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Rescue Mission Game

  • Lesson
3-5
2
GeometryData Analysis and Probability
Unknown
Location: Unknown

Students play a game to learn about the four forces of flight: lift, drag, thrust, and weight. Before playing the game, students conduct a probability experiment with spinners and record their results in tally tables and bar graphs. They then use their findings to select spinners with the greatest probability of helping them win the game. In a portion of the game, students use ordered pairs to plot points on the coordinate plane to show their flight path.

This lesson was adapted from Travel in the Solar System in Mission Mathematics II: Grades 3‑5, a NASA/NCTM project, NCTM 1997.

Background Information 

When we look at large airliners and helicopters, it seems impossible for such huge objects to lift off the ground and fly. Flight is possible because of four forces (pushes or pulls) that act on the aircraft.

Two of the forces are lift and weight. Lift is the upward force that works against the force of weight, the force that holds the aircraft down. Lift is created by the effect of airflow over and under the wings of airplanes or the blades of helicopters. Wings are usually thicker on the front edge and thinner on the back edge. This shape allows the air moving over the wing to move faster, and consequently, to have less pressure. The air moving under the wing reveals more slowly and results in more pressure pushing up on the wing. Thus, the force pushing up on the wing is greater that the force pushing down.

The other two forces of flight are thrust and drag. Thrust is the push or the pull forward that causes aircraft to move. The engines create thrust. Drag is an opposite force that slows the aircraft. Drag is caused by the surfaces of the aircraft that interrupt or deflect the smooth airflow around the aircraft. Some things that affect the amount of drag are the flaps; the ailerons; and the size, shape, and position of the wings.

1181 plane 

Getting Started 

As you introduce or review the forces of flight, ask questions to focus students' attention on a diagram with arrows to show the direction associated with each of the four forces. For example, ask which force pulls things to the ground.

As you present the Rescue Mission Game activity sheet, introduce the game students will be playing. They are pilots of rescue helicopters. Their mission is to fly their helicopters to the top of a mountain to rescue lost hikers.

pdficon  Rescue Mission Game Activity Sheet 

As you discuss the Rescue Mission Game activity sheet, explain how the spinner determines in which direction to move. For example, if the pointer lands on Lift, students move their helicopter up one space. Ask them the following questions:

In which direction they should move if it lands on Drag. [Left]

On Thrust? [Right]

On Weight? [Down]

When students cannot move in the direction indicated by the spinner, they stay in the same position for that turn.

Show students the starting point of the game and ask them to think about the flight path for their mission. Ask students the following questions:

In which directions they must go to reach the mountaintop. [Up and to the right]

Which forces will be most helpful. [Lift and thrust] Why?

Developing the Activity 

Part 1: Getting Ready for the Mission 

As you discuss the Rescue Mission Game activity sheet, explain that since the lost hikers are cold and hungry, the pilot needs to get to the top of the mountain quickly. Ask students to compare the spinners.

Class Conversation 

Use the following questions to guide the class conversation:

  • How are the spinners alike? How are they different?
  • Which spinner do you think will help your helicopter get to the mountaintop the fastest? Why do you think so?
  • How can we test the spinners to check our predictions?

After discussing their suggestions, ask students to work with a partner to spin each spinner 50 times and to record all results in a tally table.

Spinner C Tally Table
 Lift          
Thrust
 
 
Drag
 
 
Weight
 
 

When all data have been collected, help students display their data in bar graphs.

Results of 50 Spins
1181 50 spins

Each bar graph should be discussed and interpreted. Help students see that on spinner C, all forces have the same chance for the pointer to land on them. Since there is 1 chance out of 4 equal chances that the pointer will land on Lift, the probability is ?.

Class Conversation 

Use the following questions to guide the next discussion.

Compare the regions in spinner C. How many of the same size do you see? [4]

How many different forces are on spinner C? [4]

Is it less likely, equally likely, or more likely that the pointer will land on Lift than on Weight, Drag, or Thrust?

What is the likelihood, or probability, of landing on Thrust? On Drag? On Weight?

Does the pointer have the same chance of landing on each force? Why do you think that?

Next, ask students to look closely at their graphs for spinner C to interpret the results of their experiment.

Since the probability is the same for each force on spinner C, what should the graphs look like? Why?

Do your bar graphs show this?

Which bars are taller? Shorter?

What does the bars' appearance show you?

Repeat this analysis process with each spinner.

When it is your turn how can you use your graphs to help you decide which spinner to use on that turn?

Students should keep all spinners for the Rescue Mission Game.

Part 2: Playing the Rescue-Mission Game 

Introduce or review how to read and write ordered pairs to name a location on a coordinate grid. Practice using the spinners to determine moves on the game board. Ask students to predict how many spins will be needed to reach the top of the mountain.

Students then play the game with a partner to see which helicopter can rescue the lost hikers on the mountaintop first. As they take turns, students should record the following data:

  • Which spinner is selected for the turn
  • Where the pointer lands (lift, thrust, weight, or drag)
  • How the student moves (up, right, down, or left)
  • The ordered pair that names the point to which they move
Turn Number 
 
I Selected This Spinner 
 
Pointer Landed On 
 
Direction in Which I Moved 
 
Place Where I Landed
 
1
 
C
 
Lift
 
Up
 
(0,1)
 
2
 
D
 
Thrust
 
Right
 
(1,1)
 
3
 
D
 
Lift
 
Up
 
(1,2)
 

Students can record the flight path on the game-board grid by plotting the points for each student in different colors. When finished, students can connect the points to show the flight path.

Extensions 

  1. Make a new board game that favors other spinners. Let students examine their findings for each spinner and decide which spinner will help them reach the new goal fastest. Then have them play the game to test their predictions.
  2. Make up a new spinner. Have students make a new game board that would best suit this spinner. Have them play a game to test their hypothesis. For students familiar with negative and portative integers, the new game boards can extend into the other quadrants of the coordinate plane.
  3. Present this problem: Suppose that a helicopter uses three gallons of fuel for each turn needed to rescue the hikers. Calculate and graph the amounts of fuel used in each game played.
 

Questions for Students 

  1. Did it take more spins, fewer spins, or the predicted number of spins to reach the mountaintop? How can you explain this result?
  2. Look at the ordered pairs of numbers that name the points where you landed. Do you notice any patterns in these ordered pairs?
  3. How did each partner record his or her flight paths? Explain how this graph shows what happened as you took turns.
 

Learning Objectives

Students will:

  • Identify and use the four forces of flight
  • Collect, organize, and interpret data
  • Construct tally table and bar graphs
  • Determine the likeliness or probability of success
  • Read and write ordered pairs
  • Use ordered pairs to plot points on a grid

Common Core State Standards – Mathematics

Grade 3, Measurement & Data

  • CCSS.Math.Content.3.MD.B.3
    Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ''how many more'' and ''how many less'' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Grade 5, Geometry

  • CCSS.Math.Content.5.G.A.1
    Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Grade 5, Geometry

  • CCSS.Math.Content.5.G.A.2
    Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.