# Designing Cell Phone Games. An 8th-grade unit on linear functions

Size: px
Start display at page:

## Transcription

1 Designing Cell Phone Games An 8th-grade unit on linear functions

2 Designing Cell Phone Games Copyright 2006 by SRI International. This material is based upon work supported by the National Science Foundation (NSF ). Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. The project is a collaboration among Center for Technology in Learning SRI International Principal Investigator: Jeremy Roschelle The Charles A. Dana Center at the University of Texas, Austin Co-Principal Investigator: Bill Hopkins University of Massachusetts, Dartmouth Co-Principal Investigator: Stephen Hegedus The University of Texas at Austin Co-Principal Investigator: Susan Empson Virginia Polytechnic Institute and State University Co-Principal Investigator: Deborah Tatar Writing and Editing: Jennifer Knudsen, Ken Rafanan, Phil Vahey, Gucci Estrella Editing and Document Management: Ken Rafanan, Gucci Estrella, Rebecca Moniz, Meredith Ittner Design: Ken Rafanan, Lynne Peck Theis Editorial Advice: Jeremy Roschelle, Deborah Tatar, Bill Hopkins, Jim Kaput This unit is inspired by and based on the work and ideas of Jim Kaput.

3 Working at TexStar Games Welcome to the headquarters of TexStar Games, Inc. We make games for cell phones teens love them! Other game design companies are cutting into our business so we need to make improvements. That s why you have been hired. To make TexStar Games more competitive you will Use mathematics to analyze our game designs; for example, determine how to make characters move across the screen. Analyze our business. This will require a lot of mathematics. Now s the time to learn it! With the materials in this book, you will learn about functions, both proportional and nonproportional. You will also learn the real truth about average rates. And you will understand the connections between tables, graphs, and algebraic expressions. Don t worry, it will all be clear by the time you are done! All this math will help us in our business, but you will also use it in later math classes and in your life. Keep that in mind as we move ahead. Designing Cell Phone Games 1

4 Cell Phone Games and Design A few facts about cell phone game design will help you in this unit. Electronic games on cell phones, on consoles, on computers all must be designed (created) by a team of people. The team works together, but there are different jobs to do. Designers come up with ideas for games and rules for how the game will work. A designer must think about how realistic the game is and what rules will make the game fun and just difficult enough. Math is used in doing this. Programmers take the ideas and turn them into games. They use mathematics and logic to write programs. Artists make the images you see on the phone as you play. They must use math to think about how big to make the images on the screen and how much room their art will take up. Business staff make sure the business is running smoothly. They are in charge of things like employee salaries and tracking how much money the company is saving and spending. Cell phone designers, programmers, and artists get paid for their work in different ways. Sometimes all these people work for a company like TexStar Games, and they get a paycheck every month. Other times, the programmers, designers, and artists work on their own and get paid for each piece of work they do. The cell phone business is growing, and it s likely that more designers, programmers and artists will be needed in the future. Knowing math helps. 2 Designing Cell Phone Games

5 Yari, The Yellow School Bus TexStar Games is working with a traditional windup toy company to design new games for younger kids. We need to analyze the motion of the real toy. Then we can make our cell phone version. Our partner s best selling toy is Yari, The Yellow School Bus. 1. Watch the movie of the actual windup toy Yari, The Yellow School Bus moving along a centimeter ruler. Open the file Yari.swf. Run it several times. Answer the following: A. How many centimeters (cm) did Yari travel? B. How many seconds did Yari travel? Explain Each time you give a number answer, explain how you know. C. Using A & B, calculate Yari s speed (how fast Yari traveled) for this trip. D. Explain how your answers for A, B, and C are related. 2A. In the movie, when did Yari go fastest? (circle your answer.) Beginning Middle End 2B. In the movie, when did Yari go slowest? (circle your answer.) Beginning Middle End 3. Using the movie and stop action, fill in the table and make the graph. seconds 1 cm Designing Cell Phone Games 3

6 Our First Cell Phone Game Our programmer has made our first cell phone game. It has a picture of Rita, The Red School Bus, which is used in the game. We want to compare the motion of the classic windup toy Yari to our character in the cell phone game named Rita, The Red School Bus. 1. Open the Java MathWorlds file named FirstGame1.smw. Use the play button to watch the trip of the character in the simulation and the graph. Run the simulation as many times as you need to answer the following. A. How many centimeters (cm) did Rita travel? B. How many seconds did Rita travel? C. What was the Rita s speed? 2. Using step and play, watch how the graph builds as the character moves. Explain how the graph and the simulation are related. 3. Complete the table below: seconds 1 cm Designing Cell Phone Games

7 4. Describe how A. the trips of the cell phone character and the real windup toy are the same. B. the trips of the cell phone character and the real windup toy are different. For Your Information In mathematics, we often simplify things so that we can work with them. Two ways we simplify are using averages and creating models. Rita is a model of the classic windup toy, Yari. The cell phone game character is a model of the real windup toy. It simplifies the motion of the windup toy. Models always simplify the real thing in some ways. Designing Cell Phone Games 5

8 Controlling Characters with Graphs: Texas Road Rally We need to set up the mathematics controllers for the new game, Texas Road Rally. We can use graphs to control motion. Remember: we ll make the game cool later! In road rally races, cars compete as they travel from town to town. For Your Information Graphs, tables and equations are mathematical representations. Each can show the same motion in a different way. 1. Open Roadrally1.smw. It shows the Yellow Rose team car in the Texas Road Rally. The car starts in El Paso and stops in Big Spring. Run the file, watching the simulation and graph. A. When the car stops, how far has it traveled and how much time has passed? B. When the car has traveled for one hour, how far has it gone? C. How fast is this car going? Explain how you know in two ways. Think about your answers to A and B or use other ideas. D. Change the speed of the car using the graph window. It still must start in El Paso and stop in Big Spring. Use the same ideas to find the new speed. What is the new speed? 6 Designing Cell Phone Games

