Indirect Measurement and Similar Right Triangles Lab
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
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|Timeframe: 60-90 minutes|
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|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?|
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|PA Core Standards / Next Generation Science Standards|
|T & E Education||Science Education||Mathematics Education||Computer Science||CEW|
|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|