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How do ratios and proportions enable the solving of problems involving similar objects? |
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3. Student Learning Map
- Topic:08. Ratios, Proportions, and Similarity (Chapter 8)
- Subject(s):Math
- Days:17
- Grade(s):9, 10
Key Learning:
The concepts of ratios, proportions and similarity are strongly interrelated and necessary for solving problems with similar figures.
Unit Essential Question(s):
Concept: Similar Polygons
PH: 8.2
MCD: 7.3
Concept: Proving Triangles Similar
PH: 8.3
MCD: 7.4, 7.5
Lesson Essential Question(s):What are the similarities and differences between ratios and proportions? (A)
Lesson Essential Question(s):How can triangle similarity be used to indirectly find missing lengths? (A)
(ET)Concept: Similarity in Right Triangles
PH: 8.4
MCD: 8.1
Concept: Proportions in Triangles
PH: 8.5
MCD: 7.6
Lesson Essential Question(s):How does the altitude drawn to the hypotenuse of a right triangle demonstrate the use of a geometric mean?
(A)Lesson Essential Question(s):What is the side-splitter theorem and how does it relate to the triangle-angle bisector theorem?
(A)Lesson Essential Question(s):How are the ratios for perimeter and area of similar figures related?
(A)Vocabulary:
Additional Information:
Prentice Hall Geometry Textbook Chapter 8 (8.1-8.6)
Geometry (McDougal/Littell-Jergensen/Brown/Jergensen) Textbook Chapter 7 (7.1-7.6), Chapter 8 (8.1), and Chapter 11 (11.7)
Calculator
Pasco Mathematics Performance Tasks (PMPT): Big John, No Wet Feet, Top of the Tree
Also include Language Arts Benchmarks: LA.910.1.6.1 (use of vocabulary), LA.910.1.6.2 (read and discuss text), LA.910.1.6.5 (relate new vocabulary), and LA.910.3.1.3 (use organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn Diagram)).
Resources:
Acquisition Lesson:
Extending Thinking Lesson: