9 Calculating slope of a ramp
Provided by Kenan Fellows Program.
In this lesson, students build a ramp and calculate its slope at different heights. They will also test cars to see how the height of the ramp affects speed.
- Practice calculating slope
- Check their testing for outliers
- Determine how the height of a ramp affects speed
One class period
- boards or other materials to be used as a ramps
- textbooks, blocks, or other materials for raising the ramps
- toy cars (not the ones students designed for this unit)
- measuring tape or meter stick
- Calculating the slope of your ramp
- Document by the author
- Open as PDF (22 KB, 2 pages; also available as Microsoft Word document)
Student should know how to measure slope.
- Begin class with a short discussion about why slope is important and when we use slope: hills, roads, sports fields, ski slopes, and so on. Ask students to think of as examples of slope and share their ideas. Provide examples that illustrate why it is important to be able to calculate slope.
- Distribute the Calculating the Slope of Your Ramp worksheet and materials. Have students get into their groups.
- Students begin by building a ramp. They should take a board and put two textbooks under one end. To prevent them from having to chase the car after each release, they will place the lower end near the wall (but not up against it).
- Next students will measure the rise (the distance from the highest point on the ramp straight to the floor). They will mark this spot on the floor with tape and use this same point to measure run. Each student will record this measurement in the chart on the worksheet.
- Students then measure the run (the distance along the floor from where the ramp touches the floor to the point on the floor that was marked in the previous step). Each student will record this measurement in the chart on the worksheet.
- At this point, each student should calculate the value of the slope: slope = rise ÷ run. They will record the result in the chart on the worksheet.
- To determine the time it takes for the car to travel down the ramp, groups should designate three people to be timers and one person to release the car. The timers will measure the time from when the car is released until the back wheels leave the ramp. They will average the three times and record the results. Remind students that an outlier is a piece of data that is considerably different in value than the rest of the data. When comparing the three times, they should check for an outlier. If repeating the experiment will provide more accurate data, then they should release and time again before changing the ramp.
- For the second trial, students will add two more books and repeat steps 4–7.
- For the third trial, add two more books and repeat steps 4–7.
- Students finish up by answering the final questions on the lab sheet.
Evaluate answers on student worksheets for correctness and understanding.
North Carolina curriculum alignment
- Goal 1: Number and Operations -The learner will understand and compute with real numbers.
- Objective 1.02: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Goal 2: Measurement - The learner will understand and use measurement concepts.
- Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.
- Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
- Goal 1: The learner will design and conduct investigations to demonstrate an understanding of scientific inquiry.
- Objective 1.01: Identify and create questions and hypotheses that can be answered through scientific investigations.
- Objective 1.05: Analyze evidence to:
- explain observations.
- make inferences and predictions.
- develop the relationship between evidence and explanation.
- Objective 1.06: Use mathematics to gather, organize, and present quantitative data resulting from scientific investigations:
- Analysis of data.
- Prediction models.
- Goal 2: The learner will demonstrate an understanding of technological design.
- Objective 2.02: Use information systems to:
- Identify scientific needs, human needs, or problems that are subject to technological solution.
- Locate resources to obtain and test ideas.
- Objective 2.03: Evaluate technological designs for:
- Application of scientific principles.
- Risks and benefits.
- Constraints of design.
- Consistent testing protocols.
- Objective 2.02: Use information systems to: