Prep for Teachers
Create envelopes containing one die and two game pieces for each pair of students in your class. Create copies of the Game Board, and the Game Rules and Score Sheet. Bookmark all Web sites used in the lesson on each computer in your classroom, and cue the video to the appropriate starting point. When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.
Announce to the class that they are going to play a game. Teachers should decide beforehand appropriate prizes for winners. Break the class into pairs. To each pair, distribute the Game Rules and Score Sheet organizer, one Game Board organizer, a ruler, and a packet containing a die and two pennies.
Read and discuss the game rules with the class, making certain they are understood. Game rules include:
Each game has two players. Both players will use their game pieces to mark where they land after each roll (if using pennies, one player will use a penny face up, the other face down to distinguish them).
Place the game pieces on the "0" (start) space over the player number of their choice.
Take turns rolling the die. Alternate who goes first. Players move their game piece according to the number on the die. Even number rolls move up, odd number move down.
Both players start with 20 points.
A game ends when one player goes off the game board either above start or below start.
If a player goes off the game board above start, that person adds ten points plus the number on the die to their total score.
If a player goes off the game board below start, nothing is added to the player's score. The other player adds the point total of their space to their total score.
A player wins when their point total is 100 or greater.
Note: There are several ways to play the game. The directions above have students play until someone goes off the high and low part of the board. This method can be time consuming. To shorten the length of the game, you can fix the number of rolls each student is allowed to take. For instance, each player takes 10 rolls and writes down where they are. This is the number of points they receive for that game, and then they compute their total score. If they go off the top or bottom, they get a bonus of, say 10 points, and the opponent gets no score for that game.
Give the class a signal to start playing the game. After ten minutes, stop the games and ask each pair how many games they have played. (Answers will vary) Ask each group the number of moves played in their shortest games. (One) Ask what caused such a short game. (The first player rolls an odd number on the first roll of the dice. This causes the player's penny to go off the board below the start space.) Ask students to consider a change to the game board that prevents a player from losing on their first throw of the die. (Extend the game board below start the same number of spaces as above start.) Ask your student if they extend the game board below start, how will they label it so that it is different than the spaces above start? (Entertain various ideas.) Introduce the idea of placing a negative sign in front of the number less than zero. (-3). They could place a positive sign to indicate numbers greater than zero (+3) or they could just put no sign (3). Draw a number line on the board and say a number. Have students point to the position of the number on the number line. Write a number on the board and have students' say it orally, (-4 is said, "negative 4." 5 is said, "five" or "positive 5") then point to the position. (Point out that zero has no sign and is said, "zero.")
Give students another game board with the lines marked below the start space with the start/0 indicated. Have students write the numbers in the given places.
After students add spaces to the board, let them continue playing the game. Stop them when another ten minutes is up. Ask students how many games each pair has played. (Answers will vary.) Ask them if the games were longer this time. (The games should be longer and more interesting.) Ask them why they played fewer and longer games. (By extending the game board below start, there were more spaces on the game board, and more room for play.)
Tell students to look at the game board from start space to the end that added points. Ask students what mathematical figure it could represent? (A number line from 0 to 10.) Tell students that by extending our game board to include numbers less than zero, our number line has been expanded. We will have to give that part of our new number line a name. Tell students that they will now investigate how the Cyberchase kids handled a similar problem.
Explain to your students that they will be examining the concept of "below zero" or "less than zero" using a video clip from the PBS series Cyberchase. There's a new problem in Cyberspace. Hacker has taken the Cybercouncil hostage, threatening to scramble each of the council member's cyber sites unless they declare him ultimate ruler of Cyberspace. The council is being held in the Cyber Grand Tower by Buzz and Delete while Hacker is recharging. The Cyberchase crew's mission is to rescue the council for Motherboard.
CUE the tape to where the Cyberchase crew exits the Tower. Provide students with a FOCUS FOR MEDIA INTERACTION, asking students to determine out how the crew located the 18th floor. PLAY the tape. STOP when Matt labels the second floor. Ask students how the kids located the 18th floor. (They numbered the floors, making a huge ruler.) Ask your students how the kids got to the various floors? (They used a window washer platform.) Why did they have to use it? (The elevators were jammed and the stairways were locked.)
FAST FORWARD the tape to where Matt says "Ladies and gentlemen, I present to you the 18th floor." Provide a FOCUS FOR MEDIA INTERACTION asking the class to explain why the crew missed the right floor? PLAY the tape. STOP when Matt says "We're back in business." Ask the class why the crew missed the right floor? (They started at one rather than zero.) Ask students what point value the start space had in the game? (Zero) Is zero a number? (Yes. It has a definite location on the number line like every other number.) How did the Cyberchase team correct their mistake? (They renumbered the floors starting with zero.)
Tell your students that Buzz and Delete drag the Cybercouncil all over the Tower, which causes the crew to miss the right floor again. Motherboard receives a locator signal from Dr. Marbles, and she contacts the crew to tell them where to move next. FAST FORWARD the tape to where Dr. Marbles shows his locator and says, "I hope Motherboard picks up my signal."
Provide a FOCUS FOR MEDIA INTERACTION asking students what did the crew use to simplify the up and down movements. PLAY the tape. PAUSE when Jackie remarks after Inez uses the number line "...down three more levels." Ask your students how the crew simplified the up and down movements. (Inez drew a number line.) Was the crew able to complete all of Motherboard's movements? (No.) Why? (The last movement takes them to zero and they cannot go down any more.)
