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Invitation to Integers (Grade 5-7)

Master Teacher

Deb Childs

Time Allotment

90-minute class period

Overview

In this lesson students will find zero pairs and add integers using zero pairs and a number line. Students will generalize rules for adding integers. The class will view approximately 10 minutes of video divided into three segments. The Internet will be used to reinforce integer addition. Students will complete a matching activity on the Internet that will help them practice adding integers.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

find zero pairs
add integers
relate integers to real world activities
solve simple mental inequalities

South Carolina Standards

These Standards can be found online at Office of Curriculum Standards.

Mathematics Grade 6-8

Sixth Grade: Number and Operations

I G 1. Use integers to describe real-world phenomena in order to develop meanings for integers.

Seventh Grade: Number and Operations

I G 1. Compare and order integers.

III B 1. Use models and numbers, to develop

and analyze the algorithms for computing with integers.

III B 2. Add integers to solve a variety of applied and mathematical problems.

Media Components

Video

Math Talk, Lesson 10: "Both Sides of Zero" concentrates on finding zero pairs and adding integers.

Web Site

Quia, pronounced Key-uh and short for Quintessential Instructional Archive, provides a variety of educational services. This page on the site, Quia.com, looks at "Adding and Subtracting Positive and Negative Numbers." Click on the game that says "matching." There is an index to the terms. Students can play several rounds of an adding positive and negative numbers game.

Materials

Teacher:

overhead counters of 2 different colors (If available, the counters should be the same two colors as the student counters. If not write + and _ signs on the overhead counters).

Timer or clock with second hand (optional)

Student:

marker (1 per student)
2-color counters (13 counters per student)
sentence strip or a copy of the number line (Activity Sheet 1/1 per student)

Groups of 2:

3x5 or 4x6 note cards (at least 5 cards per group)

Prep for Teachers

Bookmark the Web site on the computer for the students.

Obtain an AverKey (optional).

Cue the video to the first clip where you see the cartoon hostess and parrot disappear for the third time. You will hear: "You know what happens when you add positive and negatives? You put your eye out? No, watch this sketch." Play dough heads appear.

Make a transparency of Activity Sheet 1.

Introductory Activity

Step 1: Ask the students when 11 plus 2 equals 1. (When telling time. Two hours after 11:00 a.m. is 1:00 p.m.)

Step 2: Provide a Focus for Media Interaction by asking students to look for how negative three and positive five make two. Show the first video clip. PAUSE after the screen shows -3 + 3 = 0. You will hear "Boy those are violent little fellows." Listen to responses to the question how -3 and +5 = +2. You will probably hear about the bad guys eating the good guys or one color eating another color.

Learning Activities

Step 1: Give out counters. Agree on which color will represent positive and which will represent negative. (Note to Teacher: Usually 2-color counters have a red side that is often modeled as negative.) Model each problem in the video clip on the overhead as students manipulate their counters. Place 3 negative counters on the desk or overhead. Place 5 positive counters on the surface. Remove zero pairs (1 positive and 1negative).

You will be left with 2 positive counters as the answer. Repeat with -9 + 4 = -5 and -3 +3 = 0. Ask students "When would you see -3 + 3 = 0, outside of a math classroom or textbook?" (Borrow and pay back $3."Mother may I" taking 3 steps forward, 3 steps backward. Temperature dropping 3 degrees below zero and then rising 3 degrees. Football team losing 3 yards and then gaining it back. A dieter losing 3 pounds and gaining it back. Diving 3 feet below sea level and then coming back up.)

Ask students to show the following problems and solutions with their counters. Solve the equations and discuss the answers one at a time. -8 + 5 =

-3. 5 + (-3) = +2. 8 +(-2) = +6. -6 + 6 = 0. Write each problem down after the student has modeled it. You may wish to use raised signs or parentheses on the "plus a negative" problems as was demonstrated in the previous four problems. Remind students when there is no sign in front of a number, it is assumed to be positive.

Step 2: FAST FORWARD the video until you hear "She's a self-assured little tyke" and see the cartoon hostess and parrot disappear. Then you will see and hear "Pauline's Perilous Pyramid." Provide a Focus for Media Interaction by asking students to look for another way to add integers. PAUSE when you hear "I'll get you next time" and see a box that says UNTIL NEXT TIME. Ask how this clip demonstrated adding positive and negative integers in a different way from the counters used previously. (Number line).

Step 3: Either give students the number lines you have made, or make number lines from -25 to 25 using sentence strips. Label by 5's but put hash marks for each integer between the multiples of 5. (See Activity Sheet 1). Ask them if there is any way you can get to the top without using the zapper. Remember you must stay in the range between -25 and +25. REWIND the video until you see the gameboard for Pauline's Perilous

Pyramid. FREEZE FRAME at that spot. Guide the students through one example. Start with 5 and jump to -15. Then jump somewhere besides -10.

