AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Weeks: / 1- 3

Instructional Unit Plan

Unit 7Georgia Performance Standards

M7G1a / Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
M7G1b / Recognize that many constructions are based on the creation of congruent triangles.
M7G2a / Demonstrate understanding of translations, dilations, rotations, or reflections and relate symmetry to appropriate transformations.
M7G3a / Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.
M7G3b / Understand the relationship among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.
M7G4a / Describe three-dimensional figures formed by translations and rotations of plane figures through space.
M7G4b / Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.
Unit 7 Framework Enduring Understandings
Three-dimensional objects can be created from two-dimensional plane figures through transformations and rotations.
A three-dimensional object can be built by stacking congruent or similar plane figures / Unit 7 Framework Essential Questions
When rotating or translating plane figures through space, what solids can be formed?
What is the relationship among the volumes of cylinders, cones, and spheres?
If I stack congruent similar plane figures, what kind of solids are formed?
Vocabulary
SphereCylinderBases of cylinder
ConeBase of coneRight circular cone
Plane figuresCross sectionEllipses
PolyhedronBases of prismsRectangular prism
PyramidRight pyramidRight rectangular prism
Lateral faces of a pyramid / Literacy GPS
GPS Reading Across the Content Area Standards
ELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
Unit 7 Assessment
GPS Framework Unit 7 Slices and Shadows, Culminating Task “Cool Cross Sections,” p. 25 of 26
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 1

Georgia Performance Standards

M7G4a / Describe three-dimensional figures formed by translations and rotations of plane figures through space.
M7G1a / Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
M7G1b / Recognize that many constructions are based on the creation of congruent triangles.
M7G2a / Demonstrate understanding of translations, dilations, rotations, or reflections and relate symmetry to appropriate transformations.
Unit 7 Framework Enduring Understandings
Three-dimensional objects can be created from two-dimensional plane figures through transformations and rotations.
A three-dimensional object can be built by stacking congruent or similar plane figures / Unit 7 Framework Essential Questions
When rotating or translating plane figures through space, what solids can be formed?
What is the relationship among the volumes of cylinders, cones, and spheres?
If I stack congruent similar plane figures, what kind of solids are formed?
. Vocabulary
SphereCylinder
Bases of cylinderOblique cylinder
ConeBase of cone
Oblique coneRight circular cone
VolumePlane figures / Literacy GPS
GPS Reading Across the Content Area Standards
ELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
ELA7RC4 The student establishes a context for information acquired by reading across subject areas
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 1
Warm-Up / Quick Practice
Mental Math: Findfractional parts of whole numbers (for example, 2/3 of 24, 1/5 of 80)
Distinguish between an inverse proportional relationship and a direct proportional relationship
Translate verbal phrases to algebraic expressions
Skill Mastery: Convert in customary units of measurements / Problem Solving
Solve problems involving data on graphs
Holt Mathematics Course 2, Teacher-selected problems from Chapter 7
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

4.1.1

/ Foundation for M7G1
M7G2
M7G4 / Review basic concepts and vocabulary involving geometric solids / Holt Mathematics Course 2, “Introduction to Three-Dimensional Figures,” pp. 580 - 583 / Models of geometric solids

4.1.2

/ Foundation for M7G1
M7G2
M7G4 / Review strategies to determine volume of geometric solids / Holt Mathematics Course 2, “Volume of Prisms and Cylinders” and “Volume of Pyramids and Cones,” teacher-selected problems from pages 588 – 589 and 592 – 593 / Calculators

4.1.3

/ M7G4a / Discover how rotations of plane figures can produce three-dimensional objects
Relate properties of the plane figures to the area and volume of the three-dimensional objects / GPS Framework Unit 7 Slices and Shadows, “Rotations in Sand,” pp. 7 – 9 of 26 / Isosceles triangle constructed on
heavy cardboard
Ruler
Container of damp sand

