published by
the Concord Consortium
supported by
the National Science Foundation

This web-based graphing activity explores the similarities and differences between Velocity vs. Time and Position vs. Time graphs. It interactively accepts user inputs in creating "prediction graphs", then provides real-time animations of the process being analyzed. Learners will annotate graphs to explain changes in motion, respond to question sets, and analyze why the two types of graphs appear as they do. It is appropriate for secondary physical science courses, and may also be used for remediation in preparatory high school physics courses. Resource includes interactive activity, lesson plan, and assessment with answer key.

Users must register to access full functionality of all the tools available with SmartGraphs, which include databases for classroom record-keeping and assessment and access to authoring tools for teachers wishing to customize SmartGraph content.

This item is part of the Concord Consortium, a nonprofit research and development organization dedicated to transforming education through technology.

6-8: 2A/M2. Logical connections can be found between different parts of mathematics.

9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

4. The Physical Setting

4F. Motion

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

6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

Next Generation Science Standards

Disciplinary Core Ideas (K-12)

Forces and Motion (PS2.A)

The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)

Crosscutting Concepts (K-12)

Patterns (K-12)

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

Cause and Effect (K-12)

Cause and effect relationships may be used to predict phenomena in natural systems. (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)

Construct and interpret graphical displays of data to identify linear and nonlinear relationships. (6-8)

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

Constructing Explanations and Designing Solutions (K-12)

Constructing explanations and designing solutions in 6–8 builds on K–5 experiences and progresses to include constructing explanations and designing solutions supported by multiple sources of evidence consistent with scientific ideas, principles, and theories. (6-8)

Construct an explanation that includes qualitative or quantitative relationships between variables that predict 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)

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 describe and/or support scientific conclusions and design solutions. (6-8)

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

Functions (8)

Use functions to model relationships between quantities. (8)

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.

High School — Algebra (9-12)

Reasoning with Equations and Inequalities (9-12)

A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

High School — Statistics and Probability^{?} (9-12)

Interpreting Categorical and Quantitative Data (9-12)

S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Making Inferences and Justifying Conclusions (9-12)

S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

SmartGraphs: Describing Velocity. (2010). Retrieved October 21, 2014, from The Concord Consortium: http://concord.org/stem-resources/describing-velocity

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This cost-free article describes results of research in Grades 4, 6, and 8 on student understanding of motion. Findings suggest that students as young as Grade 6 can, with instruction, change entrenched incorrect concepts to construct accurate ideas about force and motion.

This is a microcomputer-based motion lab developed for cooperative learning groups. Students collaborate to predict shape of motion graphs, then analyze their own misconceptions.