Preplanning questions:
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(1) Why
do we teach this unit to secondary school students?
Quadratics can solve many real-life problems involving area and projectile motion. It is not only the access to understanding calculus, but also the access to understanding science, such as gravity, and many other subjects. Quadratics allow us to analyze the relationships between variables.
Using quadratic graphs people could estimate values for some given values. By studying quadratic functions, students are able to apply
their understanding of quadratics to variety of real-world, model real-world
data with quadratics, graph them, find solutions for them. Quadratics is primarily used to find the curve that objects take when they fly through the air. Today, we know quadratics can be used to find shapes, circles, ellipses, parabolas, and more. Quadratics is used in the design of products in almost every field, such as car industrial, entertainment,
astronomy, etc. |
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(2) A mathematics project connected to this unit: Topic: Parabola Selfie Poster Students will find parabolas in the real world. For example, the shape of a banana, the shape of a bridge,
the shape of the brand of McDonald's, etc. This project may be done alone or in pairs. Aims: Students will know that there are many things in the real world designed using quadratics, and the graph of quadratic functions can be found throughout nature. Students will find out that a parabola is a curve, a conic section, and a graph of the quadratic function. Students will learn how to use the graphing calculator to generate an equation for their parabola. They will know how to analyze the graph by finding characteristics. Process: Step 1:
Modeling: All students will study a sample poster with the teacher. They will learn how to use Desmos to generate an equation for a parabola on a picture.
They will get to know what they are supposed to do. Step 2:
Find two parabolas in the real world. One is found in nature, and another one is found in manmade items. Take a photo with each of them. Printed out and put on the poster. It can be in black and white. Step 3:
Students will upload that picture into Desmos. They will adjust the scale of the graph to match the dimensions of the parabola in the picture. Finally,
they will generate two quadratic equations for both of their parabolas.
Printed out the graphs and put on the poster. Step 4: Students will analyze the parabolas in terms of the axis of symmetry, vertex, domain,
range, max value, min value, etc. Students will put all of these analyses on the poster. Step 5:
Students will write any funny things and ideas that they encountered or found out when doing this project. They will put all of them on the poster. Timing: They have
4 weeks to do this project. Normally, I will ask them to submit their poster two weeks before the end of the quarter. Then during the last two weeks, students could exchange ideas based on the posters on the wall. Assessment: On the poster, students must show all the items required in the rubric. I will remind them to check each item when doing the poster. The poster should be made neat and organized and submitted on time. This project will be 20% of the total grade.
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(3) Assessment and evaluation: Formative assessment: (1) Each class,
students will work on small group activities and finish a short worksheet. I
will assess students' level of understanding based on their works on these worksheets. (2) Students will have homework for each section. I will grade only for homework completion.
Every two weeks I will offer a one-on-one conversation with each student to check their homework completion and address any issue they encountered. (5%) (3) Every week,
students will do a homework quiz. I will not grade on these quizzes. Summative
assessment: There will be a unit test (15%) and a project (20%) to do for each student. This test and the project will be used to test students' comprehension of materials. |
Elements of
your unit plan:
a)
Give a numbered list of the topics of the 10-12 lessons in this unit in the
order you would teach them.
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Lesson |
Topic |
|
1 |
Investigating Quadratic
Functions in Vertex Form |
|
2 |
Investigating
Quadratic Functions in Standard Form |
|
3 |
Completing the Square |
|
4 |
Graphical Solutions of
Quadratic Equations |
|
5 |
Factoring Quadratic
Equations |
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6 |
Solving Quadratic
Equations by Completing the Square |
|
7 |
The Quadratic Formula |
|
8 |
Transforming Quadratic
functions |
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9 |
Modeling with Quadratic
data with Real-World Problems |
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10 |
Review and Unit Test |
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