Embedded Files
Critical Area 1: Congruence with Transformations (9 weeks)
Critical Area 1: Congruence with Transformations (9 weeks)
In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this Area, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
Common Core State Standards
Congruence G-CO.A.1-5
Congruence G-CO.B.6-8
Congruence G-CO.C.9-11
Congruence G-CO.D.12-13
MP.3 Construct viable arguments and critique the reasoning of others
MP.5 Use appropriate tools strategically
Evidence Pieces
Rigid Motion ( Task | Digital Task | Digital Task (ES) | Rubric)
Are the Triangles Congruent? (Task | Digital Task | Digital Task (ES) | Rubric)
Prove ABCD is a Parallelogram (Task | Digital Task | Digital Task (ES) | Rubric)
Construct This! (Task | Digital Task | Digital Task (ES) | Rubric)
Construct This Advanced (Will not be provided this year)
Common Activities/Lessons
Are The Triangles Congruent (Trapezoids) (Geogebra)***********
Geogebra: Construct Parallelogram****
Critical Area 2: Similarity With Transformations (4 weeks)
Critical Area 2: Similarity With Transformations (4 weeks)
Students apply their earliest experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of geometric figures and use similarity to solve problems.
Common Core State Standards:
Similarity, Right Triangles, and Trigonometry G-SRT.A.1-3
Similarity, Right Triangles, and Trigonometry G-SRT.B.4-5
MP.3 Construct viable arguments and critique the reasoning of others
MP.6 Attend to precision
Evidence Pieces
Common Activities/Lessons
Critical Area 3: Right Triangle Trigonometry (4 weeks)
Critical Area 3: Right Triangle Trigonometry (4 weeks)
Students apply similarity in right triangles to understand right triangle trigonometry, with particular attention to the Pythagorean Theorem and its relationship to circles.
Common Core State Standards
Similarity, Right Triangles, and Trigonometry G-SRT.B.4-5
Similarity, Right Triangles, and Trigonometry G-SRT.C.6-8
MP.1 Make sense of problems and persevere in solving them
MP.8 Look for and express regularity in repeated reasoning
Evidence Pieces
Common Activities/Lessons
Critical Area 4: Circles (4 weeks)
Critical Area 4: Circles (4 weeks)
Students build on their understanding of similarity to investigate relationships between circles. Students explore and prove relationships between parts of circles. Students understand how these parts relate to segment lengths and angle measures, and how this relates back to similarity.
Common Core State Standards:
Circles G-C.A.1-3
Circles G-C.B.5
Expressing Geometric Properties with Equations G-GPE.A.1
MP.7 Look for and make use of structure
Evidence Pieces
Common Activities/Lessons
Critical Area 5: Geometric Measurement and Modeling (9 weeks)
Critical Area 5: Geometric Measurement and Modeling (9 weeks)
Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line. Students will use geometric shapes, their properties and their measurements to describe physical environments.
Common Core State Standards
Geometric Measurement and Dimension G-GMD.A.1 and 3
Geometric Measurement and Dimension G-GMD.B.4
Modeling with Geometry G-MG.A.1-3
Expressing Geometric Properties with Equations G-GPE.B.4-7 (Depending on IC)
MP.2 Reason abstractly and quantitatively
MP.4 Model with mathematics
Evidence Pieces
Water Tanks (Task | Digital Task | Rubric)
Visualizing 2D to 3D (Task | Digital Task | Rubric)
Day at the Beach (Task | Digital Task | Rubric)
Common Activities/Lessons
Critical Area 6: Applications of Probability (4 weeks)
Critical Area 6: Applications of Probability (4 weeks)
Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.
Common Core State Standards
Conditional Probability and the Rules of Probability S-CP.A.1-5
Conditional Probability and the Rules of Probability S-CP.B.6-7
MP.1 Make sense of problems and persevere in solving them
MP.6 Attend to precision
Evidence Pieces
Common Activities/Lessons
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