Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 1 / Weeks: / 1- 3

Instructional Unit Plan

Unit 3 Georgia Performance Standards

M6N1d / Add and subtract fractions and mixed numbers with unlike denominators.
M6N1e / Multiply and divide fractions and mixed numbers.
M6N1f / Use fractions, decimals, and percents interchangeably.
M6N1g / Solve problems involving fractions, decimals and percents.
M6A1 / Students will understand the concept of ratio and use it to represent quantitative relationships.
M6A2c / Use proportions to describe relationships and solve problems, including percent problems.
Unit 3 Framework Essential Questions
How can I tell which form of a rational number is most appropriate in a given situation?
When I multiply two fractions, how can I be sure that my answer is correct?
When I subtract two fractions, how can I be sure that my answer is correct?
How do I find a common denominator?
When I multiply one number by another number, do I always get a product bigger than my original number?
When I divide one number by another number, do I always get a quotient smaller than my original number?
What information do I get when I compare two numbers using a ratio?
What kinds of problems can I solve by using ratios? / Unit 3 Framework Enduring Understandings
Fractions, decimals, and percents can be used interchangeably.
The relationships and rules that govern whole numbers, govern all rational numbers.
In order to add or subtract fractions, we must have like denominators.
When we multiply one number by another number, we may get a product that is bigger than the original number, smaller than the original number or equal to the original number.
When we divide one number by another number, we may get a quotient that is bigger than the original number, smaller than the original number or equal to the original number.
Ratios use division to represent relationships between two quantities.
Unit 3Assessment
GPS Framework, Grade 6, Unit 3, Fractions, Decimals, Ratios, and Percents, Culminating Task “Science Fair Task,” pp. 17 - 20 of 20 / Vocabulary
Proportion
Ratio
Rational number
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 1

Georgia Performance Standards

M6N1e / Multiply and divide fractions and mixed numbers.
M6N1g
M6A1 / Solve problems involving fractions, decimals, and percent.
Students will understand the concept of ratio and use it to represent quantitative relationships.
Unit 3 Framework Enduring Understandings
The relationships and rules that govern whole numbers, govern all rational numbers.
When we divide one number by another number, we may get a quotient that is bigger than the original number, smaller than the original number or equal to the original number.
Ratios use division to represent relationships between two quantities. / Unit 3 Framework Essential Questions
When I divide one number by another number, do I always get a quotient smaller than my original number?
What kinds of problems can I solve by using ratios?
Vocabulary
Proportion
Ratio
Rational number
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 1
Warm-Up/Quick Practice
Mental 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 numbers
Determine the mean, median and mode for a data set
Skill Mastery: Estimate the sum of difference to the nearest whole number / Problem Solving
Estimate and solve single- and multi-step problems
Use variables to represent the unknown quantity
Apply the Make an Organized List strategy to solve process problems
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

2.1.1

/ M6N1f / Use fractions, decimals, and percents interchangeably. / GPS Framework Unit 3 Fractions, Decimals, and Percent, “Representing Rational Numbers on the Number Line”, p. 6 of 20
HM Course1, Exploration 7-8 / Number line
Copy of task
Exploration 7-8 transparency

2.1.2

/ M6N1f / Use fractions, decimals, and percents interchangeably. / GPS Framework Unit 3 Fractions, Decimals and Percent, “Reaching the Goal, pp. 7, 8 of 20 / Copy of task

2.1.3

/ M6N1e / Model multiplication of rational numbers / MIC: Reallotment, pp. 20 – 21
HM Course 1, Lab 5-7 / Grid paper
Fraction bars

2.1.4

/ M6N1e / Recognize the similarities between division of decimals and division of fractions
Use multiplication to verify the accuracy of division computations / GPS Framework Unit 3 Fractions, Decimals and Percent, “Dividing Rational Numbers,” pp. 9 – 10 of 20
HM Course1, Lab 5-9, p. 268 / Grid paper
Fraction bars

