Title: Quadratics and Realistic Domain

Author: Jenni Darlow

Grade: Algebra I

Date to be taught: 5^th six weeks

Length of lesson: 1 class period

Objectives:

Students will be able to:

Understand the concept of realistic domain

Use a parabola to identify a situation

Use a parabola to illustrate a situation

Use the equation of a parabola to extrapolate about the situation

Construct a parabola given a real-life situation

Identify the realistic domain of a situation

TEKS addressed:

(a) Basic understandings

(3) Function concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students use functions to determine one quantity from another, to represent and model problem situations, and to analyze and interpret relationships.

(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.

(b) Knowledge and skills

(A.1)  Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

The student is expected to:

(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

(E) interpret and make decisions, predictions, and critical judgments from functional relationships.

(A.2)  Foundations for functions. The student uses the properties and attributes of functions.

The student is expected to:

B)  identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

(C)  interpret situations in terms of given graphs or creates situations that fit given graphs

(A.9)  Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions.

The student is expected to:

(A)  determine the domain and range for quadratic functions in given situations;

(D)  analyze graphs of quadratic functions and draw conclusions

Engage:

Teacher does	Student does
Have students in groups of 3 or 4. Give each group a scenario of a football game in which they are trying to catch a pass. Give the students a drawing of the first half of the throw and ask them where they need to be to catch the ball	Students discuss the problem in their groups and decide on the best answer
Call on each group. If they are correct, it is a touchdown and they get 7 points. If they are incorrect, they get another chance, but only for a field goal which is 3 points	Students tell the class the answers and if they are incorrect, they come up with another answer.

Evaluate: Teacher evaluates students abilities to extend a parabola in order to answer a question illustrating a scenario

Explore:

Teacher does	Student does
Give students worksheets with various parabolas representing different things and various quadratic formulas	Students will match up the parabolas with the equations that they think best fit.
Walk around and check students’ answers. If they are all correct, its another touchdown and they get 7 more points. If they are not all correct they have try again for 3 points	Students will show teacher their answers and correct them if they need to.
Teacher will then hand out another worksheet with word problems on it relating to the parabolas and equations from the first worksheet. The questions will involve making predictions for the situation represented by the parabola and equation.	Students will work in their groups to answer the questions. Students should recognize that they cannot simply plug numbers into the formula for every situation because the answer would not be realistic. This introduces realistic domain.
Teacher will walk around and check answers. Again, if they are correct, it is 7 points per question, with 3 possible for a correct answer the second time.	Students will show and explain their answers and correct them if necessary.

Evaluate:

Teacher will evaluate students’ answers and if they understand how quadratic equations can represent real-life situations and if they understand realistic domain.

Explain:

Teacher does	Student does
Call on various students to share their answers to the problems on the worksheet	Tells class the answer
Ask class if they agree with the answer. Call on a different student to say why they agree or disagree with the answer given	Students tell the rest of the class how they came up with the answer. They should discuss the idea of realistic domain and that answers obtained from just plugging numbers into the formula might give an answer that does not make sense for the situation.

Evaluate: Teacher will evaluate students’ ability to explain their answers and how they obtained them.

Extend:

Teacher does	Student does
Ask students what it is about a ball being thrown in the air, or a water fountain that makes it have a parabolic shape	Students will think about the properties of different situations and what makes them parabolic
Ask students to construct a parabola and estimate an equation given a situation	Students will attempt to construct a parabola, by a simple sketch, and to come up with a quadratic equation that represents a situation

Evaluate: Teacher will evaluate students’ ability to go from a situation to a parabola and an equation.

Based on the number of points the students have acquired, they get to choose a prize (candy), the size of which is determined by the points.