Updated 7/16/2014

Advanced 7th Grade Math Curriculum Map2014- 2015 School Year A (NEW 6th grade course)

First Semester Second Semester

Unit 1The Number

System

Unit 2Expressions, Equations,

andInequalities

Unit 3Ratio and

ProportionalReasoning

Unit 4

Geometric Reasoning

Unit 5

Statistics

Unit 6

Probability

Unit 7

Introductionto

Linear Functions

(5 weeks) (5 weeks) (7 weeks) (6 weeks) (4 weeks) ( 4 weeks) (3 weeks)

Common Core Georgia Performance Standards

MCC7.NS.1MCC7.NS.2MCC7.NS.3MCC.8.NS.1MCC.8.NS.2

Introduction of square roots and cube roots

portion of MCC.8.EE.2

REVIEW: MCC6.NS.1-4

MCC7.EE1MCC7.EE2MCC7.EE.3MCC7.EE4aMCC6.EE.8

MCC7.EE.4bMCC.6.EE.9

REVIEWMCC.6.EE.1-8

MCC.6.RP.1MCC.6.RP.2MCC.6.RP.3

MCC.6.RP.3aMCC.6.RP.3bMCC.6.RP.3cMCC.6.RP.3dMCC.7.RP.1

MCC.7.RP.2a,b,c,dMCC.7.RP.3MCC.7.G.1

ONE WEEK OF FINALS

MCC.6.G.1MCC.6.G.2MCC.6.G.4MCC.6.G.3MCC.7.G.2MCC.7.G.3MCC.7.G.4MCC.7.G.5MCC.7.G.6

MCC.6.SP.1MCC.6.SP.2MCC.6.SP.3MCC.6.SP.4MCC.6.SP.5

MCC.6.SP.5aMCC.6.SP.5bMCC.6.SP.5cMCC.6.SP.5d

MCC7.SP.5MCC7.SP.6

MCC7.SP.7: a,bMCC7.SP.8: a,b,c

MCC.8.F.1MCC.8.F.2 MCC.8.F.3

MCC.8.EE.5MCC.8.EE.6MCC.8.F.4MCC.8.F.5

*Standards for Mathematical Practice are addressed throughout the year!

1

Updated 7/16/2014Course: Advanced 7th Grade YEAR A (for 6th grade students) YEAR A Grade Level: 6

Unit 1: The Number System7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.7.NS.1a Describe situations in which opposite quantities combine to make 0.7.NS.1b Understand p + q as the number located a distance │q│from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p ─ q = p + (─q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (─1)(─1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is

a rational number. If p and q are integers then−( pq )= (−p )

q= p

(−q ) . Interpret quotients of rational numbers by describing real-world

contexts.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.8.NS.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2).8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

2

Updated 7/16/2014

Course: Advanced 7th Grade YEAR A(for 6th grade students) YEAR A Advanced Grade 7 – Unit 1:The Number System FIRST SEMESTERDay 1 Day 2 Day 3 Day 4 Day 5August 4 August 5 August 6 August 7 August 8

Introductions, review syllabus, set expectations for student-centered, task-based instruction

Pre-test/Diagnostic Test Review Integers and Absolute Value 7.NS.1

Comparing and ordering integers and other rational numbers7.NS.1

Assessment over day 3 and day 4

Day 6 Day 7 Day 8 Day 9 Day 10August 11 August 12 August 13 August 14 August 15Add/subtract integers7.NS.1

Add/subtract integers7.NS.1

Show me the sign task7.NS.1

Debits/Credits Task7.NS.1

Review Combining integers (add/subtract only)7.NS.1

Day 11 Day 12 Day 13 Day 14 Day 15August 18 August 19 August 20 August 21 August 22Multiplying & Dividing Integers7.NS.2

Patterns of Multiplication and Division Task

Patterns of Multiplication and Division Task Independent Instruction

Independent Practice Deep Freeze Task“Spotlight Task”

Day 16 Day 17 Day 18 Day 19 Day 20August 25 August 26 August 27 August 28 August 29Independent Practice Models for Teaching Operations

of Integers.Models for Teaching Operations of Integers.

Models for Teaching Operations of Integers.

Mastery Check on Integers

Day 21 Day 22**Start Sept 8th Day 23 Day 24September 1 September 2 September 3 September 4 September 5

Labor Day[School Closed for Students]

Professional Learning Day

Rational or Irrational Reasoning?(8th Grade Frameworks)

Rational or Irrational Reasoning?(8th Grade Frameworks)

Independent Practice

Day 25 Day 26 Day 27 Day 28 Day 29September 8 September 9 September 10 September 11 September 12Culminating Activity: Whodunit? The Undoing of (-7).

Culminating Activity: Whodunit? The Undoing of (-7).

Review Unit 1 Review Unit 1 Assessment Unit 1

3

Updated 7/16/2014Unit 1:The Number System

Essential Questions What models can be used to

show addition and subtraction of positive and negative rational numbers?

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

How can I use models to prove that opposites combine to 0?

What real life situations combine to make 0?

How do I use a number line to model addition or subtraction of rational numbers?

How do I convert a rational number to a decimal using long division?

What is the difference between rational and irrational numbers?