9 2. Open but DO NOT RUN Roadrally2.smw. It shows graphs of the Yellow Rose team car and the Longhorn team car ready to travel from San Antonio to Beaumont. A. Sketch the graph of the two cars trips on the same axes and fill in the boxes. Speed of Each Car Fastest Car B. Use the graph window to change the speed of each car so that the other car is faster this time. Now fill in the same information as in A. Speed of Each Car Fastest Car C. By looking at the position/time graphs of two cars in a rally, how can you predict which one will win? D. Explain how the cars speeds and their graph lines are related to one another. Designing Cell Phone Games 7

10 3. Below are ideas to use in other games. Please help our programmers by drawing graphs on the axes provided. Test out your graph using Roadrallytest3.smw. Make up your own characters for the Green Iguana and Blue Sky team cars. Note: There is more than one way to draw the graph for most of these. A. Draw a graph of a race in which the Green Iguana and Blue Sky team cars start at the same position and travel the same distance but at different speeds. B. Draw a graph of a race in which the two characters start at the same position and travel the same amount of time, but Green Iguana is faster than Blue Sky. 8 Designing Cell Phone Games

11 C. Draw a graph of a race in which the two characters start at the same position and travel the same distance, but Blue Sky finishes two hours before Green Iguana. D. Draw a graph of a race in which Green Iguana starts at the starting line (0 miles), and Blue Sky starts 50 miles ahead (50 miles). The two characters finish at the same position and the same time. E. Draw a graph of a race in which Green Iguana starts at the starting line and Blue Sky starts 50 miles ahead. The two characters travel at the same speed and travel the same distance. Designing Cell Phone Games 9

12 Controlling Characters with Equations So far, our graphs of moving characters have shown the relationship between time and position where the character is at what time. Equations show that same relationship with numbers and symbols. This means: give us any time, and we can find the position of the character at that time. We need to be able to control our characters with graphs as well as equations (also called algebraic expressions). The equations are so efficient! Let s work on a game with robots. We need to set up the mathematics to make our robot move at different speeds. 1. Open Shakey.smw, which shows Shakey the Robot. A. Run the simulation. How fast is Shakey going? How do you know? 10 Designing Cell Phone Games

13 B. Look at the table, the graph, and the algebraic expression window. Record the graph, table, and equation below. Graph Table Equation x (seconds) y (cm) C. To answer these questions, run the Shakey.smw file using step as much as you need to. How is time represented in the table? In the equation? How is position represented in the table? In the equation? How is speed represented in the table? In the equation? Designing Cell Phone Games 11

14 D. Change the graph so that Shakey moves slowly. Write down the table and equation for each graph. Then make Shakey move fast and write down the new information. Slow Shakey Graph Table Equation x (seconds) y (cm) Fast Shakey Graph Table Equation x (seconds) y (cm) E. Describe how to write an equation if you have the table and graph that go with it. Use the tables, graphs, and equations above to help you. If you are not sure yet, just make your best guess. 12 Designing Cell Phone Games

15 2. Let s try another way to learn how to write equations from tables. No more algebra and table windows to help! Open Roberta.smw. Variables and Letters Here we use t and p as the variables in our equations instead of x and y. A. First, fill in the p column in the table below. Fill in the mathematical rule to get p, when you know t. Roberta t (time in seconds) Rule to get p p (position in cm) st: Describe the pattern in the time column. 2nd: Describe the pattern in the position column. 3rd: Use those patterns to find the relationship that connects the time and the position in each row t p B. For every second that Roberta travels, how many centimeters does the robot move? At what rate does Roberta move? How does this rate relate to your rule? Describe the pattern in the position column. Use those patterns to find the relationship that connects the time and the position in each row. C. Write the equation that will work for any row that could be in the table. Designing Cell Phone Games 13

16 3. Open Gliderhal.smw. Go through the same steps as in Question 2 to find the equation for these two robots motion. Glider t (time in seconds) Rule to get p p (position in cm) st: Describe the pattern in the time column. 2nd: Describe the pattern in the position column. 3rd: Use those patterns to find the relationship that connects the time and the position in each row. Equation: t p Hal t (time in seconds) Rule to get p p (position in cm) st: Describe the pattern in the time column. 2nd: Describe the pattern in the position column. 3rd: Use those patterns to find the relationship that connects the time and the position in each row. 10 t p Equation: 4. Explain, in your own words, how to use a table to find an equation that represents a character s motion. 14 Designing Cell Phone Games

17 5. Use what you have learned to help Monica figure out the relationship between her salary and the time (number of months) she works. Monica is one of TexStar s best programmers. Every month, she earns a salary of \$8,200. The programming team took the weekend off they only left us a blank table to use. So, you have to do most of the work this time. Make a representation (graph, table, or equation) so that she can choose any month (where January is month 1) and find out how much she has earned so far that year. Equation: Months \$ earned Designing Cell Phone Games 15

18 One to Another You have seen how graphs, equations and tables can each represent a character moving at a certain speed. Now complete all the representations for each speed or rate. The axes of each graph are labeled for you. You can use any variable when writing equations. In Controlling Characters with Equations, we used t for time and p for position. In most, we used x and y. Name your own variable for each situation below. Just make sure that you use the same variables in your table and equation. Example: Gonzalo runs at a constant speed of 2 meters every second. Table Graph Equation _x y (seconds) (meters) 0 0 y =2 x A toy robot moves on average 4 centimeters every 2 seconds. Table Graph Equation (seconds) (cm) Designing Cell Phone Games

