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-Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Week: 1

Instructional Unit PlanGrade 6 Unit 6 Georgia Performance Standards

M6G1a Determine and use lines of symmetry.M6G1b Investigate rotational symmetry, including degree of rotation.

Grade 6 Unit 6 Framework Essential Questions

How do you determine lines of symmetry? What do they tell us?How do you determine rotational symmetry? What does it tell us?What do degrees of rotation have to do with rotational symmetry?How is symmetry used in areas such as architecture and art? In what other areas is symmetry important?

Grade 6 Unit 6 Framework Enduring Understandings

An object may be asymmetrical, have one line of symmetry, or many lines of symmetry.Symmetry exists in nature and in man-made objects.Symmetry is an important concept in art, architecture, and in many other fields.

Vocabulary

AsymmetricalAxis of symmetryLine of symmetryLine symmetryReflectional symmetryRotationRotational symmetrySymmetry

Literacy GPS

ELA6RC3a Demonstrate an understanding of contextual vocabulary in various subjects

ELA6W2a Produce technical writing that follows an organizing structure

ELA6LSV1b Ask relevant questions

ELA6LSV1c Respond to questions with appropriate information

Grade 6 Unit 6 Assessment

GPS Framework Unit 6 Symmetry, Culminating Task “Symmetry Task,” pp. 9 – 12 of 12

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Week: 2

Georgia Performance Standards

M6G1a Determine and use lines of symmetry.M6G1b Investigate rotational symmetry, including degree of rotation.


An object may be asymmetrical, have one line of symmetry, or many lines of symmetry.Symmetry exists in nature and in man-made objects.Symmetry is an important concept in art, architecture, and in many other fields.


How do you determine lines of symmetry? What do they tell us?How do you determine rotational symmetry? What does it tell us?What do degrees of rotation have to do with rotational symmetry?How is symmetry used in areas such as architecture and art? In what other areas is symmetry important?

Vocabulary

Asymmetrical Axis of symmetryLine of symmetry Line symmetryReflectional symmetry RotationRotational symmetry Symmetry

Literacy GPS






Warm-Up/Quick PracticeMental Math: Use compatible numbers to calculate change from whole dollar amounts (For example, if you spent $7.42 and paid with $20.00, think I need one dollar for the coins, so I have used $8, and 8 + 12 = 20 so I get back $12; then think 42 and what number equals 100 so I know I get 58 cents, so my change is $12.58)Define terms associated with a circleDecompose numbers into their prime factorizationAdd integers

Problem SolvingSolve routine problems and non-routine problems involving the Draw a Picture strategy HM Course 2, “Problem Solving Strategies,” p. 752

Focus LessonsRef#

State Standards

Objectives Resources Materials

3.1.1 M6G1b Understand the actions and vocabulary involved in rotational symmetry

Holt Mathematics Course 1, “Transformations” Kinesthetic Experience and Reaching All Learners with a focus on rotations, p. 460

Paper to trace shapesGraph paperScissors

3.1.2 M6G1a Develop skills with rotational symmetry

Holt Mathematics Course 1, “Transformations,” pp. 461 – 462

If technology is available, Grade 6 GPS Framework Unit 6 Symmetry, “Line and Rotational Symmetry,” p. 5 of 12

Student work from previous lesson for examples of rotations

3.1.3 M6G1a Explore symmetry of figuresIdentify lines of symmetry within polygons

Grade 6 GPS Framework Unit 6 Symmetry, “Quadrilateral Symmetry,” pp. 7 - 8 of 12Holt Mathematics Course 1, “Line Symmetry,” pp. 464 – 467

Blank paper easy to fold and cutScissorsMaterials to display student-made examples of line symmetry

3.1.4 M6G1aM6G1b

Create designs with line and rotational symmetry

Grade 6 GPS Framework Unit 6 Symmetry, “Create Your Own Logo,” pp. 8 – 9 of 12Note: Continue as a homework assignment in week 2

Art materials for students to create logos

3.1.5 See Variety of Instructional Tasks

Variety of Instructional Tasks

Weekly Focus: Apply symmetry skills with “Line and Rotational Symmetry” or “Rotational Symmetry” from Grade 6 GPS Framework Unit 6 Symmetry, pp. 5 - 6 of 12 (computer use)

Maintenance: Solve non-routine word problems with “Something’s Fishy” and “Secret Recipe” from HM Course 1, pp. 279 and 399.

Maintenance: Build integer fluency with “Ups and Downs” from HM Course 2, p. 133.

Exploration: Explore the development of measurement standards with Grade 6 GPS Framework Unit 7 Scale Factor, “The History of Measurement,” pp. 5 – 6 of 16.

Intervention:

Homework

Weekly Focus: Model and define line and rotational symmetry

Maintenance: Use data from graphs or charts to answer questions and make inferences

Skill: Add integers

Refer to HM Course 1 and Course 2

Reflection with ClosureWhy do symmetric designs and logos appeal to so many people? Do I find myself preferring those designs rather than asymmetrical figures as well? Do I regularly see any example of symmetry being used in areas such as architecture and art? Is there any symmetry in the design of our school?

Journal How is the concept of congruence related to symmetry?Why is it necessary to locate the point of rotation used with models of rotational symmetry?Why can points of rotation be located only on or outside the original figure, but not within it?

Evidence of Learning (Assessments)Weekly Focus: Selected HM Course 1 Chapter 8 items Skill Mastery: Add integers (1) 312 + -435 = (2) -406 + -645 = (3) 765 + -877 = (4) -35 + -45 + -13 + -20 = (5) 58 + -60 + -52 + -24 =Performance Task:Culminating Task: GPS Framework Unit 6 Symmetry, Culminating Task “Symmetry Task,” pp. 9 – 12 of 12

-Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Weeks: 2- 7

Instructional Unit Plan

Grade 6 Unit 7 and Grade 7 Unit 5 Georgia Performance Standards

M6M1 Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.

