published by
the Concord Consortium
supported by
the National Science Foundation

This is the portal to SmartGraphs, a project developed to promote learner understanding of graph functions through use of interactive digital graphing tools. The project goals are threefold: 1) Development of free digital graphing activities which are scaffolded to allow learner inputs, 2) Classroom testing of the graphing tools to document their effectiveness, and 3) Dissemination of free authoring tools for teachers to allow creation and sharing of new activities as open education resources. Each activity includes the interactive activity, lesson plan, and assessment with answer key.

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.

Please note that this resource requires
Java.

Editor's Note:SmartGraphs are appropriate for use in physical science courses from Grade 6-10, but can also be adapted for preparatory physics courses to assist in student remediation. Users must register to access full functionality of all the tools available with SmartGraphs, which include graph sketching, acquiring and sharing real-time data, creating databases for classroom record-keeping and assessment, and access to authoring tools. (Registration is free.)

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

Patterns can be used to identify cause and effect relationships. (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)

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)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Use mathematical representations of phenomena to describe explanations. (9-12)

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2B. Mathematics, Science, and Technology

6-8: 2B/M1. Mathematics is helpful in almost every kind of human endeavor—from laying bricks to prescribing medicine or drawing a face.

9-12: 2B/H3. Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments.

9. The Mathematical World

9B. Symbolic Relationships

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.

9C. Shapes

6-8: 9C/M4. The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters that are useful when making predictions about the phenomena being graphed.

6-8: 9C/M6. The scale chosen for a graph or drawing makes a big difference in how useful it is.

9-12: 9C/H3b. The position of any point on a surface can be specified by two numbers.

11. Common Themes

11C. Constancy and Change

9-12: 11C/H4. Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.2 Reason abstractly and quantitatively.

Geometry (K-8)

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

5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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.

Ratios and Proportional Relationships (6-7)

Analyze proportional relationships and use them to solve real-world
and mathematical problems. (7)

7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Functions (8)

Define, evaluate, and compare functions. (8)

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

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.

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion Unit Title: Special Collections

This free collection will impress teachers in the way it promotes depth of understanding about graphs. Learners use interactive digital tools to predict how a motion graph will look, then they watch as the computer simulates process in real time. Next, they place inputs on the graphs and use language to explain what is happening. Finally, they compare their own predictions with the simulated process to analyze why the graphs appear as they do. As with all Concord Consortium materials, the resources are subjected to rigorous classroom testing to ensure their effectiveness.

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