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Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 2 Weeks: 1- 5

Instructional Unit Plan

Grade 7 Unit 3 Georgia Performance Standards

M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.

Grade 7 Unit 3 Framework Enduring Understandings

Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Properties of real numbers hold for all rational numbers.Positive and negative numbers are often used to solve problems in everyday life.

Grade 7 Unit 3 Framework Essential Questions

When are negative numbers used and why are they important?Why is it useful for me to know the absolute value of a number?What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?What properties and conversions do I need to understand in order to simplify and evaluate algebraic expressions?

Grade 7 Unit 3 Assessment

GPS Framework, Grade 7, Unit 3, Rational Reasoning, Culminating Task “A Poster,” pp. 32 – 35 0f 35

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

VocabularyAbsolute value Associative propertyCommutative property Distributive propertyIntegers Natural numbersNegative numbers Opposite numbersPositive numbers Rational numbersSign Whole numbers

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 2 Week: 1

Georgia Performance Standards

M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?

Why is it useful for me to know the absolute value of a number?

Vocabulary

Absolute valueIntegersNatural numbersNegative numbersOpposite numbersPositive numbersSignWhole numbers

Literacy GPS



ELA6LSV1b Asks relevant questions

ELA6LSV1c Responds to questions with appropriate information


Warm-Up/Quick PracticeMental Math: Subtract whole numbers, working left to right with regrouping (for example, with 142 – 94 = , start with 142 – 90 = 52, and then 52 – 4 = 48)Determine the GCF and LCM for a given pair of numbersDetermine the mean, median and mode for a data setSkill Mastery: Compare and order rational numbers

Problem Solving Solve real-world problems involving percentsHolt Mathematics, Course 1 and Holt Mathematics, Course 2

Focus LessonsRef # State

StandardsObjectives Resources Materials

2.1.1 M7N1a, b, d Solve problems involving time zones

Grade 7 MIC Operations, “Positive and Negative” What Time Is It There? and World Time Zones, pp. 1 – 4

Student Activity Sheet 1, p. 75ScissorsTape

2.1.2 M7N1a, b, d Use positive and negative numbers to solve problems involving time change between different time zones

Grade 7 MIC Operations, “Positive and Negative,” World Time Zones, pp. 5 – 6 and “Additional Practice Section A,” p. 52

Student work from previous lesson

2.1.3 M7N1a, b, c, d Use positive and negative numbers to describe elevation relative to the sea levelModel combination of integers on a vertical number line in a real-world context using concept of absolute value

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Helicopters and Submarines,” pp. 10 - 12 of 35

Transparency of pp. 13 – 14Copies of pp. 13 - 14

2.1.4 M7N1b, c, d Compare and order positive and negative numbers on a number lineUse a vertical number line for elevation to add and subtract integers

Grade 7 MIC Operations, “Walking along the Number Line” Ordering the Numbers, pp. 12 – 15

Optional: Large number strip like the one on page 12

2.1.5 See Variety of Instructional Tasks

Variety of Instructional Tasks

Weekly Focus: Solve problems involving integers and absolute value using Holt Mathematics Course 2, pp. 76 – 78. (Note: It is expected that at times teachers may have alternate instructional tasks they would prefer to use in place of those listed in the plans. Teachers need to be sure the activities meet the objective listed and are presented in ways to foster student communication and team work.)

Maintenance: Apply knowledge of factors and least common multiples with the “Reaching All Learners" Activity from HM Course 1, p. 229.

Maintenance: Identify characteristics of quadrilaterals with the “Reaching All Learners” activity and “Sports Link” from HM Course 1, pp. 443 and 445.

Exploration: Develop spatial sense with “Parallel Line Relationships” from HM Course 1, pp. 432 – 433.

Intervention:

Homework

Weekly Focus: Identify integers on a number line; compare and order integers

Maintenance: Solve word problems involving percent

Skill: Compare and order rational numbers

Refer to Holt Mathematics Course 1 and Course 2

Reflection with Closure

Does it matter whether a number line is drawn vertically or horizontally when solving a problem? Explain your answer.Create a real-life situation where absolute value can be applied.

Journal

Describe how to compare the following types of numbers when it comes to which is larger: two positive numbers (2) two negative numbers(a) a positive and a negative number.

