Embedded Assessment: Teacher will monitor the student s knowledge of subtraction of integers using the additive inverse, as they model the processes presented. Reteaching: Students will review subtracting of integers using Reteaching Worksheet #3 and receive small group instruction based on individual needs. Summative Assessment: Extension: Students will create their own problems involving subtraction of integers using a foldable of their choice. (With answers!) Students will explain in writing the process of subtraction of integers. Given several examples, students will show their understanding of positive and negative integers by justifying why their answers are correct, in numbers and words. (Summative Assessment Worksheet) Authors: Susan Oppenheim Melvin J. Berman Hebrew Academy Rockville, Maryland Rossalind SmithRandall Lemmel Middle School Baltimore City, Maryland

6 HOW TO MAKE A FOLDABLE VOCABULARY BOOK 1. Fold a sheet of notebook paper in half like a hot dog. (Lengthwise) 2. On one side, cut every third line. This usually results in 10 tabs. 3. Label the tabs. TRIFOLD BOOK 1. Fold a sheet of 81 2 x 11 inch paper into thirds. 2. Use this book to make charts with 3 columns Or rows. FOLDED BOOK 1. Make a half book. Fold a sheet of 8 1/2 x 11 inch paper in half like a hot dog. 2. Fold it in half again, like a hamburger. TWOTAB BOOK 1. Take a folded book and cut up the valley of the inside toward the mountain top. This forms two tabs. From Dinah Zike s Teaching Mathematics with Foldables, Glencoe McGraw Hill

7 ADDITION RULES FOR ADDITION AND SUBTRACTION OF INTEGERS 1. When adding integers and the signs are the same, (both positive or both negative) add the absolute values and use the same sign. Ex. 4 8= When adding integers and the signs are different, subtract the absolute values an use the sign of the number with the larger absolute value. Ex. 11 ( 4) = 7 12 (6) = 6 SUBTRACTION 1. To subtract an integer, add its opposite.

8 VOCABULARY WORDS Integer The whole numbers and their opposites. Ex , 3, 2, 1, 0, 1, 2, 3, 4, 5 negative integers positive integers Positive integer An integer that is greater than zero. Negative integer An integer that is less than zero. Number line a line that goes into infinity in both directions Absolute value The distance a number is from zero on a number line. < less than > greater than Zero pairs A positive integer and a negative integer Graph The process of placing a point on a number line at its proper location. Additive inverse The opposite of an integer. The sum of an integer and its additive inverse is zero. Ex. 5 5 = 0

9 Grocery Store Library Home Playground School East TEACHER/STUDENT RESOURCE SHEET

10 NAME WORKSHEET #2 WORKSHEET FOR ADDITION OF INTEGERS WITH COUNTERS USE COUNTERS TO FIND EACH SUM. DRAW A PICTURE OF YOUR ANSWER (5) (6)

11 NAME WORKSHEET #3 WORKSHEET FOR SUBTRACTION OF INTEGERS Subtract using your counters. Draw the answers (7) ( 12) (20) Subtract using a number line. Draw the number line and show your work

12 NAME WORKSHEET #1 WORKSHEET FOR INTEGERS AND ABSOLUTE VALUE Write an integer for each situation C below 0 2. a profit of \$ A. D feet above sea level 5. a withdrawal of \$ a bonus of \$ B.C. 8. going up 6 stairs 9. loss of 25 pounds Evaluate each expression

13 NAME

14 RETEACHING WORKSHEET #1 WORKSHEET FOR INTEGERS AND ABSOLUTE VALUE Write an integer for each situation. 1. loss of 82 pounds 2. a bonus of \$ B.C feet above sea level degrees Celsius below 0 6. a profit of \$ A.D. 8. going up 12 stairs 9. a withdrawal of \$940 Evaluate each expression

15 NAME RETEACHING WORKSHEET #2 RETEACHING WORKSHEET FOR ADDITION OF INTEGERS WITH COUNTERS USE COUNTERS TO FIND EACH SUM. DRAW A PICTURE OF YOUR ANSWER (2) (9)

16 NAME RETEACHING WORKSHEET #3 RETEACHING WORKSHEET FOR SUBTRACTION OF INTEGERS Subtract using your counters. Draw the answers (2) (3) (9) (10) (17) Subtract using a number line. Draw the number line and show your work (8) (7)

17 NAME SUMMATIVE ASSESSMENT 1. Draw a number line. Show the problem 7 2. Be sure to label and use arrows for directions. 2. Draw a number line. Show the problem Be sure to label and use arrows for directions. WRITE AN INTEGER FOR EACH SITUATION. 3. A gain of 8 yards feet below sea level (19) (20) 9. What are zero pairs? 10. What is an additive inverse? 11. What are the rules for adding integers? 12. What are the rules for subtracting integers?

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