Instructional Unit Plan
Unit 9 Georgia Performance Standards
M6A2a / Analyze and describe patterns arising from mathematical rules, tables, and graphs.M6A2b / Use manipulatives or draw pictures to solve problems involving proportional relationships.
M6A2c / Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.
M6A2d / Describe proportional relationships mathematically using y=kx, where k is the constant of proportionality.
M6A2e / Graph proportional relationships in the form y=kx and describe characteristics of the graphs.
M6A2f / In a proportional relationship expressed as y=kx, solve for one quantity given the values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y=kx.
M6A2g / Use proportional reasoning (a/b=c/d and y=kx) to solve problems.
M6A3 / Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.
Unit 9 Framework Enduring Understandings
Double number lines, models, and manipulatives are helpful in recognizing and describing proportional relationships.
The equation y = kx describes a proportional relationship in which y varies directly as x.
Proportional relationships can be represented using rules, tables, and graphs.
Many problems encountered in everyday life can be solved using proportion. / Unit 9 Framework Essential Questions
What is a proportion?
How can proportions be used to solve problems?
How can proportional relationships be described using the equation
y = kx?
How can proportional relationships be represented using rules, tables, and graphs?
How can the graph of y = kx be interpreted for different contexts?
How can algebraic expressions be used to model real-world situations?
How can we solve simple algebraic equations, and how do we interpret
the meaning of the solutions?
Unit 9 Assessment
GPS Framework Unit 9 Direct Proportion, Culminating Task “Want Ads,” pp. 17 – 20 of 20 / 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
Vocabulary
Constant of proportionalityDirect proportion (Direct variation)
EquationProportion
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 1
Georgia Performance Standards
M6A2a / Analyze and describe patterns arising from mathematical rules, tables, and graphs.M6A2b / Use manipulatives or draw pictures to solve problems involving proportional relationships.
M6A2c / Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.
M6A2g / Use proportional reasoning (a/b=c/d and y=kx) to solve problems.
M6A3 / Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.
Unit 9 Framework Enduring Understandings
Double number lines, models, and manipulatives are helpful in recognizing and describing proportional relationships.
The equation y = kx describes a proportional relationship in which y varies directly as x.
Proportional relationships can be represented using rules, tables, and graphs.
Many problems encountered in everyday life can be solved using proportion. / Unit 9 Framework Essential Questions
What is a proportion?
How can proportions be used to solve problems?
How can proportional relationships be described using the equation
y = kx?
How can proportional relationships be represented using rules, tables, and graphs?
How can the graph of y = kx be interpreted for different contexts?
How can algebraic expressions be used to model real-world situations?
How can we solve simple algebraic equations, and how do we interpret
the meaning of the solutions?
Vocabulary
Constant of proportionality
Direct proportion (Direct variation)
Equation
Proportion / 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: / 4 / Week: / 1
Warm-Up/Quick Practice
Mental Math: Multiply multiples of ten
Use formulae to find the surface area and volume of common geometric solids
Determine the GCF and LCM for a given pair of numbers
Divide decimals / Problem Solving
Estimate and solve single- and multi-step problems
Use variables to represent the unknown quantity
Apply the Make an Organized List and Work Backwards strategies to solve process problems
HM Problem Solving Strategies, pp. 748 and 742
Focus Lessons
Ref
# / State Standards / Objectives / Resources / Materials4.1.1
/ M6A2b, g / Model proportional relationships / Holt Mathematics Course 1, Hands-On Lab “Explore Proportions,” pp. 360 - 361 / Counters of two different colors4.1.2
/ M6A2b, c, gM6A3 / Develop strategies to solve problems involving proportions / GPS Framework Unit 9 Direct Proportion, “Picturing Proportions,” pp. 6 – 8 of 20 / Transparency or copies of the problems from the task
4.1.3
/ M6A2b, c, gM6A3 / Develop strategies to solve problems involving proportions / GPS Framework Unit 9 Direct Proportion, “Fruit Punch” and “Puzzling Percentages,” pp. 5 – 6 and 9 – 11 of 20 / Transparency or copies of the problems from the task
4.1.4
/ M6A2a, c, gM6A3 / Identify proportional relationships among quantities / GPS Framework Unit 9 Direct Proportion, “Analyze Tables,” pp. 13 – 14 of 20 / Transparency or copies of the tables from the task
4.1.5 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus: Solve rate problems with “Reaching All Learners” from HM Course 1, p. 353.