Provide students with a FOCUS FOR MEDIA INTERACTION, asking the class to determine what changes Inez makes to the number line to locate the Cybercouncil? PLAY the tape from the previous pause point and PAUSE when Digit says "Negative numbers are less than zero." Ask your students how Inez changed the number line, and how the Cyberchase team's solution relates to making the penny game last longer? (Inez extended the number line to include those numbers less than zero, and students extended the game board to include numbers less than zero.) How did Inez show the difference between those numbers above zero and below zero? (She used a negative sign in front of the numbers below zero.) What did she call these numbers? (Negative.) What statement did Digit make about the negative numbers? (Negative numbers are less than zero.)
Provide students with a FOCUS FOR MEDIA INTERACTION, asking students to name the floor Jackie says the council was on when she used the number line. PLAY the tape and STOP when Matt says, "Let's go." Ask students what floor Jackie thinks the council was on. (-3)
FAST FORWARD the tape to where Motherboard says "Sorry, they moved again." Provide a FOCUS FOR MEDIA INTERACTION asking students to describe Digit's mistake when moving to level negative five. PLAY the tape. STOP when Digit says "Now they're going to get it." (Digit moved up rather than down, thinking that -5 was greater than -3.)
What did Inez say about negative five and negative three? (Negative five is less than negative three.) How did Jackie show Digit that negative five was less than negative three? (Using the number line she explained that negative numbers get smaller the further you go below zero.)
Ask your students if - 8 is less than - 1? (Yes) Why? (Because -8 is further below zero on the number line than -1.) Ask students if - 9 is less than 0? (Yes) Why? (- 9 is way below zero.)
In what direction did the crew move to locate the council? (Down two floors.)
FAST FORWARD to the beginning of the "Cyberchase For Real" epilogue. Provide a FOCUS FOR MEDIA INTERACTION asking students to determine what Harry's problem is. PLAY the tape. PAUSE when Harry says, "It's the one sport I haven't practiced." Ask your students what Harry's problem is. (Harry needs a score of 50 points to qualify for the team. He's good at some sports, but stinks at others. Harry is afraid that some of his sport totals will cause him to have a negative total, making 50 points difficult to achieve. Bowling is a sport that he didn't practice.) Ask your students if Harry scores negative 20, how many points will he need to get to zero? (20)
Provide a FOCUS FOR MEDIA INTERACTION by asking what Harry's score is after skating. START the tape and PAUSE when Harry says, "I'm going to have to kick it up a notch just to get to zero." What is Harry's score after skating? (-10) Ask your students how many points he needs to get to zero? (10) How many points does he need to get to 50? (60) Ask your students to explain why he needs 60 points to reach his goal of fifty points. (Ten points will get him out of the negative score to zero. Then he needs fifty additional points to get to fifty. Ten points plus fifty points equals sixty total points.)
Provide a FOCUS FOR MEDIA INTERACTION by asking how many points Harry had after gymnastics. START the tape and PAUSE when you see Harry with a bowling ball saying "Ok, I'm ready." How many points did Harry have after gymnastics? (10) Ask your students if they think all the judge's scores were fair? Why? (Answers will vary. The first judge gives Harry a -20 for a sloppy landing, even though he did all the routines on the bar.) Ask your students how many more points does Harry need to reach his goal of fifty points? (40)
Ask your students if they think Harry will make it based on what you have seen of his sport talents? (Answers will vary.) Provide a FOCUS FOR MEDIA INTERACTION asking students to view the tape and see if Harry makes the team. START the tape and STOP after the judge says to Harry, "We want you to try again next time." Did Harry make the team? (No, he had 40 points instead of the 50 he needed. He needed 10 more points.) Why did the judge invite Harry back next time? (He made a good comeback.)
Ask students to summarize what they have learned. (The number line can be extended to include numbers less than zero. Numbers less than zero are called negative numbers and they use a negative sign to make them different from numbers greater than zero.
Ask your students to log on to Space Coupe activity on the Cyberchase Web site at http://pbskids.org/cyberchase/games/negativenumbers/index.html. Ask students to read the scenario for the activity. What is their task in the game? To win the game, students must fly the space coupe above and below sea level to destroy all of Hacker's virus pods. To move the coupe, students must type in positive and negative numbers, positive for up, negative for down. Provide a FOCUS FOR MEDIA INTERACTION, asking students to complete the activity, using their knowledge of the number line to shoot down as many virus pods as possible. As students advance to the next level, time is will be shortened by one minute and the number of pods will increase by one.
After students have completed a few rounds of the activity, ask students how they calculated the distance between the virus pods and the coupe. (By counting the total number of spaces from the coupe to the virus pod.) How did they determine whether the number was positive or negative (The number was positive if they wanted the coupe to go up on the number line, and negative if they wanted the coupe to go down.) What does this activity teach us about positive and negative numbers? (This activity teaches them that positive and negative numbers tell us direction and distance; that the number line is made up of positive and negative numbers, and zero.) [Note: It is only the sum of the distances between the numbers if one number is positive and one is negative. It does not work for numbers having the same sign.]
Have students look at a map and find locations that are below sea level. Also, have them find the highest point in each state of the United States.
Have students look up the highest and lowest temperatures of each state of the United States.
- Invite a banker or accountant to discuss how positive and negative numbers are used in dealing with money.
- Invite a member of municipal government to discuss emergency plans for days large movements of temperature up or down are anticipated.