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8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Unit 3: Geometry (Pythagorean Theorem, Similarity: Angles, Parallel lines, and Triangles, Transformations, and Volume) Time Frame: 36 β 42 days Connections to Previous Learning: In Unit 1, students learned to evaluate expressions and equations with exponents. Unit 2 is about solved equations. In previous grades, students have worked with triangles and classifying triangles. In previous grades, students made scale drawings of geometric figures and solved problems involving angle measure, surface area, and volume. In Grade 7, students found the volume of prisms and pyramids. In Grade 8, students expand on the general concept of volume to explore the volume of rounded objects (specifically cylinders, cones and spheres). Moreover, students draw on their knowledge of exponents (particularly squares and cubes) from Unit 1 when finding missing sides of a right triangle and the volume and utilize their knowledge of solving equations to solve for the radius given a volume. Focus within the Grade Level: Students will apply their knowledge of squares, cubes, square roots, cube roots, and solving to solve problems like π₯ 2 = π and π₯ 3 = π. Students will apply their prior knowledge of triangles to the specific qualities of right triangles and find the missing side lengths of right triangles in various real world 2-D and 3-D situations. They will also apply the concepts of squares and square roots. Students will apply the concept of the Pythagorean Theorem to find the height or radius of a cone given the slant height and either the height or radius, while studying volume. Geometric sense allows students to comprehend space and shape. Students analyze the characteristics and relationships of shapes and structures; engage in logical reasoning, and use tools and techniques to determine measurement. Students learn that geometry and measurement are useful in representing and solving problems in the real world as well as in mathematics. Through application in real-world contexts, students learn the volume formulas for cylinders, cones and spheres. They then apply these formulas to not only find the volume of objects, but also missing dimensions such as the radius or height. Part A: Solve π₯ 2 = π and Pythagorean Theorem Part B: Similarity Part C: Transformations Part D: Solve π₯ 3 = π and Volume Connections to Subsequent Learning: Students will extend the concept of similar triangles to find sloe of linear lines. Students will extend these concepts to trigonometry. At the high school level, students will apply transformations to numbers, functional representations, and data. They will experiment with transformations in the plane where they will do rigid motion transformations, transformations in terms of a function, and transformations such as stretches that lead to shapes that are not similar or congruent. Students will use this understanding in high school when they use volume formulas of cylinders, pyramids, cones and spheres to solve problems, use geometric shapes to model real-life objects, apply concepts of density based on volume, and solve design problems using geometric methods. Unit 1 Clover Park School District 6/20/16 Page 1 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Common Core Standards in this unit: οΆ Indicates was presented to students in the 7th grade curriculum in the Clover Park School District. Work with radical and integer exponents. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form π₯ 2 = π and π₯ 3 = π, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that β2 is irrational. Understand and apply the Pythagorean Theorem. 8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Understand congruence and similarity using physical models, transparencies, or geometry software. οΆ 8.6.A.1 8.6.A.1.A 8.6.A.1.B 8.6.A.1.C οΆ 8.G.A.2 οΆ 8.G.A.3 οΆ 8.G.A.4 οΆ 8.G.A.5 Verify experimentally the properties of rotations, reflection, and translations: Lines are taken to lines, and line segments to line segments of the same length Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflection, translations, and dilations: given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. οΆ 8.G.C.9 Unit 1 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Clover Park School District 6/20/16 Page 2 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Mathematical Practices 1. 