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: Develop algebraic reasoning with “Summary” and “Check Your Work,” from MIC Comparing Quantities, pp. 32 – 33.
Intervention: / Homework
Weekly Focus: Solve proportion problems
Maintenance: Identify line and rotational symmetry
Skill: Divide decimals
Refer to Holt Mathematics Course 1
Reflection with Closure
There are many situations in food/drink preparation when ratio and proportions are used to solve a problem. Have I ever informally used those concepts to solve a problem in my past? Are there any possible situations coming up where I can see myself applying those concepts?
Journal
How are percents related to proportions?
Are all percents a type of proportion? Explain.
Explain how a percent can be greater than 100%.
How are equivalent fractions related to proportional reasoning?
Evidence of Learning (Assessments)
Weekly Focus: Selected HM Course 1Chapter 7items
Skill Mastery:Divide decimals
0.08 ÷ 0.004 6.012 ÷ 1.2 5.24 ÷ 0.4 19.81 ÷ 0.07
Performance Task:
Culminating Task:
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 2
Georgia Performance Standards
M6A2a / Analyze and describe patterns arising from mathematical rules, tables, and graphs.M6A2d / Describe proportional relationships mathematically using y=kx, where k is the constant of proportionality.
M6A2e / Graph proportional relationships in the form y=kx and describe characteristics of the graphs.
M6A2f / In a proportional relationship expressed as y=kx, solve for one quantity given the values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y=kx.
M6A2g / Use proportional reasoning (a/b=c/d and y=kx) to solve problems.
M6A3 / Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.
Unit 9 Framework Enduring Understandings
Double number lines, models, and manipulatives are helpful in recognizing and describing proportional relationships.
The equation y = kx describes a proportional relationship in which y varies directly as x.
Proportional relationships can be represented using rules, tables, and graphs.
Many problems encountered in everyday life can be solved using proportion. / Unit 9 Framework Essential Questions
What is a proportion?
How can proportions be used to solve problems?
How can proportional relationships be described using the equation y = kx?
How can proportional relationships be represented using rules, tables, and graphs?
How can the graph of y = kx be interpreted for different contexts?
How can algebraic expressions be used to model real-world situations?
How can we solve simple algebraic equations, and how do we interpret
the meaning of the solutions?
Vocabulary
Constant of proportionality
Direct proportion (Direct variation)
Equation
Proportion / Literacy GPS
ELA6RC3a Demonstrate an understanding of contextual vocabulary in various subjects
ELA6LSV1b Ask relevant questions
ELA6LSV1c Respond to questions with appropriate information
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 2
Warm-Up/Quick Practice
Mental Math: Front-end multiplication (for example, with 264 x 3, think 200 x 3 = 600, then 600 plus 60 x 3 for 780 and then 780 plus 4 x 3 for 792)
Decompose numbers into their prime factorization
Calculate percent of a given whole number or money amount
Simplify numeric expressions / Problem Solving
Estimate and solve single- and multi-step problems
Use variables to represent the unknown quantity
Apply the Make a Table and Find a Pattern strategies to solve process problems
HM Problem Solving Strategies, pp. 744 and 743
Focus Lessons
Ref
# / State Standards / Objectives / Resources / Materials4.2.6
/ M6A2a, d, e, f, g /Introduce representing proportional relationships on graphs
/ GPS Framework Unit 9 Direct Proportion, “Making Sense of Graphs,” pp. 12 – 13 of 20 / Transparency or copies of graph from the task4.2.7
/ M6A2a, d, e, f, g / Recognize constant rates of changeApply arrow math strategy to find rates of change
/ MIC Expressions and Formulas, “Formulas” Supermarkets, pp. 12 – 13GPS Framework Unit 9 Direct Proportion, “AnalyzingTables”, pp 14 of 20 / Optional: Calculators
4.2.8
/ M6A2a, d, e, f, g / Recognize constant rates of changeUnderstand the relationship among equations, tables, and graphs
/ MIC Expressions and Formulas, “Formulas” Taxi Fares including Reaching All Learners Extension, pp. 14 – 15Extend to record equations along with arrow notation / Graph paper
Optional: Calculators
4.2.9
/ M6A2a, d, e, f, g / Recognize that a constant rate of change exists between the variables in linear relationships / MIC Expressions and Formulas, “Formulas” Stacking Cups, pp. 16 - 17Extend to using cups of different sizes and graphing results / Centimeter rulers for each group
Styrofoam cups with measurable rims, with at least four cups of each size
4.2.10 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus:Find equivalent ratios with “Reaching All Learners” from HM Course 1, p. 357.