Key Vocabulary Additive Inverse Multiplicative Inverse Absolute Value Integers Irrational Numbers Natural Numbers Negative Numbers Opposite Numbers Positive Numbers Rational Numbers Repeating Decimal Terminating Decimal Zero Pair Square roots Cube Roots

Prerequisite Skills positive and negative numbers are used together to describe quantities having opposite directions or values; use positive

and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. rational numbers are points on the number line. numbers withopposite signs indicate locations on opposite sides of 0 on the number line; recognize that the opposite of the

opposite of a number is the number itself, e.g.,−(−3 )=3, and that 0 is its own opposite

absolute value of a rational number is its distance from 0 on the number line interpret absolute value as magnitude for a positive or negative quantity in a real-world situation

Suggested Learning Resources/Performance

Tasks

See next page for 7th grade resources and performance tasks.

CCGPS Standards Addressed:7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.7.NS.1a Describe situations in which opposite quantities combine to make 0.7.NS.1b Understand p+q as the number located a distance |q| fromp, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.7. NS.1c Understand subtraction of rational numbers as adding the additive inverse, p−q=p+(−q ). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (−1 ) (−1 )=1and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. 7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.MCC8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. MCC8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^2).8.EE.2Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

4

Updated 7/16/2014Unit 1: Learning Tasks and Performance Tasks

SP: Skills Practice FAL: Formative Assessment Lesson Unit 1

LT: Learning Task CT: Culminating Task Key StandardsPT: Performance Task

NS.1NS.1a NS.1b NS.1c NS.1d NS.2 NS.2a NS.2b NS.2c NS.2d NS.3

Unit 1 Framework Task: What's Your Sign? LT x x x x x

Unit 1 FrameworkTask: Helicopters & Submarines LT

Unit 1 Framework Task: Hot Air Balloons LT x x x x xUnit 1 Framework Task: Debits and Credits PT x x x x xUnit 1 Framework Task: Multiplying Integers LT x x x x

Unit 1 FrameworkTask: Multiplying Rational Numbers LT x x x x

Unit 1 FrameworkTask: Patterns of Multiplication & Division LT x x x x

Unit 1 FrameworkTask: The Repeater Vs. the Terminator LT x x

CMP: Accentuate the Negative Investigation 2 LT x x x xCMP: Skills Practice (7th gd.) SP x x

Coach Book LT/PT x x x x x x

CMP: Accentuate the Negative Investigation 3 LT x x x xCMP: Accentuate the Negative Investigation 4 LT x x x x

Exemplars Volume 10We Think Math is Really Fine PT x x x x x

Exemplars Volume 10 ATT&T Choice PT x x x xExemplars Volume 10 Cookie Caper PT x x x xExemplars Volume 10 Gobble, Gobble, Gobble PT x

Exemplars Volume 10The Sweetest Time of the Year PT x x

Exemplars Volume 10 Candy Box PT x x x xExemplars Volume 10 Indoor Paintball field Trip PT x x x xExemplars Volume 10 Lugging Water II PT x xExemplars Volume 10 Mrs.McNair New Walkway PT x x xExemplars Volume 10 Pyramids of Giza PT x xExemplars Volume 10 Tiffany's cand Making PT x x x x

5

Updated 7/16/2014Buines

Course: Advanced 7th Grade Year A Mathematics Grade Level: 7Unit 2: Expressions and Equations and Inequalities

7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

7.EE.3Solve multi step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, ‐ ‐fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

7.EE.4Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve ‐problems by reasoning about the quantities.

7.EE.4aSolve word problems leading to equations of the form px + q = r and p(x+q) = r, where p, q, and rare specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

6.EE.8 Write an inequality of the form 𝑥>𝑐 or 𝑥<𝑐 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝑥>𝑐 or 𝑥<𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

7.EE.4bSolve word problems leading to inequalities of the form px + q > ror px + q < r, where p, q, and rare specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Represent and analyze quantitative relationships between dependent and independent variables.6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

6

Updated 7/16/2014

7

Updated 7/16/2014Advanced Grade 7(for 6th grade students)—Unit 2:Expressions and Equations and InequalitiesDay 1 Day 2 Day 3 Day 4 Day 5September 15 September 16 September 17 September 18 September 19Introduction of vocabulary and translating expressions7.EE.1Rational Numbers Test

Properties/combining like terms7.EE.1

Properties/combining like terms with distributive property7.EE.1

Adding and subtracting algebraic expressionsDistributing and Factoring Using Area task 7.EE.1

More practice of adding and subtracting algebraic expressions7.EE.1

Day 6 Day 7 Day 8 Day 9 Day 10September 22 September 23 September 24 September 25 September 26

Review of day 2 – day 6Evaluate algebraic expressions Algebra Magic task7.EE.2

Simplifying expressions7.EE.2 Assessment of

day 2 – day 9

Translating equations/solving one step equations with integers (addition and subtraction property of equality)7.EE.37.EE.4

Day 11 Day 12 Day 13 Day 14 Day 15September 29 September 30 October 1 October 2 October 3Translating equations/solving one step equations with integers (addition and subtraction property of equality)7.EE.37.EE.4

One step equations with integers (multiplication and division property of equality)7.EE.37.EE.4

Solving one step equations with fractions and decimals7.EE.37.EE.4

Review of one step equations with integers

Mastery Check One Step Equations

FALL BREAK October 6th – 10th

Day 16 Day 17 Day 18 Day 19 Day 20October 13 October 14 October 15 October 16 October 17Two step equations with integers7.EE.37.EE.4

Two step equations with rational numbers7.EE.37.EE.4

Two step equations review Steps to Solving Equations FALFrameworks

Steps to Solving Equations FALFrameworks

Day 21 Day 22 Day 23 Day 24 Day 25October 20 October 21 October 22 October 23 October 24

Introduction to solving and graphing inequalities, Want Ads (6th Grade Frameworks Unit 4)7.EE.4

Solving and graphing inequalities7.EE.4

Solving and graphing inequalities, expressions and equations reviewTV and Video Games task

Solving and graphing inequalities. Assessment of Unit 2

8

Updated 7/16/2014Unit 2:Expressions and Equations and Inequalities

Unit 2 color coded boxes

Prerequisite Skills number sense computation with whole numbers and decimals, including

application of order of operations addition and subtraction of common fractions with like

denominators computation with all positive and negative rational numbers data usage and representations

Enduring Understandings Variables can be used to

represent numbers in any type mathematical problem.

