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
- Where is building structures that hold weight prevalent?
- Why are triangles the strongest shape?
- What needs to be known about triangles in order to build a structurally sound platform?
- What forces act on the structure?
ACS (Real world applications; career connections; societal impact)
- Real World Applications: Right triangle trigonometry can be used in the structural engineering of bridges and buildings.
- Career Connections: Structural engineering, Architectural engineering, Civil Engineering, Mechanical Engineering, Designers, and Builders.
- 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.
Unit Academic Standard
A.SSE.1 Interpret expressions that represent a quantity in terms of its
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
a. Factor a quadratic expression to reveal the zeros of the function
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.
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
Students often confuse the purpose of trigonometry. They do not understand where trigonometric functions come from in regards to their previous knowledge of functions.
How to Make This a Hierarchical Unit
How to Make This a Hierarchical Unit