Maintenance: Identify solid figures with “Poly-Cross Puzzle” including the Extend activity from HM Course 1, p. 588.
Maintenance:Find values for unknown quantities withHM Course 1 supplemental resources.
Exploration: Investigate probability concepts with "Reaching All Learners” fromHM Course 1, pp. 669 and 673.
Intervention: / Homework
Weekly Focus: Solve for the missing quantity in a proportion
Maintenance: Find missing side measurements of similar figures
Skill: Simplify numeric expressions
Refer to Holt Mathematics Course 1
Reflection with Closure
In the earlier grades, we used to do puzzles with In/Out boxes. Were we actually doing algebra at that time?
Journal
Can all proportional relationships be represented on a graph?
Explain how you can determine if the numerical relationship is proportional from studying the graph and from studying the table.
How much information from the table is needed to create the graphical representation?
Evidence of Learning (Assessments)
Weekly Focus: Selected MIC Expressions and FormulasSection C items
Skill Mastery:Simplify these numeric expressions.
(32 – 4) – 8 ÷ 2 = 75 – 25 ÷ 5 + 20 x 4 = 4 X 16 ÷ 4 + ( 4 + 12)2 = 9 + 16 + ( 5 – 3 )3 ÷ 2 =
Performance Task:
Culminating Task:
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 3
Georgia Performance Standards
M6A2a / Analyze and describe patterns arising from mathematical rules, tables, and graphs.M6A2b / Use manipulatives or draw pictures to solve problems involving proportional relationships.
M6A2c / Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.
M6A2d / Describe proportional relationships mathematically using y=kx, where k is the constant of proportionality.
M6A2e / Graph proportional relationships in the form y=kx and describe characteristics of the graphs.
M6A2f / In a proportional relationship expressed as y=kx, solve for one quantity given the values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y=kx.
M6A2g / Use proportional reasoning (a/b=c/d and y=kx) to solve problems.
M6A3 / Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.
Unit 9 Framework Enduring Understandings
Double number lines, models, and manipulatives are helpful in recognizing and describing proportional relationships.
The equation y = kx describes a proportional relationship in which y varies directly as x.
Proportional relationships can be represented using rules, tables, and graphs.
Many problems encountered in everyday life can be solved using proportion. / Unit 9 Framework Essential Questions
What is a proportion?
How can proportions be used to solve problems?
How can proportional relationships be described using the equation y = kx?
How can proportional relationships be represented using rules, tables, and graphs?
How can the graph of y = kx be interpreted for different contexts?
How can algebraic expressions be used to model real-world situations?
How can we solve simple algebraic equations, and how do we interpret
the meaning of the solutions?
Vocabulary
Constant of proportionality
Direct proportion (Direct variation)
Equation
Proportion / Literacy GPS
ELA6RC3a Demonstrate an understanding of contextual vocabulary in various subjects
ELA6LSV1c Respond to questions with appropriate information
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 3
Warm-Up/Quick Practice
Mental Math: Front-end multiplication
Find missing side measurements of similar figures
Find the unit cost
Add, subtract, multiply, and divide fractions and mixed numbers / Problem Solving
Solve problems involving similar triangles
Refer to HM Course 1, Chapter 7 additional resources
Focus Lessons
Ref
# / State Standards / Objectives / Resources / Materials4.3.11
/ M6A2a, d, e, f, g / Recognize constant rates of changeUnderstand the relationship among equations, tables, and graphs
/ MIC Expressions and Formulas, “Formulas” Bike sizes, pp. 18 - 21 / Activity Sheets 1 and 2, pp. 69 – 70Optional: Transparency of Activity Sheet 1, calculators
4.3.12
/ M6A2a, b, c, d, e, f, gM6A3 / Identify proportional relationships and represent with tables, graphs, and algebraic expressions / GPS Framework Unit 9 Direct Proportion, “View Tube Experiment,” pp. 15 – 16 of 20 / Cardboard tubes of varying length
Metric tape measure or meter sticks (one for each student group)
Copies of problem from the task
4.3.13
/ M6A2a, b, c, d, e, f, gM6A3 / Identify proportional relationships and represent with tables, graphs, and algebraic expressions / GPS Framework Unit 9 Direct Proportion, “View Tube Experiment,” pp. 15 – 16 of 20 / Student work from the previous lesson
4.3.14
/ M6A2a, b, c, d, e, f, gM6A3 / Solve problems involving direct proportion / GPS Framework Unit 9 Direct Proportion, Culminating Task “Want Ads,” pp. 17 – 20 of 20 / Want Ads that include jobs with hourly rates listed
Copies of problem from the task
4.3.15 / See Variety of Instructional Tasks
Variety of Instructional Tasks
Weekly Focus: Recognize linear or nonlinear relationships with Hands-On Lab “Explore Linear and Nonlinear Relationships” from HM Course 1, “pp. 644 – 645
Maintenance: Identify solid figures with “Poly-Cross Puzzle” including the Extend activity from HM Course 1, p. 588.