19 2. A sloth moves on average meters every second. Table Graph Equation (seconds) (m) 0 0 p =.5 t An Australian Tiger Beetle runs on average 2.5 meters every seconds. Table Graph Equation (seconds) (m) Designing Cell Phone Games 17

20 4. Instead of speed or rate of motion we can make the same representations for other rates, such as money earned per month. A. Sergei, a beginning game designer at our company, earns an average of \$5,000 per month. Table Graph Equation (months) (\$) B. In a quiz game, players get points for every correct answer. Table Graph Equation (correct (points) answers) 0 0 p =3 a Designing Cell Phone Games

21 5. A toy car moves meters every second. Table Graph Equation (seconds) (m) A helicopter flies up into the sky at 5 meters per second. Table Graph Equation (seconds) (m) Designing Cell Phone Games 19

22 Better Games We need to make mathematical controls for Reynaldo, Bommakanti, and Geneva, who will be used in a retro arcade game for cell phones. The equations are more complicated because these characters all start at different places. Open Better1.smw. 1. Run the simulation. Predict what the graph will look like for each character s motion, by sketching three lines on the axes below. Don t forget to label your lines. 2. Now open the graph window. Run the file several times. Pay attention to the graph and the simulation and how they work together. A. Was your prediction right? Explain why or why not. B. Where did each character begin its motion? How does the graph represent this? C. What is the speed of each character? Which character was fastest? Which character was second fastest? Which character was slowest? D. How did you know which character was fastest? 20 Designing Cell Phone Games

23 3. You can find the equations for these characters movements, using the method we learned in Controlling Characters with Equations. A. Let s start with Reynaldo. We want to find the mathematical rule to get p, when you know t. 1st: Describe the pattern in the time column. 2nd: Describe the pattern in the position column. t (time in seconds) Rule to get p p (position in cm) rd: Use those patterns to find the relationship that connects the time and the position in each row. Equation: t p B. For every second that Reynaldo travels, how many centimeters does he move? How does this relate to your rule? C. Write the equation that will work for any row that could be in the table. The equation for finding p when you know t is: p = t + 5 Designing Cell Phone Games 21

24 D. Write the three steps from question 3C in your own words. Use the same steps for Geneva and Bommakanti to find equations for their motions. Geneva t (time in seconds) Rule to get p p (position in cm) st: 2nd: rd: 5 10 t p Equation: Bommakanti t (time in seconds) Rule to get p p (position in cm) 1st: nd: rd: 5 10 t p Equation: 22 Designing Cell Phone Games

25 4. For A D below, use math to describe the motion for one character only. Do the following: Decide on a start position and speed for your character. Fill in the equation that will go with it. Sketch the graph that will go with it and label your axes. Use the file, Better4.smw, to see if you were right. If you were not right, correct your equation. A. Start position: Speed: Equation: B. Start position: Speed: Equation: C. Start position: Speed: Equation: D. Start position: Speed: Equation: Designing Cell Phone Games 23

26 Wendella s Journey: Moving At Different Speeds In our game, Lost in the Pines, Wendella the dog makes many journeys through the magical Lost Pines Woods. On her journeys, Wendella moves Forward slowly when she is in the swamp. Forward faster when she is on the road. Wendella stops and barks for help when she is in quicksand. We need many journeys and stories to use in our game. Help us set up the math and tell the story for each journey. Your work is very important. Remember you are doing the math that will make the game work. 1. Open BUT DO NOT RUN the file for Wendella s first journey, Wendella1.smw. Using the graph for this journey, predict how Wendella will travel. Finish the story below. Wendella started out fast on the road. She was happy to be on her journey. Then 24 Designing Cell Phone Games

27 2. Here is a different journey that Wendella took. A. Mark on the graph below, show when Wendella was in the swamp, in the quicksand, and on the road. Mark the times on the minutes axis. B. For each line segment in the graph above, find the number of minutes Wendella traveled, the number of meters she traveled, and her speed. You can make a table to keep it all organized. C. Choose one line segment in the graph not the first one and explain how you found Wendella s speed for that segment. Designing Cell Phone Games 25

28 3. Open the file Wendella3.smw for the third journey. The graph is also shown below. A. Run the file. Wendella does something new here! Write a story to go with Wendella s journey. B. What did Wendella do 6 minutes after starting this journey? C. How does the graph show this motion? D. What is her speed between 6 and 8 minutes? 26 Designing Cell Phone Games

29 4. Open the file Wendella4.smw, and do the following. A. Change the graph so that Wendella goes forward and backward at least twice in her journey. Run the graph to make sure it works. B. Record your graph on the axes provided. C. Write a story to go with this Wendella journey. D. One of the programmers doesn t understand what is happening in the graph. Explain how to use the graph to get Wendella to go backward in her journey. Designing Cell Phone Games 27

30 5. We need more journeys and stories. Using Wendella5.smw, make your own graph showing Wendella s next journey. Sketch the graph on the axes. Write a story to match your graph. Story: 28 Designing Cell Phone Games

31 Money Matters We re glad you helped us with some great designs for our cell phone games. But TexStar Games has to make money too! Please help us with some business problems. 1. We keep a record of how much money we have in the bank. When we make money, we add it to our bank account. When we spend money, we take it out of our bank account. The amount of money (in \$) that we have in the bank on any day is called our bank account balance. On the last day of each month, we check our bank account balance and we graph it, comparing month to balance. Help us understand what happened to our bank account this year. A. Open the file Bankaccount.smw, which shows our bank account balance over the past year. Run the simulation to see how the bank account balance changed from month to month. Using the graph, simulation, and tables, answer the questions below. Fill in the graph below. Designing Cell Phone Games 29