Evidence of Learning (Assessments)

Weekly Focus: Selected Grade 7 MIC Operations Section A itemsSkill Mastery: Compare and order rational numbers. List in order from least to greatest.

(1) 4.2 4 1/3 4.022 4 2/5 4.3 (2) 5 3 ½ 6.6 4 3/5 ¾ (3) 2.5 ¾ 1 1/6 9/8 2Performance Task:Culminating Task:



M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Positive and negative numbers are often used to solve problems in everyday life.


What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?

Vocabulary

IntegersNegative numbersOpposite numbersPositive numbersSign

Literacy GPS






Warm-Up/Quick PracticeMental Math: Recognize compatible numbers (for example, 71 and 29 are compatible, equaling 100; 120 and 180 are compatible, equaling 300)Determine the mean, median, and mode for a data setAdd and subtract fractions and mixed numbersSkill Mastery: Multiply and divide decimals

Problem Solving Estimate and solve single- and multi-step problemsUse variables to represent the unknown quantityApply the Logical Reasoning strategy to solve process problems



2.2.6 M7N1c, d Model the relationship between adding and subtracting integers

Grade 7 MIC Operations, “Walking Along the Number Line” Ronnie the Robot, pp. 16 – 19

Colored tape or rope or long stringCards with positive and negativenumbers

2.2.7 M7N1c, d Practice adding and subtracting integers with a number line and arithmetic trees

Grade 7 MIC Operations, “Calculating with Positive and Negative Numbers” Adding and Subtracting, pp. 22 – 26 (through problem 7)

Student Activity Sheet 2, p. 76

2.2.8 M7N1c, d Continue to practice adding and subtracting with integers using the Integer Game and using arithmetic trees

Grade 7 MIC Operations, “Calculating with Positive and Negative Numbers” Adding and Subtracting and “Additional Practice Section C” Problem 3, pp. 26 - 27 and 55

Student work from the previous lesson

2.2.9 M7N1a, c, d Add and subtract integers using two-color counters

Holt Mathematics Course 2, “Adding Integers” and “Subtracting Integers,” pp. 82 – 84 and 88 - 90

Two-color counters



Weekly Focus: Model subtraction of integers with “Hands On Lab” from HM Course 2, pp. 86 – 87.

Maintenance: Order numbers on a number line with “Using the Number Line” from GPS Framework, Grade 7, Unit 3, Rational Reasoning, pp. 12 - 14 of 35. Choose additional sets of rational numbers for students to order on a number line.

Maintenance: Identify angles and review related vocabulary with “Angle Relationships” from HM course 1, pp. 426 – 427.

Exploration: Investigate and explain the big ideas of equality with “Math Background” from HM Course 1, p.76. Provide Euclid’s five axioms to students. They work in pairs or groups to model the axioms algebraically and with real world examples. Mathematics Framework “Task Using the Number Line” pp. 12-14

Intervention:

Homework

Weekly Focus: Add and subtract integers

Maintenance: Compare and order positive and negative integers

Skill: Multiply and divide decimals



When adding two integers, how can one determine if the sum will be positive, negative, or zero?How are zero pairs used in the modeling of addition and subtraction of integers?

Journal

Draw pictures to model the addition problem -3 + 5 = ___ using three different strategies. Which strategy do you prefer and why?


Weekly Focus: Selected Grade 7 MIC Operations Sections B and C items Skill Mastery: Multiply and divide decimals (1) 200 x 0.004 = (2) 4.3 x 2.8 = (3) 380 x 0.125 (4) 0.01 ÷ 100 = (5) 85 ÷ 0.5 = (6) 4.416 ÷ 19.2 =Performance Task:Culminating Task:



M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?

Vocabulary

IntegersNegative numbersOpposite numbersPositive numbersSign

Literacy GPS






Warm-Up/Quick PracticeMental Math: Recognize compatible numbersDecompose numbers into their prime factorizationMultiply and divide fractions and mixed numbersSkill Mastery: Add and subtract fractions and mixed numbers

Problem Solving Develop algebraic reasoning skillsInvestigate exchange strategies to solve equality problemsMIC Comparing Quantities, “Compare and Exchange,“ pp. 1 - 3



2.3.11 M7N1c, d Find the mean of a data set that contains negative and positive numbers

Grade 7 MIC Operations, “Calculating with Positive and Negative Numbers“ Temperatures and Altitudes, pp. 28 - 30

