1 / 49

Geometry

Geometry. Grade 7 – Module 6. Session Agenda. Module Overview Focus on Topics and Lessons Module in Review Implementation Discussions. Session Objectives. Gain an understanding of the content enveloped in Module 6. Understand what was, what is, and why the change.

keaira
Download Presentation

Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Grade 7 – Module 6

  2. Session Agenda • Module Overview • Focus on Topics and Lessons • Module in Review • Implementation Discussions

  3. Session Objectives • Gain an understanding of the content enveloped in Module 6. • Understand what was, what is, and why the change. • See how geometry concepts from here forward are starting to take shape. • Gain the knowledge necessary to implement with fidelity.

  4. Curriculum Overview of A Story of Ratios

  5. Grade 7 Module 6 Overview • Let’s look at: • Foundational Standards (p.5) • Focus Standards (p.4) • Mathematical Practice Standards (p.5-6) • Table of Contents and Narrative

  6. Topic A: Unknown Angles • 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. • Prerequisites: G4 M4 and G7 M3 • Goal is to build fluency in these difficult problems • Build recognition and use of structure MP.7

  7. Complementary and Supplementary Angles Lesson 1 / Example 1 The measures of two supplementary angles are in the ratio of . Find the two angles.

  8. Solving for Unknown Angles Using Equations Lesson 2 / Exercise 4 Two lines meet as the common vertex of two rays. In a complete sentence, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of . Find the measurements of and .

  9. Solving for Unknown Angles Using Equations Lesson 3 / Example 3 Two lines meet at the common vertex of two rays. In complete sentences, describe the relevant angle relationships in the diagram. Set up and solve an equation to find the value of . Find the measurements of angles and .

  10. Solving for Unknown Angles Using Equations Lesson 3 / Example 4 Two lines meet at a point. Set up and solve an equation to find the value of . Find the measurement of one of the vertical angles.

  11. Solving for Unknown Angles Using Equations Lesson 4 / Example 3 The measurement of an angle is the measurement of its supplement. Find the measurement of the angle.

  12. Topic B: Constructing Triangles 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. New Terminology New Tools New Approach

  13. Correspondence Lesson 5 / Example 2 Two identical triangles are shown below. Give a correspondence that matches equal sides and equal angles.

  14. Drawing Geometric Shapes Lesson 6 / Exploratory Challenge Use a ruler, protractor, and compass to complete the following: 3 segments: , , Complementary angles, one of Vertical angles, one of 3 circles: , , 3 adjacent angles: , , Rectangle , , Segment: , cut a segment using your compass Segment AB; Circle with center A and radius AB, and circle with center B and radius BA.

  15. Drawing Geometric Shapes Lesson 6 / Exploratory Challenge Use a ruler, protractor, and compass to complete the following:

  16. Drawing Geometric Shapes Lesson 6 / Exploratory Challenge Use a ruler, protractor, and compass to complete the following:

  17. Drawing Parallelograms Lesson 7 / Exercise 1 Use a setsquare, ruler and protractor to construct parallelogram so the measurement of , , the measurement of , and the altitude to is .

  18. Drawing Triangles Lesson 8 / Exploratory Challenge A triangle is to be drawn given the following conditions: the measurements of two angles are and , and the length of a side is . Note that where each of these measurements is positioned is not fixed.

  19. Three Sides ConditionTwo Sides and the Included Angle Condition Lesson 9 / Exploratory Challenge 4 • has side lengths cm, cm, and . Draw under the same conditions. Use your compass and protractor to draw the sides of . Use your ruler to measure side lengths. Leave all construction marks as evidence of your work, and label all side and angle measurements. • Under what condition is drawn? Compare the triangle you drew to two of your peers’ triangles. Are the triangles identical? Did the condition determine a unique triangle? Use your construction to explain why.

  20. Two Angles and a Given Side Lesson 10 / Exploratory Challenge 3 • A triangle has angles and and side cm. Draw triangle under the same condition. Leave all construction marks as evidence of your work, and label all side and angle measurements. • Under what condition is drawn? Compare the triangle you drew to two of your peers’ triangles. Are the triangles identical? Did the condition determine a unique triangle? Use your construction to explain why.

  21. Conditions on Measurements that Determine a Triangle Lesson 11 / Exploratory Challenge 1&2 Are there conditions on the lengths of the sides of a triangle? Are there conditions on the measures of the angles in a triangle?

