Walk the Plank

• ## Walk the Plank

Periods: 1
Author: Samuel E. Zordak

### Instructional Plan

To prepare for this lesson, draw a line on a sturdy plank of wood that is 6 inches from one end. Then, draw additional lines at 12‑inch intervals. During the activity, students will stand with their feet straddling these lines.

Place a bathroom scale and a textbook on the floor, about six feet apart. Place the plank of wood so that one end rests firmly on the scale and the other end rests on the book. The line drawn 6 inches from one end of the plank should lie along the center of the scale. (Be sure to test the arrangement prior to class to ensure that it is safe for students.)

Provide the following explanation to students about the forthcoming math investigation. (Since the lesson is called "Walk the Plank," it may be fun to invoke a pirate accent while reading.)

Belay your talk, lads and lasses! Yo ho ho… ye all have performed handsomely as math students, but I’m afraid there are just too many of you in this here classroom. So today, some of ye are going to walk the plank!

(Point to the plank.) Aye, mateys! This here plank stretches between a scale and a textbook. Don’t ye be scared — it’s plenty sturdy. See? (Demonstrate its strength by walking across the plank.) As ye walk across it, we’ll record the weight shown on the scale. To show ye scallywags how to do it properly, I’ll go first.

Distribute the Walk the Plank Activity Sheet to students, and explain how the chart is to be filled in.

Step on the plank so that your feet straddle the line down the center of the scale. Read aloud the weight shown on the scale. (The weight shown will be significantly more than your actual weight, because it includes the weight of the plank.) On the chalkboard or overhead projector, make a note of the weight.

Ask the class, "Do you think this is my actual weight?" Students should realize that the weight shown on the scale includes the weight of the plank. (Although it may seem trivial, this is an important question to ask. When students realize that their actual weight will not be displayed, they will be more likely to participate. Still, when students walk the plank, use care with those who are particularly self conscious.) Step off the plank.

Start at the line nearest the scale. Use the chart on the activity sheet to record the weight. Step left, and move to the next line on the plank. Again, read and record the weight. Continue moving to the left and recording the weight at each line. If it becomes difficult to read the weight, invite a student to read the weight as you move across the plank. As you move and say the weight aloud, remind students to fill in their charts.

After you have moved the entire way along the plank, ask the following questions:

• Plot the points on a graph. What do you notice? [The points occur in a straight line; that is, the relationship between weight and distance is linear.]
• Where is the y intercept? [The y‑intercept is approximately equal to the weight of the teacher plus the weight of the plank.]
• Where is the x intercept? [The x‑intercept is approximately equal to the length of the plank.]
• Approximately, what is the slope? Is it positive or negative? [The slope is negative, and its absolute value is equal to the combined weight of the teacher and the plank divided by the length of the plank.]

Then, allow student(s) to walk the plank. If possible, select a student whose weight is approximately half of your own weight. When the line for this student is graphed, the slope of the line will be half of the slope for your line. Then, select several other students at random. (Because weight is a sensitive subject, choose students carefully, and do not force any student to participate. To avoid an awkward situation, you may want to ask for volunteers rather than select students.)

Allow students to discuss the questions on the activity sheet. To fill the time and extend the thinking of those groups who finish the worksheet and are waiting for others to finish, use the extension activities below.

The activity sheet can be reviewed after all groups have discussed the question, or you may have students complete it for homework.

If necessary, you can refer to the Walk the Plank Answer Key.

### Assessments and Extensions

Assessment Options

Observe student answers during the class discussion, and check their written answers on the activity sheet.

Extensions

1. Use a longer plank to perform the same experiment. How do the results differ?
2. What happens when two students simultaneously walk the plank?
3. Place two textbooks 12 feet apart. Between them, place a scale. Arrange a 12 foot plank so that its ends rest on the textbooks and the middle of it lies on the scale. What happens when two students simultaneously walk the plank, one on either side of the scale?
4. For the linear equation y = mx + b, what is the value of the x-intercept in terms of m and b?

### Questions and Reflections

Questions for Students

1. Why is the slope of the graph negative?

[As the person moved away from the scale, the weight displayed on the scale decreased.]

2. Why does the weight shown on the scale not accurately reflect your weight?

[The weight shown will be significantly more than your actual weight, because it includes the weight of the plank.]

3. When a student whose weight was about half of the teacher's walked across the plank, what did you notice about the slope of that student's line on the graph?

[The slope of the line was about half of the teacher's line.]

Teacher Reflection

• Was students’ level of enthusiasm/involvement high or low? Explain why.
• What student actions allowed you to determine that students did or did not have an adequate understanding of the material? How did you use that information to adjust the lesson?
• Were you able to challenge the high achievers in your class? If so, how? If not, what could have been done to provide more challenge?
• Was this lesson appropriate for your students? If not, what could you do to make it more appropriate?

### Objectives and Standards

Students will:

• Recognize that a real world situation is linear.
• Create a graph and write an equation for various linear functions.
• Determine the slope, equation, and x‑intercept of a linear function.
Common Core State Standards – Mathematics

6th to 8th

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.

9th to 12th

• Number & Quantity
• CCSS.Math.Content.HSN-VM.C
Perform operations on matrices and use matrices in applications.

9th to 12th

• Algebra
• CCSS.Math.Content.HSA-REI.B
Solve equations and inequalities in one variable.

9th to 12th

• Functions
• CCSS.Math.Content.HSF-TF.B
Model periodic phenomena with trigonometric functions.

6th to 8th

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.

6th to 8th

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.

3rd to 5th

• CCSS.Math.Content.5.MD.A
Convert like measurement units within a given measurement system.
• CCSS.Math.Content.7.SP.B
Draw informal comparative inferences about two populations.
Common Core State Standards – Practice
• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.
• CCSS.Math.Practice.MP3
Construct viable arguments and critique the reasoning of others.