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
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
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
The activity sheet can be reviewed after all groups have
discussed the question, or you may have students complete it for
If necessary, you can refer to these solutions to the activity sheet.
Observe student answers during the class discussion, and check their written answers on the activity sheet.
- Use a longer plank to perform the same experiment. How do the results differ?
- What happens when two students simultaneously walk the plank?
- 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?
- For the linear equation y = mx + b, what is the value of the x-intercept in terms of m and b?
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.]
- 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
- Was this lesson appropriate for your students? If not, what could you do to make it more appropriate?
- 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
Grade 6, Expression/Equation
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Grade 6, Expression/Equation
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Grade 6, Expression/Equation
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Grade 7, Expression/Equation
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.''
Grade 8, Expression/Equation
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Grade 8, Expression/Equation
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Grade 8, Functions
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Grade 8, Stats & Probability
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Common Core State Standards – Practice
Make sense of problems and persevere in solving them.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.