Understand the difference in an expression and an equation.

Expressions you simplify and equations you solve for the variable’s value.

Write and solve multi-step equations including all rational numbers.

Some equations may have more than one solution and understand inequalities.

Suggested Learning Resources/ Performance

TasksSee next page for learning

resources and performance tasks.

CCGPS Standards Addressed:

MCC7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. MCC7.EE.3 Solve multi step real life and mathematical problems posed with positive and ‐ ‐negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. MCC7.EE.4 Use variables to represent quantities in a real world or mathematical problem, and‐ construct simple equations and inequalities to solve problems by reasoning about the quantities.MCC7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x+q) = r, where p, q, and rare specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. 6.EE.8 Write an inequality of the form 𝑥>𝑐 or 𝑥<𝑐 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝑥>𝑐 or 𝑥<𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams.7.EE.4bSolve word problems leading to inequalities of the form px + q > ror px + q < r, where p, q, and rare specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. Represent and analyze quantitative relationships between dependent and independent variables.6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Key Vocabulary Variable Numerical expression Algebraic expression Term Coefficient Constant Equation Inequality

Essential Questions How can we represent values using variables? What is the difference in an expression and an equation? How do I simplify expressions? How can we use variables to solve equations? How do I determine the difference in equations and

inequalities? How do I solve and graph inequalities? How can I tell the difference between an expression, equation

and an inequality? How do equations and inequalities represent real life

situations?

9

Updated 7/16/2014Unit 2: Learning Tasks and Performance TasksSP: Skills Practice CT: Culminating Task Unit 2LT: Learning Task PT: Performance Task Key StandardsFAL: Formative Assessment Lesson EE.1 EE.2 EE.2a EE.2b EE.3 EE.4 EE.4a EE.4bMath's Cool Module 1, Lesson 4 (1.4) x Math'sCool Module 5, Lesson 2 (5.2) x Algebra'Scool Module 1, Lesson 2 (1.2) x Algebra'Scool Module 1, Lesson 3 (1.3) x x Algebra'Scool Module 1, Lesson 5 (1.5) x Algebra'Scool Module 2, Lesson 3 x Algebra'Scool Module 2, Lesson 4 x Algebra'Scool Module 2, Lesson 5 x Algebra'Scool Module 3, Lesson 1 x x Algebra'Scool Module 3, Lessons 3-5 x Algebra'Scool Module 4, Lesson 1 x x Unit 2 Framework Task: Area & Algebra LT x x Unit 2 Framework Task: Algebra Magic PT x x x x Unit 2 Framework Task: Calendar Equations LT x x x x Unit 2 Framework Task: The Drop PT x x x Unit 2 Framework Task: Inequality Statements LT x

Unit 2 FrameworkTask: Steps to Solving Equations FAL x x x

Unit 2 Framework Task: Population Equations CT x x x x Coach Book SP x x x x xCMP: Accentuate the Negative Investigations 2, 4 LT x CMP: Skills Practice SP x x x x xCMP: Moving Straight Ahead Investigations 1-4 LT x x x xExemplars Volume 10 Indoor Paintball Field Trip PT x Exemplars Volume 10 Mrs.McNair's New Walkway PT x

Exemplars Volume 10Tiffany's Candle Making Business PT x

Exemplars Volume 10 AT&T Choice Dilemma PT x Exemplars Volume 10 Basketball Packaging PT x Exemplars Volume 10 Gobble, Gobble, Gobble PT x Exemplars Volume 10 The Sweetest Time of the Year PT x

10

Updated 7/16/2014

Course:Advanced 7th Grade Year A Mathematics(for 6th grade students) Grade Level: 6Unit 3: Ratios and Proportional Relationships

MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.MCC6.RP.2 Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎: 𝑏 with 𝑏 ≠ 0, (b not equal to zero), and use rate language in the context of a ratio relationship.MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. MCC6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.MCC6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.MCC7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. MCC7.RP.2 Recognize and represent proportional relationships between quantities.MCC7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.MCC7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.MCC7.RP.2c Represent proportional relationships by equations. For example, if total cost tis proportional to the number nof items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.MCC7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r)where r is the unit rate.MCC7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.MCC7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

11

Updated 7/16/2014Advanced Grade 7 (for 6th grade students) —Unit 3: Ratios and Proportion

Day 1 Day 2 Day 3 Day 4 Day 5October 27 October 28 October 29 October 30 October 31

It Is On Sale Task (6th Grade Unit 4 Frameworks)

Review ratios, proportions, and coordinate plane7.RP.1 7.PR.2

Review ratios, proportions, and coordinate plane7.RP.1 7.PR.2

Review unit rate7.RP.2

Introduce relations/functions Domain, range, and input/output tables7.RP.2

Day 6 Day 7 Day 8 Day 9November 3 November 4 November 5 November 6 November 7

Write an equation for a function table.7.RP.2

Teacher PL Day[No School for Students]

Optimizing Security CamerasFAL (6th Grade Unit 2 Frameworks)

Optimizing Security CamerasFAL (6th Grade Unit 2 Frameworks)

Optimizing Security CamerasFAL (6th Grade Unit 2 Frameworks) Solutions Discussion.

