Author:
Jennifer Dunmire
Subject:
Mathematics, Geometry, Measurement and Data, Trigonometry
Material Type:
Activity/Lab
Level:
Middle School, High School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards (5)

Indirect Measurement and Similar Right Triangles Lab

Indirect Measurement and Similar Right Triangles Lab

Overview

On a hike with her children, Mrs. Thompson noticed the reflection of the top of a pine tree in a puddle in the path. Her son, who is almost a foot taller than she is, could not see the top of the tree in the puddle until he moved. Why did her son need to move to see the top of the tree? How can they use similar right triangles and indirect measurements to find the height of the tree?

Using Similar Right Triangles and Indirect Measurement in real world settings.

 

Title: Indirect Measurement and Similar Right Triangles Lab

 

Section Name = Short Lesson Overview 1 sentence (Not to exceed 250 words)
  1. On a hike with her children, Mrs. Thompson noticed the reflection of the top of a pine tree in a puddle in the path. Her son, who is almost a foot taller than she is, could not see the top of the tree in the puddle until he moved. Why did her son need to move to see the top of the tree? How can they use similar right triangles and indirect measurement to find the height of the tree?

 

Attach Section Resources/Links: Any worksheets, presentations, illustrations, assessments or activities. (Preferably in PDF)

Data Recording Sheet: https://docs.google.com/document/d/1ALOVlIFgnPwSPh3orSAOxhVh9lrpVaM9wz7DYGVoIHY/edit?usp=sharing

 

Bell Ringer: https://docs.google.com/document/d/19SWTlDufw6xkF4-_PYtgUP9XCD-6EGHZeMHqoC5d0aM/edit?usp=sharing

 

Rubric: https://drive.google.com/file/d/0BxV1LO6iHp1yZmRuV1JVbGIxT1k/edit


 

Main Content Section  (Visible in Student View) (In Bee lesson example, it was left blank)


 

 

Add to Instructor’s Notes:

 

Timeframe: 60-90 minutes

 

Stage 1 - Desired Results

Big Idea(s)& Essential Questions
Big Ideas: On a hike with her children, Mrs. Thompson noticed the reflection of the top of a pine tree in a puddle in the path. Her son, who is almost a foot taller than she is, could not see the top of the tree in the puddle until he moved. Why did her son need to move to see the top of the tree?
Essential Questions:
  • How do I plan and conduct a simple investigation?
  • How do I decide to change my plan of action (cause-effect relationship)?

 

Students Will KnowStudents Will Be Doing
  • Content specific vocab
  • Tech Ed
  • Science
  • Math
  • Computer Science
  • Career Ed
  • Steps of design process
  • Creating and solving proportions to find the height of an elevated object.
  • Converting measurements
  • Creating and revising blueprints

 

Stage 2 - Evidence of Understanding

Assessments (Formative and Summative):Performance Task(s)
  • Informal Formative Assessments throughout unit (i.e. classroom observations, questioning)
  • Formal assessments on:
  • Individual Course Summative Assessments
  • Create and revise blueprints
  • Calculate the height of an elevated object using indirect measurement.

 

Stage 3 - Lesson Learning Targets

Learning Activities: Learning targets are written from the students perspective. I can…
  • Work through the Engineering Design process by identifying and applying key components in the process.
  • Create a blueprint to identify materials and measurements necessary to see the elevated object.
  • Describe and analyze data from completing an experiment.
  • Solve problems and make adjustments to my blueprints to improve the overall design.
  • Convert measurements to create a simpler problem (inches to feet)
These should lead up to answering the Essential Question(s).
  • I can….