Maintenance: Find values for unknown quantities with HM Course 1 supplemental resources.
Exploration: Investigate probability concepts with "Reaching All Learners” fromHM Course 1, pp. 669 and 673.
Intervention: / Homework
Weekly Focus: Solve proportion problems
Bring in cardboard tubes (paper towel, toilet tissue, wrapping paper) for Lesson 4.3.12
Maintenance: Solve one-step equations, including exponents
Skill: Find the unit cost
Refer to Holt Mathematics Course 1
Reflection with Closure
Can I always represent an algebraic equation on a graph? Why do we do this?
Journal
When graphing information from the table or an equation, how do you know which information is to be represented on the x axis and the y axis?
Can a proportional relationship result in a graph that slopes down from left to right? Why or why not?
Can all proportional relationships be represented on a line graph rather than discrete points of data?
Evidence of Learning (Assessments)
Weekly Focus: Selected MIC Expressions and FormulasSection C and HM Course 1Chapter 7 items
Skill Mastery:Find the cost for one of each of the items.
3 cookies for $1.98 7 books $21.95 a dozen donuts for $4.23
Performance Task:
Culminating Task: GPS Framework Unit 9 Direct Proportion, Culminating Task “Want Ads,” pp. 17 – 20 of 20
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Weeks: / 4- 6
Instructional Unit Plan
Unit 10 Georgia Performance Standards
M6D1a / Formulate questions that can be answered by data. Students should collect data by surveys or experiments.M6D1b / Using data, construct frequency distributions, frequency tables, and graphs.
M6D1e / Relate the data analysis to the context of the questions posed.
M6D2a / Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio.
M6D2b / Determine, and use a ratio to represent, the theoretical probability of a given event.
M6D2c / Discover that experimental probability approaches theoretical probability when the number of trials is large.
Unit 10 Framework Enduring Understandings
Trials and simulations are used to predict probability.
The probability of a given event can be represented as a fraction between 0 and 1.
Experimental probability approaches theoretical probability when the number of trials is large. / Unit 10 Framework Essential Questions
How can we determine the likelihood that an event will occur?
What is the best way to represent a given probability?
What is the difference between theoretical and experimental probability?
What is the significance of a large number of trials?
Unit 10 Assessment
GPS Framework Unit 10 Games of Chance, Culminating Task “Marbles,” pp. 11 – 13 of 13 / 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
Vocabulary
Event
Experimental probability
Probability
Theoretical probability
Atlanta Public Schools Teaching Plans / Sixth Grade / Quarter: / 4 / Week: / 4
Georgia Performance Standards
M6D2a / Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio.M6D2b / Determine, and use a ratio to represent, the theoretical probability of a given event.
M6D2c / Discover that experimental probability approaches theoretical probability when the number of trials is large.
Unit 10 Framework Enduring Understandings
Trials and simulations are used to predict probability.
The probability of a given event can be represented as a fraction between 0 and 1.
Experimental probability approaches theoretical probability when the number of trials is large. / Unit 10 Framework Essential Questions
How can we determine the likelihood that an event will occur?
What is the best way to represent a given probability?
What is the difference between theoretical and experimental probability?
What is the significance of a large number of trials?
Vocabulary
Event
Experimental probability
Probability
Theoretical probability / Literacy GPS
GPS Reading Across the Content Area Standards
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: / 4 / Week: / 4
Warm-Up/Quick Practice
Mental Math: Front-end multiplication with money amounts (for example, with $3.45 x 4, think $3 x 4 = $12, then $12 plus .45 x 4 or $12 + $1.80, for a product of $13.80)
Convert customary measurement units for length, weight, and capacity
Use formulae to find the surface area and volume of geometric solids
Divide decimals by decimals and whole numbers / Problem Solving
Solve problems involving direct proportion
Refer to HM Course 1, Chapter 1 additional resources
Focus Lessons
Ref