the Concord Consortium
the National Science Foundation
This interactive graphing activity allows learners to explore the effects of gravity on light and heavy objects. First, students use a graph sketching tool to predict the Position vs. Time and Velocity vs. Time graphs for a light ball falling 2 meters to the ground. Next, they repeat the prediction sketches for a heavy ball. Graphs are then automatically generated to show data based on actual timed trials. As students compare the accurate results to their predictions, they perform scaffolded calculations to determine the slope of a line. By the conclusion of the activity, learners are expected to discover that: 1) heavy and light objects fall at the same rate of acceleration, and 2) acceleration can be calculated from data in a Velocity vs. Time graph. Appropriate for Grades 8-12.
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 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: 4B/M3. Everything on or anywhere near the earth is pulled toward the earth's center by gravitational force.
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.
9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.
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.
11. Common Themes
6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.
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.
Next Generation Science Standards
Disciplinary Core Ideas (K-12)
Types of Interactions (PS2.B)
The gravitational force of Earth acting on an object near Earth's surface pulls that object toward the planet's center. (5)
Forces that act at a distance (electric, magnetic, and gravitational) can be explained by fields that extend through space and can be mapped by their effect on a test object (a charged object, or a ball, respectively). (6-8)
Crosscutting Concepts (K-12)
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)
Cause and Effect (K-12)
Cause and effect relationships may be used to predict phenomena in natural systems. (6-8)
Scientific Knowledge Assumes an Order and Consistency in Natural Systems (1-12)
Science assumes that objects and events in natural systems occur in consistent patterns that are understandable through measurement and observation. (6-8)
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 determine similarities and differences in findings. (6-8)
Construct and interpret graphical displays of data to identify linear and nonlinear relationships. (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)
Apply scientific ideas to construct an explanation for real-world phenomena, examples, or events. (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 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.
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.
High School — Functions (9-12)
Linear, Quadratic, and Exponential Models? (9-12)
F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
High School — Statistics and Probability? (9-12)
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.
%0 Electronic Source %D 2010 %T SmartGraphs: Was Galileo Right? %I The Concord Consortium %V 2014 %N 24 July 2014 %9 text/html %U http://smartgraphs.concord.org/act4-5.html#/shared/gravity
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