MEDIA RESOURCES FROM THE GET THE MATH WEBSITE
- The Setup (video) Optional
An introduction to Get the Math and the professionals and student teams featured in the program.
- Math in Videogames: Introduction (video)
Julia Detar, a videogame designer who creates online games, describes how she got involved in the gaming world, gives an introduction to the mathematics used in computer programming languages, and poses a videogame-related math challenge.
- Math in Videogames: Take the challenge (web interactive)
In this interactive activity, users try to solve the challenge posed by Julia Detar in the introductory video segment.
- Math in Videogames: See how the teams solved the challenge (video)
The teams use algebra to solve the videogame challenge in two distinct ways.
- Math in Videogames: Try other videogame challenges (web interactive)
This interactive provides users additional opportunities to plot a path for a submarine so it will reach a target location in as few moves as possible, and avoid hitting any obstacles.
For the class:
- Computer, projection screen, and speakers (for class viewing of online/downloaded video segments)
- One copy of the “Math in Videogames: Take the challenge” answer key (download DOC | PDF)
- One copy of the “Math in Videogames: Try other videogame challenges” answer key (download DOC | PDF)
For each student:
- One copy of the “Math in Videogames: Take the challenge” handout (download DOC | PDF)
- One copy of the “Math in Videogames: Try other videogame challenges” handout (download DOC | PDF)
- One graphing calculator (Optional)
- Rulers, grid paper, chart paper, chart paper, whiteboards/markers, overhead transparency grids, or other materials for students to display their math strategies used to solve the challenges in the Learning Activities.
- Colored sticker dots and markers of two different colors (optional)
- Computers with internet access for Learning Activities 1 and 2. (Optional)
(Note: These activities can either be conducted with handouts provided in the lesson and/or by using the web interactives on the Get the Math website.)
BEFORE THE LESSON
Prior to teaching this lesson, you will need to:
- Preview all of the video segments and web interactives used in this lesson.
- Download the video clips used in the lesson to your classroom computer(s) or prepare to watch them using your classroom’s internet connection.
- Bookmark all websites you plan to use in the lesson on each computer in your classroom. Using a social bookmarking tool (such as delicious, diigo, or portaportal) will allow you to organize all the links in a central location.
- Make one copy of the “Math in Videogames: Take the challenge” and “Math in Videogames: Try other videogame challenges” handouts for each student.
- Print out one copy of the “Math in Videogames: Take the challenge” and the “Math in Videogames: Try other videogame challenges” answer keys.
- Get rulers, graph paper, chart paper, grid whiteboards, overhead transparency grids, etc. for students to record their work during the learning activities.
- Get colored stickers (optional) and colored markers, for students to mark the coordinates and paths of the asteroid and spaceship in Learning Activity 1.
Note: the stickers should be in two different colors–one to mark the coordinates and path of the asteroid and the other for the spaceship.
- Begin with a brief discussion about videogames. For instance, ask students to discuss their favorite videogames.
- Explain that today’s lesson focuses on the use of math in videogames. Ask students to brainstorm how they think mathematics might be used in videogaming (in creating the games, as well as playing them). If any of your students have ever designed their own games, ask them to discuss the math involved in the process.
- Explain that today’s lesson features video segments and web interactives from Get the Math, a program that highlights how math is used in the real world. If this is your first time using the program with this class, you may choose to play the video segment The Setup, which introduces the professionals and student teams featured in Get the Math.
- Introduce the video segment Math in Videogames: Introduction by letting students know that you will now be showing them a segment from Get the Math, which features Julia Detar, a videogame designer who creates online games for the company Arkadium. Ask students to watch for the math that she uses in her work and to write down their observations as they watch the video.
- Play Math in Videogames: Introduction. After showing the segment, ask students to discuss the different ways that Julia Detar uses math in her work. (Sample responses: She uses a programming code, which can be written using algebraic expressions and equations. She uses the code in order to move objects like spaceships and asteroids across the screen, one frame at a time. She uses functions to control objects by assigning a number, or input, to a variable that results in a specific output or movement, producing the action that you see in a videogame. She also uses algebraic reasoning, coordinate graphing, linear equations and rate of change or slope to create her games.)
