ZERO IS OUR HERO
Grades 6 - 9

The rules and algorithms used for the addition of signed numbers will be long remembered when they are discovered by the student. These rules are established by patterns found in real-life settings. When students see these patterns so that they discover the rules, understanding is inherent. And to practice, we employ competition and challenge. Following the game format of Math Talk, students will become interactive participants in introductory and practice activities involving positive and negative numbers. So, let the games begin!

"Math Talk: Positive and Negative Numbers: Both Sides of Zero (Lesson 104)"

Students will be able to:

• demonstrate proficiency when adding integers
• discover a set of rules which can be applied to the addition of signed numbers
• recognize the use of signed numbers in real life settings

Per student

• Math-Mat (Attach two pages together as indicated)
• 15-20 pennies

1 for every student pair

• Index Card
• Marker
• 1 piece of adhesive tape
• Calculators (optional)

Adequate supplies to be shared in groups

• Rulers
• Markers
• Glitters
• stars
• old magazines
• other art materials

Integers: positive and negative whole numbers

Say: "Today we are going to begin our adventure by looking for very small numbers. With a partner, think of all the numbers you know and love, and then, without revealing your choice, write the smallest number you can think of on this index card." Each student pair should have an index card, a marker, and piece of adhesive tape. Say: "After you have selected your very small number, tape your index card to the board at the front of the room. Keep all numbers in a long row." Give students 2 or 3 minutes to display their index card. "Now I need one or two volunteers who will help me arrange these numbers from smallest to largest. You will be our 'game show assistants' and all other students will be our 'audience participants.' " Once students are selected, have them go to the row of index cards and be prepared to rearrange the cards (from smallest to largest). Select an 'audience' student to choose the smallest number they see. Game show assistants will then move the index card with that number to the far left of the row. Select a second student to find the next smallest number and have assistants place it to the right of the smallest number. Encourage discussion about correct placement of these numbers, and continue arranging and rearranging until the numbers are placed smallest to largest, from left to right. Say: "Now let's discuss what characteristics very small numbers have. How do we know one number is smaller that another? What comparisons do we seem to be making? Have we found the smallest number in existence?" Allow students to discuss these questions.

To give students a specific responsibility while viewing, introduce Math Talk segment with the following directions: "Today we are going to see if Buster's smallest number is on our list. As you watch Maria and Buster, listen for his smallest number."

BEGIN tape at the start of Math Talk #104. To allow students to check Buster's smallest number against their list, PAUSE tape immediately following Buster, the parrot, describing zero as a number "beneath contempt." Ask students to discuss the following questions using the numbers displayed by the class: "Was zero on our list of smallest numbers? Did we select zero as the smallest number? Did we find any smaller numbers than zero?" Answers will vary based on student contributions. Say: "Now let's see what small numbers Maria wants to introduce." Distribute a Math-Mat to each student. To give students a specific responsibility while viewing say: "On your Math-Mat, write Buster's smallest number in his speech bubble. As you watch the video, look for Maria's ideas about very small numbers. When you hear her describe her smallest numbers, write that description in the speech bubble next to her picture.
RESUME tape.
After Maria describes 'negative numbers,' PAUSE tape to verify that students captured the phrase, "a negative number is a number less than zero." Say: "Do you see that we are comparing numbers to zero, our hero, to help us understand their size? Where have you seen or used negative numbers in your daily lives?" Give students an opportunity to share their ideas. Record this brainstorm session on the board. If students do not suggest negative temperature readings, introduce this use of negative numbers. Say: "Stanley, Maria and Buster's friend, has some special talents. Let's see where he has experienced negative numbers." To give students a specific responsibility for viewing say: "As you watch Stanley compete, list his scores on our Math-Mat. We'll see how talented Stanley really is."

RESUME tape and allow students to watch and record Stanley's antics. At the end of the song "Less Than Zero," stop tape. (Note: If you find that students are having a difficult time recording the information, use the pause feature to allow them more time.) Say:

"Let's compare Stanley's scores on his four events by finding his total scores for each event. Use your mathematics skills to complete a note to Stanley about his overall performance." Give students an opportunity to complete Activity II on the Math-Mat. Say: "When we made our list of uses of negative numbers, many of you realized that we see them everyday in our weather patterns. Here is a game show that has an interesting temperature problem." To give students a specific responsibility while viewing, say: "As you watch this game show, decide how you would answer this temperature question if you were a participant. Record your answer in Activity III."

RESUME tape and play until game show host asks, "How many degrees did the temperature drop?" Stop tape. Say: "Record your answer to this question on your Math-Mat." To give students a specific responsibility for viewing say: "Now let's see how your answer compares with our TV students."

RESUME tape and play to the end of the game show and until Maria says, "Never mind, Buster." STOP tape. Say: "How many of you got Luiza's answer?" Allow students to respond by raising their hands. Say, "How many of you got Chris' answer?" Students raise hands. "How many of you see that BOTH answers are correct?" Teacher gives round of applause when students raise their hands to affirm this answer! Say: "Now let's extend our Square One Challenge to the weather map in Activity III. With the help of our trusty thermometer, find out how many degrees the temperature changed in each of these cities. Locate the city on the map, and record the temperature change at that point. Let's see how many you can complete in 6 minutes. Okay, everyone, begin!" Allow students to work in pairs if they prefer and time this activity. At the end of 6 minutes, students should make groups of 4 students and compare their results. Say: "Now let's find a set of rules that will help us find how much the temperature changes. Did you notice that sometimes you added the values and sometimes you subtracted? Let's look for a set of rules that will help us decide when to add and when to subtract. I think these 'clay creatures' in the next segment will help us understand how to combine positive and negative numbers."

