Parabola Sliders
Curator: Sophia Borden
Parabola Sliders is an activity that allows students to explore how changes in the equation of a quadratic function affect the graph.
Grade Level: Many different grade levels
PSSM Content Standard: Algebra
CCSSM Content Standard:
CCSS.Math.Content.5.G.A.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).
CCSS.Math.Content.HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Math Content: Coordinate Grids, Quadratic Equations, Graphing, Transformations
Evaluation
What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?
The activity focuses on learning about how changes in the coefficients of a quadratic equations affect its graph. It emphasizes relational understanding by how it shows the changes in the equations affecting the graphs.
How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?
The learning takes place primarily by students observing the changes of a, b, and c in the quadratic equation and making predictions of how that change affects the graph in relation. Students will need as background knowledge that the standard equation for a parabola is ax^2 + bx + c.
What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?
The technology helps the learners by being able to see instantly how a change in an equation affects the graph. It also helps by providing a visual representation of what is happening instead of tabular. The technology also helps by allowing students to compare multiple graphs at the same time.
How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)
The technology is intended to enhance the learning of Quadratic Equations and transformations of functions, something already integral to the curriculum in Algebra and Functions, Statistics, and Trigonometry.
How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)
The technology can be used in many different ways. It can be used by the teacher to explain a certain concept, by students individually to make observations about what is happening with the graphs, or even by students in a group to discuss their observations and predict what a certain change will do to the graph.
How are important differences among learners taken into account?
The technology allows students to view visual graphs of the functions which will help visual learners, auditory learners will be reached through discussions about students’ observations of the effects the changes of the functions have on the graph.
What do teachers and learners need to know? What demands are placed on teachers and other "users"? What knowledge is needed? What knowledge supports does the innovation provide (e.g., skills in using particular kinds of technology)?
Users of the technology need to be comfortable using GeoGebra, specifically making graphs and sliders that can change the function. The technology helps students understand conceptually how the coefficients of a polynomial affect the graph of the function.
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