 

 

Lesson Procedures:   
MaterialsActivitiesPresentationsAssessments
Bell ringer::Classroom Materials
  • Work through Bell Ringer with students to frame the premise of the problem. https://docs.google.com/document/d/19SWTlDufw6xkF4-_PYtgUP9XCD-6EGHZeMHqoC5d0aM/edit?usp=sharing
  • Present the materials to the students with descriptions of what they will be using when they develop their plan for the blueprint to solve for the height of the elevated object. Divide students into groups of 3 or 4. Students should create individual blueprints to present to the other members of their team based on their own individual height. Team members will discuss the pros and cons of each sketch and then combine their blueprints into the final product.
Procedures:1.     Review the Engineering by Design Process2.    Introduce the Problem: On a hike with her children, Mrs. Thompson noticed the reflection of the top of a pine tree in a puddle in the path. Her son, who is almost a foot taller than she is, could not see the top of the tree in the puddle until he moved. Why did her son need to move to see the top of the tree?   Problem: Create a blueprint including each group member’s height to use proportions and indirect measurement protocols to find the height of an elevated object.3.  Present and display the materials to the students to identify these materials.  Divide the students into groups of 3-4. Provide independent time for each individual student to develop his/her brief to present to the other members of the group as well as choose an elevated object and take preliminary measurements. Groups will discuss the pros and cons of each brief and then create their blueprint. 4. Each group will verify measurements and then calculate the height of the elevated object. TEACHER NOTE: Students should be allowed to adjust and remeasure as necessary.5.    Groups will work on their calculations and record their observations. Recordable data could include: student height, student distance from the mirror, distance from the mirror to the bottom or a point underneath the elevated object. 6. Groups will analyze their results and determine the cause of what they observed. Students will then make adjustments to their blueprint based on their actual findings using colored pencils for evidence of adjustments. All group members must approve of the changes. 7. Groups will present their overall findings to the class. Discussion points should include: What adjustments were made to the blueprint and why? Identify some of the differences in the initial blueprint and the final. Pros and Cons for specific design elements. Did certain design features matter? Did the adjustments make sense? Identify any design flaws that you would make adjustments to in the future.
  •  Groups will present their overall findings to the class through a PowerPoint or Google Slides. Discussion points should include: Which design elements needed adjusted on the blueprint? Identify some of the differences in the different blueprints. Pros and Cons for specific design elements. Did certain design features matter? Did the adjustments work? Identify any design flaws that you would make adjustments to in the future.

 


 

 

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PA Core Standards / Next Generation Science Standards
T & E EducationScience EducationMathematics EducationComputer ScienceCEW
 3.2.7B B. Apply process knowledge to make and interpret observations. • Measure materials using a variety of scales. • Describe relationships by making inferences and predictions. • Communicate, use space / time relationships, define operationally, raise questions, formulate hypotheses, test and experiment, • Design controlled experiments, recognize variables, and manipulate variables. • Interpret data, formulate models, design models, and produce solutions. 3.2.7CC. Identify and use the elements of scientific inquiry to solve problems. • Generate questions about objects, organisms and/or events that can be answered through scientific investigations. • Evaluate the appropriateness of questions. • Design an investigation with limited variables to investigate a question. • Conduct a two-part experiment. • Judge the significance of experimental information in answering the question. • Communicate appropriate conclusions from the experiment. 3.2.7D D. Know and use the technological design process to solve problems. • Define different types of problems. • Define all aspects of the problem, necessary information and questions that must be answered. • Propose the best solution. • Design and propose alternative methods to achieve solutions. • Apply a solution. • Explain the results, present improvements, identify and infer the impacts of the solution.  CC.2.2.7.B.3 Model and solve real world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representationsCC.2.1.7.D.1Analyze proportional relationships and use them to model and solve real-world and mathematical problems.CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them. Standard - CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multi-step problems.Standard - CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.Standard - CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations.Standard - CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.Standard - CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them.Standard - CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools.Standard - CC.2.3.8.A.3 Understand and apply the Pythagorean Theorem to solve problems.Standard - CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.Standard - CC.2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.Standard - CC.2.3.HS.A.14 Apply geometric concepts to model and solve real world problems. 13.3.5A. Explain how student attitudes and work habits transfer from the home and school to the workplace. B. Explain the importance of working cooperatively with others at both home and school to complete a task. C. Identify effective group interaction strategies, such as, but not limited to:  Building consensus  Communicating effectively  Establishing ground rules  Listening to others