VITAL INFORMATION
Subject(s):
Mathematics
Topic or Unit of Study:
Graphing and Quadratic Equations
Grade/Level:
10
Time Allotment:
1 class period. 55 Min. per class.
Summary:
Given a basic understanding of ordered pairs, solving quadratic equations, T-charts and graphing on coordinate grids, students will learn how predict the appearance of resulting parabolic graphs based on the values of the various X-terms in a given quadratic equation.
Goals and Objective:
10th Grade AIMS Tests contain problems requiring students to identify parabolic graphs of simple quadratic equations. This lesson will enable students to the placement and orientation of such graphs based on the X-values.
Standards:
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AZ- Arizona Academics Standards
Performance Objective PO 1: Graph a quadratic equation with lead coefficient equal to one.
Performance Objective PO 6: Determine changes in the graph of a linear function when constants and coefficients in its equation are varied.
USA- ISTE: Profiles for Technology Literate Students (includes NETS for Students)
Performance Objective 2: Make informed choices among technology systems, resources, and services. (1, 2)
Performance Objective 6: Evaluate technology-based options, including distance and distributed education, for lifelong learning. (5)
Performance Objective 7: Routinely and efficiently use online information resources to meet needs for collaboration, research, publications, communications, and productivity. (4, 5, 6)
Performance Objective 8: Select and apply technology tools for research, information analysis, problem-solving, and decision-making in content learning. (4, 5)
LESSON ACCOMODATIONS
Content:
As the instructor for this lesson, I will need to know the mathematical concepts to be presented. In addition, I will need to know how to develop these concepts in Power Point and how to demonstrate them on an interactive Smart Board. Various web resources will also be incorporated within the lesson.
Multiculturalism & Diversity:
Multiculturism: In the practice phase of this lesson, students will work with ALEKS software which is “an artificially intelligent assessment and learning system.” This software assesses student progress and tailors practice activities to fit the needs of the individual learner. ALEKS also offers the added benefit of allowing students to toggle back and forth between English and Spanish as a support to Spanish speaking English language learners.
Special Needs: This lesson is designed to address the needs of all students while offering support for English language learners. English language learners will be supported through an emphasis on vocabulary and heterogeneously grouped cooperative learning and computers.
Lesson Integration:
This lesson could be related to either science or sports. Parabolas relate to the path of movement of many kinds of moving bodies under the influence of gravity. The path of anything from a basket ball free throw to a sub orbital rocket can be described in terms of Parabolas.
IMPLEMENTATION
Rationale:
Throwing a basketball from different places on the basketball court requires different shaped trajectories or parabolic curves to guide the ball to the intended destination. Though calculations of this type are not done directly on the basketball court, an intuitive understanding of parabolas is demonstrated by how hard and at what angle the ball is thrown. AIMS Mathematics Test contains content relating to this.
Focusing Event:
I will have students do calculations using a quadratic equation to complete a T-chart and then place the ordered pairs on a Coordinate Grid until enough points are placed to plot a parabola. Then I will have the students work with an interactive-parabola web resource to interactively learn the relationships of the various X values to see how they influence the resulting graph.
Teaching Procedures:
This lesson assumes that students have a basic understanding of how to solve quadratic equations, record results on T-Charts, and graph results on a co-ordinate grid.
Procedures:
Introduction: Using Power Point the Instructor will present a quick review of vocabulary and distribute a glossary of terms. The instructor will then do a review of producing ordered pairs from a quadratic equation.
Activity: Class will be divided into heterogeneous teams of four, pairing an ELL student with several English Models. Each team will then be given four transparencies or thin sheets of paper with matching coordinate grids. Each Team member will be given a quadratic equation to solve that has been selected to exhibit a different resulting characteristic. Upon completion of the graphs, the Teams will then stack their graphs and align the X and Y axes. The students will note that each graph displays different appearances. The students will then be encouraged to develop theories to explain why the graphs look the way they do. After the students have developed their hypotheses, the Teams will then be directed to the following web resource: SeeingMath Quadratic Transformer.
This web resource allows student to enter various X values into a quadratic equation while observing the resulting parabolic graph. In this way the Team members can test the validity of their hypotheses.
Assessment: Assessment of this activity will include a teacher checklist, evaluation of the team hypotheses, and a post test that challenges students to look at a quadratic equation and predict where the vertex will reside on a coordinate grid and in what direction the parabola will open. The assessment will also challenge students to look at a simple quadratic equation and match it to the parabola that would result, without solving for ordered pairs.
Follow-up: The instructor will prescribe tailored practices on the computer using ALEKS to reinforce as needed and Spanish speaking ELL students will have the ability to supplement this activity with tutorials offered in Spanish.
Attachments
- Parabola Predictions Lesson for Smart Board Power Point Lesson
- Parabola Predictions Work Sheet Coordinate Grid for graphing parabola
- Vocabulary Sheet
Links
- ALEKS Home ALEKS is a web-based, artificially intelligent assessment and learning system. ALEKS offers a Spanish option in lessons
- SeeingMath Quadradic Transformer Interactive web resource used to demonstrate how various X values influence the resulting parabolic graph
Formative Check:
The instructor will check student progress during the lesson by collecting the Parabola Prediction Work Sheets that each team member contributes to the group assignment. In addition the instructor will go about and make notations in the Parabola Prediction Evaluation Matrix to for the basis of ALEKS guided practice and reinforcement.
Attachments
- Parabola Prediction Evaluation Matrix A quick check list of skills to be used to base ALEKS practice activities for individual students.
Student Participation:
During this activity, students will solve quadratic equations, develop T Charts and graph the results. In addition students will work cooperatively to develop a hypostasis regarding the behavior of quadratic equations based on their X-values. Students will use a web based recourses to test and possible modify their hypotheses. Ultimately students will be able to predict the appearance of a parabola by looking at the X value.
Closure:
Using the SeeingMath Quadratic Transformer, the instructor will pull the class together and pose a series of questions about altering the appearance of a Parabola. The instructor will try to get the class to answer as a group.
Given the following quadratic equation:
y = x² + x - 1
What will the Y value of the vertex be?
What way will the parabola open?
What X value would you change to make the parabola wider?
How would you move the vertex up relating to the Y axis on the coordinate glide?
How can you invert the parabola to open in the opposite direction?
Assessment/Rubrics:
Attachments
- Parabola Prediction Evaluation Matrix A quick check list of skills to be used to base ALEKS practice activities for individual students.
- Parabola Prediction Quiz
- Parabola Predictions Rubric
MATERIALS AND RESOURCES
Instructional Materials:
Attachments
- Parabola Prediction Work Sheet Coordinate Grid for graphing parabola
Resources:
- Materials and resources:
Various handout and quizes - Technology resources:
Firefox, PowerPoint, Smart Board, LCD Projector and Computer
SmartBoard Requires:
Pentium 150 MHz processor (450 MHz or faster recommended)
128 MB of RAM (256 MB recommended)
Available powered USB or serial port
Approximately 160 MB of free hard disk space for a full installation
Windows NT 4.0 (SP6), Windows 98 operating system or later
Microsoft Internet Explorer 5.0 or later (6.0 recommended)
Macromedia Flash player version 7.0.19 or later (recommended)
Requirements for SMART Video Player
Pentium 450 MHz processor (700 MHz or faster recommended)
Windows 98 operating system or later. Does not run on the Windows NT operating system.
Microsoft DirectX 8.1 End-User Runtime or later - The number of computers required is 5.
- Students Familiarity with Software Tool:
Currently not known.