3. 5. 7. Unit 1 Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically. Look for and make sure of structure. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision. 8. Look for and express regularity in repeated reasoning. Clover Park School District 6/20/16 Page 3 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 1 Desired Results Transfer Goals Students will be able to independently use their learning toβ¦ - Understand and apply the Pythagorean Theorem. - Understand congruence and similarity using physical models, transparencies, or geometry software. - Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Meaning Goals UNDERSTANDINGS Students will understand thatβ¦ ο· Right triangles have a special relationship among the side lengths which can be represented by a model and a formula. ο· The Pythagorean Theorem can be used to find the missing side lengths in a coordinate plane and real-world situations. ο· The Pythagorean Theorem and its converse can be proven. ο· Reflections, translations, and rotations are actions that produce congruent geometric objects. ο· Dilation is a transformation that changes the size of a figure but not the shape. ο· If the scale factor of a dilation is greater than 1, the image resulting from the dilation is an enlargement, and if the scale factor is less than 1, the image is a reduction. ο· A two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of transformations. ο· Two shapes are similar if the lengths of all the corresponding sides are proportional and all the corresponding angles are congruent. ο· Two similar figures are related by a scale factor, which is the ratio of the lengths of corresponding sides. ο· Congruent figures have the same size and shape. If the scale factor of a dilation is equal to 1, the image resulting from the dilation is congruent to the original figure. Unit 1 ESSENTIAL QUESTIONS Clover Park School District 6/20/16 ο· ο· ο· ο· ο· ο· ο· ο· ο· Why does the Pythagorean Theorem apply only to right triangles? How does the knowledge of how to use right triangles and the Pythagorean Theorem enable the design and construction of such structures as a properly pitched roof, handicap ramps to meet code, structurally stable bridges, and roads? How can the Pythagorean Theorem be used for indirect measurement? How do indirect measurement strategies allow for the measurement of items in the real world such as playground structures, flagpoles, and buildings? What are transformations and what effect do they have on an object? What does the scale factor of a dilation convey? How can transformations be used to determine congruency or similarity? What angle relationships are formed by a transversal? How do we determine the volume of rounded objects? Page 4 8th grade Mathematics Curriculum Guide β Unit 3 Geometry ο· ο· ο· 2016 β 2017 When parallel lines are cut by a transversal, corresponding angles, alternate interior angles, alternate exterior angles, and vertical angles are congruent. Rounded object volume can be calculated with specific formulas. Pi is necessary when calculating volume of rounded objects. Acquisition Goals Students will knowβ¦ ο· The Pythagorean Theorem. ο· When to apply the Pythagorean Theorem. ο· Properties of rotations, reflections and translations ο· Exterior angle and angle sum of triangles. ο· The names and properties of angles created when parallel lines are cut by a transversal. ο· Angle-angle criterion for similarity of triangles. ο· The volume formulas for cylinders, cones and spheres. Students will be skilled atβ¦ ο· Explaining a proof of the Pythagorean Theorem and its converse. (8.G.6) ο· Using the Pythagorean Theorem to solve for a missing side of a right triangle given the other 2 sides in both 2-D and 3-D problems. (8.G.7) ο· Applying the Pythagorean Theorem to solve problems in real-world contexts. (8.G.7) ο· Applying the Pythagorean Theorem to find the distance between two points in the