Students use a simple seesaw to visualize solving a two- or three-step mathematics equation, while solving a basic structural engineering weight balance problem in the process. They solve two-step equations on a worksheet and attempt to solve the challenge of "balancing a beam" through hands-on problems. The use of sensor equipment for correct position monitoring aids students in balancing the structure, as well as balancing the equation as they solve it on paper.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
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- Common Core State Standards for Mathematics: Math
- 1. Write and evaluate numerical expressions involving whole-number exponents. (Grade 6)  ...show
- 6. 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)  ...show
- 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (Grade 6)  ...show
- 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (Grade 7)  ...show
- 7. Solve linear equations in one variable. (Grade 8)  ...show
- International Technology and Engineering Educators Association: Technology
- New York: Math
- 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. (Grade 6)  ...show
- Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (Grade 7)  ...show
- Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (Grade 7)  ...show
- Demonstrate how to solve two-step equations.
- Identify terms in the mathematical equation.
- Explain the use of sensors in a system, especially in feedback control.
- Explain the importance of solving equations in basic structural design.
- 2 buckets or containers with large handles
- 1 2 x 4 wooden beam, 6 ft (2 m) long
- 2 2 x 4 wooden beam, 3 ft (1 m) long
- 2 2 x 4 wooden beam, 2 ft (0.6 m) long
- 4 wood screws, 2-3 in (5 cm – 8 cm) long
- metal rod, ¾ inch (2 cm) diameter
- 2 rubber bands
- 1 elastic (bungee) cord
- 1 ball bearing (same inner diameter as metal rod)
- LEGO MINDSTORMS NXT robot, such as the NXT Base Set (5003402) for $159.98 at https://shop.education.lego.com/legoed/en-US/catalog/product.jsp?productId=5003402& isSimpleSearch=false&ProductLine=NXT
- LEGO MINDSTORMS Education NXT Software 2.1, available as a single license (2000080) for $39.97 or a site license (5003413) for $271.96 at https://shop.education.lego.com/legoed/en-US/catalog/product.jsp?productId=prod120017&isSimpleSearch=false&ProductLine=LEGO+MINDSTORMS+Education+NXT
- computer, loaded with NXT 2.1 software
- multiple objects of the same weight and size, to use as weights (such as bulk packages of water bottles or sandwich bags filled with sand) (Note: Water bottles of 11 fluid ounces [325 ml] were used successfully with the set-up described in this activity, and as much as 24 bottles were used on each side without functionality problems. However, heavier objects may work.)
- several plastic bags or containers for the objects
|Stiff, simple structures whose length is much longer than its width and height, and are used in buildings and large structures to resist bending.|
|Simple machine that balances weight along a bar.|
|A device that measures or "senses" something (temperature, distance, level of light/darkness).|
Before the Activity
- Gather materials and make copies of the pre-assessment, worksheet and post-assessment handouts.
- Assemble the seesaw, as shown in Figures 2-4. The design of the seesaw can vary; what is provided in this activity is simply a suggested design. The most important thing is for the beam to be balanced. A bungee cord wrapped around the bottom of the 6 ft. beam assists in correctly balancing the beam after each use. Attach the hooks of the bungee cord to the metal rod on each side, and then wrap it around the legs.
- Attach two ultrasonic sensors to ports 1 and 4 of the LEGO NXT unit.
- Construct the set-up shown in Figure 5 using the provided building instructions. Once complete, attach the set-up onto the seesaw, keeping both sensors equidistant from the seesaw fulcrum (legs). Use rubber bands and the pegs in the back of each sensor structure to securely attach them around the 6 ft. beam.
- Create the NXT program that incorporates the two sensors, so that both sensors are incorporated and programmed with respect to a reference distance. Figures 6-7 denote the general program structure.
- Position the seesaw near a whiteboard for student use. Place buckets on both sides of the seesaw.
- Using objects of equal weight and size, start placing the appropriate amount of objects on the seesaw. For example, in the equation 3n + 5 = 20, you would know in advance that n = 5. So place 5 water bottles inside 3 closed, opaque bags, since the coefficient in front of the variable "n" is 3. Along with 5 loose water bottles, place the bags with the bottles inside on the left bucket of the seesaw, since "3n + 5" is on the left side of the equation. On the right side of the equation is a 20. So place 20 loose bottles on the right bucket of the seesaw.
- Depending on how many equations assigned for students to work out, take sufficient objects and bags and arrange them for each equation. Place the objects in bags in advance so that it is easy to transition from equation to equation during the activity. Ensure that the bags are closed and fully opaque so that students cannot see inside each bag. For each equation, ensure that the amounts of objects in each bag are equal.
With the Students
- Direct students to keep the concept of weight balance in mind, where an equal amount of weight is placed on both sides of a fulcrum in order for balance to be achieved. Initially, have them assume that the weight is placed equidistant from the middle of the seesaw. Have them imagine that the top beam of the seesaw is a part of a building, and that their objective is to "balance the beam" using mathematics, particularly the method of two-step equations. Work out the problem in Beam Example so that the students can see how math is incorporated in the design of real-world structures.
- Hand out to each student a Seesaw Worksheet of equations to work on for 15 minutes. Have them form groups of 4-5 students each and work on the entire sheet.
- Assign one question from the worksheet to each group to carry out using the seesaw and the whiteboard.
- Give each group time to solve their assigned problem step-by-step using the classroom whiteboard and seesaw at the same time. For example, to solve for n in the equation 3n + 5 = 20, we subtract 5 from both sides. So, the group is also expected to remove 5 water bottles from each bucket. To finally solve for n, each side is divided by 3. In a similar fashion, the load in each bucket must be divided by 3. So, one bag is left on one side, while a certain amount of water bottles are left on the other side. In this way, students solve for the amount of water bottles in each bag, and students open the bags to verify.
- If a group incorrectly solves the equation, the beam should be unbalanced, and the class should hear the NXT beep. If this occurs, warn them that the beam is unbalanced, and that the building is tilting too much. Have them re-check their calculations to correct the imbalance.
- Seesaw Worksheet (pdf)
- Seesaw Worksheet (docx)
- Seesaw Worksheet Answer Key (pdf)
- Seesaw Worksheet Answer Key (docx)
- Seesaw Pre-Assessment (pdf)
- Seesaw Pre-Assessment (docx)
- Seesaw Pre-Assessment Answer Key (pdf)
- Seesaw Pre-Assessment Answer Key (docx)
- Seesaw Post-Assessment (pdf)
- Seesaw Post-Assessment (docx)
- Seesaw Post-Assessment Answer Key (pdf)
- Seesaw Post-Assessment Answer Key (docx)
- Beam Example (pdf)
- Beam Example (docx)
- Have an adult standing nearby to control the motion of the seesaw as students transfer weight from one bucket to another. It also helps if team members using the seesaw set-up help to stabilize the seesaw's motion and work together.
Activity Embedded Assessment
© 2013 by Regents of the University of Colorado; original © 2011 Polytechnic Institute of New York University
AMPS GK-12 Program, Polytechnic Institute of New York University
Last modified: February 4, 2016