  22. Conditions on Measurements that Determine a Triangle Lesson 11 / Exploratory Challenge 2d Is there a “Three Angles” condition for unique triangle?

  23. Two Sides and a Non-Included Angle Lesson 12 / Exploratory Challenge 1 • Use your tools to draw provide , , and . • What makes this drawing challenging? • Use a ruler and compass to locate .

  24. Two Sides and a Non-Included Angle Lesson 12 / Exploratory Challenge 2 • Use your tools to draw provide , , and .

  25. Two Sides and a Non-Included Angle Lesson 12 / Exploratory Challenge 3 Use your tools to draw provide , , and . Conclusions based on the results of Exploratory Challenges 1-3?

  26. Checking for Identical Triangles Lesson 14 / Examples 1-2

  27. Using Unique Triangles to Solve Real World and Mathematical Problems Lesson 15 / Exercise 2 Quadrilateral is a model of a kite. Diagonals and represent the sticks that help keep the kite rigid.

  28. Mid-Module Assessment • Assessment • Progression Toward Mastery Rubric • Exemplary Student Responses

  29. Topic C: Slicing Solids 7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Slicing 3-Dimensional figures by a plane and the resulting 2-Dimensional slices.

  30. Slicing a Right Rectangular Prism with a Plane Lesson 16 / Exercises 5-6

  31. Right Rectangular Pyramid Lesson 17 Bla

  32. Right Rectangular Pyramid Lesson 17

  33. Slicing a Right Rectangular Pyramid with a Plane Lesson 17 / Example 5

  34. Slicing on an Angle Lesson 18 / Example 1

  35. Slicing on an Angle Lesson 18 / Example 3

  36. Understanding 3-Dimensional Figures Lesson 19 / Exercise 2 If slices parallel to the tabletop are taken of this figure, then what would each slice look like? Given the level slices that you determined, how many unit cubes are in the figure?

  37. Topic D: Problems Involving Area and Surface Area 7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

  38. Real World Area Problems Lesson 20 / Example 2 Ten targets are being painted as shown in the following figure. The radius of the smallest circle is , and each successive, larger circle is more in radius than the circle before it. A “tester” can of red and of white paint is purchased to paint the target. Each can of paint covers . Is there enough paint of each color to create all ten targets?

  39. Mathematical Area Problems Lesson 21 / Example 1 Examine the change in dimension and area of squares as the lengths and widths are increased by the given amount.

  40. Area Problems with Circular Regions Lesson 22 / Problem Set #4 The diameters of four half circles are sides of a square with side lengths of Find the exact area of the shaded region.

  41. Surface Area Lesson 23 / Exercise 4 Determine the surface area of the right prism.

  42. Surface Area Lesson 24 / Example 3 A right rectangular pyramid has a square base with side lengths of 10 inches. The surface area of the pyramid is . Find the height of the four lateral triangular faces.

  43. Topic E: Problems Involving Volume 7.G.B.6 Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

  44. Volume of Right Prisms Lesson 25 / Example 3 Two containers are shaped like right triangular prisms, each with the same height. The base area of the larger container is more than the base area of the smaller container. How many times must the smaller container be filled with water and poured into the larger container in order to fill the larger container?

  45. Volume of Composite 3-Dimensional Objects Lesson 26 / Example 2 Find the volume of the right prism shown whose base is the region between two right triangles. Use two different strategies.

  46. Real-World Volume Problems Lesson 27 / Exit Ticket Jim wants to know how much his family spends on water for showers. Water costs $1.50 per 1000 gallons. His family averages 4 showers per day (total). The average length of a shower is 10 minutes. He places a bucket in his shower and turns on the water. After one-minute, the bucket has 2.5 gallons of water in it. About how much money does his family spend on water for showers in a month (30 days)?

  47. End-of-Module Assessment • Assessment • Progression Toward Mastery Rubric • Exemplary Student Responses

  48. Module 6 in Review • Take a few moments to discuss, with those around you, the major highlights of the Module. • Likes • What was and what is • Concerns • Major Takeaways

  49. Key Points • Student transitioning to more complex levels of geometry • Using algebra to solve unknown angle problems • Explore the structure of triangles • Determine the conditions that determine unique triangles • Identify identical triangles and use their relationship to solve problems • Describe the slices of three-dimensional figures • Apply strategies for area, surface area, and volume in solving real world and mathematical problems

More Related