# Do You Even Lift

 Author: Kevin Metzger Unit Title: Do You Even Lift Grade: 10 Subject: Geometry/Algebra II Estimated Duration: 9-48minute class periods Unit Activities: Activity 1: How high are the bleachers? Activity 2: How high are the bleachers? Activity 4: Creating a quadratic with Data Background Knowledge:  Students will need a background knowledge of similar triangles.  In order to complete activity 1, students will use similar triangles to find the height of the football stadium bleachers.  Also, students will need to know parts of a triangle including sides, angles, as well as the relationships between all of those parts.   Date: July 2014
##### The Big Idea (including global relevance)

Building structures such as buildings and bridges has become more or less an art work.  Consider downtown Cincinnati with Music Hall, Great American Ball Park, as well as Union Terminal.  These structures are not only eye catching, but structurally sound.  They are made in such a way as to hold significant amounts of weight as well as promote safety for those that venture inside of their vast rooms.  The methods used to build these remarkable designs has been dated back to the years of Pythagoras as well as the Pythagorean Theorem.  Right triangles are the most sturdy shapes to use in architecture, and a thorough analysis of them may lead to significant understanding of how structures are built.

##### The Essential Question
1. What geometric designs promote effective building of structures such as buildings or bridges?
2. How can right triangle trigonometry be used in structural designs?
##### Justification for Selection of Content

Trigonometry is prevalent in almost all aspects of mathematics.  It is introduced in Math 2 and carried on from topic to topic up through the Calculus courses.  Right triangle trigonometry is used on high-stakes testing including the OGT which all sophomores must take in the state of Ohio in order to graduate.  Last year, 41% of the co-taught Math 2 classes failed the Ohio Graduation Test.  Also, the ACT uses right triangle trigonometry in some of its questions.  Throughout the year I get many students asking for ACT help, specifically for right triangle trigonometry.

Using right triangle trigonometry to build structures is widely used in architectural engineering as well as the engineering of bridges.  By having students build a single platform that holds weight, they are considering architecture of buildings as well as bridges.  Right triangle trigonometry also has a wide variety of applications outside of structural engineering.  Students will consider these applications in Math 3, Pre-calculus, and Calculus courses.  They learn the basics of trigonometry in Math 2, which is the attended audience of this unit.

##### The Challenge

Students will be required to build a platform using the following materials:

• 3 8x8 pieces of wood 1/2in thick wood flooring.
• 4 36 inch wood dowel rods.
• Hot Glue

The students will be competing against each other to build a platform that holds the most weight.  Students will be graded on how they use right triangles to build a platform.  The students will be restricted by the following:

• The platform must be at least 9 inches off of the ground.
##### The Hook

As the facilitator of the lesson, I will show students different applications of right triangle trigonometry.  I will hook the students by having them take part in an engaging Engineering Design Team activity.

Students will be given 20 sheets of construction paper, 20 sheets of printer paper, and scotch tape to design a platform that holds the most weight. Students will realize what structures hold the most weight and what shapes make up each of the structures.

##### Teacher's Guiding Questions
1. Where is building structures that hold weight prevalent?
2. Why are triangles the strongest shape?
3. What needs to be known about triangles in order to build a structurally sound platform?
4. What forces act on the structure?
##### ACS (Real world applications; career connections; societal impact)
1. Real World Applications:  Right triangle trigonometry can be used in the structural engineering of bridges and buildings.
2. Career Connections:  Structural engineering, Architectural engineering, Civil Engineering, Mechanical Engineering, Designers, and Builders.
3. Societal Impact:  The general society has taken a vast appreciation for right triangle trigonometry and structural engineering.  People want to be in buildings that do not collapse because of faults in the engineering of the buildings.
##### Engineering Design Process (EDP)

Students will follow the Engineering Design Process when building their platforms.  The idea behind this unit is for students to see the problems when designing structures and buildings.  They will see that the structures or buildings are required to hold a certain amount of weight.  The fact that they are building a scale version of a basic structure will allow them to easily apply the problems to real world situations.  The students will be required to work in Engineering Design teams and present their ideas to other groups at the end of their experiments.  Students will be given the opportunity to refine their designs after they test to see how much weight their first design can hold.

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

Lesson 1:  Basic Right Triangle Trigonometry

-       Day 1:  Review of Pythagorean Theorem, pre assessment (Activity 1 Worksheet A) and hook activity (as stated above in the “hook” section).

-       Day 2: The Big Idea and Essential questions will be answered prior to completing Activity 1 Worksheet B and Worksheet C.  Students will measure the height of the bleachers in the football stadium.  They will use mirrors as well as measuring tape to create two right triangles.  They will then use Pythagorean Theorem to find all of the sides of each triangle.  Finally, they will use similar triangles to find the overall height of the bleachers.

-       Day 3:  Special Right Triangles and Trigonometry

-       Day 4:  Activity 2 Worksheet E.  Students will meet with their Engineering Design teams to cover the EDP for their platforms.  They will need to develop a plan for building their structure while following the EDP.

-       Day 5:  Angles of elevation and depression

Lesson 2:  Structure Build

-       Day 6:  Activity 3 Worksheet F.  Students will build their structures.

-       Day 7:  Students will test their structure and record the overall weight that their structure could hold before it breaks.

-       Day 8:  Students will refine their design.

-       Day 9: Activity 4 Worksheet G.  Students will test their new design and present their findings to the other groups using Activity 4 Worksheet H.

-       Day 10 (1/2 day):  Post Assessment Activity 4 Worksheet I

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

CBL:  Activity 1, Activity 3

EDP:  Activity 2, Activity 4

##### Misconceptions

Students often confuse the purpose of trigonometry. They do not understand where trigonometric functions come from in regards to their previous knowledge of functions.

www.pearsonsuccess.net

##### How to Make This a Hierarchical Unit

Right triangle trigonometry is used in Math 1, Math 2, Math 3, and pre-calculus at Milford High School.  I focused this unit on the basics of right triangle trigonometry.  We could also increase the level of rigor by having students calculate the angle between the ground and their support beams.  This would allow for the Math 3 and Pre-calculus students to see the application of right triangles in their curriculum.

##### Reflection

1.     The students were able to find the solution that resulted in concrete meaningful action.  During the phase of students testing their designs, they were able to successfully conclude the concept of right triangles played a major role in their designs.  Students used right triangle trigonometry to determine why their building may have collapsed.

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 where students tend to struggle in mathematics.  Almost 80% of my students will move on to a vocational school setting.  Creating a lesson where they can use their hands allows them to better understand this type of mathematics.

3.

The chart above 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.

4.     I believe the purpose for selecting the unit was met.  Students were able to learn the EDP and also obtain mastery of the concept.  They stayed engaged the entire time we completed the lesson.

5.     Next time I implement this lesson I will try to incorporate more right triangle trigonometry.  The lesson can be so rich with mathematics, but I chose to only focus on the basics.