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
Unit Academic Standard
Factor a quadratic expression to reveal the zeros of the function it defines.
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Interpret the parameters in a linear or exponential function in terms of a context.
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:
- Trebuchet Kits (I used the ones at: http://www.pitsco.com/Physical_Science/Simple_Machines/Catapults_and_Trebuchets/Kits/Trebuchet_Kits)
- TINspire CX Calculators (these are provided as I have a class set of 30 in my classroom)
- 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)
- Clay (to make the projectile mass)
- Metal washers (to make the counterweight mass)
- String (to make the counterweight height)
- X Acto Knife
- Needle-nose pliers
- Glue (hot glue or wood glue)
Pre-Unit Assessment Instrument
1.1.1a; Worksheet a
Post-Unit Assessment Instrument
1.3.8i; Worksheet i