2.1.5

/ M6N1e / Recognize the similarities between division of decimals and division of fractions
Use multiplication to verify the accuracy of division computations / GPS Framework Unit 3 Fractions, Decimals and Percent, “Taking a Break”, p. 10 of 20
HM Course 1, Exploration 5-9 / Number line
Grid paper
Exploration 5-9 transparency
Variety of Instructional Tasks
Weekly Focus: Model percent and relate to fractions and decimals, HM Course 1, pp. 380 -- 383
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: Technology Lab “convert Between Percents, Decimals, and Fractions”, calculator activity
Intervention: Lesson Tutorial video, “Writing Decimals as Percents” http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm1/player.html?contentSrc=6046/6046.xml
http://my.hrw.com/math06_07/nsmedia/tools/Decimal_Fractions/Decimal_Fractions.html online tool for multiplying decimal fractions / Homework
Weekly Focus: Estimate and solve fraction division problems
Maintenance: Solve one-step or multi-step word problems involving whole numbers or decimals
Skill: Estimate the sum or difference to the nearest whole number
Refer to Holt Mathematics Course 1
Reflection with Closure
When using only the algorithm, how can you verify the accuracy of your quotient?
What does the expression 1/2 ÷ 3/8 really mean? Explain how you know that the solution will be greater than one.
If percent means ‘out of one hundred’ what do they mean by 125%?
Journal
Describe how to find the product of a mixed number and a fraction.
Describe how to divide a decimal fraction by a decimal fraction.
When have I heard the term percent in real life?
Evidence of Learning (Assessments)
Weekly Focus: Selected HM Course 1 Chapter 7 items; products from framework tasks
Skill Mastery: Estimate the sum or difference to the nearest whole number
6.7 + 3.2 + 4.1 + 5.9 = 23.56 + 101.32 + 79.09 + 235.6 = 347.69 - 238.98 = 1,098.72 - 898.76 =
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 2

Georgia Performance Standards

M6A1 / Students will understand the concept of ratio and use it to represent quantitative relationships.
M6N1f / Use fractions, decimals, and percents interchangeably.
M6N1g / Solve problems involving fractions, decimals and percents.
Unit 3 Framework Enduring Understandings
Fractions, decimals, and percents can be used interchangeably.
Ratios use division to represent relationships between two quantities. / Unit 3 Framework Essential Questions
How can I tell which form of a rational number is most appropriate in a given situation?
What information do I get when I compare two numbers using a ratio?
What kinds of problems can I solve by using ratios?
Vocabulary
Proportion
Ratio
Rational number / 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
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 2
Warm-Up/Quick Practice
Mental 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 set
Add and subtract fractions and mixed numbers
Skill Mastery: Multiply and divide decimals / Problem Solving
Estimate and solve single- and multi-step problems
Use variables to represent the unknown quantity
Apply the Make a Table strategy to solve process problems
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

2.2.6

/ M6N1f, g
M6A1 / Use fractions, decimals, and percents interchangeably. / GPS Framework Unit 3 Fractions, Decimals and Percent, “Reading Circle Graphs,” pp. 11– 12 of 20 / Fraction circles

2.2.7

/ M6N1f
M6A1 / Use fractions, decimals, and percents interchangeably. / http://illuminations.nctm.org/ActivityDetail.aspx?ID=60 Circle Grapher, “How I divide my 24 hour day”
HM Course 1, Problem Solving 5-9

2.2.8

/ M6N1f, g
M6A1 / Model division by decimals, fractions, and mixed numbers
Rename fractions to divide without inverting
Practice traditional strategy of inverting to divide / GPS Framework Unit 3 Fractions, Decimals and Percent, “Dividing Rational Numbers,” pp. 13 – 14 of 20
http://www.europa.com/~paulg/mathmodels/eggdiv.html

2.2.9

/ M6N1f, g
M6A1 / Use benchmark fractions to estimate and calculate percent / MIC More or Less, “Discounts” Percents and Fractions, pp. 13 – 15 / Student Activity Sheet 2, p. 56
Optional: Calculators

2.2.10

/ M6N1f, g
M6A1 / Solve real world problems involving fractions and percent / MIC More or Less, “Many Changes,” Design a Sign, pp. 18 – 19 / No additional materials required
Optional: Calculators
Variety of Instructional Tasks
Weekly Focus: Solve percent problems involving sales tax with Problems 3, 8 and 9 from HM Course 1, p. 396.
Maintenance: Use factors of numbers with “Journal” and “Reaching All Learners” from HM Course 1, pp. 172 and 174. http://illuminations.nctm.org/ActivityDetail.aspx?ID=29 The Product Game
Maintenance: Identify angles and review related vocabulary with “Angle Relationships” from HM course 1, pp. 426 – 427.
Exploration:
http://www.europa.com/~paulg/mathmodels/eggmult.html
http://www.europa.com/~paulg/mathmodels/eggdiv.html - These two websites use egg cartons to model multiplication and division of fractions.
Intervention: http://illuminations.nctm.org/ActivityDetail.aspx?ID=44 Fraction Model II, interchanging fractions, decimals, and percents / Homework
Weekly Focus: Solve problems involving sale prices
Maintenance: Multiply and divide fractions and mixed numbers
Skill: Multiply and divide decimals
Refer to Holt Mathematics Course 1
Reflection with Closure
Can you find percents of fraction or decimal amounts?
Why are percents useful in comparing quantities?
Why is it important to know the original quantity when using percents?
Journal
Why are so many discounts and sales advertised as 20% or 25% off?
Evidence of Learning (Assessments)
Weekly Focus: Selected MIC More or Less Section B items and products from tasks
Skill Mastery: Multiply and divide decimals
1.3 x 0.4 = 5.32 x 1.2 = 0.07 x 0.04 =
0.6 / 0.02 = 0.9 / 0.3 = 16.8 / 2.1 =
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 3

