**Teacher's Guiding Questions**

- What motion does the projectile follow throughout its course of flight?
- What do you need in order to maximize the distance of the trebuchet?
- What important piece of information do you need in order to find the maximum height of a quadratic?

**ACS (Real world applications; career connections; societal impact)**

Applications: Students will be considering the motion of a projectile through its course of flight. This closely resembles what the military does when analyzing the flight of a weapon or missile. Also, this closely resembles what NASA considers when analyzing the flight of a rocket into space

Career Connections: Students will see military applications. Also, students can correlate this to any type of projectile motion. This could mean aerospace engineering, and mechanical engineering.

Societal Impact: How could the maximum height of a projectile affect a society? If a projectile reaches a certain height then it reaches a certain linear distance. This could have a major impact especially in missile launches.

**Engineering Design Process (EDP)**

Students will use the engineering design process when considering how to create their trebuchet with the materials they are given. Also, using the challenge based learning framework, students will complete the following activities throughout the lesson:

- Use the engineering design process to develop a trebuchet and launch a projectile.
- Apply the data they receive from their launches to quadratic equations.
- Analyze the quadratic equations
- Determine the maximum height and test this value using their trebuchets.

##### Unit Academic Standard

F.IF.4 For a function that models a relationship between two quantities,

interpret key features of graphs and tables in terms of the quantities,

and sketch graphs showing key features given a verbal description

of the relationship. *Key features include: intercepts; intervals where*

*the function is increasing, decreasing, positive, or negative; relative*

*maximums and minimums; symmetries; end behavior; and periodicity.*

F.IF.7 Graph functions expressed symbolically and show key features

of the graph, by hand in simple cases and using technology for more

complicated cases.★

a. Graph linear and quadratic functions and show intercepts,

maxima, and minima.

b. Graph square root, cube root, and piecewise-defined functions,

including step functions and absolute value functions.

F.BF.1 Write a function that describes a relationship between two

quantities.★

a. Determine an explicit expression, a recursive process, or steps for

calculation from a context.

b. Combine standard function types using arithmetic operations.

*For example, build a function that models the temperature of a*

*cooling body by adding a constant function to a decaying exponential,*

*and relate these functions to the model.*

F.BF.3 Identify the effect on the graph of replacing *f(x) *by *f(x) + k,*

*k f(x), f(kx)*, and *f(x + k) *for specific values of *k *(both positive and

negative); find the value of *k *given the graphs. Experiment with

cases and illustrate an explanation of the effects on the graph using

technology. *Include recognizing even and odd functions from their*

*graphs and algebraic expressions for them.*

##### Tentative Schedule

Day 1: Introduction to quadratics

Graphing Quadratics: Basic transformations

Day 2: Graphs and Transformations

Day 3: Activity 1 Worksheet A: Students will use what they learned in class to complete graphs and transformations of quadratic functions.

Day 4: Activity 1 Worksheet B: Students will be introduced to the idea of the project through the Smart Board Notebook presentation. They will then be asked to complete the Engineering Design Process (worksheet B). This is where they can develop guiding questions and a possible model for their trebuchet launcher.

Day 5: Activity 1 Worksheet B: After the introduction, there may need to be another day to complete Worksheet B.

Day 6: Discussion of standard form and properties of quadratic equations (Smart Board Notebook presentation).

Day 7: Discussion of converting vertex to standard form as well as how to create graphs from standard form equations.

Day 8: Activity 2 Worksheet C: Practice converting from standard form to vertex form.

Day 9: Activity 2 Worksheet D: Students will build their trebuchets

Day 10: Activity 2 Worksheet D: Students will build their trebuchets.

Day 11: Creating quadratic equations given a data set. Students will use graphing calculators, and Microsoft Excel.

Day 12: Activity 3 Worksheet E: Practice creating equations given a data set.

Day 13: Activity 3 Worksheet F: Creating a quadratic equation given the data they obtain from several launches of their trebuchet.

Day 14: Activity 4 Worksheet G: Students will convert their standard form equation to a vertex form and find the maximum height their trebuchet will reach. They will then refine their design and see if they can reach the theoretical maximum.

Day 15: Extra day just in case they need extra time to refine their design.

##### Where the CBL and EDP appear in the Unit

- Activity 1 Worksheet B represents the EDP

Students will use this design plan to fabricate an actual trebuchet. They will then use the trebuchet to make several launches. After each launch they will record the maximum height of their projectile. Using this data they will create a quadratic equation that best represents their data, theoretically find the maximum height, then refine their design.

- Activity 2 Worksheet D represents the CBL

##### Misconceptions

1. Students will confuse the transformations of quadratic functions. They often confuse which part of the equation forces the parent function to move left, right, up, or down.

2. Students may not understand why a quadratic function needs at least three points to develop a solid relationship between input and output values.

##### Additional Resources

www.pearsonsuccess.net

##### Pre-Unit Assessment Instrument

##### Post-Unit Assessment Instrument

##### Results: Evidence of Growth in Student Learning

After teaching the Unit, present the evidence below that growth in learning was measured through one of the instruments identified above. Show results of assessment data that prove growth in learning occurred.