32 Find the following and explain how you know (from the graph, table, or simulation). Beginning balance. Ending balance. Months in which our balance increased. Months in which our balance decreased. Month with highest increase in balance. Months during which the balance did not change at all. Month in which the balance was the highest. B. Write a sentence or two that describes what happened to our bank account balance over the year. Make up your own explanations for what might have happened. For example: The balance decreased between January and February. This is because we had to pay for a lot of artwork for a new game. C. Our goal was to have \$60,000 in our bank account by the end of the year. By how much did we miss our goal? 30 Designing Cell Phone Games

33 D. Our goal for next year is to end the year with \$110,000 in our bank account. We would like to put the same amount of money in the bank each month. Complete the graph below to show this. E. Use the graph you made to answer the following questions. How much money do we need to put in the bank each month to reach our goal? How can we predict what our balance will be each month? Designing Cell Phone Games 31

34 2. We have two new games, Texas Road Rally and Planet Eaters. Next month, we want to start selling just one of them. To help us decide which one to sell, we let kids in the Electronic Gaming Afterschool Club use our games for 14 days. At the end of each day, we graphed the total number of times each game had been played altogether. A. About how many times had each game been played after 1 day? 4 days? 10 days? 14 days? B. Compare the kids use of the two games over the 14 days. C. We care about selling games kids really like to play. Using the information in the graph, advise us: Which game should we start selling next month? Make your own decision, and defend it with mathematics. (There is no one right answer.) 32 Designing Cell Phone Games

35 Mathematically Speaking: Graphs to know In order to understand graphs, it helps to know some by sight. Sketch a graph for each of the following movements. Use what you learned in the Wendella game and the Bank Account activity to think about these more general situations. An object moving, then speeding up. A bank account with its amount increasing and then increasing at a higher rate. An object moving forward, then moving the backward. A bank account s money increasing and then decreasing. An object standing still (not moving). A bank account whose amount is not changing. Designing Cell Phone Games 33

36 Crab Velocity In our other games, characters can move forward and backward, or up and down. We already know how to calculate their speed. But there s a bit more to it than that. Help us learn how to use velocity in our games. Velocity? It s just speed but with direction! + (positive) for up or forward - (negative) for down or backward Our crab characters, Karla and Lenny, move up and down above the water (on the rocks) and below it. The water level is at 0 meters. Positive positions are above the water line. Negative positions are below the water line. 1. Open the file Crab1.smw, run the simulation, and find Karla s speed: Lenny s speed: Karla s velocity: Lenny s velocity: 34 Designing Cell Phone Games

37 2. Open file Crab2.smw. The graph shows the motion of Lenny, Karla and their children Dolores, Antonia, and Orlando. A. Find the velocity of each crab in the family. Karla: Lenny: Dolores: Antonia: Orlando: B. Using what you already learned, write the equation for Antonia s motion. C. Predict the equation for Dolores motion. Use the algebraic expression window to see if you are right. D. Compare the equations for Antonia s and Dolores motions. Designing Cell Phone Games 35

38 3. Using Crab3.smw, make a graph for each situation below. Then, sketch the graph and write an equation for your graph. Remember, the water level is at position Designing Cell Phone Games

39 4. Open TemperatureGauge4.smw. The graph shows the temperature inside TexStar Games supercomputer used for running simulations. Zane, our supercomputer technician, can t run a simulation unless the computer s temperature is at least 30 degrees below freezing (-30 degrees Celsius). A. Find the speed of the temperature change in the supercomputer. B. Find the velocity of the temperature change in the supercomputer. C. If the temperature inside the computer starts at 0 degrees Celsius and the rate of temperature change stays the same, how long must Zane cool the computer before he can run a simulation? You can change the graph to help you, but you must keep the rate of temperature change the same. Explain how you got your answer: D. Change the graph so that the starting temperature is 20 degrees Celsius. If the rate of temperature change stays the same, how long must Zane cool the computer before he can run a simulation? Explain how you got your answer: Designing Cell Phone Games 37

40 Wolf and Red Riding Hood We need you to test a new game based on the fairy tale, Red Riding Hood. In this game, Red Riding Hood (RRH) and the Wolf start from Home and move toward Grandma s House. RRH moves at two velocities during the journey. The Wolf moves at the same velocity the whole time. The Wolf must arrive at Grandma s House at exactly the same time as RRH. Then he can devour her. Help us find the trick so that the Wolf always arrives at exactly the same time as RRH. 1. Open Wolf1.smw. Use the graph to: A. Describe RRH s trip to Grandma s. Include how long it took her to get there and estimates of her two velocities. B. Predict the Wolf s velocity so that he and RRH meet at Grandma s, at exactly the same time. C. Test your prediction by changing the Wolf s graph and running the simulation. Were you right? Why or why not? Revise until you get it right. 38 Designing Cell Phone Games

41 2. The next round of the game is Wolf2.smw. Again, there are two velocities for RRH, we need to find the one for the Wolf to catch her at Grandma s House. A. Use the graph to find the Wolf s velocity. What is the Wolf s velocity? B. Explain how to use graphs to find the Wolf s velocity, when you have a graph of RRH s journey. 3. Use Wolf3.smw to predict the Wolf s velocity with an equation. A. Using the algebraic expression window, predict the Wolf s velocity, check and revise until you get it right. What is the Wolf s velocity? B. Explain how to use equations to find the Wolf s velocity, when you have an animation of RRH s journey. 4. We can use graphs or equations to find the Wolf s velocity. Explain the advantages and disadvantages of each. Designing Cell Phone Games 39