coordinate system. (8.G.8) ο· Describing a series of transformations that exhibits congruence between two congruent figures. (8.G.2) ο· Describing transformations (dilations, translations, rotations, and reflections) with words and with coordinates. (8.G.3) ο· Describing a series of transformations that exhibits similarity between two similar figures. (8.G.4) ο· Finding the measures of angles using transversals, the sum of angles in a triangle, the exterior angles of triangles. (8.G.5) ο· Determining if triangles are similar using the angle-angle criterion. (8.G.5) ο· Justifying congruence or similarity of figures using a series of transformations. (8.G.2 and 8.G.4) ο· Finding the volume of rounded objects in real-world contexts. (8.G.9) ο· ο· Unit 1 Giving volume in terms of 3.14 or π (8.G.9) Finding a missing dimension given the volume of rounded object. (8.G.9) Clover Park School District 6/20/16 Page 5 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning toβ¦ Part A: Solve ππ = π and Pythagorean Theorem 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form π₯ 2 = π and π₯ 3 = π, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that β2 is irrational. Understand and apply the Pythagorean Theorem. 8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Explanations, Examples, and Comments Previous learning - Vocabulary Cards Points, Lines, Planes, and Angles (Holt Course 3: 7-1) Angles in Triangles (Holt Course 3: 7-3) Explanations: ο· Students should verify, using a model, that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle. Students should also understand that if the sum of the squares of the 2 smaller legs of a triangle is equal to the square of the third leg, then the triangle is a right triangle. ο· Through authentic experiences and exploration, students should use the Pythagorean Theorem to solve problems. Problems can include working in both two and three dimensions. Students should be familiar with the common Pythagorean triplets. ALD Target H: Understand and apply the Pythagorean theorem Unit 1 Clover Park School District 6/20/16 - Acute angle (4th) Angle (4th) Distance (4th) Measure (4th) Obtuse angle (4th) Right angle (4th) Right Triangle (4th) Coordinates (5th) Measurement (5th) Ordered pairs (5th) Coordinate plan (6th) Edge length (6th) Vertices (6th) Graph (7th) Triangle (right, scalene, acute, obtuse, equilateral, isosceles) (7th) Page 6 8th grade Mathematics Curriculum Guide β Unit 3 Geometry - Level 1 student should be able to identify the hypotenuse and the legs of a right triangle given the side lengths or an image of a right triangle. Level 2 student should be able to apply the Pythagorean theorem to determine whether or not a given triangle is a right triangle, given its side lengths. They should be able to find the distance between two points on a horizontal or vertical line in a two-dimensional coordinate system. Level 3 students should be able to apply the Pythagorean theorem to determine the unknown side lengths of right triangles and to find the distance between two points in a coordinate system in two dimensions. Level 4 students should be able to apply the Pythagorean theorem to find the distance between two points in a coordinate system in three dimensions. 2016 β 2017 Converse (8th) Degree (8th) Height (8th) Hypotenuse (8th) Leg (pertaining to the Pythagorean theorem) (8th) Origin (8th) Power (8th) Pythagorean theorem (8th) Square root (8th) X-coordinate (8th) Y-coordinate (8th) Item Specs Version 2.0 - Target H Item Specs Version 3.0 - Target H Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning toβ¦ Part B: Similarity Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Explanations, Examples, and Comments Previous learning - Vocabulary Cards and some more geometry Cards Ratios and Proportions (Holt Course 3: 5-1and 5-4) Point, Line, line segment, ray, triangle Explanations Students can informally prove relationships with transversals. ο· Unit 1 Show that m ο3 + m ο 4 + m ο5 = 180Λ if l and m are parallel lines and t1 & t2 are transversals. Clover Park School District 6/20/16 - Acute angle (4th) Angle (4th) Line (4th) Obtuse angle (4th) Point (4th) Protractor (4th) Ray (4th) Right angle (4th) Straight angle (4th) Page 7 8th grade Mathematics Curriculum Guide β Unit 3 Geometry ο1 + ο2 + ο3 = 180Λ. Angle 1 and Angle 5 are congruent because they are corresponding angles ( ο5 ο ο1 ). ο1 can be substituted for ο5 . ο 4 ο ο2 because alternate interior angles are congruent. ο 4 can be substituted for ο2 . Therefore m ο3 + m ο 4 + m ο5 = 180Λ ο· Students can informally conclude that the sum of a triangle is 180o (the angle-sum theorem) by applying their understanding of lines and alternate interior angles. ο· In the figure to the right, line x is parallel to line yz: ο· Angle a is 35 o because it alternates with the angle inside the triangle that measures 35 o. Angle c is 80 o because it alternates with the angle inside the triangle that measures 80 o. Because lines have a measure of 180 o, and angles a + b + c form a straight line, then angle b must be 65 o (180 β 35 + 80 = 65). Therefore, the sum of the angles of the triangle are 35 o + 65 o + 80 o. Unit 1 Clover Park School District 6/20/16 - 2016 β 2017 Vertex (4th) Line segments (5th) Parallel (5th) Perpendicular (5th) Adjacent angles (7th) Complementary angles (7th) Linear pairs of angles (7th) Supplementary angles (7th) Triangle (right, scalene, acute, obtuse, equilateral, isosceles) (7th) Vertical angles (7th) Angle-angle criterion (8th) Congruent (8th) Converse (8th) Exterior angles of triangles (8th) Measure of an angle (8th) Measure of a line segment (8th) Similar (8th) Similar Triangles (8th) Transversal (8th) Page 8 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning toβ¦ Part C: Transformations Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.1: Verify experimentally the properties of rotations, reflection, and translations: - 8.G.A.1a: Lines are taken to lines, and line segments to line segments of the same length. - 8.G.A.1b: Angles are taken to angles of the same measure. - 8.G.A.1c: Parallel lines are taken to parallel lines. 8.G.A.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflection, translations, and dilations: given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Explanations, Examples, and Comments Vocabulary Cards ALD Target G: Understand congruence and similarity using physical models, transparencies, o geometry software. Level 1 students should be able to identify reflections, rotations, and translations and the result of these right motions on figures. Level 2 students should be able to construct reflections and translations of figures in a coordinate plane and identify dilations and the results of dilations on figures. Level 3 students should be able to understand and describe the impact of a transformation on a figure and its component parts with or without coordinates. They should be able to use or describe a sequence of Unit 1 Clover Park School District 6/20/16 - Polygon (3rd) Rectangle (3rd) Rhombus (3rd) Square (3rd) Acute angle (4th) Angle (4th) Distance (4th) Figure (4th) Line (4th) Measure (4th) Obtuse angle (4th) Point (4th) Page 9 8th grade Mathematics Curriculum Guide β Unit 3 Geometry transformations to determine or exhibit the congruence of two figures. They should also be able to construct rotations and dilations of figures in a coordinate plane. Level 4 students should be able to describe a sequence that exhibits the similarity between two shapes and understand that the angle measures are unchanged. Item Specs Version 2.0 - Target G Item Specs Version 3.0 - Target G 2016 β 2017 - Unit 1 Clover Park School District 6/20/16 Protractor (4th) Ray (4th) Right angle (4th) Straight angle (4th) Vertex (4th) Coordinates (5th) Line segments (5th) Measurement (5th) Ordered Pairs (5th) Parallel (5th) Perpendicular (5th) Sequence (5th) Coordinate plane (6th) Edge length (6th) Vertices (6th) Adjacent angles (7th) Complementary angles (7th) Graph (7th) Linear pairs of angles (7th) Parallelogram (7th) Supplementary angles (7th) Trapezoid (7th) Triangle (right, scalene, acute, obtuse, equilateral, isosceles) (7th) Vertical angles (7th) Congruent (8th) Converse (8th) Dilate (8th) Dilation (8th) Measure of an angle (8th) Measure of a line segment (8th) Proportional relationship (8th) Reflect (8th) Reflection (8th) Rotate (8th) Rotation (8th) Similar (8th) Similar Triangles (8th) Page 10 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 - - Transformations (8th) Translate (8th) Translation (8th) Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning toβ¦ Part D: Solve ππ = π and Volume 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form π₯ 2 = π and π₯ 3 = π, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that β2 is irrational. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Explanations, Examples, and Comments Vocabulary Previous learning - Circle Radius Diameter Chord Circumference Area Explanations ο· Students should verify, using a model, that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle. Students should also understand that if the sum of the squares of the 2 smaller legs of a triangle is equal to the square of the third leg, then the triangle is a right triangle. Unit 1 - Clover Park School District 6/20/16 Volume (4th) Surface area (6th) Base of 3-D figures (7th) Circle (7th) Circumference (7th) Diameter (7th) Pi (7th) Radius (7th) Cone (8th) Cube (8th) Cube root (8th) Cylinder (8th) Height (8th) Sphere (8th) Square (8th) Square root (8th) Slant height Page 11 8th grade Mathematics Curriculum Guide β Unit 3 Geometry Stage 2 - Evidence SAMPLE Assessment Evidence PERFORMANCE TASK(S): See Day 32, Day 35, and Matchsticks: lesson, resource Evaluative Criteria: Common Assessment See Sample Assessments for Unit 3. Washington State: Materials to help districts and others understand the organization and content of the standards and the content and evidence base used to support the standards: http://mathpractices.edc.org/pdf/Rational_Exponents.pdf Washington State: Instructional materials, Resources and Course Support: http://www.k12.wa.us/Mathematics/Resources.aspx Washington State: Professional Learning Support: http://www.k12.wa.us/Mathematics/profdev.aspx Washington State: General Assessment Resources: http://www.k12.wa.us/Mathematics/Assessment.aspx 2016 β 2017 OTHER ASSESSMENT EVIDENCE: SBA Sample Items 8.G.2 (G.141) 8.G.3 (G.142) 8.G.5 (G.129) 8.G.2 (G.146) 8.G.7 (H.002) 8.G.8 (H.143) 8.G.9 (A.001) 8.G.4 (G.321) 8.G.9 (B.128) 8.G.9 (B.132) 8.G.4 (B.010) 8.G.3 (B.059) 8.G.7 (B.433) 8.G.9 (F.011) 8.G.7 (F.016) 8.G.3 (F.559) 8.G.9 (A.271) SBA Review by Target SBA Review Target G SBA Review Target H1 Unit 1 Clover Park School District 6/20/16 Page 12 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 SBA Review Target H2 SBA Review Target I Stage 3 β Learning Plan Sample Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning LEARNING ACTIVITIES: Additional Resources: A suggested guide to layout of unit by days Part A: Pythagorean theorem 8.EE.2 and 8.G.B.6, 7, and 8 Day 1: Lab: What is the Pythagorean Theorem? Day 2: Discovering the Pythagorean Theorem: lesson, resources Day 3: Holt Course 3: 4-8 The Pythagorean Theorem and - Watson Saves: from Yummy math problem Day 4: Holt Course 3 Companion Guide: 4-9A Day 5: Tunnel Vision: from Making Sense of Problem Solving and - Holt Geometry: 5-7 The Pythagorean Theorem Part A: 8.EE.2 and 8.G.B.6, 7, and 8 Stations Activity: Properties of Right Triangles Comparing TVs: Task from Georgia Steep Hikes: from Yummy math Pythagorean Theorem: more practice worksheets Proving Triangles are Right Triangles: more practice worksheets Pythagorean Triples: more practice worksheets Using the Pythagorean Theorem to Find Missing Dimensions: more practice worksheets Think Tac Toe Pythagorean Theorem Day 6: Holt Geometry: 5-8 Applying Special Right Triangles - Fish Tale: from Yummy math problem Day 7 : additional day if needed - Holt Algebra 1: 1-5 challenge - School Yard: lesson, resources Part B: Similarity 8.G.A.5 Day 8: Lines and Angles - Properties of Angle Pairs: Station Activity (Discovery of rules) - Holt Geometry: 3-1 Lines and Angles Unit 1 Clover Park School District 6/20/16 Part B: Similarity 8.G.A.5 Properties of Angle Pairs: Station Activity Properties of Lines Cut by Transversals: Station Activity Page 13 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 3 β Learning Plan Sample Day 9: Parallel Lines and Angles - Holt Course 3: 7-2 Parallel and