Day 10 Day 11 Day 12 Day 13 Day 14November 10 November 11 November 12 November 13 November 14

Revisit relations/functions Domain, range, and input/output tables7.RP.2

Find the missing values and write the equation for a function table. 7.RP.2

Direct variation7.RP.2

Direct variation7.RP.2

Indirect variation7.RP.2

Day 15 Day 16 Day 17 Day 18 Day 19November 17 November 18 November 19 November 20 November 21

Indirect variation7.RP.2

Fish in a Lake Task (Spotlight Task 7th Grade Unit 3 Frameworks) 7.RP.2,3

Fish in a Lake Task (Spotlight Task 7th Grade Unit 3 Frameworks) 7.RP.2,3

Direct and Indirect review Direct and Indirect Assessment

Thanksgiving Break November 24th – 28th

Day 20 Day 21 Day 22 Day 23 Day 24December 1 December 2 December 3 December 4 December 5Sales tax/gratuities/discountIce cream task7.RP.3 – Nov 10th

Percent increase and decrease7.RP.3

Simple interest7.RP.3 Review day 20 – day 22 Assessment of

day 20 – day 23

Day 25 Day 26 Day 27 Day 28 Day 29December9 December 10 December 10 December 11 December 12Use a proportion to find the missing value and scale factor (percent).7.G.1

Area and scale drawing7.G.1

Area and scale drawing7.G.1

Creating a scale map task7.G.1 Review –Finish Nov 21st

Day 30 Day 31 Day 32 Day 33 Day 34December 15 December 16 December 17 December 18 December 19Re-teach/Review Re-teach/Review Re-teach/Review Re-teach/Review Semester Exam

Winter Break December 22nd- January 2nd

12

Updated 7/16/2014Unit 3: Ratios and Proportional Relationships

Essential Question What information do I get when I compare

two numbers using a ratio? What kinds of problems can I solve by

using ratios? How do I compute unit rate in tables,

graphs, equations and diagrams? How do I compute unit rate in real-world

problems? How do I use ratios and their relationships

to solve real world problems? How do I recognize proportional

relationships between quantities? How do I represent proportional

relationships between quantities? How do I solve multistep ratio problems

using proportional relationships? How do I solve multistep percent problems

using proportional relationships? How do I represent proportional

relationships by equations? How do I solve problems involving scale

drawings of geometric figures? How do I compute actual lengths and areas

from a scale drawing? How do I reproduce a scale drawing at a

different scale?

Key Vocabulary

Multiplicative inverse Percent rate of change Ratio Proportion Scale factor Percent Proportion Quantity Rate Rational Number Unit Ratio

Prerequisite Skills number sense computation with whole numbers and decimals, including

application of order of operations addition and subtraction of common fractions with like

denominators measuring length and finding perimeter and area of

rectangles and squares characteristics of 2-D and 3-D shapes data usage and representations

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, 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, 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

Suggested Learning Resources/ Performance TasksSee next pages for resources and performance tasks.

CCGPS Standards Addressed:MCC6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.MCC6.RP.2 Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎: 𝑏 with 𝑏 ≠ 0, (b not equal to zero), and use rate language in the context of a ratio relationship.MCC6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. MCC6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. MCC6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.MCC6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. MCC6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2Recognize and represent proportional relationships between quantities.7.RP.2aDecide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.7.RP.2bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.7.RP.2cRepresent proportional relationships by equations. For example, if total cost tis proportional to the number nof items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.7.RP.2dExplain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r)where r is the unit rate.7.RP.3Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

13

Updated 7/16/2014Unit 3: Learning Tasks and Performance Tasks

CT: Culminating Task SP: Skills Practice Unit 3PT: Performance Task LT: Learning Task Key StandardsFAL: Formative Assessment Lesson RP.1 RP.2 RP.2a RP.2b RP.2c RP.2d RP.3 G1Math'sCool Module 7, Lessons 2-7 x Math'sCool Module 10, Lesson 1 x Algebra'Scool Module 4, Lesson 2 x Unit 3 Framework Task: What is Unit Rate? LT x Unit 3 Framework Task: Orange Fizz Experiment LT x x x Unit 3 Framework Task: Creating a Scale Map PT x x xUnit 3 Framework Task: Which is the better deal? LT x x Unit 3 Framework Task: Patterns &Percents LT x x x x Unit 3 Framework Task: Nate & Natalie's Walk PT x x x x x Unit 3 Framework Task: Developing a Sense of Scale FAL x x x x x x Exemplars Math Volume 10 We Think Math is Really Fine PT x Exemplars Math Volume 10 At&T Choice Dilemma PT x Exemplars Math Volume 10 Cookie Caper PT x x Exemplars Math Volume 10 Dance-a-thon PT x Exemplars Math Volume 10 Gobble, Gobble, Gobble PT x x Exemplars Math Volume 10 The Sweetest Time of the Year PT x x Exemplars Math Volume 10 Tiffany's Candle Making Business PT x

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (for 6th grade students)

Unit 4: Geometric Reasoning

Solve real-world and mathematical problems involving area, surface area, and volume.MCC6.G.1 Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

MCC6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉 = 𝑙𝑤h and 𝑉 = 𝑏h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

MCC6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

MCC6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining pointsith the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