- Ask students to describe the challenge that Julia Detar posed to the teens in the video segment. (In a game Julia designed, an asteroid is moving on a collision course with a spaceship. The challenge is to plot a linear path for the spaceship so it won’t crash into the asteroid. Students need to plot the next two moves for the spaceship to avoid hitting the asteroid. )
LEARNING ACTIVITY 1
- Explain that the students will now have an opportunity to solve the problem, which involves plotting a linear path for the spaceship.
- Ask students to think of situations in their daily life where they may need to apply the concept of finding a linear path or two linear paths that intersect. (Sample responses: When you take a trip you may want to stop at specific locations along the highway. Today, you can use a GPS (global positioning system) or websites like Google Maps that even ask if you want to insert specific route points so you can determine important spots that you want to avoid (like the road leading to a sports stadium at game time)).
- Discuss why you would need more than one variable to identify location (GPS devices estimate distance and location using at least 4 satellites to calculate position). (Sample responses: For position on a street or highway, you would need a cross street for more accuracy; for navigation you need latitude and longitude; at least two coordinates are needed for a point of intersection.)
- Review the following terminology with your students:
- Linear: in a straight line.
- Coordinates: an ordered pair of numbers that identify a point on a coordinate plane.
- Constant rate: a ratio that compares two different units that are changing in the same way.
- Slope: a ratio or rate of change. Slope represents the change in the y-values to the change in the x-values on a coordinate graph using any two points on a line. It is a ratio of the vertical change to the horizontal change.
- Function: a relation in which every input (x-value) has a unique output (y-value).
- Distribute the “Math in Videogames: Take the challenge” handout. Let your students know that it is now their turn to solve the challenge that Julia Detar posed to the teams in the video. Explain that in the activity, students should plot the points of the asteroid’s path, select coordinates, and plot the points for the linear path of their spaceship as they complete the questions on the handout.
- Ask students to work in pairs or small groups to complete the “Math in Videogames: Take the challenge” handout. Use the “Math in Videogames: Take the challenge” answer key as a guide to help students as they complete the activity. Note: The handout can be used by itself or in conjunction with the “Math in Videogames: Take the challenge” activity on the website.
- If you have access to multiple computers, ask students to work in pairs to explore the interactive and complete the handout.
- If you only have one computer, have students work in pairs to complete the assignment using their handouts and grid or graph paper and then ask them to report their results to the group and input their solutions into the online interactive for all to see the results.
- Review the rules listed on the handout.
- As students complete the challenge, encourage them to use the following 6-step mathematical modeling cycle to solve the problem:
- Step 1: Understand the problem: Identify variables in the situation that represent essential features (For example, x represents the moves right or left, and y represents moves up or down; slope may be represented by an “a” or “m” and the y-intercept using a “b”.)
- Step 2: Formulate a model by creating and selecting multiple representations (For example, students may use visual representations in graphing, algebraic representations such as slope and an equation of a line, a transformation notation to show a translation, or an explanation/plan written in words.)
- Step 3: Compute by analyzing and performing operations on relationships to draw conclusions (For example, operations include solving for slope– the relationship between the change in y-values and the change in x-values that allows a student to conclude the steepness of the path or rate of change.)
- Step 4: Interpret the results in terms of the original situation (The results of the first three steps should be examined in the context of the challenge to avoid a collision.)
- Step 5: Ask students to validate their conclusions by comparing them with the situation, and then either improving the model or, if acceptable,
- Step 6: Report on the conclusions and the reasoning behind them. (This step allows a student to explain their strategy and justify their choices in a specific context.)
- Ongoing Assessment: Ask students to reflect upon the following:
- How can you use the linear equations for both paths (the asteroid and ship) to solve for a point of intersection or collision?
- Is there only one point that a collision or intersection can occur? How do you know? (You may wish to have students solve graphically to determine that there are several possibilities for the equations, and therefore, for a point of intersection. An extension would be to have students solve the system of equations using another method, such as substitution or elimination.)