Perpendicular Lines Parallel Lines and Transversals: worksheet Angles in Triangles: worksheet Similar Triangles worksheet Day 10: Parallel Lines and Angles - Holt Geometry: 3-2 Angles Formed by Parallel Lines and Transversals Stage 3 MATERIALS BY STANDARD(S): Day 11: Parallel Lines and Angles - Angles, draw the picture: Activity PowerPoint (review of angle pairs/notes) - Holt Geometry: 3-3 Proving Lines Parallel Day 12: Parallel Lines and Angles - City Design: Activity PowerPoint Day 13: Parallel Lines and Angles - City Design: Activity day 2 and review Day 14: Triangles - Holt Course 3: 7-3 Angles in Triangles Day 15: Triangles - Holt Geometry: 4-2 Angle Relationships in Triangles Estimate days 11-13 Holt Course 3: 7-6 Congruence Holt Course 3 Curriculum Companion: 7-6A Hands-On Lab: Explore congruence Holt Geometry: 12-1 Reflections Holt Geometry: 12-2 Translations Holt Geometry: 12-3 Rotations Holt Course 3: 7-7 Transformations Holt Geometry: 12-4 Compositions of Transformations Holt Course 3: 5-6 Dilations Holt Geometry: Dilations Holt Course 3 Curriculum Companion: 7-7A Similarity & Congruence Transformations Holt Course 3 Curriculum Companion: 7-7B Identifying Combined Transformations Day 16: Triangles - Whatβs Your Angle Activity: from Making Sense of Problem Solving Day 17: Similar Figures - Holt Course 3: 5-5 Similar Figures Day18: Similar Figures - Holt Course 3: 5-7 Indirect Measurement Day 19: Similar Triangles - Holt Geometry: 7-3 Triangle Similarity: AA, SSS, SAS Unit 1 Clover Park School District 6/20/16 Page 14 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 3 β Learning Plan Sample Day 20: Similar Triangles - This is Similar Activity: from Making Sense of Problem Solving or - Identifying Similar Triangles: lesson, resources Part C: Transformations 8.G.A 1, 8.G.A.2, 8.G.A.3, and 8.G.A.4 Day 21: Congruence of Figures - Holt Course 3: 7-6 Congruence - Holt Course 3 Curriculum Companion: 7-6A Hands-On Lab: Explore congruence Day 22: Transformations Reflections - Holt Geometry: 12-1 Reflections Part C: Transformations 8.G.A 1, 8.G.A.2, 8.G.A.3, and 8.G.A.4 Transformations: Station Activity Translations and Rotations: Station Activity Aaronβs Design: problem Transformations: small activity or little quiz Day 23: Transformations Translations - Holt Geometry: 12-2 Translations Day 24: Transformations Rotations - Holt Geometry: 12-3 Rotations Day 25: Transformations - Holt Course 3: 7-7 Transformations and/or - Holt Geometry: 12-4 Compositions of Transformations Day 26: Transformations - Representing and Combining Transformations: lesson, resources Day 27: Dilations - Holt Course 3: 5-6 Dilations Day 28: Dilations - Holt Geometry: Dilations Day 29: Transformations - Holt Course 3 Curriculum Companion: 7-7A Similarity & Congruence Transformations - Combining Transformations: worksheet Unit 1 Clover Park School District 6/20/16 Page 15 8th grade Mathematics Curriculum Guide β Unit 3 Geometry 2016 β 2017 Stage 3 β Learning Plan Sample Day 30: Transformations - Holt Course 3 Curriculum Companion: 7-7B Identifying Combined Transformations Part D: Volume 8.G.C.9 Day 31: Circles and π - What is π? Activity : The Mystery Ratio Activity (review from 7th, but good lab activity to reviw) Day 32: Volume of Cylinders - Which glass of soda would you pick (good opener to get students thinking about volume) - http://mrmeyer.com/threeacts/youpourichoose/ - Holt Course 1 Lesson 10-8 Volume of Cylinders Day 33: Volume of Cylinders - Holt Course 3 Lesson 8-5 Volume of Prisms and Cylinders Part D: Volume 8.G.C.9 Comparing Spheres and Cylinders (Georgia Task) Making Sense of Problem Solving H.12 Picking up the Garbage How full is your glass? (Georgia Task) Gift Box Dilemma (North Carolina Task) Volume of Cylinders, Cones, and Spheres: Station Activity Day 34: Volume of Cones - Holt Course 3 Lesson 8-6 Volumes of Pyramids and Cones Day 35: Volume of Spheres - Holt Course 3 lesson 8-9 Spheres Day 36: Volume of Cylinders, Cones, and Spheres - Meltdown (North Carolina Task) good problem or - I Scream for Ice Cream and Hankβs Tanks: worksheet Common Assessment Semester Cumulative Assessment Unit 1 Clover Park School District 6/20/16 Page 16