MCC7.G.3 Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (for 6th grade students)YEAR A Unit 4: Geometric Reasoning SECOND SEMESTERDay 1 Day 2 Day 3 Day 4 Day 5January 5 January 6 January 7 January 8 January 9

ProfessionalLearning

Second Semester Begins Pre-AssessmentIntroduce types of angles/

MCC.6.G.1 MCC.6.G.2

Day 6 Day 7 Day 8 Day 9 Day 10January 12 January 13 January 14 January 15 January 16

MCC.6.G.4 MCC.6.G.3

Practice writing and solving simple equations for an unknown angle in a figure.7.G.5

Practice writing and solving simple equations for an unknown angle in a figure.7.G.5

I have a secret angle taskAssessment of day 3 – day 5

Day 11 Day 12 Day 13 Day 14 Day 15January 19 January 20 January 21 January 22 January 23NO SCHOOLMLK Holiday Review polygons

7.G.2

Construct geometric shapes7.G.2

Review parts of a circle and the formulas for the area and circumference of a circle7.G.4

Real world practice of area and circumference of a circle7.G.4

Day 16 Day 17 Day 18 Day 19 Day 20January 26 January 27 January 28 January 29 January 30Real world practice of area and circumference of a circle7.G.4

Saving Sir Cumference task7.G.4

Review 3-D shapes and formulas for volume and surface area7.G.3

Practice solving real-world problems involving volume 7.G.6

Day 21 Day 22 Day 23 Day 24 Day 25February 2 February 3 February 4 February 5 February 6

Saving Sir Cumference task7.G.4

Review 3-D shapes and formulas for volume and surface area7.G.3

Practice solving real-world problems involving volume 7.G.6

Practice solving real-world problems involving surface area7.G.6 Three Little Pigs Builder task

7.G.6

Day 26 Day 27 Day 28 Day 29 Day 30February 9 February 10 February 11 February 12 February 13Review day 11 – day 15 Assessment of day 11 – day 15 Cross sections of right

rectangular prims and right rectangular pyramids7.G.3

ReviewUNIT Assessment

Next week Winter Break…

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Updated 7/16/2014February 16 Winter Break February 16 Winter Break February 16 Winter Break February 16 Winter Break February 16 Winter Break

17

Updated 7/16/2014Course: Advanced 7th Grade YEAR A (for 6th grade students)YEAR A Unit 4: Geometric Reasoning

number sense

Prerequisite Skills number sense computation with

whole numbers and decimals, including application of order of operations

addition and subtraction of common fractions with like denominators

measuring length and finding perimeter and area of rectangles and squares

characteristics of 2-D and 3-D shapes

angle measurement data usage and

representations

Key Vocabulary Additive Inverse Multiplicative Inverse Absolute Value Integers Natural Numbers Negative Numbers Opposite Numbers Positive Numbers Rational Numbers Repeating Decimal Terminating Decimal Zero Pair

Essential Questions When is it appropriate to use area, surface area, and volume? How can we find the area of figures? How can we cut and rearrange irregular polygons in order to find their area? How can we use one figure to determine the area of another? Is there a common way to calculate area? How do you know? How can shapes be combined to create new shapes? How can a shape be broken down into smaller shapes? How do we figure the area of a shape without a formula for that shape? How are the areas of geometric figures related to each other? How can the formulae for the area of plane figures be used to solve problems? How can we find the area of regular and irregular polygons when you don’t have a specific formula? How can I use manipulatives and nets to help compute the surface areas of rectangular and triangular prisms? How can I use surface areas of plane figures to derive formulas for the surface areas of solid figures? How can I use formulas to compute the surface area of rectangular and triangular prisms? What kinds of problems can be solved using surface areas of rectangular and triangular prisms? How can I interpret and sketch views of rectangular and triangular prisms? How can I construct nets for rectangular and triangular prisms? How can you model finding surface area and volume of rectangular and triangular prisms? How can I use formulas to determine the volumes of fundamental solid figures? How can I determine the appropriate units of measure that should be used when computing the volumes of a right rectangular prism? What kinds of problems can be solved using volumes of fundamental solid figures? How does the fractional edge length affect the volume of a prism? How does the volume of a prism change when using different sized cubes to measure space?

CCGPS Standards Addressed:Solve real-world and mathematical problems involving area, surface area, and volume.MCC6.G.1 Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.MCC6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉 = 𝑙𝑤h and 𝑉 = 𝑏h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.MCC6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.MCC6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining pointsith the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.MCC7.G.3 Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. MCC.7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. MCC.7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.MCC.7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.MCC.7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.MCC.7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (for 6th grade students)YEAR A

Enduring Understandings

Students will… Cross-sections of three-dimensional objects can be formed in a variety of ways, depending on the angle of the cut with the base of the object. The area of irregular and regular polygons can be found by decomposing the polygon into triangles, squares, and rectangles. “Pi” () is the relationship between a circle’s circumference and diameter. Parallelograms and rectangles can be used to derive the formula for the area of a circle. Approximate volumes of simple geometric solids may be found using estimation Formulas may be used to determine the volume of fundamental solid figures. Approximate surface area 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. Formulas may be used to compute the surface area of right rectangular prisms. Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes Solve real-world and mathematical problems involving area Decipher and draw views of rectangular and triangular prisms from a variety of perspectives Recognize and construct nets for rectangular and triangular prism Find the surface area of rectangular and triangular prisms by using manipulatives and by constructing nets Determine the surface area of rectangular and triangular prisms by substituting given values for their dimensions into the correct formulas; Solve real-world that require determining the surface area of rectangular and triangular prisms Measure and compute volume with fractional edge length using cubic units of measure Find the volumes of right rectangular prisms by substituting given values for their dimensions into the correct formulas Make the connection that finding the volume given the length (l) x width (w) is the same as the base (B) Solve real-world problems that require determining the volume of right rectangular prism Coordinate geometry can be useful tool for understanding geometric shapes and transformations