4.1.4

/ M7G4a
M7G1a, b
M7G2a / Make a three-dimensional model of a solid by translating a rectangle through space / GPS Framework Unit 7 Slices and Shadows, “Translations and Prisms,” pp. 10 – 11 of 26
GPS Framework Unit 7 Slices and Shadows, “One More Time Around”, pp 10 – 11 of 16 / Refer to tasks
4.1.5 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus: Review geometric solids using HM Course 2, “Journal,” p. 583.
Maintenance: Use manipulative to solve problems. Refer to supplemental HM Course 2 materials.
Maintenance: Generate and model equivalent ratios. Refer to supplemental HM Course 2 materials.
Exploration: Investigate the surface area of similar prisms with “Hands-On Lab 10-5” from HM Course 2, pp. 602 – 603.
Intervention: / Homework
Weekly Focus: Solve problems involving spheres, cones, and cylinders
Maintenance: Distinguish between an inverse proportional relationship and a direct proportional relationship
Skill: Convert in customary units of measurements
Reflection with Closure
Describe five three-dimensional figures that can be formed by stacking congruent or similar plane figures. Explain what is stacked to form each three-dimensional figure suggested.
Journal
If a cone, a cylinder, and a sphere have the same radius and height, describe the relationships among the volumes of the cone, the sphere, and the cylinder. Use examples and sketches to illustrate your answer
Evidence of Learning (Assessments)
Weekly Focus: Teacher-selected HM Course 2 items
Skill Mastery:Convert in customary units of measurements
(1) 7 ft = ___ in (2) 72 in = ___ yd (3) 15 qt = ___ pt (4) 10 c = ___ fl oz (5) 30 qt = ___ gal ___qt
Performance Task:
Culminating Task:
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 2

Georgia Performance Standards

M7G4b / Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.
M7G3a / Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.
M7G3b / Understand the relationship among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.
N7N1c / Add, subtract, multiply, and divide positive and negative rational numbers.
N7N1d / Solve problems using rational numbers.
Unit 7 Framework Enduring Understandings
Cross sections of three-dimensional objects can be formed in a variety of ways, depending on the angle of the cut with the base of the object.
Parallel cross sections of the same solid may be similar or congruent plane figures. / Unit 7 Framework Essential Questions
What plane figures can I make by slicing a cube by planes? What about when I use cones, prisms, cylinders, and pyramids instead of cubes?
If I stack congruent or similar plane figures, what kinds of solids are formed?
How can I be sure that I have found all possible cross-sections of a solid?
Vocabulary
Cross section Cylinder
ConeSphere
Plane figures Ellipses
PolyhedronBases of prisms
Lateral faces of prismsRectangular prism
Right rectangular prismPyramid
Lateral faces of a pyramidRight pyramid / Literacy GPS
GPS Reading Across the Content Area Standards
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
ELA7RC4 The student establishes a context for information acquired by reading across subject areas
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 2
Warm-Up / Quick Practice
Mental Math: Find fractional parts of whole numbers
Determine the volume of cones and cylinders
Solve two-step equations
SM: Add and subtract fractions and mixed numbers / Problem Solving
Solve routine and non-routine problems using variousstrategies
Holt Mathematics Course 2, “Problem Solving Strategies,” pp. 752 - 761
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

4.2.6

/ M7G4b / Describe, name, and sketch cross-sections of a cube / GPS Framework Unit 7 Slices and Shadows, “Cross-Section of a Cube,” pp. 13 and 17 of 26 / Clay or play-dough
Dental floss

4.2.7

/ M7G4b / Explore cross-sections of cylinders, cones, and spheres / GPS Framework Unit 7 Slices and Shadows, “Crazy with Cross-Sections,” pp. 18-19 of 26 / Clay or play-dough
Dental floss

4.2.8

/ M7G4b
M7G3a, b
M7N1c, d
M7P1a, b / Explore shadow of a three-dimensional figure
Explore cross-sections of a pyramid and discover similarity / GPS Framework Unit 7 Slices and Shadows, “Shadows,” p. 20 of 26 and “Similar Cross Sections,” p. 21 of 26 / Cube constructed from cardboard
Light source
Large piece of paper
Clay or play-dough to construct
pyramids
Ruler

4.2.9

/ M7G4b / Explore the cross-section of an oval cylinder / GPS Framework Unit 7 Slices and Shadows, “Vase,” p. 22 of 26 / Copies of tasks
Access to clay or play-dough
Toilet paper roll
4.2.10 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus: Solve problems involving geometric solids with “Focus on Problem Solving”HM Course 2, p. 595.
Maintenance: Solve problems involvingratios with “Miles per Hour” and “Miles per Gallon” from MIC Ratios and Rates, pp. 4 – 7.
Maintenance: Apply reasoning skills with “Water Works” and “Magic Cubes” from HM Course 2, pp. 316 and 614.
Exploration: Investigate how changing dimensions of a pyramid affects its volume with Technology Lab “Explore Changes in Dimensions” from HM Course 2, p. 609.
Intervention: / Homework
Weekly Focus:Explore cross-sections of solids
Maintenance:Apply knowledge of volumes a cylinder, cone, and sphere
Skill: Add and subtract fractions and mixed numbers
Reflection with Closure
Describe the cross-sections of a cube, pyramid, cylinder, cone, and sphere.
Journal
Describe all the possible shadows of a cube. Explain how to hold the cube to obtain each shadow.
Evidence of Learning (Assessments)
Weekly Focus: Teacher-selected HM Course 2 items
Skill Mastery:Add and subtract fractions and mixed numbers
(1) 3 7/8 + 2 ¼ = (2) 4 ¾ - 2 3/5 = (3) 4 ½ + 3 7/8 + 2 ¾ = (4) 5 1/8 - 2 5/8 = (5) 4 ¾ + 2 7/8 =
Performance Task:
Culminating Task:
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 3

Georgia Performance Standards

M7G4a / Describe three-dimensional figures formed by translations and rotations of plane figures through space.
M7G4b / Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.
M7G1a / Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
M7G1b / Recognize that many constructions are based on the creation of congruent triangles.
M7G2a / Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.
Unit 7 Framework Enduring Understandings
Cross sections of three-dimensional objects can be formed in a variety of ways, depending on the angle of the cut with the base of the object.
Parallel cross sections of the same solid may be similar or congruent plane figures. / Unit 7 Framework Essential Questions
What plane figures can I make by slicing a cube by planes? What about when I use cones, prisms, cylinders, and pyramids instead of cubes?
How can I be sure I have found all possible cross-sections of a solid?
Vocabulary
SphereCylinder
Bases of cylinderCone
Base of coneRight circular cone
Plane figuresCross section
EllipsesPolyhedron
Bases of prismsRectangular prism
Right rectangular prismPyramid
Lateral faces of a pyramidRight pyramid / Literacy GPS
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
ELA7RC4 The student establishes a context for information acquired by reading across subject areas
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 3
Warm-Up / Quick Practice
Mental Math: Compare prices to find the better deal(for example, 5 pounds for $19.99 or 3 pounds for $12.99)
Describe the results of the transformation of a three-dimensional figure
Analyze relations from a table
SM: Evaluate algebraic expressions / Problem Solving
Solve problems involving data and geometric figures
HM Course 2, “Problem Solving on Location,” pp. 512 - 513
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

4.3.11

/ M7G4b / Describe a solid from its cross sections / GPS Framework Unit 7 Slices and Shadows, “What’s My Solid?” pp. 23 - 24 of 26 / Copies of task, “What’s My Solid?”
Plain paper to sketch

4.3.12

/ M7G4a, b
M7G1a, b
M7G2a / Apply knowledge of cross-sections of solids and the result of moving a two-dimensional figure through space to create a three-dimensional figure / GPS Framework Unit 7 Slices and Shadows, Culminating Task “Cool Cross Sections,” p. 25 of 26
Assign pairs and pass out handouts for culminating activity, “Cool Cross Sections,” p. 25 of 26. / Copies of culminating activity “Cool
Cross Sections”
Markers
Rulers
Large sheets of paper

4.3.13

/ M7G4a, b
M7G1a, b
M7G2a / Apply knowledge of cross-sections of solids and the result of moving a two-dimensional figure through space to create a three-dimensional figure / GPS Framework Unit 7 Slices and Shadows, Culminating Task “Cool Cross Sections,” p. 25 of 26
Students are to work in pairs to complete this culminating activity. / Copies of tasks
Markers
Rulers
Large sheets of paper

4.3.14

/ M7G4a, b
M7G1a, b
M7G2a / Apply knowledge of cross-sections of solids and the result of moving a two-dimensional figure through space to create a three-dimensional figure / GPS Framework Unit 7 Slices and Shadows, Culminating Task “Cool Cross Sections,” p. 25 of 26
Presentations of culminating activity / Student projects
4.3.15 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus:Sketch and describe cross-sections of three-dimensional figures with “Extension Cross Sections” from HM Course 2, pp. 612 – 613.
Maintenance: Solve problems involving ratios with “Miles per Hour” and “Miles per Gallon” from MIC Ratios and Rates, pp. 4 – 7.
Maintenance: Apply reasoning skills with “Water Works” and “Magic Cubes” from HM Course 2, pp. 316 and 614.
Exploration: Investigate how changing dimensions of a pyramid affects its volume with Technology Lab “Explore Changes in Dimensions” from HM Course 2, p. 609.
Intervention: / Homework
Weekly Focus:Apply knowledge of cross-sections of solids and the result of moving a two-dimensional figure through space to create a three-dimensional figure
Maintenance: Solve problems involving the volume of three-dimensional figures
Skill:Evaluate algebraic expressions
Reflection with Closure
Can a given cross-section be a part of more than one type of solid? Explain or give an example.
Journal
Is it possible for a right rectangular prism to have a cross section that is a rhombus? Explain why it is not possible or explain how it is possible.
Evidence of Learning (Assessments)
Weekly Focus: Teacher-selected HM Course 2 items
Skill Mastery:Evaluate algebraic expressions
(1) t + 108 = (2) t² + 3 - t = (3) 2³ + t² = (4) 4 + t ÷ 6 · 2 =
Performance Task:
Culminating Task:
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Weeks: / 4- 9

Instructional Unit Plan

Unit 8Georgia Performance Standards

This unit provides an opportunity to apply all seventh grade mathematics performance standards. Refer to the weekly cover sheets.
Unit 8 Enduring Understandings
Proficiency in computing with positive and negative numbers is vital to success in real life.
Algebraic expressions may be used to represent relationships between variables when solving problems.
Proportional relationships can be represented using words, rules, tables, and graphs.
Inverse operations and the basic properties of our number system are essential to understanding and solving linear equations.
Constructions and transformations can be used to verify congruence.
Two shapes are similar if all of the corresponding angles are congruent and the lengths of all the corresponding sides are proportional. The ratio of these corresponding sides is known as a scale factor. / Unit 8 Framework Essential Questions
How can I formulate questions, gather data, display and decipher the results?
How do I add, subtract, multiply, and divide using positive and negative rational numbers?
What role does solving equations play in solving real world problems?
How can I use congruent triangles to justify geometric constructions?
How could using the coordinate plane help me understand properties of reflections, translations, and rotations?
How can I be sure that I have found all possible cross-sections of a solid?
How does an inverse proportion differ from a direct proportion?
Vocabulary
Grade level vocabulary presented through the year / Literacy GPS
GPS Reading Across the Content Area Standards
ELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
Unit 8 Assessment
GPS Framework Unit 8Show What We Know, presentations of final projects
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 4

Georgia Performance Standards

M7G1a / Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
M7G2a / Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.
M7G2b / Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.
M7G3a / Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.
M7G3b / Understand the relationship among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length rations and area ratios to determine side lengths and areas of similar geometric figures.
M7G3c / Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape.
Unit 8 Framework Enduring Understandings
Constructions and transformations can be used to verify congruence.
Two shapes are similar if all of the corresponding angles are congruent and the length if all corresponding sides are proportional. The ratio of these corresponding sides is known as a scale factor. / Unit 8 Framework Essential Questions
How can I use congruent triangles to justify geometric constructions?
How could using the coordinate plane help me understand properties of reflections, translations, and rotations?
What information do I need to know in order to be assured that two figures are similar and/or congruent?
Vocabulary
Grant
Profit
Slogan
Logo
Cartesian plane / Literacy GPS
GPS Reading Across the Content Area Standards
ELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.
ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.
ELA7RC4 The student establishes a context for information acquired by reading across subject areas
AtlantaPublic SchoolsTeaching Plans / Seventh Grade / Quarter: / 4 / Week: / 4
Warm-Up / Quick Practice
Mental Math: Compare prices to find the better deal
Identify the cross-section of a solid
Describe a graph given a situation
SM: Evaluate numerical expressions. / Problem Solving
Solve problems involving data on graphs
Holt Mathematics Course 2, Teacher-selected problems from Chapter 7
Focus Lessons

Ref #