Georgia Performance Standards

M6N1f / Use fractions, decimals, and percents interchangeably.
M6N1g / Solve problems involving fractions, decimals and percents.
M6A1 / Students will understand the concept of ratio and use it to represent quantitative relationships.
Unit 3 Framework Enduring Understandings
Fractions, decimals, and percents can be used interchangeably.
Ratios use division to represent relationships between two quantities. / Unit 3 Framework Essential Questions
How can I tell which form of a rational number is most appropriate in a given situation?
What information do I get when I compare two numbers using a ratio?
What kinds of problems can I solve by using ratios?
Vocabulary
Proportion
Ratio
Rational number / 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
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Week: / 3
Warm-Up/Quick Practice
Mental Math: Recognize compatible numbers
Decompose numbers into their prime factorization
Multiply and divide fractions and mixed numbers
Skill Mastery: Divide by two-digit divisors / Problem Solving
Develop algebraic reasoning skills
Investigate exchange strategies to solve equality problems
MIC Comparing Quantities, “Compare and Exchange,“ pp. 1 - 3
Focus Lessons

Ref #

/ State
Standards / Objectives / Resources / Materials

2.3.11

/ M6N1f, g
M6A1 / Solve real world problems involving fractions and percent
Identify the fraction, decimal, and percent relationship / MIC More or Less, “Many Changes” Profit Fractions, pp. 20 - 21 / Student Activity Sheets 3 and 4,
pp. 57 - 58
Calculators
Optional: Colored pencils and scissors

2.3.12

/ M6N1f
M6A1 / Use benchmark fractions to estimate and calculate percent / MIC More or Less, “Discounts” Percents and Fractions, pp. 13 – 14 / Additional teacher-written problems

2.3.13

/ M6N1f, g
M6A1 / Solve real world problems involving percent / GPS Framework Unit 3 Fractions, Decimals, and Percent, “Free Throws” and “Ice Cream and Cake,” pp. 14 – 16 of 20 / Copies of problems from task

2.3.14

/ M6N1f
M6A1 / Solve real world problems involving percent / GPS Framework Unit 3 Fractions, Decimals, and Percent, Culminating Activity “Science Fair,” pp. 17 – 20 of 20 / Copies of problems from task

2.3.15

/ M6N1d,e,f,g
M6A1
M6A2 / Solve problems using the four arithmetic operations with rational numbers. / GPS Framework Unit 3 Fractions, Decimals, and Percent, Culminating Activity “Science Fair,” pp. 17 – 20 of 20 / Copies of the task
Optional: Grid paper
Variety of Instructional Tasks
Weekly Focus: Solve challenging percent problems with Problems 16 - 17 from HM Course 1, p. 397.
Maintenance: Use factors of numbers with “Journal” and “Reaching All Learners” from HM Course 1, pp. 172 and 174. http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 The Factur Game
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: Represent quantities as fractions, decimals and percents
Maintenance: Apply order of operations to simplify numeric expressions
Skill: Divide with two-digit divisors
Refer to Holt Mathematics Course 1
Reflection with Closure
Explain when 40% is a larger amount than 60%.
If 90% of the people surveyed agree on an issue, does it necessarily mean that a lot of people agree?
Journal
Explain how you can find any percent of a number as long as you can calculate 10% and 1% of that number.
Evidence of Learning (Assessments)
Weekly Focus: Selected MIC More or Less Section C items
Skill Mastery: Divide with two-digit divisors
604 ÷ 13 275 ÷ 34 5,962 ÷ 22 7304 ÷ 36
Performance Task:
Culminating Task: GPS Framework, Grade 6, Unit 3, Fractions, Decimals, Ratios, and Percents, Culminating Task “Science Fair Task,” pp. 17 - 20 of 20
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 2 / Weeks: / 4-5

Instructional Unit Plan