M6M2a Measure length to the nearest half, fourth, eighth, and sixteenth of an inch.M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6M2c Compare and contrast units of measure for perimeter, area, and volume.M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6G1d Interpret and sketch simple scale drawings.M6G1e Solve problems involving scale drawings.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M7G2a Demonstrate understanding of (translations), dilations, (rotations, reflections, and relate symmetry to appropriate transformations).

M7G2bGiven a figure in the coordinate plane, determine the coordinates resulting from a (translation), dilation, (rotation, or reflection).

M7A3aPlot points on a coordinate plane.

M7G3a Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.

M7G3bUnderstand 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.

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Weeks: 2- 7

Instructional Unit PlanGrade 6 Unit 7 and Grade 7 Unit 5, continued

Grade 6 Unit 7 and Grade 7 Unit 5 Framework Enduring Understandings

It is important to be able to convert from one unit of measure to another within the same system of measurement.Ratios, proportions, and scale factors are used to solve many problems encountered in everyday life.The ratios of corresponding sides of similar figures are constant.Scale factors are used to create scale drawings.Two shapes are similar if the lengths of all the corresponding sides are proportional and all the corresponding angles are congruent.If the scale factor of a dilation is greater than 1, the image resulting form the dilation is an enlargement. If the scale factor is less than 1, the image is a reduction.Two similar figures are related by a scale factor, which is the ratio of the lengths of the corresponding sides.The sides and perimeters of similar figures are related by the square of the scale factor.Scale factors, length ratios, and area ratios may be used to determine missing side lengths and areas in similar geometric figures.Congruent figures have the same size and shape.

Grade 6 Unit 7 and Grade 7 Unit 5 Framework Essential Questions

Why is it important to be able to convert from one unit of measurement to another?How do you determine the most appropriate unit of measure for measuring lengths, areas, and perimeters of simple plane figures?How can scale factors, ratios, and proportions be used to represent the relationships that exist between similar figures?How can scale factors, ratios, and proportions be used to solve problems related to similar figures?How can I tell if two figures are similar?In what ways can I represent the relationships that exist between similar figures using the scale factor, length ratios, and area ratios?What strategies can I use to determine missing lengths and areas of similar figures?Under what conditions are similar figures congruent?

Vocabulary

Ratio Proportion Scale drawingsScale factor Similar figures DilationPerimeter Corresponding sides Corresponding anglesArea Similar figures Congruent figures

Literacy GPS


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Grade 6 Unit 7 and Grade 7 Unit 5 Assessment

GPS Framework Unit 7 Scale Factor, Culminating Task “Designer’s Challenge,” pp. 13 – 16 of 16Grade 7 GPS Framework Unit 5 Staying in Shape , Culminating Task “Club Logo,” pp. 32 – 33 of 33



M6G1a Determine and use lines of symmetry.M6G1b Investigate rotational symmetry, including degree of rotation.M6M1 Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional

relationships.M6M2a Measure length to the nearest half, fourth, eighth, and sixteenth of an inch.M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6M2c Compare and contrast units of measure for perimeter, area, and volume.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.

Grade 6 Unit 6 and Unit 7 Framework Enduring Understandings

An object may be asymmetrical, have one line of symmetry, or many lines of symmetry.

It is important to be able to convert from one unit of measure to another within the same system of measurement.Ratios, proportions, and scale factors are used to solve many problems encountered in everyday life.

Grade 6 Unit 6 and Unit 7 Framework Essential Questions

How do you determine lines of symmetry? What do they tell us?How do you determine rotational symmetry? What does it tell us?

Why is it important to be able to convert from one unit of measurement to another?How do you determine the most appropriate unit of measure for measuring lengths, areas, and perimeters of simple plane figures?

Vocabulary

Asymmetrical Axis of symmetryLine of symmetry Line symmetryReflectional symmetry RotationRotational symmetry Symmetry

Ratio Proportion

Literacy GPS






Warm-Up/Quick PracticeMental Math: Use compatible numbers to calculate change from whole dollar amountsRecognize and extend patterns represented in a tableRecognize or calculate fraction, decimal, and percent equivalentsSubtract integers

Problem SolvingSolve problems involving circle measurement Solve problems involving circle graphsRefer to HM Course 1 and HM Course 2 materials

Focus Lessons

-Ref#

State Standards


3.2.6 M6G1aM6G1b

Recognize and describe line and rotational symmetry

Grade 6 GPS Framework Unit 6 Symmetry, Culminating Task “Symmetry Task,” pp. 9 – 12 of 12

Copies of task for individual students or group work

3.2.7 M6M1M6M2bM6A1

Use metric units to estimate lengthConvert units within the metric system

Grade 6 MIC Models You Can Count On, “Choose Your Model” Meter Spotting and problems 5 – 9, pp. 52 - 54

Meter stick for each group of students

3.2.8 M6M1M6A1

Understand the significance of standardized units in measurementConvert customary and metric units of length, using proportional relationships

Grade 6 GPS Framework Unit 7 Scale Factor, “New Unit,” p. 7 of 16Holt Mathematics Course 1, “Converting Customary Units” including Reaching All Learners, pp. 496 – 499

Copies of benchmark pencil from the task for each groupInch and centimeter rulers RulersOptional: Calculators

3.2.9 M6M2bM6M2c

Measure area with metric or customary units

Grade 6 MIC Reallotment, “Measuring Area” Area, pp. 26 - 29

Cm rulers, inch rulers, and cm grid paper for each studentMeter stick, scissors, and self-stick notes for each group



Weekly Focus: Estimate and measure length of classroom items with customary and metric units.

Maintenance: Solve non-routine word problems with “Something’s Fishy” and “Secret Recipe” from HM Course 1, pp. 279 and 399.

Maintenance: Build integer fluency with “Ups and Downs” from HM Course 2, p. 133.

Exploration: Explore the development of measurement standards with Grade 6 GPS Framework Unit 7 Scale Factor, “The History of Measurement,” pp. 5 – 6 of 16.

Intervention:

Homework

Weekly Focus: Solve word problems involving conversion of measurement units

Maintenance: Complete “Create Your Own Logo” activity from week 1

Skill: Subtract integers


Reflection with ClosureWhy is it so very important to identify the unit used when giving a measurement? What are some possible problems that could occur when the appropriate unit is not clearly stated?

Journal What do mathematicians mean when they say no measurement is truly exact?What is the difference between precision and accuracy in measurement?

Evidence of Learning (Assessments)Weekly Focus: Selected HM Course 1 Chapter 9 items Skill Mastery: Subtract integers (1) 60 – 54 = (2) -76 - 84 = (3) 127 – (-98) = (4) -91 – (-67) = (5) 705 – (-859) =Performance Task:Culminating Task:



M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6G1d Interpret and sketch simple scale drawings.M6G1e Solve problems involving scale drawings.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M7G2a Demonstrate understanding of (translations), dilations, (rotations, reflections, and relate symmetry to appropriate transformations).




Ratios, proportions, and scale factors are used to solve many problems encountered in everyday life.The ratios of corresponding sides of similar figures are constant.


How can scale factors, ratios, and proportions be used to represent the relationships that exist between similar figures?How can scale factors, ratios, and proportions be used to solve problems related to similar figures?

Vocabulary

ProportionRatio

Literacy GPS






Warm-Up/Quick PracticeMental Math: Make compatible decimals when adding (for example, with 1.79 + 3.40, take .60 from the first addend and add it to the second for an easier new problem, 1.19 + 4.0)Solve one-step equations, including exponentsDetermine the mean, median, and mode for a data setMultiply and divide integers

Problem SolvingSolve routine problems and non-routine problems involving the Make a Table strategyHM Course 2, “Problem Solving Strategies,” p. 757

Focus LessonsRef#

State Standards


3.3.11 M6G1c, dM6A1

Understand the relationship among the angles and sides of similar figures

Holt Mathematics Course 1, “Similar Figures” Motivate and Reaching All Learners, pp. 366 - 367

ProtractorsRulersSimilar Polygons (Teaching Tools)

3.3.12 M6G1c, d, e M6A1M7G2aM7G3a, b

Understand the relationship among the angles and sides of similar figures Create scale drawings

Grade 7 GPS Framework Unit 5 Staying in Shape, “Dilations in the Coordinate Plane,” pp. 9 – 18

Copies of taskGrid paper—each student needs six grids

3.3.13 M6G1c, d, e M6A1M7G2aM7G3a, b

Understand the relationship among the angles and sides of similar figures Create scale drawings

Grade 7 GPS Framework Unit 5 Staying in Shape, “Dilations in the Coordinate Plane,” pp. 9 – 18

Student work and materials from previous lesson

3.3.14 M6G1c, d, eM7G2aM7G3a, b

Sketch scale drawingsIntroduce the term scale factor

Grade 6 GPS Framework Unit 7 Scale Factor, “A Common Misconception about Scaling,” pp. 8 - 9 of 16 and “Similar Figures,” pp. 10 – 12 of 1

Copies of tasks for each student group and transparency of problems


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Weekly Focus: Estimate and measure angles with “Palmanova” from Grade 6 MIC Figuring All the Angles, pp. 42 – 43. (Protractors are required.)

Maintenance: Solve problems involving constant area and changing perimeter. Refer to supplemental HM Course 1 materials.

Maintenance: Create designs with line and rotational symmetry (for school, favorite team, family, self or simply an artistic expression), based on “Create Your Own Logo” from the GPS Framework Unit 6 Symmetry, pp. 8 – 9 of 12.

Exploration: Investigate less common measurement strategies with “Body Length and Fathom” and “Other Measures for Length” from Grade 7 MIC Made to Measure, pp. 8 – 9.

Intervention:

Homework

Weekly Focus: Create simple scale drawings

Maintenance: Model and define line and rotational symmetry

Skill: Multiply and divide integers


Reflection with ClosureHow might movie producers use scale drawings in their productions? Are there any other professions where the ability to sketch scale drawings would be beneficial?

JournalHow many pairs of corresponding sides must you compare in order to calculate the scale factor of similar figures?How can corresponding angle measurements stay the same in similar figures when all the corresponding side lengths are not?

Evidence of Learning (Assessments)Weekly Focus: Selected HM Course 1 Chapter 7 items Skill Mastery: Multiply and divide integers (1) -7 (-14) = (2) -56 (101) = (3) 74 (-71) = (4) -1248/ -13 = (5) 7627 ÷ -29 =Performance Task:Culminating Task:



M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6G1d Interpret and sketch simple scale drawings.M6G1e Solve problems involving scale drawings.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M7G2a Demonstrate understanding of (translations), dilations, (rotations, 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.



Ratios, proportions, and scale factors are used to solve many problems encountered in everyday life.The ratios of corresponding sides of similar figures are constant.Scale factors are used to create scale drawings.

Grade 6 Unit 7 Framework Essential QuestionsHow can scale factors, ratios, and proportions be used to represent the relationships that exist between similar figures?How can scale factors, ratios, and proportions be used to solve problems related to similar figures?Why do we need scale drawings?

VocabularyProportionRatioScale drawingsScale factorSimilar figures

Literacy GPSELA6RC3a Demonstrate an understanding of contextual vocabulary in various subjects




Warm-Up/Quick PracticeMental Math: Make compatible decimals when addingOperations with intergersCalculate percent of a given whole number or money amountSolve one-step equations

Problem SolvingSolve real world problems involving measurement

HM Course 2, “Problem Solving on Location,” pp. 622 – 623

Focus LessonsRef#

State Standards


3.4.16 M6G1c, d, eM6A1M7G2aM7G3a, b

Investigate the connections that need to be made between the original and the resulting figure

Grade 7 MIC Ratios and Rates, “Scale Factor” Smaller or Larger? pp. 41 – 42

Centimeter rulersCalculators


Determine and use scale factors Grade 7 MIC Ratios and Rates, “Scale Factor” Enlarged or Reduced through question 13, pp. 42 – 45

Centimeter paperCentimeter rulersCalculators


Apply scale factor and ratio tables to solve problems

Grade 7 MIC Ratios and Rates, “Scale Factor” Enlarged or Reduced through question 16, pp. 44 – 46Grade 7 GPS Framework Unit 5 Staying in Shape, “Making Copies,” p. 26 of 33

Centimeter paperCentimeter rulersCalculatorsSamples of enlarged and reduced copies

3.4.19 M6G1c, d, eM6A1M7G2a, bM7A3a

Use a given rule to transform a shape on a coordinate planePredict how figures on coordinate planes will be affected by a given rule

Grade 7 GPS Framework Unit 5 Staying in Shape, “Changing Shapes,” pp. 19 - 20 of 33

Grid paper Transparency or copies of tasks for each student group



Weekly Focus: Investigate dilations with “Playing with Dilations” from Grade 7 GPS Framework Unit 5 Staying in Shape, pp. 7 – 8 of 33. (Computer use)

Maintenance: Solve problems involving constant area and changing perimeter. Refer to supplemental HM Course 1 materials.

Maintenance: Create designs with line and rotational symmetry (for school, favorite team, family, self or simply an artistic expression), based on “Create Your Own Logo,” from the Grade 6 GPS Framework Unit 6 Symmetry, pp. 8 – 9 of 12.

Exploration: Investigate less common measurement strategies with “Body Length and Fathom” and “Other Measures for Length” from Grade 7 MIC Made to Measure, pp. 8 – 9.

Intervention:

Homework

Weekly Focus: Compare lengths and angles in similar and non-similar figures

Maintenance: Use data from graphs or charts to answer questions and make inferences

Skill: Solve one-step equations


Reflection with ClosureWhat are some strategies that would help me determine the scale factor most efficiently?Based on your knowledge thus far, what does it mean for two figures to be similar?

Journal How does knowledge of factors and multiples help to determine which scale factors are most appropriate when creating a scale drawing?Why are most scale drawings smaller than the actual real-life references? When might it be effective to create a scale drawing larger than the real-life reference?

Evidence of Learning (Assessments)Weekly Focus: Selected Grade 7 MIC Ratios and Rates Section D items Skill Mastery: Solve one-step equations (1) -5 + v = 3 (2) 13.2 + k = 4.7 (3) t – 5.9 = 4.8 (4) y – 16 = -5 (5) s + 11.8 = 13.1Performance Task:Culminating Task:



M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M7G3a Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding

parts.




Two shapes are similar if the lengths of all the corresponding sides are proportional and all the corresponding angles are congruent.If the scale factor of a dilation is greater than 1, the image resulting form the dilation is an enlargement. If the scale factor is less than 1, the image is a reduction.Two similar figures are related by a scale factor, which is the ratio of the lengths of the corresponding sides.The sides and perimeters of similar figures are related by the square of the scale factor.Scale factors, length ratios, and area ratios may be used to determine missing side lengths and areas in similar geometric figures.Congruent figures have the same size and shape.


How can I tell if two figures are similar?In what ways can I represent the relationships that exist between similar figures using the scale factor, length ratios, and area ratios?What strategies can I use to determine missing lengths and areas of similar figures?Under what conditions are similar figures congruent?

Vocabulary

Dilation Perimeter AreaScale factor Ratio ProportionCorresponding sides Similar figures Corresponding anglesCongruent figures

Literacy GPS





Warm-Up/Quick PracticeMental Math: ‘Balance’ to subtract (for example, for 87 – 48 =, add two to each number to make the problem 89 – 50 =; also known as ‘same difference’)Convert customary and metric measurement units for length, weight, and capacityDivde fractions and mixed numbersAdd, subtract, multiply, and divide decimals

Problem SolvingSolve routine and non-routine problems using the Work Backwards strategy HM Course 2, “Problem Solving Strategies,” p. 755

Focus LessonsRef#

State Standards


3.5.21 M7G3a, b, c Identify tessellating triangles within larger trianglesDiscover how side lengths of the interior tessellating triangles relate to the larger triangle

Grade 8 MIC It’s All the Same, “Tessellations” Triangles Forming Triangles and Tessellations, pp. 1 - 3

Student Activity Sheet 1, p. 75Scissors

3.5.22 M7G3a, b, c Identify sets of parallel lines within a triangle Draw families of parallel lines that form a triangle tessellation

Grade 8 MIC It’s All the Same, “Tessellations” It’s All in the Family, pp. 4 - 5

Student Activity Sheet 2, p. 76RulersOptional: Drawing triangles

3.5.23 M6G1cM6A1M7G3b

Discover the relationship between area and perimeter of original figures and their reductions or enlargements

Grade 7 GPS Framework Unit 5 Staying in Shape, “Growing Logos,” pp. 21 – 22 of 33

Copies of task, p. 21 of 33

3.5.24 M6G1cM6A1M7G3a, b

Investigate similarity Grade 8 MIC It’s All the Same, “Similarity” Similar Shapes, p. 22 and Angles and Parallel Lines, p. 29

Blank paperScissors


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Weekly Focus: Use map scales to determine actual distances between locations with “Reaching All Learners” from HM Course 1, p. 375.

Maintenance: Create scale drawings with Culminating Task “Designer’s Challenge” from Grade 6 GPS Framework Unit 7 Scale Factor, pp. 13 – 16 of 16.

Maintenance: Subtract or multiply fractions with “Reaching All Learners” from HM Course 1, pp. 245 and 255.

Exploration: Investigate use of geometric shapes in famous architectural sites with “Reaching All Learners” from HM Course 1, p. 567.

Intervention:

Homework

Weekly Focus: Solve problems involving similar figures

Maintenance: Solve problems involving conversion of measurement units

Skill: Add, subtract, multiply, and divide decimals


Reflection with ClosureIf two figures are similar, describe the relationships between their (a) general shapes, (b) angle measures, and (c) side lengths.

JournalDescribe two ways to determine congruency of two figures.Why is it important to compare corresponding parts when determining the similarity of two figures?

Evidence of Learning (Assessments)Weekly Focus: Selected Grade 8 MIC It’s All the Same Section B items Skill Mastery: Add, subtract, multiply, and divide decimals (1) 61.9 + 213.56 + 97.3 (2) 576.18 - 239.8 (3) 238.7 X 4.8 (4) 4.236 ÷ 0.6 (5) 8.084 ÷ 1.2Performance Task:Culminating Task: GPS Framework Unit 7 Scale Factor, Culminating Task “Designer’s Challenge,” pp. 13 – 16 of 16



M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M7G3a Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding

parts.

M7G3bUnderstand 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.



If the scale factor of a dilation is greater than 1, the image resulting form the dilation is an enlargement. If the scale factor is less than 1, the image is a reduction.Two similar figures are related by a scale factor, which is the ratio of the lengths of the corresponding sides.Scale factors, length ratios, and area ratios may be used to determine missing side lengths and areas in similar geometric figures.Congruent figures have the same size and shape. If the scale factor of a dilation is equal to one, the image resulting from the dilation is congruent to the original figure.


What strategies can I use to determine missing lengths and areas of similar figures?In what ways can I represent the relationships that exist between similar figures using the scale factor, length ratios, and area ratios?

Vocabulary

Scale factorEnlargementReductionRatio tableProportion

Literacy GPS





Warm-Up/Quick PracticeMental Math: ‘Balance’ to subtract Determine the GCF and LCM for a given pair of numbersDecompose numbers into their prime factorizationExpress decimals as percents

Problem SolvingUse tables and graphs to examine variation that occurs within a group and variation that occurs between groups.Analyze data in various ways to determine how they are centered (mean, median, and mode) and how they are spread.HM Course 1 and HM Course 2

Focus LessonsRef#

State Standards


3.6.26 M6G1cM6A1M7G3a, b

Create similar trianglesIdentify similar plane figures

Grade 8 MIC It’s All the Same, “Similarity” Point to Point, pp. 23 – 26

Student Activity Sheet 3, p. 77Ruler for each studentCompass for each student

3.6.27 M6G1cM6A1M7G3a, b

Visually compare geometric figures for similarityDescribe similarities by listing corresponding partsDescribe the relationship between the areas of similar figures

Grade 7 GPS Framework Unit 5 Staying in Shape, “Similar Triangles,” pp. 23 – 25 of 33


3.6.28 M6G1cM6A1M7G3a, b

Demonstrate an understanding of the relationships between scale factors and length ratios of similar figures

Grade 7 GPS Framework Unit 5 Staying in Shape, “Similar Pentagons,” pp. 27 – 29 of 33


3.6.29 M6G1cM6A1M7G3a, b, c

Identify similar triangles Review similarity

Grade 8 MIC It’s All the Same, “Similarity” problems 12 – 15 and Check Your Work, pp. 30 – 34

Student Activity Sheet 4, p. 78Optional: Additional copies of p. 30



Weekly Focus: Create similar figures with “Reaching All Learners” from HM Course 2, pp. 301 and 305.

Maintenance: Create scale drawings with Culminating Task “Designer’s Challenge” from Grade 6 GPS Framework Unit 7 Scale Factor, pp. 13 – 16 of 16.

Maintenance: Subtract or multiply fractions with “Reaching All Learners” from HM Course 1, pp. 245 and 255.

Exploration: Investigate use of geometric shapes in famous architectural sites with “Reaching All Learners” from HM Course 1, p. 567.

Intervention:

Homework

Weekly Focus: Solve real-world similarity problems

Maintenance: Operations with decimals

Skill: Express decimals as percents


Reflection with ClosureExplain how you can use scale factor to determine how the area of an enlarged figure compares to the area of the original figure.

JournalIf two figures are similar with a scale factor of 5, describe how the perimeters of the two figures compare. Describe how their areas compare. Draw pictures with measurements labeled and justify your answers.

Evidence of Learning (Assessments)Weekly Focus: Selected Grade 8 MIC It’s All the Same Section C items Skill Mastery: Express decimals as percents (1) 1.45 (2) 0.00018 (3) 7.5 (4) 0.004 (5) 0.34Performance Task:Culminating Task: Grade 7 GPS Framework Unit 5 Staying in Shape , Culminating Task “Club Logo,” pp. 32 – 33 of 33

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Weeks: 7- 9

Instructional Unit PlanGrade 6 Unit 8 Georgia Performance Standards

M6G2a Compare and contrast right prisms and pyramids.M6G2b Compare and contrast cylinders and cones.M6G2c Interpret and sketch front, back, top, bottom, and side views of solid figures.M6G2d Construct nets for prisms, cylinders, pyramids, and cones.M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6M2c Compare and contrast units of measure for perimeter, area, and volume.M6M3a Determine the formula for finding the volume of fundamental solid figures.M6M3b Compute the volumes of fundamental solid figures, using appropriate units of measure.M6M3c Estimate the volumes of simple geometric solids.M6M3d Solve application problems involving the volume of fundamental solid figures.M6M4a Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.M6M4b Compute the surface area of right rectangular prisms and cylinders using formulae.M6M4c Estimate the surface area of simple geometric solids.M6M4d Solve application problems involving surface area of right rectangular prisms and cylinders.

-Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Weeks: 7- 9

Instructional Unit PlanGrade 6 Unit 8, continued


Various views of solid figures may be interpreted and sketched to provide a 2-dimensional representation of a 3-dimensional figure.Nets for prisms, cylinders, pyramids, and cones may be constructed.Approximate volumes of simple geometric solids may be found using estimation.Formulas may be used to determine the volume of fundamental solid figures.Approximate units of measure should be used when computing the volumes of fundamental solid figures.Approximate surface areas of simple geometric solids may be found using estimation.Manipulatives and the construction of nets may be used in computing the surface area of right rectangular prisms and cylinders.Formulas may be used to compute the surface area of right rectangular prisms and cylinders.Volumes of right prisms and cylinders may be compared and contrasted.


How can I interpret and sketch various views of solid figures?How can I construct nets for prisms, cylinders, pyramids, and cones?How can I use formulae to determine the volumes of fundamental solid shapes?How can I determine the appropriate units of measure that should be used when computing the volumes of fundamental solid figures?What kinds of problems can be solved using volumes of fundamental solid figures?How can I estimate the surface areas of simple geometric solids?How can I use manipulatives and nets to help compute the surface areas of right rectangular prisms and cylinders?How can I use surface areas of plane figures to derive the formulas for the surface areas of solid figures?What kinds of problems can be solved using surface areas of right rectangular prisms and cylinders?How do the volumes of right rectangular prisms and pyramids compare?How do the volumes of cylinders and cones compare?

Vocabulary

Base of a cone, pyramid, cylinder, and prismCylinder Edge FaceLateral faces Net PolyhedronPrism Surface area VolumeCone Cube Pyramid

Literacy GPS





Grade 6 Unit 8 Assessment

GPS Framework Unit 8 Solids, Culminating Task “Three Little Pig Builders,” pp. 22 – 29 of 29

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Week: 7Georgia Performance Standards

M6G1c Use the concepts of ratio, proportion, and scale factors to demonstrate the relationships between similar plane figures.M6A1 Students will understand the concept of ratio and use it to represent varying quantities.M6G2a Compare and contrast right prisms and pyramids.M6G2b Compare and contrast cylinders and cones.M6G2c Interpret and sketch front, back, top, bottom, and side views of solid figures.M6G2d Construct nets for prisms, cylinders, pyramids, and cones.

M7G3aUnderstand similarity; visually compare geometric figures for similarity; describe similarities by listing corresponding parts.

M7G3bUnderstand 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.



Two similar figures are related by a scale factor, which is the ratio of the lengths of the corresponding sides.Scale factors, length ratios, and area ratios may be used to determine missing side lengths and areas in similar geometric figures.


Various views of solid figures may be interpreted and sketched to provide a 2-dimensional representation of a 3-dimensional figure.Nets for prisms, cylinders, pyramids, and cones may be constructed.


In what ways can I represent the relationships that exist between similar figures using the scale factor, length ratios, and area ratios?What strategies can I use to determine missing lengths and areas of similar figures?


How can I interpret and sketch various views of solid figures?How can I construct nets for prisms, cylinders, pyramids, and cones?

VocabularyDilation Proportion RatioScale factor Similar figures

Base of a prism Cube CylinderEdge Face Lateral facesPolyhedron Prism




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Warm-Up/Quick PracticeMental Math: ‘Balance’ to subtract decimals (for example, with 6.43 – 3.72 = , add 0.28 to each number so the subtrahend is a whole number for an easier problem of 6.71 – 4.0 = )Calculate tips, tax, and discountsSolve one-step equations, including exponentsEvaluate numerical expressions

Problem SolvingSolve routine and non-routine problems using the Logical Reasoning strategyHM Course 2, “Problem Solving Strategies,” p. 759

Focus LessonsRef#

State Standards


3.7.31 M6G1cM6A1M7G3a, b

Apply similarity to solve indirect measurement problems

Grade 8 MIC It’s All the Same, “Similarity” Shadows, Takeoff, and You Don’t Have to Get Your Feet Wet pp. 27 – 28 and 31

Meter stickMaterials for group work and presentation

3.7.32 M6G1cM6A1M7G3a, b, c

Apply similarity to solve indirect measurement problems

Grade 7 GPS Framework Unit 5 Staying in Shape, “Shadow Math,” pp. 29 – 31 of 33Introduce the Culminating Task “Club Logo,” from Grade 7 GPS Framework Unit 5 Staying in Shape, pp. 32 – 33 of 33


3.7.33 M6G2a, c Interpret and sketch views of three-dimensional figures from different perspectives

Holt Mathematics Course 1, Hands-On Lab “Draw Views of Three-Dimensional Figures,” pp. 564 - 565

Centimeter cubesBlank paperOptional: Lab 10-6 Recording Sheet

3.7.34 M6G2a, b, d Introduce nets to create a rectangular prism, a square pyramid, a cylinder and a cone

Holt Mathematics Course 1, Hands-On Lab “Model Three-Dimensional Figures,” pp. 580 – 581Note: Save nets for lesson 3.9.41

Art paperScissorsTape



Weekly Focus: Construct figures from centimeter cubes for partners to draw from three different views.

Maintenance: Identify solid figures with “Poly-Cross Puzzle” including the Extend activity from HM Course 1, p. 588.

Maintenance: Create plane figures or simple designs on blank paper or grid paper. Trade designs with a partner. Partners then must create a figure/design similar to the original.

Exploration: Develop algebraic reasoning with “Arrow Language” Wandering Island and Airline Reservation from MIC Expressions and Formulas, pp. 3 - 5.

Intervention:

Homework

Weekly Focus: Complete work on “Club Logo” Culminating Task

Maintenance: Integer operations

Skill: Evaluate numerical expressions


Reflection with ClosureWhich professions would require an ability to understand different perspectives of 3-D figures?

JournalWhy is it challenging to sketch a two-dimensional drawing of a three-dimensional figure?Is it possible that a figure could have the same view from any perspective?How many different ways could you create a net for a given rectangular prism?

Evidence of Learning (Assessments)Weekly Focus: Selected Grade 8 MIC It’s All the Same Section C and Grade 6 MIC Reallotment Section E items Skill Mastery: Evaluate numerical expressions (1) (3 + 2)³ + 6 = (2) (3 + 7)² + 3 x 2² = (3) 25 ÷ 5 + 3³ x 2 = (4) 48 + ( 2 x 3)² - 4 x 2 =Performance Task:Culminating Task:



M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6M2c Compare and contrast units of measure for perimeter, area, and volume.M6M3a Determine the formula for finding the volume of fundamental solid figures.M6M3b Compute the volumes of fundamental solid figures, using appropriate units of measure.M6M3c Estimate the volumes of simple geometric solids.M6M3d Solve application problems involving the volume of fundamental solid figures.M6M4a Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.M6M4b Compute the surface area of right rectangular prisms and cylinders using formulae.M6M4c Estimate the surface area of simple geometric solids.M6M4d Solve application problems involving surface area of right rectangular prisms and cylinders.

Grade 6 Unit 8 Framework Enduring UnderstandingsApproximate volumes of simple geometric solids may be found using estimation.Formulas may be used to determine the volume of fundamental solid figures.Approximate units of measure should be used when computing the volumes of fundamental solid figures.Approximate surface areas of simple geometric solids may be found using estimation.Manipulatives and the construction of nets may be used in computing the surface area of right rectangular prisms and cylinders.Formulas may be used to compute the surface area of right rectangular prisms and cylinders.Volumes of right prisms and cylinders may be compared and contrasted.

Grade 6 Unit 8 Framework Essential QuestionsHow can I estimate the volumes of simple geometric solids?How can I use formulae to determine the volumes of fundamental solid shapes?How can I determine the appropriate units of measure that should be used when computing the volumes of fundamental solid figures?What kinds of problems can be solved using volumes of fundamental solid figures?How can I estimate the surface areas of simple geometric solids?How can I use manipulatives and nets to help compute the surface areas of right rectangular prisms and cylinders?How can I use surface areas of plane figures to derive the formulas for the surface areas of solid figures?What kinds of problems can be solved using surface areas of right rectangular prisms and cylinders?

VocabularyBase of a cylinder, prismCylinder EdgeFace Lateral facesNet PolyhedronPrism Surface areaVolume

Literacy GPSELA6W2a Produce technical writing that follows an organizing structure



Warm-Up/Quick PracticeMental Math: ‘Balance’ to subtract decimals Convert customary measurement units for length, weight, and capacityRecognize and extend patterns represented in a tableCompute with rational numbers

Problem SolvingSolve real-world problems involving percentsHM Course 1 and HM Course 2

Focus LessonsRef#

State Standards


3.8.36 M6M4a, b, c, dM6G2d

Introduce the concept of surface area Create nets to represent rectangular prisms

Grade 6 MIC Reallotment, “Surface Area and Volume” Packages, including the extension activity, pp. 49 - 50

Centimeter cubesCentimeter grid paperScissors

3.8.37 M6M2b, cM6M3a, b, c, d M6M4a, b, c, d

Understand the difference between volume and surface areaCompare and contrast the measurement units used for surface area and volume

Grade 6 MIC Reallotment, “Surface Area and Volume” Measuring Inside, pp. 51 - 53

One small tissue box or a similar boxes for each group

Centimeter cubes

3.8.38 M6M3a, b, c, d Solve problems involving the volume of prisms and cylinders

Grade 6 GPS Framework Unit 8 Solids, “Rain,” pp. 13 – 14 of 29

Copies of problems from the taskCalculators

3.8.39 M6M4a, b, c, d Investigate strategies to find the surface area of a cylinder

Grade 6 GPS Framework Unit 8 Solids, “Cylinder Task” parts a through e, pp. 8 – 12 of 29

Copies of problems from the taskCalculators


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Weekly Focus: Solve problems involving volume of rectangular prisms with “Boxing Bracelets,” from Grade 6 GPS Framework Unit 8 Solids, pp. 15 – 19 of 29.

Maintenance: Identify solid figures with “Poly-Cross Puzzle” including the Extend activity from HM Course 1, p. 588.

Maintenance: Create plane figures or simple designs on blank paper or grid paper. Trade designs with a partner. Partners then must create a figure/design similar to the original.

Exploration: Develop algebraic reasoning with “Arrow Language” Wandering Island and Airline Reservation from MIC Expressions and Formulas, pp. 3 - 5.

Intervention:

Homework

Weekly Focus: Determine the surface area and volume of cylinders

Maintenance: Model and define line and rotational symmetry

Skill: Compute with rational numbers


Reflection with ClosureWhy do I need to know about volume?As people wrap gifts for family members and friends, they often miscalculate the amount of wrapping paper they will need. Why is that such a common error?

JournalWhat is the difference between volume and capacity?Why is it often difficult to compare volumes of prisms with different dimensions?In the real world, who would need to calculate the exact volume or surface area of these geometric solids?

Evidence of Learning (Assessments)Weekly Focus: Selected MIC Reallotment Section E items Skill Mastery: Compute with rational numbers 1) 4.8 x 2.38 = (2) 0.04872 ÷ 0.24 = (3) 3 7/8 + 13 4/5

(4) 10 1/4 - 7 5/6 = (5) 1,201 – 986.29 = (6) 4.62 + 21.45 + 13 = Performance Task:Culminating Task:

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 3 Week: 9Georgia Performance Standards

M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6M3a Determine the formula for finding the volume of fundamental solid figures.M6M3b Compute the volumes of fundamental solid figures, using appropriate units of measure.M6M3c Estimate the volumes of simple geometric solids.M6M3d Solve application problems involving the volume of fundamental solid figures.M6M4a Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.M6M4b Compute the surface area of right rectangular prisms and cylinders using formulae.M6M4c Estimate the surface area of simple geometric solids.M6M4d Solve application problems involving surface area of right rectangular prisms and cylinders.

Grade 6 Unit 8 Framework Enduring UnderstandingsFormulas may be used to determine the volume of fundamental solid figures.Approximate units of measure should be used when computing the volumes of fundamental solid figures.Approximate surface areas of simple geometric solids may be found using estimation.Manipulatives and the construction of nets may be used in computing the surface area of right rectangular prisms and cylinders.Formulas may be used to compute the surface area of right rectangular prisms and cylinders.Volumes of right prisms and cylinders may be compared and contrasted.Volumes of cylinders and cones may be compared and contrasted.

Grade 6 Unit 8 Framework Essential QuestionsHow can I use formulae to determine the volumes of fundamental solid shapes?How can I determine the appropriate units of measure that should be used when computing the volumes of fundamental solid figures?What kinds of problems can be solved using volumes of fundamental solid figures?How can I estimate the surface areas of simple geometric solids?How can I use manipulatives and nets to help compute the surface areas of right rectangular prisms and cylinders?How can I use surface areas of plane figures to derive the formulas for the surface areas of solid figures?What kinds of problems can be solved using surface areas of right rectangular prisms and cylinders?How do the volumes of right rectangular prisms and pyramids compare?How do the volumes of cylinders and cones compare?

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VocabularyBase of a cone, pyramid, cylinder, prismCone Cube CylinderEdge Face Lateral facesNet Polyhedron PrismPyramid Surface area Volume





Warm-Up/Quick PracticeMental Math: Multiply multiples of ten (for example, 70 x 30, 4 x 600)Convert metric measurement units for length, weight, and capacityDetermine the mean, median, and mode for a data setDetermine the sales price.

Problem Solving Solve routine and non-routine problems using the Guess and Check strategy HM Course 2, “Problem Solving Strategies,” p. 754

Focus Lessons

Ref#

State Standards


3.9.41 M6M2b, cM6M3a, b, c, d

Find the volume of irregular solids constructed with cubesExplore the volume of a square pyramid, cones, and cylinders

Grade 6 MIC Reallotment, “Surface Area and Volume” Reshaping, pp. 54 - 56

Centimeter cubes for each groupThe nets from lesson 3.7.34

3.9.42 M6M2b, cM6M3a, b, c, d

Find the volume of irregular solids constructed with cubesExplore the volume of a square pyramid, cones, and cylinders

Grade 6 MIC Reallotment, “Surface Area and Volume” Reshaping, pp. 56 - 58

Optional: Calculators

3.9.43 M6M4b, c, d Find the surface areas of prisms, (pyramids) and cylinders

Holt Mathematics Course 1, “Surface Area,” pp. 582 – 585

Optional: Nets of shapes made during the unit

3.9.44 M6M2bM6M3b, c, dM6M4b, c, d

Solve problems involving volume and surface area

Grade 6 GPS Framework Unit 8 Solids, Culminating Task “Three Little Pig Builders,” pp. 22 – 29 of 29

Copies of problems for each student or group


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Weekly Focus: Construct and compare rectangular prisms and triangular prisms with “Reaching All Learners” from HM Course 1, p. 573.

Maintenance: Determine surface area of rectangular prisms with “Reaching All Learners” from HM Course 1, p. 583.

Maintenance: Interpret data from circle graphs. Refer to cross-curricular grade level resources or newspapers.

Exploration: Explore probability concepts with “Georgia Link” and “Earth Science Link” from HM Course 2, pp. 631 and 635.

Intervention:

Homework

Weekly Focus: Solve real-world problems involving volumes and surface area

Maintenance: Operations with fractions

Skill: Determine the sales price.


Reflection with ClosureThese formulas are hard to remember. How can I just estimate the volume and surface area of these solids?

JournalHow would skills at calculating volume and surface area help design the most economical packaging for new products?How would skills at calculating volume and surface area help design the most misleading packaging for new products?A change in which dimension would result in the most significant difference in a cylinder’s volume or surface area?

Evidence of Learning (Assessments)Weekly Focus: Selected HM Course 1 Chapter 10 and MIC Reallotment Section E itemsSkill Mastery: Determine the sales price. Find the sales price to the nearest cent. (1) $3.49 binder at 35% off (2) $84 tennis shoes at 20% off (3) $24.95 backpack at 25% off (4) $13.99 CD at 10% offPerformance Task:Culminating Task: Grade 6 GPS Framework Unit 8 Solids, Culminating Task “Three Little Pig Builders,” pp. 22 – 29 of 29

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