After you finish that one, let the students work individually or in groups to come up with other paths Pauline could take to win the game. You may wish to add the following limits to the rules. You may go left to right but not back "down." You may move to the left or right only one space per (left to right) row. Allow students about 5-10 minutes to complete this activity. Let groups or individuals describe other possible solutions. (Note to Teacher: See Activity Sheets 2 and 3 for some possible solutions.)

Step 4: FAST FORWARD through the cartoon hostess and parrot until you see a black and white maze that says "MATH MAN." You will hear "Math Man, no he's as sick as a pig." Provide a Focus for Media Interaction by asking students to listen for why 0 does not work in the game. STOP when you see GAME OVER, and hear Math Man. Listen for the students' responses to why zero does not work? (7 + 0 = 7, seven is not less than seven.) If your students are familiar with the symbol for less than or equal to, ask them what symbol could have replaced the < to make the statement true. If they are not familiar with this symbol, show them the symbol for less than or equal to < and greater than or equal to >. Ask the students what the "p" represented. (Some number or the unknown). Show the other numbers listed on the clip (5 No. -3 Yes.), and let the students decide which ones would make the inequality true. Ask the students for other integers that would make the inequality true? (Any negative number)

Culminating Activity

Step 1: Go the Quia Web site (http://www.quia.com/custom/66762). If you have an AverKey, you can guide the students through the matching game the first time. Provide a Focus for Media Interaction by asking students to write down any equations they miss as they play the game. Now, have the students go the Web site that has been bookmarked. Allow the students to play a few rounds of the matching game. Ask about problems they missed. Work those on the overhead. (Note to Teacher: All equations and solutions used on the Internet activity are included on Activity Sheet 4).

Step 2: Arrange the students in groups of two. Ask them to make up 5 integer problems that can be solved using the number line from +25 to -25. Each group will write the problems on one side and the answers on the other side, like a flash card. Ask groups to exchange cards with another group and check their flash cards. Put flash cards that both groups agree to be correct in one pile. Make another pile of flash cards with possible errors. (Note to Teacher: Groups that finish early can copy some of the equations from Activity Sheet 4 to include in the upcoming game.) Check all cards and destroy any with errors.

Step 3: Play "Around the World" with the flash cards. Ask the student in seat number 1 to stand beside the student in seat number 2. Show a flash card. The first one to answer correctly gets to move to seat number 3 and challenge that student. The student who did not move sits in seat number 2. If there is a tie, the two students get another card, until the tie is broken. If they both miss, they get another card, until a student answers correctly and moves to the next seat. Each student gets one guess at a card. If the student misses, he/she must remain silent while the other student has 20 seconds to answer the question correctly. The goal is to be the first student to go completely around

the room and return to his/her seat. (Note to Teacher: If your desks are not numbered, designate a pattern around the room before play begins).

Step 4: Divide the flash cards into three piles: a negative plus a negative, a positive plus a positive and a third pile in which one addend is negative and the other is positive. Ask students to hold up those cards at the front of the room. Ask the students to notice any patterns they observe. They will probably respond that a negative plus a negative is always negative, a positive plus a positive is always positive. They may need some guidance to see that when the signs are different, the answer will match the sign of the number that is farthest from zero. You may wish to write

-5 + 3 = -2 5 + -3 = +2

on the board or overhead. Negative 5 is farther from zero in the first problem so the answer is negative. Positive 5 is farther from zero in the second problem so the answer is positive. At this point they will probably notice they can find the number that is the answer by subtracting instead of walking the number line or finding zero pairs. Ask them to explain why the answer is sometimes positive and sometimes negative in these cases. They may talk about going past the zero on the number line or they may notice the answer is always the same as the addend with the larger absolute value (farthest from zero in either direction).

Step 5: In class or as homework, ask students to write a paragraph to a friend who was absent from school that day (a real student or a pretend one if all students are present). In that note they will explain how to add positive and negative numbers. Ask them to include examples of simple problems in their paragraph that illustrate adding two positive numbers, two negative numbers, and a problem where one number is positive and the other is negative. They may use the rules just discussed, the number line, or the 2-color counters demonstrated earlier, to explain the process to the absent classmate. They may wish to write about all the methods.

Cross-Curricular Extensions

Language Arts: Students will write a paragraph about how integers can be used outside of math class. (Body temperature, elevation, electrical charges, time lines, money, sports, dieting, etc.)

Science: Students can relate this to times they have completed experiments in science that involved a thermometer, elevation, etc.

Community Connections

Ask an electrician to come demonstrate the positives and negatives in his trade.

Ask a scuba diver to come talk to the class and relate how positive and negative numbers impact decisions about his dive. (How fast he can descend. How far below sea level he can go.)