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STANDARD 4.7 - All students will develop spatial sense and an ability to use geometric properties and relationships to solve problems in mathematics and in everyday life.

Note - Internet links at bottom of page

Descriptive Statement: Spatial sense is an intuitive feel for shape and space. It involves the concepts of traditional geometry, including an ability to recognize, visualize, represent, and transform geometric shapes. It also involves other, less formal ways of looking at two-and three-dimensional space, such as paper-folding, transformations, tessellations, and projections. Geometry is all around us in are, nature, and the things we make. Students of geometry can apply their spatial sense and knowledge of the properties of shapes and space to the real world.
 
Topic/Unit

Timeline

 Cumulative Progress Indicators Objectives Suggested Activities Materials Evaluation
Geometry and Spatial Sense

Timeline

  1. 4th Q
  2. 3rd Q
 Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students will:
  1. Relate two-dimensional and three-dimensional geometry using shadows, perspectives, projections and maps.
  1. Identify patterns that fold into three-dimensional figures
  2. Relate two-dimensional and three-dimensional geometry using perspectives and maps
  1. See Lesson 11-2.
  2. See Lesson 8-6.
  1. Centimeter graph paper, compass, scissors
  2. Math journal, Hot Page software
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
Timeline
  1. 1st Q
  2. 2nd Q
  3. 3rd Q
  1. Understand and describe the concepts of symmetry, similarity and congruence
  1. Verify that two triangles are congruent
  2. Diagram lines of symmetry
  3. Determine when polygons are similar and congruent
  1. See Lesson 2-4.
  2. See Lesson 5-10.
  3. See Lesson 8-4.
  1. Protractor, metric ruler, toothpicks, Math Tools software "Geometry", math journal
  2. Tracing paper, ruler, marker, Hot Page software, math journal
  3. Graph paper, Hot Page software, math journal
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
  3. Same as #2

 
 
Topic/Unit

Timeline

 Cumulative Progress Indicators Objectives Suggested Activities Materials Evaluation
Geometry and Spatial Sense
 
 
 
 

Timeline

  1. 1st Q
  2. 1st and 4th Q
  1. Identify, describe, compare, and classify plane and solid geometric figures
  1. Classify triangles and quadrilaterals
  2. Classify solid geometric figures
  1. See Lesson 2-1.
  2. See Lessons 2-5 and 11-1.
  1. Compass, protractor
  2. Math journal, Hot Page software
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
Timeline
  1. 1st Q
  2. 1st Q
  3. 1st Q
  1. Understand the properties of lines and planes, including parallel and perpendicular lines and planes, and intersecting lines and their angles of incidence.
  1. Investigate the properties of perpendicular lines
  2. Investigate the properties of parallel lines
  3. Explore the relationships among the angles formed by parallel lines and a transversal
  1. See Lesson 2-8.
  2. See Lesson 2-10.
  3. See Lesson 2-9.
  1. Tracing paper, compass, straightedge, Math Tools software "Geometry ", math journal
  2. Compass, straightedge, math journal
  3. Protractor, Math Tools software "Geometry", math journal
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. Same as #1
  3. Same as #1

 
 
Topic/Unit

Timeline

 Cumulative Progress Indicators Objectives Suggested Activities Materials Evaluation
Geometry and Spatial Sense
 
 

Timeline

  1. 1st Q
  2. 2nd Q
  3. 2nd Q
  4. 2nd Q
  5. 3rd Q
  1. Explore the relationships among geometric transformations (translations, reflections, and rotations), tessellations, (tilings), and congruence and similarity.
  1. Investigate tessellations
  2. Graph and investigate translations
  3. Graph and investigate reflections
  4. Graph and investigate rotations
  5. Use proportional reasoning to find corresponding parts of similar polygons
  1. See Lesson 2-7.
  2. See Lesson 5-9.
  3. See Lesson 5-10.
  4. See Lesson 5-11.
  5. See Lesson 8-4.
  1. Hot Page software, congruent copies of polygons, math journal
  2. Ruler, protractor, graph paper, Hot Page software, math journal
  3. Tracing paper, ruler, marker, Hot page software, math journal
  4. Graph paper, ruler, math journal
  5. Graph paper, Hot page software, math journal
  1. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet, portfolio assessment
  2. "On Your Own" examples, teaching resources provided by the publisher, Hot page record sheet
  3. Same as #2
  4. "On Your Own" examples, teaching resources provided by the publisher
  5. Same as #2