42 Secrets of Average Rate Revealed We need to use averages a lot in our work. You ve already learned about averages in math class. And, you know something about them in real life. Use what you already know to find out more about average rate. 1. When playing a game Robots Gone Awry, Deborah gets scores of 70, 87, and 99. Use what you learned in math class to find her average, or mean score. Explain how you did it. 2. Some game designers get paid for each game they make, charging different amounts for different games. In January, the designer, Sandro, sold 3 different games. Name of the Game Charge for the Game Lost in the Pines \$10,000 Robots Gone Awry \$20,000 Texas Road Rally \$6,000 A. What was total amount of money Sandro was paid in January from selling these games? B. Sandro would like to charge the same amount for each game. What would he have to charge for each game, in order to make the same total amount of money for January? C. What s the average rate (in dollars per game) that Sandro was paid, in January? Explain how you know, in two different ways. 40 Designing Cell Phone Games

43 3. Speed and velocity are rates, too. Red Riding Hood and the Wolf can help us think about average rate, using graphs. RRH s average rate is the single rate at which she could make the same journey in the same amount of time. A. You ve seen these graphs before. Each graph shows RRH moving at two different rates. First, RRH moves at meters per minute for minutes. Then, she moves at meters per minute for minutes. Predict: What is her average rate, in meters per minute? (Hint: What was the Wolf s rate, in meters per minute?) First, RRH moves at meters per minute for minutes. Then, she moves at meters per minute for minutes. Predict: What is her average rate, in meters per minute? (Hint: What was the Wolf s rate, in meters per minute?) B. Look at the work you just did in Part A. In a sentence or two, explain the relationship between RRH s average rate and the Wolf s rate. Designing Cell Phone Games 41

44 Problem Solving We still have other problems to solve at TexStar Games! Use all you have learned to help us with the following problems. 1. Think back to Lost in the Pines. Help us analyze Wendella s journeys and average rate. A. What is Wendella s average rate of motion (her average speed) on this journey? B. What is Wendella s average rate of motion (her average speed) on this journey? C. Wendella went 100 meters through the swamp in 4 minutes, then 350 meters on the road in 2 minutes. Using the graph to help you, what was her average rate, in meters per minute? 42 Designing Cell Phone Games

45 2. Marissa has worked for TexStar Games for 5 years. For the first 2 years, her salary was \$50,000 per year. Then she got a big raise. For the last 3 years, her salary has been \$70,000 per year. Marissa says, So my average yearly salary for these 5 years has been \$60,000. Her supervisor, Tanya, disagrees, Actually, Marissa s average salary has been \$62,000. The \$2,000 difference matters to them! Explain who is right and why (use the graph if it helps you). Designing Cell Phone Games 43

### Slow. Bicycle. Race. Thomas Jefferson National Accelerator Facility - Office of Science Education

Slow Bicycle Race http://educationjlaborg/ Slow Bicycle Race How slowly can you ride a bike without touching the ground? Fill in the names of your teammates on the Slow Bicycle Race Data Chart on the next

### Motion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph.

Motion Graphs It is said that a picture is worth a thousand words. The same can be said for a graph. Once you learn to read the graphs of the motion of objects, you can tell at a glance if the object in

### Lesson 19: Comparison Shopping Unit Price and Related Measurement Conversions

Comparison Shopping Unit Price and Related Measurement Conversions Student Outcomes Students solve problems by analyzing different unit rates given in tables, equations, and graphs. Materials Matching

### UNIT PLAN: EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT PLAN: EXPONENTIAL AND LOGARITHMIC FUNCTIONS Summary: This unit plan covers the basics of exponential and logarithmic functions in about 6 days of class. It is intended for an Algebra II class. The

### Use a 1/2 inch graph paper to make a multiplication matrix and allow youngsters to take turns identifying all the multiples of a target digit.

Multiplication and Division The accompanying games and activities are presented sequenced from basic to more challenging. Multiplication games are in the left hand column, division in the right with various

### not think the same. So, the consumer, at the end, is the one that decides if a game is fun or not. Whether a game is a good game.

MR CHU: Thank you. I would like to start off by thanking the Central Policy Unit for the invitation. I was originally from Hong Kong, I left Hong Kong when I was 14 years old, it is good to come back with

### Would You Like To Earn \$1000 s With The Click Of A Button?

Would You Like To Earn \$1000 s With The Click Of A Button? (Follow these easy step by step instructions and you will) This Version of the ebook is for all countries other than the USA. If you need the

### MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC

MOVIES, GAMBLING, SECRET CODES, JUST MATRIX MAGIC DR. LESZEK GAWARECKI 1. The Cartesian Coordinate System In the Cartesian system points are defined by giving their coordinates. Plot the following points:

### Tennessee Department of Education. Task: Sally s Car Loan

Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was \$15,. She made a down payment of \$43. She financed the remaining amount

### DIAMOND PROBLEMS 1.1.1

DIAMOND PROBLEMS 1.1.1 In every Diamond Problem, the product of the two side numbers (left and right) is the top number and their sum is the bottom number. Diamond Problems are an excellent way of practicing

### Summer Math for incoming Fifth Graders

Teresa walks her neighbors dogs on weekdays in the summer. Each neighbor pays her \$5.00 a week. In the next two weeks, Teresa wants to save her money to buy a new DVD. Fill in the bubbles in this graphic

### UNDERSTANDING YOUR ONLINE FOOTPRINTS: HOW TO PROTECT YOUR PERSONAL INFORMATION ON THE INTERNET

UNDERSTANDING YOUR ONLINE FOOTPRINTS: HOW TO PROTECT YOUR PERSONAL INFORMATION ON THE INTERNET SPEAKING NOTES FOR GRADES 4 TO 6 PRESENTATION SLIDE (1) Title Slide SLIDE (2) Key Points It can be really

### Granny s Balloon Trip

Granny s Balloon Trip This problem gives you the chance to: represent data using tables and graphs On her eightieth birthday, Sarah s granny went for a trip in a hot air balloon. This table shows the schedule

### Wheels Diameter / Distance Traveled

Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating

### Return on Investment (ROI)

ROI 1 Return on Investment (ROI) Prepared by Sarah Major What is ROI? Return on investment (ROI) is a measure that investigates the amount of additional profits produced due to a certain investment. Businesses

