Jennifer Crawford

Algebra For All- Week 8 Integration Assignment

5 day mini-unit- Quadratics

MMC Standards

  • A2.6.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate information (e.g., vertex, intercepts, etc.)
  • A2.6.2 Identify the elements of a parabola (vertex, axis of symmetry, and direction of opening) given its symbolic form or its graph and relate these elements to the coefficient(s) of the symbolic form of the function.
  • A2.1.3 Represent functions in symbols, graphs, tables, diagrams or words, and translate among representations.

Outcomes

  • Students will be able to move between representations of a function as a table, a graph, and an equation.
  • Students will be able to determine the maximum and minimum of a parabola.
  • Students will be able to find the axis of symmetry and the vertex of quadratics.
  • Students will compare and contrast quadratic functions when given either the table, graph, or equation.
  • Students will be able to solve quadratic functions on the graphing calculator after going through the calculator activity.
  • Students will be able to use real life situations to solve quadratic functions.

Hook- “Egg Launch Contest”

  • Mr. Rhode’s class is holding an egg launching contest on the football field. Teams of students have built catapults that will hurl an egg down the field. Ms. Monroe’s class will judge the contest. They have various tools and ideas for measuring each launch and how to determine which team wins.
  • The culminating activity will be our own class egg launch.

Lesson Plan

Title: Exploring Parabolas

Content Expectation(s):

Strand: Functions

Standard: A2.6.2

Topic: Quadratic functions

Content Expectation: Identify the elements of a parabola (vertex, axis of symmetry, and direction of opening) given its symbolic form or its graph and relate these elements to the coefficient(s) of the symbolic form of the function.

Lesson Outcome: Students will be able to understand the effect that each part of the equation has on the appearance of a graph.

Materials and Resources: Computer- using the website ( graphing calculator, graph paper, class projector with website displayed

Procedures:

  1. Students will hold a class discussion about the introduction to parabolas activity, “The Egg Launch” from NCTM Illuminations. Students will use the questions from this activity for their discussion. (Describe the usefulness of each representation (table, graph, equation) of the data. What information about these egg launches can you infer from the tables, graphs, and equations? What effect do the negative leading coefficients of the equations have on the graphs? Explain different strategies that can be used to determine the maximum height reached by an egg on its flight path. What can you say about a minimum height reached by an egg on its flight path? What can you say about any symmetry in these graphs? ) The class will then come together so the teacher can explain the next part of the lesson. Using the projector the teacher will display the Algebra For All website and explain what students will be doing in the computer lab. Students will then go down to the computer lab with the teacher. They will be working on their own computers, but sitting with a partner so they can have support if needed. Students will then complete the “Exploring Parabolas” activity. They can use the applet for graphing, graphing calculator, or graph paper to complete the activity. At the completion of the activity, students will go back to their classrooms to write in their spirals a self-reflection of the computer activity. (What was the purpose of this activity? What happens to a graph when certain parts of the equation are changed? Can you give an example? Do you need more practice?)

Assessment:

Observation will be one assessment. Were students able to complete the activity successfully? Were there questions? Did they ask for help from the teacher and/or partner? Students will be working in groups the next day on the handout, “Let’s Make a Parabola”. They will answer the questions and make the graphs. They will also write a story about their graph or give a real-world situation which is represented by the graph. The group will then show their graphs to the class and be able to explain the effect that each part of the equation has on the appearance of the graph.

Additional Notes:The teacher will know the students best. She/he may choose to have partners depending on the comfort level of the students. Some of the students may prefer to work individually. This will need to be determined before this lesson is taught.

Attachments:

Let's make a Parabola handout

SUMMARY:

The above lesson is day two out of three days. The first day would be the egg launch and the third day would be the activity, “Let’s Make a Parabola.” I feel this is a functions based approach to teaching quadratics because the lessons allow for different representations. Students will be looking at equations, tables, and graphs throughout the three days. Another reason I feel this supports a functions based approach is because students are working individually, with partners, and/or groups. During these times they are expected to work towards an understanding of the objective. In this instance they are to understand the role of each part of a quadratic equation on the appearance of the graph. The third day’s activity asks students to work in a group and be able to explain to each other what is being seen in the graphs and why. The continued exposure in different ways hopefully helps students to understand quadratic functions. A functions based approach also puts the math into real-world context. This is one reason I would lead with the egg launch activity. I also think it would be neat to watch some videos where parabolas occur- like in free throws in basketball.

Course Content Modules/AfA activities

  • (Exploring Parabolas Module)
  • (Full equation)
  • (Isolated a-value)
  • (Isolated h-value)
  • (Isolated k-value)
  • Let's make a Parabola handout
  • (projectile simulator)

Graphing Calculator Activity

  • This will be done throughout the above applets

Multiple Representations

This handout will be used for the Egg Launch Contest in which students will be asked to make tables, graphs, and written answers to questions.

Formative and Summative Assessments

  • Formative: observation, handout, journals,
  • Summative: Egg launch, News story using a given graph

5-day mini- unit

Monday:

  • Students will follow the instructions for the “Egg Launch Contest” activity.
  • Data for team A is shown in a table
  • Data for team B is given in an equation
  • Data for team C is shown in a graph
  • Students will work with a partner which will allow them to discuss, compare and contrast, move between the representations.
  • Students will journal the following questions in their spirals:
  • Describe the usefulness of each representation (table, graph, equation) of the data. What information about these egg launches can you infer from the tables, graphs, and equations? What effect do the negative leading coefficients of the equations have on the graphs? Explain different strategies that can be used to determine the maximum height reached by an egg on its flight path. What can you say about a minimum height reached by an egg on its flight path? What can you say about any symmetry in these graphs?

Tuesday:

  • Using the projector the teacher will display the Algebra For All website and explain what students will be doing in the computer lab. Students will then go down to the computer lab with the teacher. They will be working on their own computers, but sitting with a partner so they can have support if needed. Students will then complete the “Exploring Parabolas” activity. They can use the applet for graphing, but must also use their graphing calculator. At the completion of the activity, students will go back to the classroom to write in their spirals a self-reflection of the computer activity.
  • What was the purpose of this activity? What happens to a graph when certain parts of the equation are changed? Can you give an example? Do you need more practice?
  • Projection simulator (

Wednesday:

  • Let’s Make a Parabola activity
  • Stations 1 and 2 only
  • Students will work with a group for this activity instead of just a partner
  • The group will also begin brainstorming ideas for their own egg launching contest. The contest will be in the classroom with plastic eggs being used. Students will need to decide what materials will be needed to make a catapult and bring to class the following day.

Thursday:

  • Let’s Make a Parabola activity
  • Stations 3 and 4 only
  • Groups will build the catapults and begin determining the path that the egg should take.

Friday:

  • Presentations of the “Let’s Make a Parabola” activity
  • Presentations of “Classroom Egg Launch Contest”
  • Journal
  • Which group won the contest? Why?
  • Give students an additional graph
  • Students are to write a news story based on the graphs given to them.
  • (possible graph to use from Illuminations)