Optional: copies of the graph on Student Book page 29 and calculators

2.3.12 M7N1c, d Solve problems involving elevation and temperature changes

Grade 7 MIC Operations, “Calculating with Positive and Negative Numbers“ Higher and Higher, pp. 30 - 33

Optional: Transparencies of tables in lesson

2.3.13 M7N1c, d Multiply with positive and negative numbers

Grade 7 MIC Operations, “Adding and Multiplying” Calculations Using Differences and Multiplication with Positive and Negative Numbers, pp. 36 - 39 (through question 7)Mathematics Framework Tasks: “ Sums and products”, p 14-19

Optional: Calculators Copies of task

2.3.14 M7N1c, d Explore a pattern to support the rules for multiplying integers and complete arithmetic trees for integers

Grade 7 MIC Operations, “Adding and Multiplying” Multiplication with Positive and Negative Numbers, pp. 39 - 41Mathematics Framework Tasks: “ Always, Sometimes, and Never” p. 20-22

Student Activity Sheet 3, p. 77Copies of task



Weekly Focus: Model integer multiplication and division using Holt Mathematics Course 2, “Model Integer Multiplication and Division, Hands-On Lab,” pp. 92 – 93.

Maintenance: Order numbers on a number line with “Using the Number Line” from GPS Framework, Grade 7, Unit 3, Rational Reasoning, pp. 12 - 14 of 35. Choose additional sets of rational numbers for students to order on a number line.

Maintenance: Identify angles and review related vocabulary with “Angle Relationships” from HM course 1, pp. 426 – 427.

Exploration: Investigate and explain the big ideas of equality with “Math Background” from HM Course 1, p.76. Provide Euclid’s five axioms to students. They work in pairs or groups to model the axioms algebraically and with real world examples.

Intervention:

Homework

Weekly Focus: Multiply integers

Maintenance: Add and subtract integers

Skill: Add and subtract fractions and mixed numbers


Reflection with ClosureDesign a table to show rules for multiplying integers. Be sure to include all possible combinations of positive integers, negative integers, and zero.Is it possible to have a data set with a negative mean? If possible, give an example of the data set and determine its mean.

JournalWrite a strategy for multiplying two integers. Be sure to include all possible combinations—positive integers, negative integers, and zero. Verify your strategy with examples.

Evidence of Learning (Assessments)Weekly Focus: Selected Grade 7 MIC Operations Sections C and D itemsSkill Mastery: Add and subtract fractions and mixed numbers.

(1) 3 ¼ + 7 5/8 = (2) 34 4/5 + 72 1/3 = (3) 56 ½ - 38 ¾ = (4) 67 2/3 - 56 ¾ = (5) 101 2/5 + 128 ¾ + 175 2/3 =

Performance Task:Culminating Task:



M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.M7A1a Translate verbal phrases to algebraic expressions.


Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Properties of real numbers hold for all rational numbers.Positive and negative numbers are often used to solve problems in everyday life.



Vocabulary

Absolute value Associative propertyCommutative property Distributive propertyIntegers Natural numbersNegative numbers Opposite numbersPositive numbers Rational numbersSign Whole numbers

Literacy GPS





Atlanta Public Schools Teaching Plans Sixth Grade Quarter: 2 Week: 4

Warm-Up/Quick PracticeMental Math: Add using compatible numbers [for example, for 80 + 31 =, think (80 + 20) + 11 and for 262 + 150, think (260 + 140) + 2 + 10]Determine the GCF and LCM for a given pair of numbersRecognize or calculate fraction, decimal and percent equivalentsSkill Mastery: Compare and order integers

Problem Solving Estimate and solve single- and multi-step problemsUse variables to represent the unknown quantityApply an appropriate strategy to solve process problems



2.4.16 M7N1c, d Multiply and divide integers Holt Mathematics Course 2, “Multiplying and Dividing Integers, “ pp. 94 - 96

Two-color counters

2.4.17 M7N1c, d Demonstrate an understanding of even and odd numbers using algebraic expressionsUse knowledge of consecutive integers to solve problems

Grade 7 GPS Framework, Unit 3, Rational Reasoning, “Working with Integers,” pp. 25 - 31 of 35.