### Scratch Primary Lesson 4

Scratch Primary Lesson 4 Motion and Direction creativecomputerlab.com Motion and Direction In this session we re going to learn how to move a sprite. Go to http://scratch.mit.edu/ and start a new project:

### Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

### Objectives. Day Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7. Inventory 2,782 2,525 2,303 2,109 1,955 1,788 1,570

Activity 4 Objectives Use the CellSheet App to predict future trends based on average daily use Use a linear regression model to predict future trends Introduction Have you ever gone to buy a new CD or

### Physics Kinematics Model

Physics Kinematics Model I. Overview Active Physics introduces the concept of average velocity and average acceleration. This unit supplements Active Physics by addressing the concept of instantaneous

### a. In the table below, fill out the first two columns only with 8 possible combinations that will yield 20 pounds of fruit.

Name: Activity: The Bake Sale (Intro to Systems of Equations) 1. The student council is planning a bake sale to raise money for a local food pantry. They are going to be making apple and peach pies. They

### Fry Instant Word List

First 100 Instant Words the had out than of by many first and words then water a but them been to not these called in what so who is all some oil you were her sit that we would now it when make find he

### Math Matters: Why Do I Need To Know This?

Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Fourteen 1 Annuities Investment strategies Objective: To illustrate how knowing the

### Superstars Building Fry List Fluency

Sight Word Superstars Building Fry List Fluency By Jennifer Bates http://finallyinfirst.blogspot.com/ How I use this program I developed this program because I noticed many of my students were still trying

### Summer Math Packet. For Students Entering Grade 5 \$3.98. Student s Name 63 9 = Review and Practice of Fairfield Math Objectives and CMT Objectives

Summer Math Packet 63 9 = Green Yellow Green Orange Orange Yellow \$3.98 1 Green A B C D Red 8 1 2 3 4 5 Student s Name June 2013 Review and Practice of Fairfield Math Objectives and CMT Objectives 1 Summer

### PLANT TECHNICIAN SKILLS AND ABILITIES PRACTICE TEST

PLANT TECHNICIAN SKILLS AND ABILITIES PRACTICE TEST OVERVIEW Welcome to the Plant Technician Skills and Abilities Practice Test. The purpose of this Practice Test is to help you get used to the questions

### 2-1 Position, Displacement, and Distance

2-1 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:

### Learning OutcOmes \$250 never learned how to play. Key terms

Savings What do other high school students know about saving? We asked high school students to describe something they really wanted and thought they had to buy, only to realize later that they wasted

### Summer Math Exercises. For students who are entering. Pre-Calculus

Summer Math Eercises For students who are entering Pre-Calculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn

### Interpreting Distance-Time Graphs

CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Interpreting Distance- Graphs Mathematics Assessment Resource Service University of Nottingham & UC

### Final Word Problem Practice #1

Final Word Problem Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with

### THE ENVELOPE BUDGET The Easiest Budgeting Tool I Know By David Dopp

THE ENVELOPE BUDGET The Easiest Budgeting Tool I Know By David Dopp My son, who has always had a problem keeping track of his money, had tried just about every budgeting trick he had ever read. Despite

### Excerpt from "Introduction to Algebra" 2014 AoPS Inc. www.artofproblemsolving.com

Exercises 7.3.1 Five chickens eat 10 bags of scratch in 20 days. How long does it take 18 chickens to eat 100 bags of scratch? 7.3.2 Suppose a is jointly proportional to b and c. If a = 4 when b = 8 and

### Algebra I. In this technological age, mathematics is more important than ever. When students

In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,

### Keystone National Middle School Math Level 7 Placement Exam

Keystone National Middle School Math Level 7 Placement Exam ) Erica bought a car for \$,000. She had to add Pennsylvania s sales tax of 6%. The total price of the car is closest to? \$,00 \$6,000 \$,000 \$,000

### OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

### Decimals and Percentages

Decimals and Percentages Specimen Worksheets for Selected Aspects Paul Harling b recognise the number relationship between coordinates in the first quadrant of related points Key Stage 2 (AT2) on a line

### Planning a Responsive Website

Planning a Responsive Website Planning a website is important for both web designers and website owners. Planning your website before you start building it can save you time, keep your site code more accurate

### Graphing Motion. Every Picture Tells A Story

Graphing Motion Every Picture Tells A Story Read and interpret motion graphs Construct and draw motion graphs Determine speed, velocity and accleration from motion graphs If you make a graph by hand it

### Chapter 1: How to play Introduction

1. How to play Chapter 1: How to play Introduction Film transcript Whether it s Olympic, Paralympic sport, global business, or academic success there s always more behind the numbers. That s why, as the

### Stocks and Mutual Funds

LESSON 14 Stocks and Mutual Funds I ntroduction One characteristic of a market economy is private ownership of property. Property is not just land and real estate; it is anything of economic value that

### Instructor Now pick your pencils up and get this important equation in your notes.

Physics 605 Mechanical Energy (Read objectives on screen.) No, I haven t been playing with this toy the whole time you ve been gone, but it is kind of hypnotizing, isn t it? So where were we? Oh yes, we

### NCTM Content Standard/National Science Education Standard:

Title: Do These Systems Meet Your Expectations Brief Overview: This concept development unit is designed to develop the topic of systems of equations. Students will be able to graph systems of equations

### Fry Instant Words High Frequency Words

Fry Instant Words High Frequency Words The Fry list of 600 words are the most frequently used words for reading and writing. The words are listed in rank order. First Hundred Group 1 Group 2 Group 3 Group

### The Abingdon Co. Jackie. Product Information, Manual and Warranty

The Abingdon Co. Jackie Product Information, Manual and Warranty Revision 3 2 Dear Friend, 3 Welcome to the Abingdon family. Thank you for purchasing your Abingdon watch. I hope it helps you navigate for

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

### High School Functions Interpreting Functions Understand the concept of a function and use function notation.

Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.

### MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

### Statistics and Probability

Statistics and Probability TABLE OF CONTENTS 1 Posing Questions and Gathering Data. 2 2 Representing Data. 7 3 Interpreting and Evaluating Data 13 4 Exploring Probability..17 5 Games of Chance 20 6 Ideas

### Moses. July 11-12, 2015. God has a plan for us. Exodus 2-4; Jeremiah 29:11

rd 3 5 July 11-12, 2015 Moses Exodus 2-4; Jeremiah 29:11 God has a plan for us. th Connect Time (20 minutes): Five minutes after the service begins, split kids into groups and begin their activity. Remember

### A Quick Algebra Review

1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals

### Math and FUNDRAISING. Ex. 73, p. 111 1.3 0. 7

Standards Preparation Connect 2.7 KEY VOCABULARY leading digit compatible numbers For an interactive example of multiplying decimals go to classzone.com. Multiplying and Dividing Decimals Gr. 5 NS 2.1

### 1Planning Your Financial Future: It Begins Here

This sample chapter is for review purposes only. Copyright The Goodheart-Willcox Co., Inc. All rights reserved. 1Planning Your Financial Future: It Begins Here Terms Financial plan Financial goals Needs

### Cap Tables Explained

Cap Tables Explained Introduction Capitalization tables ( cap tables ) are used to record and track ownership in a company. If you are a sole proprietor, then it is not necessary to use a cap table you

### Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1

Subject: Math Grade Level: 5 Topic: The Metric System Time Allotment: 45 minutes Teaching Date: Day 1 I. (A) Goal(s): For student to gain conceptual understanding of the metric system and how to convert

### Pristine s Day Trading Journal...with Strategy Tester and Curve Generator

Pristine s Day Trading Journal...with Strategy Tester and Curve Generator User Guide Important Note: Pristine s Day Trading Journal uses macros in an excel file. Macros are an embedded computer code within

### Section 1.5 Linear Models

Section 1.5 Linear Models Some real-life problems can be modeled using linear equations. Now that we know how to find the slope of a line, the equation of a line, and the point of intersection of two lines,

### Debt: The Good, The Bad, & The Ugly EPISODE # 402

Debt: The Good, The Bad, & The Ugly EPISODE # 402 LESSON LEVEL Grades 6-8 KEY TOPICS Debt management Budgets Compound interest LEARNING OBJECTIVES 1. Understand different types of debt. 2. Learn how budgets

### c01_1 09/18/2008 1 CHAPTER 1 COPYRIGHTED MATERIAL Attitude Is Everything in a Down Market http://www.pbookshop.com

c01_1 09/18/2008 1 CHAPTER 1 Attitude Is Everything in a Down Market COPYRIGHTED MATERIAL c01_1 09/18/2008 2 c01_1 09/18/2008 3 Whether you think you can or you think you can t, you are right. Henry Ford

### UNIT AUTHOR: Elizabeth Hume, Colonial Heights High School, Colonial Heights City Schools

Money & Finance I. UNIT OVERVIEW & PURPOSE: The purpose of this unit is for students to learn how savings accounts, annuities, loans, and credit cards work. All students need a basic understanding of how

### Answers Teacher Copy. Systems of Linear Equations Monetary Systems Overload. Activity 3. Solving Systems of Two Equations in Two Variables

of 26 8/20/2014 2:00 PM Answers Teacher Copy Activity 3 Lesson 3-1 Systems of Linear Equations Monetary Systems Overload Solving Systems of Two Equations in Two Variables Plan Pacing: 1 class period Chunking

### Infographics in the Classroom: Using Data Visualization to Engage in Scientific Practices

Infographics in the Classroom: Using Data Visualization to Engage in Scientific Practices Activity 4: Graphing and Interpreting Data In Activity 4, the class will compare different ways to graph the exact

### Beating Roulette? An analysis with probability and statistics.

The Mathematician s Wastebasket Volume 1, Issue 4 Stephen Devereaux April 28, 2013 Beating Roulette? An analysis with probability and statistics. Every time I watch the film 21, I feel like I ve made the

### American Diploma Project

Student Name: American Diploma Project ALGEBRA l End-of-Course Eam PRACTICE TEST General Directions Today you will be taking an ADP Algebra I End-of-Course Practice Test. To complete this test, you will

### Have fun & we ll see you July 29th!

Student Information Page We re so proud of you for taking the time to work on math over the summer! This packet is intended for students who just finished fifth grade and will be entering middle school

Version 2.0 Online Resources Business 101 Box Office Poll...1 Box Office Poll: Making Charts...2-3 Top Ten List: Movie-Making Programs.....4 Short Answer Assessment Questions.....5 Lemonade Stand Story-Telling

### So how much does it cost?

17 Math Challenge # PERPLEXING PERCENTAGES So how much does it cost Figure This! Is a discount of 30% off the original price, followed by a discount of 50% off the sale price, the same as a discount of

### Lesson 8: Making Inferences

Lesson 8: Making Inferences Selected Content Standards Benchmarks Addressed: D-5-M Comparing experimental probability results with theoretical probability (e.g., representing probabilities of concrete

### English as a Second Language Podcast www.eslpod.com. ESL Podcast 307 Cable and Satellite TV

GLOSSARY cable TV cable television; television services that are delivered through long wires that are underground or high in the air * With cable TV you can see hundreds of channels from all around the

### VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS

### 33 DISCOUNTED PRESENT VALUE

33 DISCOUNTED PRESENT VALUE Purpose: To illustrate the idea of discounted present value with computations of the value of payments to be received in the future at different rates of interest. To use discounted

### flight attendant lawyer journalist programmer sales clerk mechanic secretary / receptionist taxi driver waiter/waitress

Work Choices UNIT 3 Getting Ready Discuss these questions with a partner. flight attendant lawyer journalist programmer sales clerk mechanic secretary / receptionist taxi driver waiter/waitress 1 Look

### Björn Bäckström, Lars Olsén and Simon Renström Copyright 2011 ClaroBet AB. Updated: May. 12, 11 You may not distribute or copy any of the text or use

Björn Bäckström, Lars Olsén and Simon Renström Copyright 2011 ClaroBet AB. Updated: May. 12, 11 You may not distribute or copy any of the text or use it in any other way except for personal use, without

### How to Use the Cash Flow Template

How to Use the Cash Flow Template When you fill in your cash flow you are trying to predict the timing of cash in and out of your bank account to show the affect and timing for each transaction when it

### Follow the Money! by Loreen Leedy

OFFICE OF THE VERMONT STATE TREASURER Follow the Money! by Loreen Leedy Follow the Money! is written and illustrated by Loreen Leedy. Copyright 2002. Published by Holiday House, Inc. Book Jacket Description:

### Factual statements in this course are made as of the date the course was created and are subject to change without notice.

1 HOW TO AVOID CHOPPY MARKETS Dr. Barry Burns Copyright 2007 Top Dog Trading IMPORTANT-READ CAREFULLY: Reproduction, translation, or distribution in any form or by any means, or storage in a data base

### Multiple Representations of Linear Relationships. 12 Real World Situations

Multiple Representations of Linear Relationships 12 Real World Situations Instructions for At the football game they expect That for every 4 people who attend. The game the concession stand Will sell 3

### Basic Pre Algebra Intervention Program

Basic Pre Algebra Intervention Program This 9 lesson Intervention Plan is designed to provide extra practice lessons and activities for students in Pre Algebra. The skills covered are basics that must

### GRADE 2 SUPPLEMENT. Set A7 Number & Operations: Numbers to 1,000 on a Line or Grid. Includes. Skills & Concepts

GRADE 2 SUPPLEMENT Set A7 Number & Operations: Numbers to 1,000 on a Line or Grid Includes Activity 1: Mystery Numbers on a 101-200 Grid A7.1 Activity 2: What s My Number? A7.7 Independent Worksheet 1:

### Scripts for Recruiters

Scripts for Recruiters Companion Script Guide for The New Recruiters Tool Kit www.greatrecruitertraining.com Copyright 2010 Scott Love 1 How to Use This Guide Use this companion script guide while watching

Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions...617.2

### The Distributive Property

The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com

### Pay per Click Success 5 Easy Ways to Grow Sales and Lower Costs

Pay per Click Success 5 Easy Ways to Grow Sales and Lower Costs Go Long! The Benefits of Using Long Tail Keywords clogged sewage line, I ll see a higher conversion How many keywords are in your pay-per-click

### Newton s Wagon Newton s Laws

Newton s Wagon Newton s Laws What happens when you kick a soccer ball? The kick is the external force that Newton was talking about in his first law of motion. What happens to the ball after you kick it?

### WHAT'S INSIDE: Your guide to... INDIANA'S GUIDE TO STUDENT SUCCESS GRADES K-2

INDIANA'S GUIDE TO STUDENT SUCCESS GRADES K-2 WHAT'S INSIDE: Your guide to... Planning for your career Preparing for college Cutting the cost of college Jose is in first grade at Heth-Washington Elementary

### By Steven Peeris, Research Analyst

1/12/2013 Personal Finance By Steven Peeris, Research Analyst NUS Students Investment Society NATIONAL UNIVERSITY OF SINGAPORE TIME IS MONEY TRADING TIME FOR DOLLARS What are we getting paid for when we

### YOU CAN COUNT ON NUMBER LINES

Key Idea 2 Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and

### Bus Rider Activities

1. To easily divide campers into two teams or groups, split down the middle of the bus, so that the campers on one side of the aisle are one team, and those on the other side are the second team. But if

### Part 1 will be selected response. Each selected response item will have 3 or 4 choices.

Items on this review are grouped by Unit and Topic. A calculator is permitted on the Algebra 1 A Semester Exam The Algebra 1 A Semester Exam will consist of two parts. Part 1 will be selected response.

### The Seasons on a Planet like Earth

The Seasons on a Planet like Earth As the Earth travels around the Sun, it moves in a giant circle 300 million kilometers across. (Well, it is actually a giant ellipse but the shape is so close to that

### Financial fitness for the future. Finances out of shape. Learn to manage your money. Managing your money

Finances out of shape. Learn to manage your money. Financial fitness for the future. Managing your money W E S T E R N U N I O N F O U N D A T I O N You want a better future. A better life. A better education.

### Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.

INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe

### STUDENT NAME: GRADE 8 MATHEMATICS

STUDENT NAME: GRADE 8 MATHEMATICS Administered October 2009 Name: Cla ss: 8th Grade TAKS Practice Test 1 1 A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group

### \$300 to Freedom in FOREX FOREX Freedom Turn \$300 into \$30,000 with FOREX Financial Freedom in as Little as 6 Months!

Turn \$300 into \$30,000 Financial Freedom in as Little as 6 Months! ereport By Robert Borowski 2004 & 2005 Evergreen Forex Inc. \$300 to Freedom in FOREX FOREX Freedom Turn \$300 into \$30,000 with FOREX Financial

### LEGAL & GENERAL HOME FINANCE. Guide to Lifetime Mortgages

LEGAL & GENERAL HOME FINANCE Guide to Lifetime Mortgages A lifetime mortgage could give you the freedom to really enjoy your retirement. We re delighted you re finding out more about lifetime mortgages.