Distribute 15-20 pennies per group of two students. To give students a specific responsibility while viewing say: "As you watch these positive and negative 'clay creatures,' we will use pennies to show the same results. Let heads represent the orange positive (+) creature and let tails represent the blue negative (-) creature. As they enter the screen, lay out one penny for each creature (heads for + and tails for -)."
RESUME tape and reduce the volume. As the first three 'negative' creatures enter, speak over the video sound and say, "Lay out three tails to represent these 'tough guys!' " As orange men parachute in say, "Lay out five heads to represent these 'positive guys!' "


PAUSE tape immediately following the 'high five' of the two remaining 'positive creatures' and ask students to show the same results with their pennies. Say: "Try these next two problems using your pennies. Record your answer on your Math-Mat." Give students two or three minutes to model the next two problems with their pennies. When all students have recorded their results, give students a specific responsibility for viewing by saying: "Check your results with the results of our clay creatures."

RESUME tape. Provide emphasis for the graphics by pointing out that the positive creatures were modeled by 'heads' and the negative creatures were modeled by 'tails.' STOP tape after the 'creature war' and as Maria wishes Stanley good luck. Say: "Now let's have our own creature war, using heads and tails as our warriors. Show each army, the positive one and the negative one, and find the results of each challenge. Record your answers next to each 'battle.' " After students have completed Activity IV on adding positive and negative numbers, have them compare their results with other students or with a calculator. Record several of the student's Rules for Adding and Subtracting Signed Numbers on the board. Say:

"Now we are ready to challenge our rules to make it to the top of Pauline's Perilous Pyramid." To give students a specific responsibility for viewing, say: "Let's help Pauline keep track of her score. Let's all shout out Pauline's score before the video announcer does!"

RESUME tape with slightly reduced volume. Encourage students to shout out the sum before it is revealed by the announcer. If students need additional time, use pause button liberally.

PLAY tape through both of Pauline's attempts and until Maria asks, "Pauline, was there any way you could have got to the top without using the Zapper?" STOP tape. Say:

"Let's give Pauline a hand getting to the top of the pyramid. (Students clap!) In Activity V, find as many paths as you can that would have allowed Pauline to make it to the top without the use of the Zapper." Give students 5-6 minutes to find several paths. To give students a specific responsibility while viewing, say: "Let's see if Buster found any of your paths. Check your results with his!"

RESUME tape and play until Maria says that Buster "is the loudest." Say: "Well, class, we have one more opportunity to challenge our positive and negative number skills. Let's get ready for Mathman!" To give students a specific responsibility for viewing, say: "Watch this blue tornado PLAY the Mathman game. When you see him make a mistake, everyone shout STOP!" When students shout Stop! or as the blue tornado is being eaten by Mathman and screen says Game Over, Stop the tape. Say: "What mistake was made?" Direct discussion to the error: 7 + 0 = 7, not 7 + 0 < 7. Say: "What does it mean to use the letter 'p' in this problem?" Collect students' ideas and record them on the board. Bring one student to the board and say:

"Let's see what Maria and Buster have to say about our list of ideas." To give students a specific responsibility while viewing, say: "As we watch the tape, my 'game show assistant' will underline all of the ideas we had about the mathematics in the Mathman Game that we see Maria and Buster discuss."

RESUME tape and verify the ideas generated by the class. PLAY video to the end of the segment and STOP tape.

Say: "It is fun to practice math skills using a game format. Now it is your turn to make a game for another student in this class that will help him/her practice the concepts we learning in our lesson, Zero Is Our Hero! On the back of your Math-Mat, make a game that uses the concepts we have just learned. You can use one of the games from our video, or you can make one up on your own. Include the rules of the game and make it an exciting adventure!" Provide students with rulers, markers, and other materials that will help them create a "Positive and Negative Game" on the back of their Math-Mat. When finished, have students exchange game boards and play this newly created game.

From a list of several mathematics topics already studied, have students select one and create a Math-Mat for other students in the school. The Math-Mat should include games, applications, history, and other activities that would help other students better understand a concept.

Select an educational video program that is appropriate for a younger audience. Show the video to the class and have them make a Math-Mat to accompany the video. Share the video and the Math-Mat with a math class at a nearby elementary school.

Have students research the activities used by breakfast cereal companies on the back of cereal boxes. Each student should design his/her own cereal box activity that uses mathematics or science topics. Include these designs in the Parent Newsletter and encourage parents to tape these creations to the back of the cereal boxes at home.

Science

Using Internet, collect weather data for several days and try to predict the weather for the next few weeks. Include temperature differences.

Compare the Fahrenheit thermometer to the Celsius thermometer. Convert one temperature F to an equivalent temperature C. When are the numerical temperatures the same?

List as many symbols as you can find which meteorologists use when making a weather map. Explain what each symbol stands for. Now list as many mathematics symbols as you can and explain what they represent.


Mathematics

Using your pennies and/or a calculator, explore the rules for subtracting, multiplying, and dividing positive and negative numbers.

Research the famous mathematician, Rene Descartes, and share his mathematical contributions (in spite of the fact that he refused to use negative numbers!)

Many number systems did not use the concept of zero. Explore the Roman Numeral System, one that did not have a symbol for zero.

Explain what is meant by using zero as a 'place holder.'

Language Arts

Write a poem or rap song that will help other students remember the rules you discovered for adding positive and negative numbers.

Art

Find out what is meant by 'negative space' in a drawing or painting. Compare that idea to the mathematical idea of a negative number.

Computers

There are many good software products to help students practice skills using positive and negative numbers. If you have access, give students time to practice their new skill using a good software product.

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Resources:

Historical Topics for the Mathematics Classroom, National Council of Teachers of Mathematics, 1989.

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