Enhanced Instructional Transition Guide

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1 Geometry: Coordinate Plane, Graphing Transformations, and Perspectives (9 days) Possible Lesson 01 (6 days) Possible Lesson 02 (3 days) POSSIBLE LESSON 02 (3 days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with districtapproved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students needs. To better understand how your district is implementing CSCOPE lessons, please contact your child s teacher. (For your convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Students sketch three-dimensional figures when given the top, side, and front views and vice versa. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at Geometry and spatial reasoning.. The student uses geometry to model and describe the physical world. The student is expected to: 7.8A Sketch three-dimensional figures when given the top, side, and front views. Supporting Standard Underlying Processes and Mathematical Tools TEKS: 7.13 Underlying processes and mathematical tools.. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: 7.13D Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. page 1 of 34

2 7.15 Underlying processes and mathematical tools.. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: 7.15A Make conjectures from patterns or sets of examples and nonexamples. 7.15B Validate his/her conclusions using mathematical properties and relationships. Performance Indicator(s): Grade 07 Mathematics Unit 04 PI 02 Given the top, side, and front views, construct a three-dimensional figure using manipulatives (e.g., cubes, tiles, etc.). Validate the model by sketching the three-dimensional figure in a journal. Standard(s): 7.15B, 7.8A, 7.13D, 7.15A ELPS ELPS.c.1E, ELPS.c.3J Key Understanding(s): Perspective views can be used to validate sketches, models, and conjectures about three-dimensional figures. Vocabulary of Instructions: front view perspectives side view top view Materials: index card (3 x 5 ) (1 per 2 students) linking cubes (15 per 2 students) linking cubes or color tiles (20 per student) math journal (1 per student) real-life three-dimensional object (various) (1 per 2 students) page 2 of 34

3 three-dimensional geometric solid (various) (1 per 2 students) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Grid Paper Cubes KEY Grid Paper Cubes Cube Sketches KEY Cube Sketches How Do I Look? KEY How Do I Look? Perspective Views KEY Perspective Views Perspective Views Practice KEY Perspective Views Practice GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator page 3 of 34

4 in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher 1 2 Topics: Engage 1 Perspectives Spiraling Review ATTACHMENTS Students use logic and reasoning skills to examine various geometric perspectives. Instructional Procedures: 1. Display teacher resource: Grid Paper Cubes and distribute handout: Grid Paper Cubes to each student. Explain to students that they will use grid paper to create a three-dimensional cube drawing for examples 1 5 on their handout. 2. Explain to students that for Example 1, they will create a three-dimensional drawing of 1 cube. Demonstrate drawing a 2 x 2 square on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. Teacher Resource: Grid Paper Cubes KEY (1 per teacher) Teacher Resource: Grid Paper Cubes (1 per teacher) Handout: Grid Paper Cubes (1 per student) TEACHER NOTE When students create the drawings for the threedimensional figures for each example on the handout: Grid Paper Cubes, instruct students to place the drawings for three-dimensional figures in the top left corner of the grid so there is room to draw the two-dimensional drawings for the front, top, and side views. TEACHER NOTE For the drawings of these three-dimensional figures, point out to students the front face of the cube is a square. The top face and right side face of the cube are parallelograms. The top face and the right page 4 of 34

Suggested Day Suggested Instructional Procedures Notes for Teacher 3. Demonstrate drawing a parallelogram with a side attached to the top side of the square on teacher resource: Grid Paper Cubes.

TEACHER NOTE For Example 4, we are not able to see if there are 2 hidden cubes, 1 hidden cube, or no hidden cubes; therefore, teacher resource: Grid Paper Cubes KEY suggests 3 possible top views. 4. Demonstrate drawing a parallelogram with its left side and top side attached to the right side of the square and parallelogram on teacher resource: Grid Paper Cubes.

5 Suggested Day Suggested Instructional Procedures Notes for Teacher 3. Demonstrate drawing a parallelogram with a side attached to the top side of the square on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. side face of a partial cube are isosceles right triangles. Shade the right side faces of the cubes. TEACHER NOTE For Example 4, we are not able to see if there are 2 hidden cubes, 1 hidden cube, or no hidden cubes; therefore, teacher resource: Grid Paper Cubes KEY suggests 3 possible top views. 4. Demonstrate drawing a parallelogram with its left side and top side attached to the right side of the square and parallelogram on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 5 of 34

Suggested Day Suggested Instructional Procedures Notes for Teacher 5. Demonstrate shading the right face of the cube on teacher resource: Grid Paper Cubes.

6 Suggested Day Suggested Instructional Procedures Notes for Teacher 5. Demonstrate shading the right face of the cube on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 6. Explain to students that for Example 2, they will create a three-dimensional model of 3 cubes. Demonstrate drawing 3 2 x 2 squares on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 6 of 34

Suggested Day Suggested Instructional Procedures Notes for Teacher 7. Demonstrate drawing 3 parallelograms with a side attached to the top side of each square on teacher resource: Grid Paper Cubes.

7 Suggested Day Suggested Instructional Procedures Notes for Teacher 7. Demonstrate drawing 3 parallelograms with a side attached to the top side of each square on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 8. Demonstrate drawing a parallelogram with its left side and top side attached to the right side of the square and parallelogram on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 7 of 34

Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 10.

8 Suggested Day Suggested Instructional Procedures Notes for Teacher 9. Demonstrate shading the right face of the cube on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 10. Explain to students that for Example 3, they will create a three-dimensional drawing of 6 cubes. Demonstrate repeating the procedures for a three-dimensional drawing of 3 cubes and then draw a row of 3 page 8 of 34

Suggested Day Suggested Instructional Procedures squares below the 3 cubes on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes.

9 Suggested Day Suggested Instructional Procedures squares below the 3 cubes on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. Notes for Teacher 11. Demonstrate drawing a parallelogram with its left side attached to the right side of the square on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 9 of 34

10 Suggested Day Suggested Instructional Procedures Notes for Teacher 12. Demonstrate shading the right face of the cube on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 10 of 34

11 Suggested Day Suggested Instructional Procedures Notes for Teacher 13. Explain to students that for Example 4, they will create a three-dimensional drawing of 6 cubes with a partial cube behind the right cube in the bottom row to create a three-dimensional drawing of 7, 8, or 9 cubes. Demonstrate repeating the procedures for a three-dimensional drawing of 6 cubes, and then draw a parallelogram and shade it on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 14. Demonstrate drawing an isosceles right triangle on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. page 11 of 34

12 Suggested Day Suggested Instructional Procedures Notes for Teacher 15. Explain to students that for Example 5, they will create a three-dimensional drawing of 11 cubes, by adding another stack of cubes behind the previous drawing. Demonstrate repeating the procedures for a threedimensional drawing of 7, 8, or 9 cubes and then draw two parallelograms on teacher resource: Grid Paper Cubes. Instruct students to replicate the drawing on their handout: Grid Paper Cubes. 16. Demonstrate drawing and shading an isosceles right triangle on teacher resource: Grid Paper Cubes. page 12 of 34

13 Suggested Day Suggested Instructional Procedures Instruct students to replicate the drawing on their handout: Grid Paper Cubes. Notes for Teacher 17. Instruct students to keep their handout: Grid Paper Cubes for future instruction. Topics: ATTACHMENTS Perspectives Explore/Explain 1 Students explore various geometric perspectives by creating and sketching a three-dimensional model when given the two-dimensional front, top, and side views, or vice versa. Instructional Procedures: 1. Display teacher Resource: Cube Sketches and instruct students to sketch this model on their handout: Grid Paper Cubes for Example 6. Allow time for students to draw the model for the three-dimensional figure. Monitor and assess students to check for understanding. Facilitate individual discussions about Teacher Resource: Cube Sketches KEY (1 per teacher) Teacher Resource: Cube Sketches (1 per teacher) Handout: Grid Paper Cubes (1 per student) Teacher Resource: How Do I Look? KEY (1 per teacher) Handout: How Do I Look? (1 per student) MATERIALS page 13 of 34

14 Suggested Day Suggested Instructional Procedures drawing three-dimensional figures, as needed. Ask: How many cubes will it take to build this figure? Explain. (Example 6: 15 cubes.) What would this figure look like from the top? (Example 6: It will look like.) What would this figure look like from the right side? (Example 6: It will look like.) What would this figure look like from the front? (Example 6: It will look like.) Notes for Teacher index card (3 x 5 ) (1 per 2 students) linking cubes (15 per 2 students) 2. Place students in pairs and distribute a 3 x 5 index card and 15 linking cubes to each pair. Instruct students to record front on the lower front edge of the card and record right on the right edge of the card. 3. Explain to students that they will use their linking cubes to create models of the 6 three-dimensional drawings from their handout: Grid Paper Cubes. Instruct student pairs to build each model with linking cubes, compare their model with the three-dimensional drawings, examine the three-dimensional model from the top, front, and side perspective views, and describe the view in a two-dimensional perspective by sketching the front, top, and side views on the same grid as the three-dimensional drawing. Remind students to use their index card as a guide to identify the top, front, and side views of the model. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions about perspective views, as needed. Ask: How many cubes did it take to build this figure? Explain. Answers may vary. One cube; etc. What would this figure look like from the top? Answers may vary. One cube; etc. What would this figure look like from the right side? Answers may vary. One cube; etc. What would this figure look like from the front? Answers may vary. One cube; etc. page 14 of 34

15 Suggested Day Suggested Instructional Procedures Notes for Teacher 4. Display teacher resource: How Do I Look? and distribute handout: How Do I Look? to each student. Instruct student pairs to use their linking cubes to create models of the three-dimensional figures using the top, front, and side perspective views, and then sketch the three-dimensional views beside each set of the two-dimensional models of the top, front, and side view. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions about the threedimensional models and two-dimensional perspective views, as needed. Ask: How many cubes did it take to build this figure? Explain. Answers may vary. 6 cubes; etc. What would the sketch of the three-dimensional figure look like? Answers may vary. ; etc. Where in the sketch is the front view? (Student should point to the front of the diagram.) Where in the sketch is the top view? (Student should point to the top of the diagram.) Where in the sketch is the side view? (Student should point to the side of the diagram.) How can the top, side, and front views be used to make a sketch of the three-dimensional figure? (The top, front, and side views provide a two-dimensional view of the three-dimensional figure.) Topics: Perspectives Explore/Explain 2 Students sketch the two-dimensional front, top, and side views when given a real-life or geometric threedimensional model. Student sketch the three-dimensional figure when given a two-dimensional view. MATERIALS real-life three-dimensional object (various) (1 per 2 students) three-dimensional geometric solid (various) (1 per 2 students) math journal (1 per student) Instructional Procedures: page 15 of 34

16 Suggested Day Suggested Instructional Procedures Notes for Teacher 1. Place students in pairs and distribute a real-life three-dimensional object (e.g., cereal box, lunch box, etc.) or a three-dimensional geometric solid (e.g., cone, cylinder, prism, etc.) to each pair. Instruct students to create a 4 column chart in their math journal, and label each column: Name, Top View, Side View, and Front View. 2. Instruct student pairs to record the name of their object or solid, sketch the top, side, and front view of each in the appropriate column in their math journal, exchange three-dimensional models with another pair of students, and repeat the process until at least 5 three-dimensional models have been recorded. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate small group discussions about the three-dimensional models and two-dimensional perspective views, as needed. Ask: What is the name of the figure? Answers may vary. Cylinder; etc. Describe the top view. Answers may vary. A circle; etc. Describe the side view. Answers may vary. A rectangle; etc. Describe the front view. Answers may vary. A rectangle; etc. 3 Topics: Perspectives Elaborate 1 Students sketch the two-dimensional front, top, and side views when given a three-dimensional model. Instructional Procedures: Spiraling Review ATTACHMENTS Teacher Resource: Perspective Views KEY (1 per teacher) Handout: Perspective Views (1 per student) page 16 of 34

17 Suggested Day Suggested Instructional Procedures Notes for Teacher 1. Distribute handout: Perspective Views to each student. Instruct students to complete the handout. Monitor and assess students to check for understanding. Facilitate individual discussions about three-dimensional models and two-dimensional sketches, as needed. Ask: Teacher Resource (optional): Perspective Views Practice KEY (1 per teacher) Handout (optional): Perspective Views Practice (1 per student) How many cubes did it take to build this figure? Explain. Answers may vary. 7; etc. Where in the sketch of the three-dimensional figure is the front view? Answers may vary. ; etc. Where in the sketch of the three-dimensional figure is the top view? Answers may vary. ; etc. Where in the sketch of the three-dimensional figure is the side view? Answers may vary. ; ADDITIONAL PRACTICE The handout (optional): Perspective Views Practice may be used as additional practice if needed. etc. Evaluate 1 MATERIALS Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. linking cubes or color tiles (20 per student) math journal (1 per student) Performance Indicator(s): page 17 of 34

18 Suggested Day Suggested Instructional Procedures Notes for Teacher Grade 07 Mathematics Unit 04 PI 02 Given the top, side, and front views, construct a three-dimensional figure using manipulatives (e.g., cubes, tiles, etc.). Validate the model by sketching the three-dimensional figure in a journal. Standard(s): 7.15B, 7.8A, 7.13D, 7.15A ELPS ELPS.c.1E, ELPS.c.3J 04/01/13 page 18 of 34

19 Grid Paper Cubes KEY Grade 7 Mathematics Unit: 04 Lesson: 02 Example 1: 1 cube Example 2: 3 cubes Front Front Top Side Top Side Example 3: 6 cubes Example 4: 7, 8, or 9 cubes Side Front Side Front Top OR Top Top OR Top 2 Hidden Cubes 1 Hidden Cube Example 5: 11 cubes Example 6: 15 cubes Side Front Side Front Top Top 2012, TESCCC 08/17/12 page 1 of 1

20 Grid Paper Cubes Grade 7 Mathematics Unit: 04 Lesson: 02 Example 1 Example 2 Example 3 Example 4 Example 5 Example , TESCCC 08/17/12 page 1 of 1

21 Cube Sketches KEY Grade 7 Mathematics Unit: 04 Lesson: 02 Draw the model of the three-dimensional figure shown below on the handout: Grid Paper Cubes for Example 6. Look for the squares, parallelograms, and isosceles right triangles in the models. Draw the front, top, and side views. Example 6 Front View Top View Note: The top view is looking from the top down with the front facing the student. Side View 2012, TESCCC 08/17/12 page 1 of 1

22 Cube Sketches Grade 7 Mathematics Unit: 04 Lesson: 01 Draw the model of the three-dimensional figure shown below on the handout: Grid Paper Cubes for Example 6. Look for the squares, parallelograms, and isosceles right triangles in the models. Draw the front, top, and side views. Example 6 Front View Top View Side View 2012, TESCCC 08/17/12 page 1 of 1

23 How Do I Look? KEY Grade 7 Mathematics Unit: 04 Lesson: 02 Use cubes to build a solid figure that is best represented by the given front, top, and side views. Sketch a model of each three-dimensional figure. Front View Example 1: Three-Dimensional Top View Side View Front View Example 2: Three-Dimensional Top View Side View 2012, TESCCC 08/17/12 page 1 of 1

24 How Do I Look? Grade 7 Mathematics Unit: 04 Lesson: 02 Use cubes to build a solid figure that is best represented by the given front, top, and side views. Sketch a model of each three-dimensional figure. Front View Example 1: Three-Dimensional Top View Side View Front View Example 2: Three-Dimensional Top View Side View 2012, TESCCC 08/17/12 page 1 of 1

25 Perspective Views KEY Grade 7 Mathematics Unit: 04 Lesson: Draw the two-dimensional front, top, and side views for each three-dimensional figure. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View c. Front View Top View Side View 2012, TESCCC 08/17/12 page 1 of 3

26 Perspective Views KEY Grade 7 Mathematics Unit: 04 Lesson: Draw the three-dimensional figure for the given two-dimensional front, top, and side views. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View c. Front View Top View Side View 2012, TESCCC 08/17/12 page 2 of 3

27 Perspective Views KEY Grade 7 Mathematics Unit: 04 Lesson: Circle the three-dimensional figure that the given views could represent. a. The top and side views of a threedimensional figure are shown below. dimensional figure are shown b. The top and side views of a three- below. Top View Side View Top View Side View Note: The cylinder is lying on its side with the two bases on the horizontal ends. Triangular Prism Cone Triangular Prism Cone Square Pyramid Triangular Pyramid Cylinder Rectangular Prism c. The top and side views of a threedimensional figure are shown below. d. The top and side views of a threedimensional figure are shown below. Top View Side View Top View Side View Note: The cone is lying on its side with the base on the horizontal end. Triangular Pyramid Cylinder Cone Rectangular Prism Triangular Prism Square Pyramid Rectangular Pyramid Rectangular Prism 2012, TESCCC 08/17/12 page 3 of 3

28 Perspective Views Grade 7 Mathematics Unit: 04 Lesson: Draw the two-dimensional front, top, and side views for each three-dimensional figure. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View c. Front View Top View Side View 2012, TESCCC 08/17/12 page 1 of 3

29 Perspective Views Grade 7 Mathematics Unit: 04 Lesson: Draw the three-dimensional figure for the given two-dimensional front, top, and side views. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View c. Front View Top View Side View 2012, TESCCC 08/17/12 page 2 of 3

30 Perspective Views Grade 7 Mathematics Unit: 04 Lesson: Circle the three-dimensional figure that the given views could represent. a. The top and side views of a threedimensional figure are shown below. dimensional figure are shown b. The top and side views of a three- below. Top View Side View Top View Side View Triangular Prism Cone Triangular Prism Cone Square Pyramid Triangular Pyramid Cylinder Rectangular Prism c. The top and side views of a threedimensional figure are shown below. d. The top and side views of a threedimensional figure are shown below. Top View Side View Top View Side View Triangular Pyramid Cone Triangular Prism Rectangular Pyramid Cylinder Rectangular Prism Square Pyramid Rectangular Prism 2012, TESCCC 08/17/12 page 3 of 3

31 Perspective Views Practice KEY Grade 7 Mathematics Unit: 04 Lesson: Draw the two-dimensional front, top, and side views for the given three-dimensional figures. a. Front View Top View Side View b. Front View Top View Side View 2012, TESCCC 08/17/12 page 1 of 2

32 Perspective Views Practice KEY Grade 7 Mathematics Unit: 04 Lesson: Draw the three-dimensional figure for the given two-dimensional front, top, and side views. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View 3. Draw the two-dimensional front and top views for the given three-dimensional solid. Three-Dimensional Solid Two-Dimensional Views Front View Top View 2012, TESCCC 08/17/12 page 2 of 2

33 Perspective Views Practice Grade 7 Mathematics Unit: 04 Lesson: Draw the two-dimensional front, top, and side views for the given three-dimensional figures. a. Front View Top View Side View b. Front View Top View Side View 2012, TESCCC 08/17/12 page 1 of 2

34 Perspective Views Practice Grade 7 Mathematics Unit: 04 Lesson: Draw the three-dimensional figure for the given two-dimensional front, top, and side views. Three-Dimensional Figure Two-Dimensional Views a. Front View Top View Side View b. Front View Top View Side View 1. Draw the two-dimensional front and top views for the given three-dimensional solid. Three-Dimensional Solid Two-Dimensional Views Front View Top View 2012, TESCCC 08/17/12 page 2 of 2

Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Unit 0: Fractions ( days) Possible Lesson 0 ( days) Possible Lesson 02 ( days) Possible Lesson 0 ( days) Possible Lesson