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Geometry is a way to understand the real world around us by basing arguments on concrete referents, modeling relationships, and applying mathematical principles to understand geometric properties and concepts using objects, drawings, diagrams, and actions.
The Story of Geometry - Unit 4: Trigonometry (Up to 24 days, End of Triad 4)
This unit focuses on problem solving & right triangles, especially trigonometry. Students gain understanding and use trigonometry, the Pythagorean Theorem (that was first introduced in eighth grade), and the relationship between the sine and cosine of complementary angles to solve problems involving all three. This is reinforced by examining trigonometric ratios for special right triangles (30°, 60°, 90°and 45°, 45°, 90°). Time permitting, students then apply trigonometry to general triangles. Further depth is achieved by reenaging with angles and side lengths, which can be embedded into this unit's instruction, and by proving additional theorems about triangle similarity not addressed in the previous unit; namely, a line parallel to one side of a triangle divides the other two proportionally, the converse of the same, and the Pythagorean Theorem proved using triangle similarity.
Unit 4 & The Need to Examine Claim 2... and CLAIM 1
Most of the geometry course is tested in Claim 3; however, the emphasis is this unit is Claim 2, Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Problem solving is always an emphasis in mathematics, but special attention is drawn to problem-solving in this unit. Students should be primarily engaged with SMP #1: Make sense of problems and persevere in solving them and SMP's 2, 7 & 8 as problem solving pathways. Teachers should devote time at the beginning of this unit (if not done before) to understand Claim 2 for themselves, especially the Assessment Targets, Task Models and Examples. This is also the only Geometry Unit with a Claim 1 Target, Target O. The Achievement Level Descriptors, Required Evidence, and Task Models greatly inform the instruction in this unit. Time should be spent examining them and using them to guide instruction.
Vocabulary, Tools & Developmental Notes from SBAC
G-SRT.C Define trigonometric ratios and solve problems involving right triangles.
G-SRT.C Define trigonometric ratios and solve problems involving right triangles.
(Target O)
(Target O)
Claim 2, Problem Solving: Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies.
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