Copies of tasks

2.4.18 M7N1a, b, c, d Compare and order rational numbersAdd, subtract, multiply, and divide integersCreate and solve problems involving rational numbersDemonstrate an understand of properties of real numbers

Grade 7 GPS Framework, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Class presentations of assignment on the following Monday

PostersAccess to supplies—markers, rulers, colored pencils, textbooks, etc.

2.4.19 M7N1a, b, c, d Create and solve problems involving rational numbers

Demonstrate an understand ofproperties of real numbers

Grade 7 GPS Framework, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Continue to work on culminating activity

PostersAccess to supplies—markers, rulers, colored pencils, textbooks, etc.



Weekly Focus: Model integer multiplication and division with “Hands On Lab” from HM Course 2, pp. 92 – 93.

Maintenance: Determine sales prices with “Reaching All Learners” from HM Course 1, p. 395.

Maintenance: Recognize fraction, decimal, and percent equivalence with “Triple Play" from HM Course 1, p. 402.

Exploration: Explore number patterns with Technology Lab “Find a Pattern in a Sequence” from HM Course 1, p. 37.

Intervention:

Homework

Weekly Focus: Solve problems involving rational numbers

Maintenance: Solve problems involving percent

Skill: Compare and order integers


Reflection with ClosureCreate a set of rules for comparing negative and positive numbers.When subtracting two negative numbers, do you always get a negative number? Why or why not? Give examples to justify your answer.

JournalHow is division of integers related to multiplication of integers? Draw a model to justify your answer.

Evidence of Learning (Assessments)Weekly Focus: Selected HM Course 1 Chapter 4 items Skill Mastery: Compare and order integers

(1) Arrange the integers in order from least to greatest. -1 0 5 -5 -2 1 -10 7Compare using < , >, or = . (2) -10 -5 (3) 2 -7 (4) -110 10 (5) 52 5 (6) -34 -14

Performance Task:Culminating Task:



M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1dM7A3a

Solve problems using rational numbers.Plot points on a coordinate plane.

M7A3bM7A3c


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Properties of real numbers hold for all rational numbers.Positive and negative numbers are often used to solve problems in everyday life.



Vocabulary

Absolute valueAssociative propertyCommutative propertyDistributive propertyIntegersRational numbers

Literacy GPS





Warm-Up/Quick PracticeMental Math: Add using compatible numbers Interpret data from a histogram or line graphAdd and subtract fractions and mixed numbersSkill Mastery: Add and subtract integers




2.5.21 M7N1a, b, c, d Compare and order rational numbersAdd, subtract, multiply, and divide integersDemonstrate an understanding of properties of real numbers

Grade 7 GPS Framework, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35 Class presentations

Culminating Activity Posters

2.5.22 M7N1a, b, c, d Compare and order rational numbersAdd, subtract, multiply, and divide integersCreate and solve problems involving rational numbers

Grade 7 GPS Framework, Unit 3, Rational Reasoning, “Culminating Activity “A Poster,” pp. 31 - 35 of 35Final touches to culminating activity; Students make appropriate changes to as suggested during presentations

Culminating Activity PostersAccess to supplies—markers, rulers, colored pencils, textbooks, etc.

2.5.23 M7A3a, b, c Plot and label points on a coordinate system

Predict what will happen to a figure when the coordinates are changed

Grade 7 MIC Operations, “Operations and Coordinates” Changing Shapes, pp. 46 - 48 (through problem 13)

Copies o f Student Activity Sheet 4,p. 78Rulers

2.5.24 M7A3a, b, c Explore the effect of a negative number on the shape of a figure in the coordinate planeInvestigate the effect of multiplication on the coordinates of given figures

Grade 7 MIC Operations, “Operations and Coordinates” Changing Shapes, pp. 48 - 49

Student work from the previous lessonRulers



Weekly Focus: Explain integer computation rules with “Reaching All Learners” and Journal” from HM Course 2, pp. 95 and 97.

Maintenance: Determine sales prices with “Reaching All Learners” from HM Course 1, p. 395.

Maintenance: Recognize fraction, decimal, and percent equivalence with “Triple Play" from HM Course 1, p. 402.

Exploration: Explore number patterns with Technology Lab “Find a Pattern in a Sequence” from HM Course 1, p. 37.

Intervention:

Homework

Weekly Focus: Add, subtract, multiply, and divide integers

Maintenance: Apply order of operations to simplify numeric expressions

Skill: Add and subtract integers



Illustrate how the Commutative Properties of Addition and Multiplication hold for all rational numbers.Illustrate how the Associative Properties of Addition and Multiplication hold for all rational numbers.

JournalWhy is there not a Commutative Property of Subtraction? Explain with examples.


Weekly Focus: Selected Grade 7 MIC Operations Section E itemsSkill Mastery: Add and subtract integers (1) -78 + -37 = (2) 765 + -129 = (3) -708 + 329 = (4) 681 – 932 = (5) -32 – ( -23) =Performance Task:Culminating Task: GPS Framework, Grade 7, Unit 3, Rational Reasoning, “A Poster,” pp. 32 – 35 of 35

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 2 Wks 6-7



M6A2a Analyze and describe patterns arising from mathematical rules, tables, and graphs. M6A3 Evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic

operations.

Unit 4 Framework Enduring Understandings

In mathematics, letters are used to represent numbers.There are conventions for using letters to represent numbers in mathematics.Algebraic expressions are used to represent relationships between numbers.Variables can be used to generalize patterns. Pictures and diagrams are helpful in recognizing relationships. Inverse operations are helpful in understanding and solving problems.

Unit 4 Framework Essential Questions

Why do we use letters to represent numbers in mathematics?Why do we need conventions in mathematics?How do I evaluate an algebraic expression?How can variables be used to describe patterns?How do I solve a one-step equation?

Unit Assessment

GPS Framework, Grade 6, Unit 4, One-Step Equations, Culminating Task “Building with Toothpicks,” pp. 11 - 14 of 14

Literacy GPS





Vocabulary

Algebraic expressionEquationVariable



M6A2a Analyze and describe patterns arising from mathematical rules, tables, and graphs. M6A3 Evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic

operations.


In mathematics, letters are used to represent numbers.There are conventions for using letters to represent numbers in mathematics.Algebraic expressions are used to represent relationships between numbers.Inverse operations are helpful in understanding and solving problems.


Why do we use letters to represent numbers in mathematics?Why do we need conventions in mathematics?How do I evaluate an algebraic expression?How can variables be used to describe patterns?How do I solve a one-step equation?

Vocabulary


Literacy GPS






Warm-Up/Quick PracticeMental Math: Recognize compatible decimals, including money amounts (for example, 0.72 and 0.28 or $4.15 + 1. 85)Solve one-step equations, including exponentsCalculate 1%, 10%, 25% and 50% of any whole number Skill Mastery: Add and subtract fractions and mixed numbers




2.6.26 M6A3 Understand combinations as a foundation for working with variables and equations

Grade 6 MIC Comparing Quantities, “Looking at Combinations” The School Store, pp. 6 – 9

Student Activity Sheet 1, p. 57Optional: Colored pencils (Same colors for each student)

2.6.27 M6A3 Write algebraic expressions to represent a real world situationExplore strategies to solve equations

Grade 6 MIC Comparing Quantities, “Equations” The School Store Revisited and Hats and Sunglasses, pp. 28 – 30


2.6.28 M6A3 Solve one-step addition and subtraction equations

Holt Mathematics Course 1, Addition Equations” and “Subtraction Equations,” pp. 74 – 76 and 78 - 89

Balance scaleCounters and markers for variablesTeacher-selected examples and practice problems

2.6.29 M6A3 Evaluate algebraic expressionsSolve one-step multiplication equations

GPS Framework Grade 6 Unit 4 One Step Equations, “Learning the Conventions for Multiplying and Dividing Letters and Numbers,” pp. 7 – 9 of 14

Counters and markers for variablesOptional: Transparency of Question 4 from the task



Weekly Focus: Use a variable to represent the unknown with “Using Letters to Represent Numbers” from GPS Framework Unit 4 One Step Equations, pp. 5 – 6 of 14.

Maintenance: Multiply and add integers using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Sums and Products,” pp. 14 - 19 of 35.

Maintenance: Solve fraction puzzles with “Fraction Riddles” from HM Course 1, p. 280.

Exploration: Investigate pi with "Discovering Pi” from GPS Framework, Unit 5 Circles and Graphs, pp. 6 -7 of 16.

Intervention:

Homework

Weekly Focus: Use algebraic expressions to represent a real situation with an unknown

Maintenance: Solve problems involving elapsed time in hours and minutes

Skill: Add and subtract fractions and mixed numbers Refer to Holt Mathematics Course 1


Why are letters used for the variables rather than another set of symbols?How many variables can be included in one algebraic expression?How are inverse operations useful when solving equations? How do these solution steps reflect the concept of balance?

Journal

Do we have to use letters in these equations? Why not just use the boxes and lines we used in elementary school? Why are n and x so common?


Weekly Focus: Selected Grade 6 MIC Comparing Quantities Section E itemsSkill Mastery: Add and subtract fractions and mixed numbers.

3 7/8 + 2 1/4 = 4 3/4 - 2 3/5 = 4 1/2 + 3 7/8 + 2 3/4 = 5 1/8 – 2 5/8 = 4 3/4 + 2 7/8 =Performance Task:Culminating Task:



M6A3 Evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.

M6A2a Analyze and describe patterns arising from mathematical rules, tables, and graphs.


In mathematics, letters are used to represent numbers.There are conventions for using letters to represent numbers in mathematics.Algebraic expressions are used to represent relationships between numbers.Variables can be used to generalize patterns. Pictures and diagrams are helpful in recognizing relationships. Inverse operations are helpful in understanding and solving problems.


Why do we use letters to represent numbers in mathematics?How can variables be used to describe patterns?How do I solve a one-step equation?

Vocabulary


Literacy GPS






Warm-Up/Quick PracticeMental Math: Recognize compatible decimals, including money amountsinterpret data from a line graph or histogramRecognize and extend patterns represented in a tableSkill Mastery: Write equations for statements

Problem Solving Develop algebraic reasoning skillsApply exchange strategies to solve equality problemsUse variables to represent unknown quantitiesMIC Comparing Quantities, “Finding Prices, “ pp. 16 – 18



2.7.31 M6A3 Solve one-step equations

Identify and evaluate expressions

GPS Framework Grade 6 Unit 4 One Step Equations, “The Ant,” pp. 10 – 11 of 14Holt Mathematics Course 1, “Variables and Expressions,” pp. 54 – 57

Copies of problem from the task

2.7.32 M6A2aM6A3

Identify patterns from tablesExpress patterns in words and with algebraic expressions

Holt Mathematics Course 1, “Translate Between Words and Math,” pp. 58 – 60

No additional materials

2.7.33 M6A2aM6A3

Identify patterns from tablesExpress patterns in words and with algebraic expressions

Holt Mathematics Course 1, “Translating Between Tables and Expresions,” pp. 62 - 65

No additional materials

2.7.34 M6A2aM6A3

Write a formula that involves a variableRecognize patterns to solve problems

GPS Framework Grade 6 Unit 4 One Step Equations, Culminating Task “Building with Toothpicks,” pp. 11 – 14 of 14

Copies of problem from the taskOptional: Toothpicks



Weekly Focus: Apply the rules of equality with “Balancing Act” from GPS Framework Unit 4 One Step Equations, p. 9 of 14.

Maintenance: Multiply and add integers using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Sums and Products,” pp. 14 - 19 of 35.

Maintenance: Solve fraction puzzles with “Fraction Riddles” from HM Course 1, p. 280.

Exploration: Investigate pi with "Discovering Pi” from GPS Framework, Unit 5 Circles and Graphs, pp. 6 -7 of 16.

Intervention:

Homework

Weekly Focus: Identify and extend number patterns

Maintenance: Solve word problems involving percent

Skill: Write equations for statements

Refer to Holt Mathematics Course 1

Reflection with ClosureCan all patterns be generalized with an algebraic expression?How many elements are needed before a pattern can be determined?How many operations can be included in generating a pattern?

JournalDo I prefer using a table or words to describe a pattern? Why are tables used so often when we talk about patterns?

Evidence of Learning (Assessments)Weekly Focus: Selected Skill Mastery: Write an equation for each statement.

(1) Two less than three times a number is thirty-seven (2) Forty-eight is four times a number (3) Some number times two is three times four plus two (4) A number increased by fourteen is equal to forty- five minus two (5) Four times a number divided by three is eighteen (6) A number decreased by five and multiplied times four is five less than sixty-

fivePerformance Task:Culminating Task: GPS Framework, Grade 6, Unit 4, One-Step Equations, “Building with Toothpicks,” pp. 11 - 14 of 14

Atlanta Public Schools Teaching Plans Accelerated Sixth Grade Quarter: 2 Wks 8-9



M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6D1b Using data, construct frequency distributions, frequency tables, and graphs.M6D1c Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots.M6D1d Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups.M6D1e Relate the data analysis to the context of the questions posedM6A1 Students will understand the concept of ratio and use it to represent quantitative relationshipsM6N1f Use fractions, decimals, and percent interchangeablyM6N1g Solve problems involving fractions, decimals and percents

Unit 5 Framework Enduring Understandings

The ratio of the circumference to the diameter of any circle is a constant approximately equal to 3.14.Formulas can be used to help us find missing measurements of figures.The area of a circle can be approximated using the area of a rectangle.Fractions, decimals, and percents help us solve problems and make sense of data.Some data sets are best displayed using circle graphs.

Unit 5 Framework Essential Questions

What is the relationship between the circumference and the diameter of a circle?How can we determine the formula for the area of a circle?When should I use a circle graph?How do circle graphs help me compare different groups?How can fractions, decimals and percents help me answer questions related to data?

Unit Assessment

GPS Framework, Grade 6, Unit 5, Circles and Graphs, Culminating Task “Data and Circle Graphs,” pp. 13 - 16 of 16

Literacy GPS





Vocabulary

DiameterCircumferenceCircle Graph



M6M2b Select and use units of appropriate size and type to measure length, perimeter, area, and volume.M6A1 Students will understand the concept of ratio and use it to represent quantitative relationships.

.


The ratio of the circumference to the diameter of any circle is a constant approximately equal to 3.14.Formulas can be used to help us find missing measurements of figures.The area of a circle can be approximated using the area of a rectangle.Some data sets are best displayed using circle graphs.


What is the relationship between the circumference and the diameter of a circle?How can we determine the formula for the area of a circle?When should I use a circle graph?

Vocabulary

DiameterCircumference

Literacy GPS






Warm-Up/Quick PracticeMental Math: Calculate elapsed time, counting on by minutes first and then hours (for example with 4:12 until 9:00, think 48 minutes gets me to 5:00 and then 4 hours more until 9:00, for a total of 4 hours and 48 minutes)Solve one-step equations, including exponentsCalculate 1%, 10%, 25% and 50% of any whole numberSkill Mastery: Solve equations




2.8.36 M6M2bM6A1

Understand the relationship between diameter and circumference

Grade 6 MIC Reallotment, “Perimeter and Area” Circles, pp. 41 - 43

Student Activity Sheet 13, p. 99CalculatorsCompassesCentimeter rulers

2.8.37 M6M2bM6A1

Explore strategies using sectors of circles to estimate the area of a circle

GPS Framework Grade 6, Unit 5 Circles and Graphs, “Deriving the Area of a Circle,” pp. 9 – 10 of 16

Four paper circles with diameters of about eight inches for each student groupScissors

2.8.38 M6M2b Develop strategies using grids and squares to determine the formula for the area of a circleApply area formula to solve real word problems

Grade 6 MIC Reallotment, “Perimeter and Area” Circles and Area, pp. 44 - 45

Student Activity Sheet 14, p. 100Calculators

2.8.39 M6M2b Solve real world problems involving the measurement of circles

Holt Mathematics Course 1, “Area of Circles,” pp. 558 - 561

Calculators



Weekly Focus: Solve problems involving measurements of circles with “Using the Equation C/d=pi” Task from GPS Framework Unit 5 Circles and Graphs, pp. 7 – 8 of 16.

Maintenance: Demonstrate an understanding of math properties using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Always, Sometimes, Never,” pp. 20 - 22 of 35.

Maintenance: Model addition and subtraction of positive and negative numbers with “Zero Sum” from HM course 1, p. 654.

Exploration: Develop spatial reasoning with “Create Tessellations” from HM Course 1, pp. 468 – 469.

Intervention:

Homework

Weekly Focus: Estimate and calculate the area of circles

Maintenance: Identify and continue patterns on tables

Skill: Solve equations



Compare and contrast circles and polygons.Why are there fewer circles than triangles and quadrilaterals in architecture?How can a circle have interior angles if it has no straight line segments?How can square units be used to determine the area of a curved figure?

Journal

Describe how you can find the area of a circle by measuring its radius or its diameter. If you need to, explain your thinking by using a specific circle. Why is your method useful?


Weekly Focus: Selected Grade 6 MIC Reallotment Section D itemsSkill Mastery: Solve equations. (1) 2m = 24 (2) 416 = 4c (3) 3s + 8 = 26 (4) 92 – 16t = 12Performance Task:Culminating Task:



M6D1a Formulate questions that can be answered by data. Students should collect data by using samples from a larger population or by conducting experiments.

M6D1b Using data, construct frequency distributions, frequency tables, and graphs.M6D1c Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs,

histograms, bar graphs, line graphs, circle graphs, and line plots.M6D1d Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups.M6D1e Relate the data analysis to the context of the questions posedM6N1g Solve problems involving fractions, decimals and percents.


.Fractions, decimals, and percents help us solve problems and make sense of data.Some data sets are best displayed using circle graphs.


When should I use a circle graph?How do circle graphs help me compare different groups?How can fractions, decimals and percents help me answer questions related to data?

Vocabulary

DiameterCircumferenceCircle Graph

Literacy GPS






Warm-Up/Quick PracticeMental Math: Calculate elapsed time, counting on by minutes first and then hours Calculate percent of a given whole number or money amountDetermine the GCF and LCM for a given pair of numbersSkill Mastery: Multiply and divide integers

Problem Solving Interpret circle graphs HM Course 1, “Music Link,” p.384.



2.9.41 M6D1eM6N1g

Interpret data displayed on circle graphs

Grade 6 MIC Picturing Numbers, “A Piece of the Pie” Fuel Gauges and How People Spend their Vacations, pp. 10 – 11


2.9.42 M6D1a, b, c, d, eM6N1g

Create a frequency table and circle graph based on survey data

Grade 6 MIC Picturing Numbers, “A Piece of the Pie” Data Collection and Ways of Traveling to School, pp. 12 - 15

Student Activity Sheets 4 and 5, pp. 68 - 69Materials to gather class dataOptional: Enlarged copy of Transportation Data

2.9.43 M6D1a, b, c, d, eM6N1g

Compare different representations of the same dataCompare data from different samples

Grade 6 MIC Picturing Numbers, “A Piece of the Pie” Ways of Traveling to School, pp. 13 - 15

Student work from previous lesson

2.9.44 M6D1a, b, c, d, eM6N1g

Create a frequency table and circle graph based on survey data

GPS Framework Grade 6 Unit 5 Circles and Graphs, Culminating Activity “Data and Circle Graphs,” pp. 13 – 16

Data from Framework taskMaterials to create circle graphs for class presentation



Weekly Focus: Recognize the connection between circles and circle graphs GPS Framework Unit 5 Circles and Graphs, “Circles and Sectors,” pp. 11 – 12 of 16.

Maintenance: Demonstrate an understanding of math properties using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Always, Sometimes, Never,” pp. 20 - 22 of 35.

Maintenance: Model addition and subtraction of positive and negative numbers with “Zero Sum” from HM course 1, p. 654.

Exploration: Develop spatial reasoning with “Create Tessellations” from HM Course 1, pp. 468 – 469.

Intervention:

Homework

Weekly Focus: Interpret data displayed on circle graphs

Maintenance: Solve one-step or multi-step word problems involving whole numbers or decimals

Skill: Multiply and divide integers


Reflection and Closure

Which benchmark fractions and percents are used when first studying a circle graph?Can circle graphs be used for either categorical or numerical data?Compare and contrast circle graphs with bar graphs and line graphs.

Journal

Do you agree or disagree that circle graphs are more valid than other representations since they do not have scales that can be manipulated?What do you think is the maximum number of categories (segments) that can clearly be represented on a circle graph?How could I explain the ways to interpret a circle graph to younger students who do not understand percents yet?

Evidence of Learning (Assessments)Weekly Focus: Selected Grad 6 MIC Picturing Numbers Section B itemsSkill Mastery: Multiply and divide integers (1) 42 x 53 = (2) 35 x 123 = (3) 132 x 56 = (4) 144 ÷ 12 = (5) 692 ÷ 4 = Performance Task:Culminating Task: GPS Framework, Grade 6, Unit 5, Circles and Graphs, “Data and Circle Graphs,” pp. 13 - 16 of 16

week 1 of the first quarter - atlanta public schools€¦ · web viewstudent activity sheet 5, p....

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