- After students have completed the activity, ask students to share their solutions and problem-solving strategies with the class through discussion and visual materials, such as chart graph paper, grid whiteboards, overhead transparency grids, etc. Encourage students to discuss how their strategy helped (or didn’t help) them avoid a collision between the asteroid and the ship. Ask students to discuss any difficulties they faced in completing the challenge and how they overcame those obstacles.
- As students present their solutions, ask them to discuss the mathematics they used in solving the challenge. (Sample responses: Using coordinate graphs to solve problems, representing functions, identifying variables and writing expressions and/or an equation of a line, finding slope or rate of change, identifying transformations.)
- Introduce the Math in Videogames: See how the teams solved the challenge video segment by letting students know that they will now be seeing how the teams in the video solved the videogame challenge. Ask students to observe what strategies the teams used and whether they are similar to or different from the strategies presented by the class.
- Play Math in Videogames: See how the teams solved the challenge. After showing the video, ask students to discuss the strategies the teams used and to compare them to the strategies presented by the class. How are they similar? How are they different? During the discussion, point out that the two teams in the video solved the videogame challenge in two distinct ways. Discuss the strategies listed in the “Math in Videogames: Take the challenge” answer key, as desired.
LEARNING ACTIVITY 2:
- Go to the Math in Videogames: Try other videogame challenges interactive. Explain to your students that they will use the web interactive to solve a series of problems similar to the one Julia Detar presented in the video segment. In this multi-level activity, students are challenged to get their submarine to a target location in as few moves as possible without hitting obstacles. After students complete the first “Level 1” challenge, they have the option to advance to a more difficult “Level 2” challenge. If they are successful again, they may advance to a “Level 3” challenge. In the middle of Level 3, students will encounter an additional “Engine Trouble” mini-challenge that asks them to calculate the distance between two points. Students may also choose to repeat a level if they would like to try to solve the same challenge in fewer moves. There are 2 possible maps for each of the 3 levels, a total of 6 different challenges students may encounter.
Note: As in Learning Activity 1, you can conduct this activity with one computer and an LCD projector in front of the entire class or your students can work in small groups on multiple computers. This can also be assigned to students to complete as an independent project or homework using the accompanying handout as a guide.
- Distribute the “Math in Videogames: Try other videogame challenges” handout. Clarify and discuss the directions.
- Ask students to complete the handout as they explore the online challenges.
Note: If you are using one computer, have your students work in pairs to plot points on graph or chart paper and to write the equation of the line connecting the ship. Have students take turns inputting their responses into the web interactive to test their choices.
- As in Learning Activity 1, encourage your students to use the 5-step mathematical modeling cycle as they develop a strategy to solve the challenges.
- After students have completed the activity, lead a group discussion and encourage students to share their strategies and solutions to the challenges. Ask students to discuss how they selected the points and linear paths to reach the target.
- Ask your students to reflect upon and write down their thoughts about the following:
- How did you determine an effective strategy for solving the challenges in this lesson? What are your conclusions and the reasoning behind them? (Sample answer: First you could find the path of the asteroid to determine which direction it was moving and then find a way to go around it. The reason for this would be to find where you shouldn’t go before you decide where you will go to avoid the collision.)
- Compare and contrast the various algebraic and graphical representations possible for the problem. How does the approach used to solve the challenge affect the choice of representations? (Sample answers: If you decide to graph the points and then think of the ship as an object that is being translated on the grid, you would use transformation notation to represent the moves; if you decide to graph the points, you can list them (either by paper and pencil or using a graphing calculator) and then plot the points to move the ship as the asteroid moves on the screen; if you want to identify the path of either the asteroid or the ship, you would graph the points and then you could show the slope using a ratio, with the final representation being the equation of the linear path.)
- Why is it useful to represent real-life situations algebraically? (Sample responses: Using symbols, graphs, and equations can help visualize solutions when there is more than one, such as all the coordinates that satisfy the linear path of the asteroid or ship.)
- What are some ways to represent, describe, and analyze patterns that occur in our world? (Sample responses: patterns can be represented with graphs, expressions, and equations to show change.)
- After students have written their reflections, lead a group discussion where students can discuss their responses. During the discussion, ask students to share their thoughts about how algebra can be applied to the world of videogames. Ask students to brainstorm other real-world situations which involve the type of math and problem solving that they used in this lesson.