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (for 6th grade students)YEAR A

Suggested Performance Tasks

Unit 56.G.1 6.G.2 6.G.4

Unit 5 Frameworks Who Put the Tang in Tangram? XUnit 5 Frameworks Rectangle Wrap-Around XUnit 5 Frameworks What’s My Area? XUnit 5 Frameworks King Arthur’s New Table XUnit 5 Frameworks Finding Surface Area XUnit 5 Frameworks How Many Ways? XUnit 5 Frameworks Volume and Cubes XUnit 5 Frameworks Packaging Our Goods X XUnit 5 Frameworks Designing Candy Cartons X X XUnit 5 Frameworks Candle Box X X XUnit 5 Frameworks Smoothie Box X X XUnit 5 Frameworks Boxing Bracelets X XUnit 5 Frameworks Culminating Task – STEM Fish Tank Foam Packaging Design X XCovering and Surrounding (CMP) Investigation 1 XCovering and Surrounding (CMP) Investigation 2 XCovering and Surrounding (CMP) Investigation 3 X XCovering and Surrounding (CMP) Investigation 4 XCovering and Surrounding (CMP) Investigation 5 XFilling and Wrapping (CMP) Investigation 1 XFilling and Wrapping (CMP) Investigation 2 XFilling and Wrapping (CMP) Investigation 3 X

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (for 6th grade students)YEAR A Unit 5: Inequalities

MCC6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.MCC6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. MCC6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions.MCC6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MCC6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data was gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A Advanced Grade 7—Unit 5: StatisticsDay 1 Day 2 Day 3 Day 4 Day 5February 23 February 24 February 25 February 26 February 27

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Updated 7/16/2014

ProfessionalLearning Day

Unit 6 Framework

MCC6.SP.1-Learning/Scaffolding task “What is a Statistical Question?” (CCGPS Framework)

MCC6.SP.2,3,4,5-Teach mean by “leveling” and as a “balance point” using manipulatives (Van de Walle)**see resource folder in POINT-Have students ask statistical questions and have the class answer them by using manipulatives. They can work in small groups to find the mean.

MCC6.SP.2,3,4,5-Learning task “Who Was the Greatest Yankee Home Run Hitter?” (CCGPS Framework)-Guide the students through creating the first graph, then let them work independently/ small group to complete the graphs

MCC6.SP.2,3,4,5-Complete task from Day 2-Independent practice on mean, median and mode

**Give the pre-assessment in anticipation for the FAL Task

Day 6 Day 7 Day 8 Day 9 Day 10March 2 March 3 March 4 March 5 March 6

MCC6.SP.4-Quiz over measures of central tendency-Review dot/line plots (this graph is done in 3rd, 4th, and 5th grade)

MCC6.SP.2,3,4,5,5c,5d-Learning/Scaffolding task “How Long is a Minute” -Option 1: Use “Where’s Waldo?” Task and collect the data. Create the kinesthetic box plot as outlined in “How Long is a Minute” with data, then continue with task.-Option 2: Have the class collect their own data from a statistical question they generate and create the kinesthetic box plot as outlined in “How Long is a Minute”?

MCC6.SP.1,2,3,4,5-Complete task from Day 6-Create foldable:Student copyTeacher copy

-Learning/Scaffolding task “Where’s Waldo?” (You will need to make color copies of the picture for this task in order for this task to work best.)

MCC6.SP. 1,2,3,4,5-Complete task from Day 7

-Learning Task “Cost of Learning” (Spotlight Task)

MCC6.SP.1,2,3

-Formative Assessment Lesson “Mean, Median, Mode and Range”

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Updated 7/16/2014Day 11 Day 12 Day 13 Day 14 Day 15March 9 March 10 March 11 March 12 March 13

MCC6.SP.1,2,3

-Formative Assessment Lesson “Mean, Median, Mode and Range”

MCC6.SP.4,5, 5a, 5b,5c,5d

-Short Cycle Tasks “Suzi’s Company” and “Candy Bars”

MCC6.SP.2,3,4,5-Introduce MAD by completing learning/scaffolding task “How Many People Are in Your Family

MCC6.SP.2,3,4,5

-Complete task from Day 14

MCC6.SP.2,3,4,5-Continue working with Box Plots and MAD using teacher/student created data (examples: shoe sizes of students, number of times students saw a movie in a theater last year, have students guess your age and record guesses, etc)-Play “Minute to Win It” Games (Games) have students record the data and create box plots, line plots; use data to find MAD

Day 16 Day 17 Day 18 Day 19 Day 20March 16 March 17 March 18 March 19 March 20MCC6.SP.2,3,4,5-Continue working with Box Plots and MAD using teacher/student created data (examples: shoe sizes of students, number of times students saw a movie in a theater last year, have students guess your age and record guesses, etc)-Play “Minute to Win It” Games (Games) have students record the data and create box plots, line plots; use data to find MAD

Culminating Task “Order Up! Fast Food Frenzy” Part I (CCGPS Framework)

Culminating Task “Order Up! Fast Food Frenzy” Part II (CCGPS Framework)

Culminating Task “Order Up! Fast Food Frenzy” Part III (CCGPS Framework)

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A Unit 5 Inequalities

Suggested Resources and Materials www.georgiastandards.org Newspaper and magazine graphs for analysis of

the spread, shape and variation of data Hollywood Box Office This rich problem focuses

on measures of center and graphical displays. Wet Heads In this lesson, students create stem-

and-leaf plots and back-to-back stem-and-leaf plots to display data collected from an investigative activity.

