Class: Algebra II

Topic: Quadratic Equations, Parabolas

Teacher: Ms. Hill


Objectives
The student will be able to identify the vertex, axis of symmetry, and zeros of the parabola by labeling the bird’s flight path.

The student will be able to write the equation of the parabola in vertex form by finding the vertex and substituting the values.

The student will be able to predict if the bird will hit by using the graph and writing if it will hit.

Anticipatory Set
A Keynote slideshow will introduce the problem. The problem is “Will the bird make a hit?”

Guided Practice
As a class we will explore GeoGebra together. In this class discussion the class will learn to fit a parabolic curve to the bird’s path and find the Axis of Symmetry. Directions will be provided. Together we will brainstorm other questions they might have about the equation, parabola, or the relationship between the two. This brainstorm will result in a list of questions students will answer throughout the continued investigation of similar problems.

Independent Practice
Students will be given three new videos and still frames from Angry Birds asking the same question: “Will the bird hit?” Using GeoGebra groups will explore parabolic properties such as the axis of symmetry, position of vertex, and location of zeros. Groups will answer the questions they posed during the brainstorming session. During independent group work time the teacher will circulate the each group to answer questions and to ask questions to guide inquiry and encourage deep thinking by having students explain why they need to answer the problems and why they solved it they way they did.

Check for Understanding
The class will reconvene to discuss groups’ progress so far. What have you discovered? What are you hung-up on? What more can we learn? Selected groups will share their insights, hang-ups, and questions. At least one group will have a very clear understanding of what problems need to be solved and how to solve them. One group will be on track but have questions on how to complete one part or another. And one group may have many problems to solve without clear understanding of how to solve them. All students can learn from these groups successes or failures. Through these preliminary presentations, off track students can gain insight to a direction to solve the problems, and students who are on track may find a problem they have not thought of. Although groups are presenting, this is a time for students to ask questions, think aloud, and talk through their understanding. At the end of this preliminary presentation session the class will create a mind map to help show relationships between the equation, shape of parabola, and other parts such as the vertex.

Independent Practice
Students will go back to their groups and continue to find the equations of the parabolas. GeoGebra will provide them with the standard form and students will write the vertex form. Students will create a presentation to explain what they learned about a parabola’s properties and equations. They will also include how they determined if the bird would hit or miss.

Closure
Students will give presentations. And tally up each groups predictions of hits and misses. As a class we will watch the videos to reveal if their predictions were correct.If their predictions were not correct, for homework students will post to the wikispace a reflection discussing why their groups predictions were off and how they could have made them more accurate.

Materials

Keynote slideshow of Angry Birds Problem, Directions for GeoGebra,
Angry Birds picture files
AB_vid1_stillframe.png
AB_vid2_stillframe.png
AB_vid3_stillframe.png
AB_vid4_stillframe.png
computers with internet access, wikispace, GeoGebra, presentation tools, SmartBoard

Duration
4 days
Day 1 Investigate GeoGebra and parabolic properties
Day 2 Write equations in standard and vertex form, start creating presentation
Day 3 Presentation day
Day 4 Presentation day

Teacher Notes: Research Info
General Question:
What are the observed behaviors and reported experiences of 11th grade Algebra II students when implementing problem-based learning?
Specific Questions:
  • What are the effects of problem-based learning on students' ability to think for themselves?
  • What are the effects of problem-based learning on students' understanding math's purpose?
  • What are the effects of problem-based learning on students' written communication skills?
Through observation, class discussion, informal interviews, wiki posts, and surveys I believe my specific questions can be answered. Students’ ability to think for themselves: students will create the list of questions regarding parabolic properties and will use a graphing tool to discover those answers in their groups. Students’ understanding math’s purpose: applying math to a game students may reveal in a post survey that they observed parabolas in other areas of their lives. Students’ written communication skills: in the presentation students must speak of their findings in a way that is clear and understood by the teacher and classmates.