Author: Tiffany Stanton Unit Title: Save Your Friends Grade: 12 Subject: Pre-Calculus Estimated Duration: 7 Days Unit Activities: Activity 2: Hook and Intro to EDP Activity 3: Challenge and Essential Questions 1.1.01a. Pre  Assessment 1.1.02b. EDP Powerpoint 1.2.04d. Trebuchet Simulator Data Sheet 1.2.04e. Trebuchet Simulator Rubric 1.3.08h. Final Presentation 1.3.08i. Post Assessment Background Knowledge:  Students will have to have prior knowledge of basic functions.  Students should know about linear and quadratic functions, however, they will learn how to link those types of equations to real world problems.  They also will be ask to derive their own equations based on their data for the first time. Date: October 2014
##### The Big Idea (including global relevance)

How can you accurately hit a specified target using a trebuchet?

Students will be given a scenario in which they will need to develop a solution.  Your friends are trapped in a shelter in the middle of a war field. They are surrounded by enemies, no one can leave and no one can enter without putting everyone in danger. They are on lock down.  Their friends will soon begin to get hungry and thirsty.  Not only are they surrounded by enemies on the ground but also in the sky.  How will you get needed supplies to your friends?

Students will be told the specified materials available to help save their friends.

The students will be given a trebuchet kit for creating each groups trebuchet.  After creating the trebuchet students will then be able to adjust the projectile mass, the counterweight height and the counterweight mass.  Students will need to build with care and precision and record their data from their different trials.  The students will then use that data to determine how accurate their trebuchet is to saving their friends.  Students will then have the ability to refine their trebuchet to be sure it is the most accurate.

##### The Essential Question
1. What is a trebuchet?
2. How does it work?
3. What math topics do you think relate to trebuchets?
4. What information is important to be sure you hit your target accurately?
##### Justification for Selection of Content

Projectile motion is a very large topic often discussed in most physics classes. However, its applications are seen in pre-calculus and calculus as well. With that being said, projectile motion applies to a variety of real-world situations. For example, the military uses projectile motion when shooting a variety of weapons. Also, NASA considers projectile motion when launching things into space.

##### The Challenge

Your friends are trapped in a shelter in the middle of a war field.  They are surrounded by enemies, no one can leave and no one can enter without putting everyone in danger. They are on lock down.  Your friends will soon begin to get hungry and thirsty.  Not only are they surrounded by enemies on the ground but also in the sky.  How will you get needed supplies to your friends when you only have one chance to get it right?

##### The Hook

I will show students a combined video of two trebuchets in history where accuracy was crucial. It also shows the importance of making refinements to a product, project, or prototype.

https://www.youtube.com/watch?v=L1EAA7pkEJ4 (trebuchets in history, highlights importance of refinements)

http://pbskids.org/dragonflytv/show/trebuchet.html (kids making a trebuchet to get supplies to a friend at a height and distance)

##### Teacher's Guiding Questions
1. What motion does the projectile follow throughout its course of flight?
2. What equation does that projectile model?
3. What do you need in order to maximize the distance of the trebuchet?

4. What important piece(s) of information do you need in order to find the maximum height and distance covered of a quadratic?

5. How do the variables of the trebuchet correlate to the variables of the quadratic equation?

##### 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: Currently many countries are experiencing this exact issue as stated in the challenge problem.  There are families in Israel that are separated from each other and from resources because of the airstrikes from Hamas in Gaza.  There are missiles being sent from Gaza into Israel and it is killing and separating many innocent people that are not even involved in the fight.  Also Iraq is experiencing this type of fighting right now with the terrorist group, ISIS.  ISIS has taken over major cities in Iraq with aggressive force.  Iraqis are scared and again they are surround by enemies in their own homes.  This will help students understand the difficulty that military have in sending help and it will help students also understand the difficulty in getting the missile strikes correct, which leads to many innocent deaths.

##### 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 unit:

1. Analyze quadratic equations that relate to projectile problems in the real-world.

a.     Occurs in 1.1.01a, 1.2.05f, 1.3.08i

2. Use the engineering design process to develop a trebuchet and launch a projectile.

a.     Occurs in 1.1.02b, 1.1.03c, 1.1.04d-e, 1.3.06, 1.3.08

3. Apply the data they receive from their launches to derive quadratic equations.

a.     Occurs in 1.2.04, 1.2.04d-e, 1.3.06, 1.3.08

4. Determine the exact settings for their trebuchet to hit the target, then test these settings using their trebuchets.

a.     Occurs in 1.3.06-07

CCSS.MATH.CONTENT.HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of the function it defines.

CCSS.MATH.CONTENT.HSF.LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSS.MATH.CONTENT.HSF.LE.A.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

CCSS.MATH.CONTENT.HSF.LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.

CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

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

1.1.2; 1.1.2b; 1.1.3; 1.1.3c, 1.3.6; 1.3.8; 1.3.8h

Students will need:

1. Trebuchet Kits (I used the ones at: http://www.pitsco.com/Physical_Science/Simple_Machines/Catapults_and_Trebuchets/Kits/Trebuchet_Kits)
2. TINspire CX Calculators (these are provided as I have a class set of 30 in my classroom)
3. TINspire Teacher Software (this allows for you to upload the Pumpkin.tns file to all the calculators and it allows you to project the calculator if students need some guidance on the activity)
4. Clay (to make the projectile mass)
5. Metal washers (to make the counterweight mass)
6. String (to make the counterweight height)
7. X Acto Knife
8. Needle-nose pliers
9. Scissors
10. Sandpaper
11. Glue (hot glue or wood glue)
##### Pre-Unit Assessment Instrument

1.1.1a; Worksheet a

##### Post-Unit Assessment Instrument

1.3.8i; Worksheet i