Stella’s Stumpers Basketball Team Weight This problem situation uses the mean to determine a missing data element.

Learning Conductor Lessons. Use the interactive applets in these standards-based lessons to improve understanding of mathematical concepts. Scroll down to the statistics section for your specific need.

From the National Council of Teachers of Mathematics, Illuminations: Height of Students in our Class. This lesson has students creating box-and-whisker plots with an extension of finding measures of center and creating a stem-and-leaf plot.

National Library of Virtual Manipulatives . Students can use the appropriate applet from this page of virtual manipulatives to create graphical displays of the data set. This provides an important visual display of the data without the tediousness of the student hand drawing the display.

Kader, Gary D. “Means and MADs.” Mathematics Teaching in the Middle School 4.6 (1999): 398-403. Print.

Franklin, C., Kader, G., Mewborne, D., Moreno, J., Peck, R., Perry, M., Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (gaise) report: A pre-k-12 curriculum framework. Alexandria, Virginia: American Statistical Association. Print.

Essential Question

How do we represent and analyze data?

What is the best way to organize a set of data?

What kinds of graphs will best represent a given set of data?

How can I describe the center of a set of data?

How can I describe the spread of a set of data?

How can I use data to compare different groups?

How do I choose and create appropriate graphs to represent data?

What conclusions can be drawn from data?

Enduring UnderstandingsStudents will… Analyze data from many different

sources such as organized lists, box-plots, bar graphs and stem-and-leaf plots

Understand that responses to statistical questions may vary

Understand that data can be described by a single number

Determine quantitative measures of center (median and/or mean)

Determine quantitative measures of variability (interquartile range and/or mean absolute deviation)

GPS Standards Addressed:MCC6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.MCC6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.MCC6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. MCC6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.MCC6.SP.5. Summarize numerical data sets in relation to their context, such as by:MCC6.SP.5.a. Reporting the number of observations.MCC6.SP.5.b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurementMCC6.SP.5.c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.MCC6.SP.5.d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Prerequisite Skills

Analyzing patterns and seeing relationships

Fluency with operations on multi-digit numbers and decimals

Key Vocabulary

Box and Whisker Plot Frequency Grouped Frequency Table Histogram Interquartile Range (IQR) Maximum Value Mean Absolute Deviation Mean Measures of Center Measures of Spread Median Minimum Value Mode Outlier Range Stem and Leaf Plot

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 5 Inequalities

Suggested Performance Tasks

Unit 56.G.1 6.G.2 6.G.4

Unit 5 Frameworks Who Put the Tang in Tangram? XUnit 5 Frameworks Rectangle Wrap-Around XUnit 5 Frameworks What’s My Area? XUnit 5 Frameworks King Arthur’s New Table XUnit 5 Frameworks Finding Surface Area XUnit 5 Frameworks How Many Ways? XUnit 5 Frameworks Volume and Cubes XUnit 5 Frameworks Packaging Our Goods X XUnit 5 Frameworks Designing Candy Cartons X X XUnit 5 Frameworks Candle Box X X XUnit 5 Frameworks Smoothie Box X X XUnit 5 Frameworks Boxing Bracelets X XUnit 5 Frameworks Culminating Task – STEM Fish Tank Foam Packaging Design X XCovering and Surrounding (CMP) Investigation 1 XCovering and Surrounding (CMP) Investigation 2 XCovering and Surrounding (CMP) Investigation 3 X XCovering and Surrounding (CMP) Investigation 4 XCovering and Surrounding (CMP) Investigation 5 XFilling and Wrapping (CMP) Investigation 1 XFilling and Wrapping (CMP) Investigation 2 XFilling and Wrapping (CMP) Investigation 3 X

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A Unit 6: ProbabilityUnit 6: Probability

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long run relative ‐frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolledroughly 200 times, but probably not exactly 200 times.

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class,find the probability that Jane will be selected and the probability that a girl will be selected.

7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny willland heads up or that a tossed paper cup will land open end down. Do the outcomes for the spinning ‐pennyappear to be equally likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 6 Probability

Key Vocabulary:

Chance Process Compound Event Empirical Event Experimental Probability Independent events Probability Probability Model Relative Frequency of Outcomes Sample space Simple Event Simulation Theoretical Probability Tree diagram

Prerequisite Skills: number sense computation with whole numbers and decimals,

including application of order of operations addition and subtraction of common fractions with like

denominators measuring length and finding perimeter and area of

rectangles and squares characteristics of 2-D and 3-D shapes data usage and representations

Enduring Understandings: Probabilities are fractions derived from modeling real world experiments and

simulations of chance. Modeling real world experiments through trials and simulations are used topredict the

probability of a given event. Chance has no memory. For repeated trials of a simple experiment, the outcome of

prior trials has no impact on the next. The probability of a given event can be represented as a fraction between 0 and 1. Probabilities are similar to percents. They are all between 0 and 1, where a probability

of 0 means an outcome has 0% chance of happening and a probability of 1 means that the outcome will happen 100% of the time. A probability of 50% means an even chance of the outcome occurring.

If we add the probabilities of every outcome in a sample space, the sum should always equal 1.

