# Mousetrap Mania

 Author: Kevin Metzger Unit Title: Mousetrap Mania Grade: 10 Subject: Geometry/Algebra II Estimated Duration: 14-48 minute class periods Unit Activities: Background Knowledge:  Students will need a general knowledge of the x,y plane.  Also, they will need to know how to plot points on the x,y plane. Date: August 2013
##### The Big Idea (including global relevance)

Linear functions have many real-world applications.  However, students only remember lines as “y = mx + b.”  Although this is a correct way to remember a line, students never see the true reason why lines are written this way.  This lesson will teach students the relationship between “x” and “y” through a real-world application.  Students will build cars that are powered by mouse traps.  They will then use these cars to generate distance versus time data.  From the data students will be able to generate a linear equation and estimate the average velocity of their car.

##### The Essential Question

1.     What does a linear equation represent?

2.     What is the slope of a linear equation?

3.     How does the slope relate to mouse trap cars?

4.     How do mouse trap cars relate to a bigger picture?

##### Justification for Selection of Content

Using mouse trap cars to generate linear equations is a great physics application.  More importantly it gives the students an opportunity to understand how linear motion occurs and how it applies to things such as driving a car.

##### The Challenge

Students will be required to use their creativity to build a mouse trap car.  However, they will need to design their car to move as quickly as possible.  Students will use this opportunity to compete with other groups to build the fastest car.

##### The Hook

As the facilitator of the lesson, I will show students different applications of linear motion.  I will show them the University of Cincinnati’s design of a car that runs solely on the power of water.  This will give them an idea of environmentally friendly vehicles.  Also, it will get them thinking about how these vehicles move.

##### Teacher's Guiding Questions

1.     How will our mouse trap cars relate to our everyday life?

2.     What is a linear equation?

3.     What relationship represents linear functions?

4.     What two variables will we use for our mouse trap cars?

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

1. Real World Applications:  The linear motion of mouse trap cars closely resemble that of actual automobiles.  By analyzing the data obtained from mouse trap cars, students will understand how automobiles obtain and maintain speed.  Also, they will have an idea on how distances relates to time.  More importantly, they will understand how the slope of a distance versus time graph represents the velocity of their car.

2. Career Connections:  The linear motion of automobiles is a large topic in mechanical engineering.  Also, car mechanics need an understanding of the relationship between distance and time.

3. Societal Impact:  The general society has taken a vast appreciation of automobiles in the last century.  As a person of this society, we need a fast and efficient way to travel.  By understanding the relationship between distance and time, students will better understand the impact of automobiles on our daily life.  Whether that means calculating gas mileage or simply how long it will take to make a trip.

##### Engineering Design Process (EDP)

Students will follow the engineering design process when constructing their mouse trap cars.  Although students will be given “kits” of materials for the cars, they will use their own creativity to actually build the car.  Students will get to choose how many wheels, how many axles, and even the size of the wheels.  More importantly, students will use the engineering design process to take data from their cars.    Then, students will be given the chance to refine their design.  As they are competing to build the fastest car, students will need to make improvements as necessary.  This data will be valuable in their understanding of linear equations.

A.SSE.1 Interpret expressions that represent a quantity in terms of its

context.★

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of

their parts as a single entity. For example, interpret P(1+r)n as the

product of P and a factor not depending on P.

A.SSE.3 Choose and produce an equivalent form of an expression

to reveal and explain properties of the quantity represented by the

expression.★

a. Factor a quadratic expression to reveal the zeros of the function

it defines.

b. Complete the square in a quadratic expression to reveal the maximum

or minimum value of the function it defines.

c. Use the properties of exponents to transform expressions for

exponential functions. For example the expression 1.15t can be rewritten

as (1.151/12)12t 1.01212t to reveal the approximate equivalent

monthly interest rate if the annual rate is 15%.

A.CED.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.

A.CED.2 Create equations in two or more variables to represent

relationships between quantities; graph equations on coordinate axes

with labels and scales.

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the

same reasoning as in solving equations. For example, rearrange Ohm’s

law V = IR to highlight resistance R.

##### Unit Activities

Tentative Schedule:

Day 1: Introduction to functions and relations.

Day 2:  Activity 1 Worksheet A:  Students will complete the egg drop activity.

Day 3:  Activity 1 Worksheet A:  Students will complete the analysis of their data from the egg drop activity.

Day 4:  Activity 1 Worksheet B:  Students will practice identifying functions and relations as well as

Day 5:  Students will work in groups on their EDP for the unit.  They will need to get an idea of what type of car they would like to build with the given materials.  They will also be required to draw a sketch of the car they would like to make.

Day 6-7:  Introduction to all three forms of linear equations via the Smart Board presentation.

Day 8:  Students will complete Worksheet D

Day 9-10:  Students will complete Worksheet

Day 11-12: Students will spend both class periods refining their design and taking final data for the challenge.

Day 13:  Students will be engaged in a “navigating” Microsoft Excel lesson.

Day 14:  Students will use Microsoft Excel to analyze their data (Worksheet F).

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

Activity 2 Worksheet C represents the EDP portion of this unit.  Students will plan how they will build scaled versions of cars that will be powered by mouse traps.  Also, In Activity 4 Worksheet F, students will have the opportunity to refine the design that they built in the previous lesson.

##### Misconceptions

1.     Students may confuse why types of relationships are linear.

2.     Students may confuse how distance and time form a linear relationship.

1.     www.pearsonsuccess.net

Worksheet G

Worksheet H

##### Results: Evidence of Growth in Student Learning
The chart below shows the amount of questions students correctly answered on the pre-assessment as well as the amount of questions answered on the post assessment.  The red bars clearly show a significant growth from pre to post assessment. ##### How to Make This a Hierarchical Unit

If this lesson was taught at a lower level, the students would only be able to write basic equations of lines.  Therefore, students would have to be given the resources to generate linear equations from data without fully understanding where the application stands mathematically.

##### Reflection

1. The students were able to find the solution that resulted in concrete meaningful action.  During the students presentations they were able to successfully describe how they obtained their data.  Also, students were able to successfully describe how their data represented a linear equation.

2. The content that I chose for this lesson was chosen based on the history of my students.  The class that I teach is a co-taught class (content teacher plus intervention specialist) where students tend to struggle in mathematics. Using mathematics in the real world helps these types of students apply the math so they can see where they would actually use the math outside of the classroom.

3. I do believe the purpose for selecting the unit was met.  Students were able to use the data to theoretically develop a linear equation.  Also, they were able to describe how the math applies to their actual process.  Finally, students were able to use the engineering design process to perfect their cars.  If I were to change anything, I would give the students more materials to work with.  This would allow the cars to go even farther than they already do.