ACS (Real world applications; career connections; societal impact)
- Real World Applications: Students will understand how objects move through certain medians such as water and air. The concept of a floating boat is very similar to the concept of a “gliding” airplane.
- Career Connections: Boat engineer, structural engineer, aeronautical engineer, Boat Designers (recreational, commercial, and military).
- Societal Impact: Students will better understand how boats work. They will understand how much weight a boat can hold as well as how much space the boat can actually take up with respect to how much weight it can hold.
Engineering Design Process (EDP)
Students will use the engineering design process when building their overall structure for their aluminum foil boats. They will have to decide how to maintain the overall constraints on size as well as how much weight the structure can hold. Students will work in engineering design teams to design the boat before actually making the boat. They will record all of their calculations in their engineering design notebooks. Students will also have a chance to refine their design after testing their first design.
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: Understanding Surface Area and Volume:
Day 1: Review of Surface Area of various 3D figures as well as pre-assessment: Activity 1 Worksheet A.
Day 2: Review of Volume of various 3D figures. Activity 1 Worksheet B
Day 3: Activity 1 Worksheet C – The Hook. Students will be given an 8.5inx11in piece of card-stock. They will be instructed to work in their engineering design teams to develop a structure that holds the most amount of water for a total of 2 minutes. This structure must be able to close and open in order to measure the amount of water.
Day 4: Activity 2 Worksheet D. Students will be given the opportunity to discuss the big idea and essential questions based on the “hook” from the previous day. This is where I will attempt to have students develop the idea of floating on their own. Students will be given the constraints of their overall challenge. They will be expected to work on the engineering design process with their engineering design teams. Students will record all steps to the engineering design process in their engineering notebooks.
Lesson 2: Surface Area and Volume in Building Boats:
Day 5: Activity 3 Worksheet E. Students will build their first structure for an aluminum foil boat that can hold 1000grams of water.
Day 6: Students will test their design Activity 3 Worksheet F.
Day 7. Students will refine their design to make it hold more weight or meet the first 1000gm requirement.
Day 8. Activity 4 Worksheet H. Students will present their overall experiment with the first and second designs. They will be expected to describe, in detail, any calculations to determine the maximum weight that their structures can hold.
Where the CBL and EDP appear in the Unit
CBL: Worksheet C, Worksheet D, Worksheet E
EDP: Worksheet D, Worksheet E, Worksheet H
Students will confuse how to find the surface area and volume of their own boats.
How to Make This a Hierarchical Unit
Surface Area and Volume is used in Math 1, Math 2, Math 3, and pre-calculus at Milford High School. I focused this unit on the 3 dimensional surface area and volume. We could also increase the level of rigor by having students study the forces on the boat including buoyant force. Most students will learn this in their physics class. However, to increase to another level of mathematics, buoyant force would be a great topic to discuss.
- 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 surface area (more than volume) played a huge role in the outcome and result of their designs. Students were able to make conclusions, using surface area, as to why their boats may not have held as much as they anticipated.
- 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.
How to Make This a Hierarchical Unit