Can You Build It?

In this WebQuest, students will be working together in groups of three to determine the feasibility of given architectural jobs and then design homes under particular constraints. The WebQuest will have students working through real applications of solving right triangles, which requires them to understand whether or not they have sufficient information given in order to proceed. Students need to have a solid foundation in evaluating trigonometric expressions, using a graphing calculator (or online calculation tool), and possess the ability to comprehend given information and determine what else is necessary to solve a problem. In addition, students will also need to apply these tools to not only right triangles but also to oblique triangles. Finally, they will have to evaluate their work and decide whether their designs will be possible under different budgets.

 

By the end of the WebQuest, students should be able to answer the following essential questions:

• How can we use trigonometry to solve real-world problems?
• How can we use concepts of trigonometry to find unknown parts of any type of triangle?
• What quantities need to be known in order to determine what is unknown?

Performance Objectives

• Students will deepen understanding of right triangles and trigonometry by applying them to a real-life context.
• Students will collaborate to develop a unique, creative project design.
• Students will utilize technology to further advance their learning.

Outcomes

• Students will be able to determine from the given information what methods of solving will be appropriate and useful.
• Students will be able to apply their calculations to a realistic context and determine the feasibility of their design.
• Students will be able to work together and combine different ideas to create one, cohesive project.

Scaffolding Knowledge

Essential Questions:

• How can we use trigonometry to solve real-world problems?
• How can we use concepts of trigonometry to find unknown parts of any type of triangle?
• What quantities need to be known in order to determine what is unknown?

Incorporating Bloom’s Taxonomy

Click link for PDF: Bloom’s Taxonomy Table

 

Gardner’s Multiple Intelligences

Click Link for PDF: Gardner’s Multiple Intelligence Table

 

Gregorc’s Mind Styles

Click Link for PDF: Gregorc’s Mind Styles Table

Sense & Meaning

The purpose of this activity is to have you consider information, make calculations, and then propose a recommendation based on what you have calculated. This process mirrors real-world problem solving and does not merely present an artificial solution that has just one correct answer. This should allow the students to connect better with the material and gain some insight as to how the formulas and concepts can help them to solve real-world problems.

Difficulty vs. Complexity

The problems addressed within this project are at an age-appropriate level of difficulty. While they may be difficult for some, we hope that the difficulty of the problems will encourage individuals to seek help from their group members and that the students will consider how best to solve the problem from among a number of potential methods of solution. The structure of the problems is that they are not constructed in a simple manner. We have included the element of uncertainty in order to promote the idea of coming up with a potential solution and potentially defending that solution (see CCSS Math Practice Standard 3).

Standards Addressed

The Mathematical Practice Standards

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

CCSS.MATH.CONTENT.HSG.MG.A.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).^*

CCSS.MATH.CONTENT.HSG.SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CCSS.MATH.CONTENT.HSG.SRT.C.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.^*

CCSS.MATH.CONTENT.HSG.SRT.D.11
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

CCSS.MATH.CONTENT.HSG.MG.A.3
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).^*

Teacher Preparation

• Examples: prior to Day One activities, students will have gone over key terms, worked through examples which are relevant to the WebQuest, and completed a formative assessment to inform instruction over the course of the unit.
• Materials: Graphing Calculators, SMART Board, Internet access, smartphones, laptop computers, calculators
• Printable handouts can be found within this page and others within the WebQuest

Key Terms

Trigonometry	The study of the relationship of the sides and angles of a triangle
Right Triangle	A triangle which contains a right angle
Hypotenuse	The side of a right triangle which is opposite the right angle
Legs	Any side of a triangle which is not the hypotenuse
Trigonometric Ratio	The quotient which results from the ratio of any two sides of a right triangle.

 

 

Alternate Outline – Accommodations

Example:

• The problem offers the opportunity for “multiple entry points” for students who are having difficulty. The teacher will use scaffolding techniques to give students of differing abilities a challenge in solving the problem. Those techniques may include giving hints, providing an alternate problem with a simpler solution, or the use of additional resources that may assist the student.
• Additionally, we have the ability to control who works with whom, and can construct groups of similar ability or mixed ability, depending on what each learner needs or what is best for the group.
• Students can access the WebQuest on their smartphones or at home if Internet access is not available in class. Additionally, a printed version of the WebQuest can be made available.
• For ELL students, we will provide access to translation tools, or simplified diagrams which rely more on numbers than words.

Suggested Follow-Up

If students need more practice on skills, visit:

• Khan Academy (www.khanacademy.com)
• Wolfram Math World (mathworld.wolfram.com)
• Kuta Worksheets (kutasoftware.com)