published by
the Concord Consortium
supported by
the National Science Foundation

This activity explores the relationship between graphs of Distance vs. Time and Velocity vs. Time by blending a motion sensor lab with student-generated digital graphs. First, learners use the online graph sketching tool to predict graphs of both distance and velocity for a toy car being pushed up a ramp and allowed to coast back down. Next, they use a motion sensor to collect data on a real toy being pushed up a ramp. Finally, they analyze differences in slope between their original predictions and the actual data from the motion sensor. See Related Materials for a similar blended-learning lab that explores simple, straight-line motion.

This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology. The Concord Consortium develops deeply digital learning innovations for science, mathematics, and engineering.

Editor's Note:Users must register to access full functionality of all the tools available with this resource, which include acquiring and sharing real-time data, and creating classroom fields for record-keeping and assessment. This resource was developed for use in middle school, but may be easily adapted for high school.

Graphs and charts can be used to identify patterns in data. (6-8)

NGSS Science and Engineering Practices (K-12)

Analyzing and Interpreting Data (K-12)

Analyzing data in 6–8 builds on K–5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. (6-8)

Analyze and interpret data to provide evidence for phenomena. (6-8)

Developing and Using Models (K-12)

Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)

Develop a model to predict and/or describe phenomena. (6-8)

Planning and Carrying Out Investigations (K-12)

Planning and carrying out investigations to answer questions or test solutions to problems in 6–8 builds on K–5 experiences and progresses to include investigations that use multiple variables and provide evidence to support explanations or design solutions. (6-8)

Conduct an investigation to produce data to serve as the basis for evidence that meet the goals of an investigation. (6-8)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 6–8 level builds on K–5 and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments. (6-8)

Use mathematical representations to support scientific conclusions and design solutions. (6-8)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4F. Motion

3-5: 4F/E1a. Changes in speed or direction of motion are caused by forces.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9. The Mathematical World

9B. Symbolic Relationships

3-5: 9B/E2. Tables and graphs can show how values of one quantity are related to values of another.

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

11. Common Themes

11B. Models

3-5: 11B/E4. Models are very useful for communicating ideas about objects, events, and processes. When using a model to communicate about something, it is important to keep in mind how it is different from the thing being modeled.

6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.

12. Habits of Mind

12C. Manipulation and Observation

6-8: 12C/M3. Make accurate measurements of length, volume, weight, elapsed time, rates, and temperature by using appropriate devices.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.2 Reason abstractly and quantitatively.

MP.4 Model with mathematics.

Geometry (K-8)

Graph points on the coordinate plane to solve real-world and
mathematical problems. (5)

5.G.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.

Expressions and Equations (6-8)

Represent and analyze quantitative relationships between
dependent and independent variables. (6)

6.EE.9 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.

Functions (8)

Define, evaluate, and compare functions. (8)

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Use functions to model relationships between quantities. (8)

8.F.4 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.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Key Ideas and Details (6-12)

RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Integration of Knowledge and Ideas (6-12)

RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

Range of Reading and Level of Text Complexity (6-12)

RST.6-8.10 By the end of grade 8, read and comprehend science/technical texts in the grades 6—8 text complexity band independently and proficiently.

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion Unit Title: Graphing

This activity blends a motion sensor lab with digital graph modeling. Students use the online graph-sketching tool to predict graphs of distance vs. time and velocity vs. time. Next, they use a motion sensor to collect data on a real toy being pushed up a ramp. Last, they analyze differences between their predictions and the actual data. Highly recommended by the editors. For beginners, try first introducing the activity directly above.

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=11796">National Science Foundation. Concord Consortium: Motion on a Ramp. Concord: The Concord Consortium, 2017.</a>

Concord Consortium: Motion on a Ramp. (2017). Retrieved July 28, 2021, from The Concord Consortium: https://learn.concord.org/resources/657/motion-on-a-ramp

National Science Foundation. Concord Consortium: Motion on a Ramp. Concord: The Concord Consortium, 2017. https://learn.concord.org/resources/657/motion-on-a-ramp (accessed 28 July 2021).

Concord Consortium: Motion on a Ramp. Concord: The Concord Consortium, 2017. National Science Foundation. 28 July 2021 <https://learn.concord.org/resources/657/motion-on-a-ramp>.

%0 Electronic Source %D 2017 %T Concord Consortium: Motion on a Ramp %I The Concord Consortium %V 2021 %N 28 July 2021 %9 text/html %U https://learn.concord.org/resources/657/motion-on-a-ramp

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