 
 
Topic/Unit

Timeline

 Cumulative Progress Indicators Objectives Suggested Activities Materials Evaluation
Geometry and Spatial Sense

Timeline

  1. 1st Q
  2. 4th Q
  3. 4th Q
  4. 4th Q
  5. 4th Q
  6. 1st Q
  1. Develop, understand, and apply a variety of strategies for determining perimeter, area, surface area, angle measure, and volume.
  1. Compute the area and circumference of a circle
  2. Derive the formula for and compute the surface area of prisms
  3. Derive the formula for and compute the surface area of cylinders
  4. Compute the volume of a cylinder
  5. Compute the volume of cones and pyramids
  6. Classify and work with the central angles and inscribed angles of a circle
  1. See Lesson 2-2.
  2. See Lesson 11-5.
  3. See Lesson 11-4.
  4. See Lesson 11-8.
  5. See Lesson 11-9.
  6. See Lesson 2-1.
  1. Math Tools software "Geometry", math journal
  2. Math journal
  3. Writing paper, tape, ruler, compass, scissors, spreadsheet software, math journal
  4. Spreadsheet software, Hot Page software, math journal
  5. Same as #4
  6. Compass, protractor
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. Same as #1
  3. Same as #1
  4. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
  5. Same as #4
  6. "On Your Own" examples, teaching resources provided by the publisher
Timeline
  1. 1st Q
  2. 3rd Q
  1. Understand and apply the Pythagorean Theorem.
  1. Investigate the Pythagorean Theorem
  2. Apply the Pythagorean Theorem in real-life problems
  1. See Lesson 2-12.
  2. See pages 359 #13 and 366 #19-#21.
  1. Geoboard, dot paper, Hot Page software, Investigations software "The Pythagorean Theorem", math journal
  2. See teacher’s edition for a list of materials needed for each activity
  1. "On Your Own" examples, teaching resources provided by the publisher, Hot Page record sheet
  2. Self assessment

 
 
Topic/Unit

Timeline

 Cumulative Progress Indicators Objectives Suggested Activities Materials Evaluation
Geometry and Spatial Sense
 
 

Timeline

  1. 3rd Q
  2. All year
  1. Explore patterns produced by the processes of geometric change, relating iteration, approximation, and fractals.
  1. Explore self-similarity and fractals
  2. Explore the patterns produced and make predictions in problem situations resulting from geometric change
  1. See Lesson 8-9.
  2. These are found throughout the text. For example, see pages 492 #13, 314 #13, 303 #9, 259 #10, 49 #14, 201 #28, and others.
  1. Compass, straightedge
  2. See Teacher’s edition for a list of materials needed for each activity
  1. "On Your Own" examples, teaching resources provided by the publisher
  2. Self assessment
Timeline
  1. All year
  2. All year
  1. Investigate, explore, and describe geometry in nature and real-world applications, using models, manipulatives, and appropriate technology.
  1. Describe instances where geometry is found in nature.
  2. Investigate real-life applications of geometry
  1. Identify the geometric concepts in the pictures on pages 56, 71, 80, 120, 208, 226, 232, 234, and others.
  2. Discuss the geometry applied in the pictures on pages 63, 61, 70, 178, 206, and others. 
  1. See teacher’s edition for a list of materials needed for each activity
  2. Same as #1
  1. Self assessment
  2. Same as #1

 
Resources

The Internet Pizza Server  -Topic: Data Collection, Unit Price, Proportions, Research, & Area of Circles, (many more
                                                           can be adapted).

Totally Tessellated  -This site will give you a comprehensive introduction to tessellations.

Online Geometry  -activities for middle or high school geometry.

Dueling Pinwheels  -Dazzle your students with this so-cool animated introductory exercise.

Pythagoras' Playground  -From this site, we will use the amazing properties of the Pythagorean Theorem to explore the
                                                     world around us.

Fractals-a fractals unit for Elementary and Middle School Students

Symmetry and Patterns  -the art of oriental carpets.  The study of symmetry offers one approach to
                                                      analyzing patterns in Oriental carpets.
A Cylinder Workshop  -Students will work with given formulas to solve for specific variables. They will calculate the volume
                                              of a cylinder and analyze the change in volume when there is a constant surface area. They will
                                              repeat the problem with a constant perimeter.