The experimental probability or relative frequency of outcomes of an event can be used to estimate the exact probability of an event.

Experimental probability approaches theoretical probability when the number of trials is large.

Sometimes the outcome of one event does not affect the outcome of another event. (This is when the outcomes are called independent.)

Tree diagrams are useful for describing relatively small sample spaces and computing probabilities, as well as for visualizing why the number of outcomes can be large.

Simulations can be used to collect data and estimate probabilities for real situations that are sufficiently complex that the theoretical probabilities are not obvious.

Essential Questions:

Why must the numeric probability of an event be between 0 and 1?

What is the likeliness of an event occurring based on the probability near 0, ½, or 1?

How can you determine the likelihood that an event will occur?

How are the outcomes of given events distinguished as possible?

What is the difference between theoretical and experimental probability?

What is the significance of a large number of trials?

How do I determine a sample space? How can you represent the likelihood of an event

occurring? How are theoretical probabilities used to make

predictions or decisions? How can you represent the probability of

compound events by constructing models? How can I use probability to determine if a game

is worth playing or to figure my chances of winning the lottery?

What is the process to design and use a simulation to generate frequencies for compound events?

Suggested Learning Resources

See next pages for learning resources and performance tasks.

CCGPS Standards Addressed:MCC7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.MCC7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.MCC7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.MCC7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.MCC7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. MCC7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomesin the sample space which compose the event.MCC7.SP.8c Design and use a simulation to generate frequencies for compound events.

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 6 Probability

28

LT: Learning Task SP: Skills Practice Unit 6PT: Performance Task CT: Culminating Task Key Standards:FAL: Formative Assessment Lesson

SP.5 SP.6SP.7 SP.7a

SP.7b SP.8

SP.8a SP.8b SP.8c

Unit 6 Frameworks Probability?? LT xUnit 6 Frameworks Heads Win! LT x x x xUnit 6 Frameworks What are Your Chances? LT x x x xUnit 6 Frameworks Probably Graphing LT x xUnit 6 Frameworks Rolling Dice LT x x x x xUnit 6 Frameworks Number Cube Sums LT x x x x x x x xUnit 6 Frameworks Dice Game Task PT x x x x x xUnit 6 Frameworks Is It Fair? PT x x x x x xUnit 6 Frameworks Charity Fair PT x x x x xUnit 6 Frameworks Designing Simulations LT x x xUnit 6 Frameworks Conducting Simulations CT x x x xUnit 6 Frameworks Evaluating Statements about Probability FAL x x x xExemplars Math Volume 10 Double Trouble Dilemma PT xCMP: What do you Expect? Investigations 1-4 LT x x x x x x x x xCMP: Skills Practice SP x x x x x x x x x

Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 6 ProbabilityDay 1 Day 2 Day 3 Day 4 Day 5

March 23 March 24 March 25 March 26 March 27

Introduce probability, tree diagrams, and sample space7.SP. 5 7.SP.8

Practice probability, tree diagrams, and sample spaceProbability on a number line task 7.SP.5 7.SP.8

Introduce /practice probability of simple events7.SP.5 7.SP.6 7.SP.7

Introduce probability of compound events7.SP.5 7.SP.6 7.SP.7

Head Winds task7.SP.5 7.SP.6 7.SP.7

Day 6 Day 7 Day 8 Day 9 Day 10March 30 March 31 April 1 April 2 April 3

Assessment of day 2—day 77.SP.5 7.SP.6 7.SP.7

Introduce simulations7.SP.8

Continue simulations7.SP.8

Designing/Conducting Simulations 7.SP.8

Unit Assessment

SPRING BREAK SPRING BREAK SPRING BREAK SPRING BREAK SPRING BREAKApril 6 April 7 April 8 April 9 April 10

April 13 April 14 April 15 April 16 April 17REVIEW FOR GeorgiaMilestones Georgia Milestones administered April 16-28

(Content dates TBD)Day 6 Day 7 Day 8 Day 9 Day 10

April 20 April 21 April 22 April 23 April 24GeorgiaMilestones administered April 16-28

(Content Area Dates TBD)

Day 11 Day 12 Day 13 Day 14 Day 15May 3 May 4 May 5 May 6 May 7

Introduce inferences by discussing population, census, surveys, and samples 7.SP.17.SP.2

Is it Valid? task from the frameworks 7.SP.1

Measures of central tendency/mean, median, mode, and outliers 7.SP.4

Measures of central tendency/mean, median, mode, and outliers 7.SP.4

Travel Times to work task 7.SP.4

Day 16 Day 17 Day 18 Day 19 Day 20January 20 January 21 January 22 January 23 January 24

AssessmentIntroduce comparing two box plots related to two populations.7.SP.37.SP.4

Compare two box plots related to two populations.7.SP.37.SP.4

Got Friends? Task 7.SP.3 7.SP.4

Got Friends? Task 7.SP.3 7.SP.4

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A Mathematics Unit 7 Introduction to Linear Functions

Unit 7: Introduction to Linear Functions

Define, evaluate, and compare functions. MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Define, evaluate, and compare functions.MCC8.F.3 Interpret the equation y = mx + bas defining a linear function, whose graph is astraight line; give examples of functions thatare not linear.MCC8.EE.5 Graph proportional relationships,interpreting the unit rate as the slope of thegraph. Compare two different proportionalrelationships represented in different ways.MCC8.EE.6 Use similar triangles to explainwhy the slope m is the same between anytwo distinct points on a non‐vertical line inthe coordinate plane; derive the equationy = mx for a line through the origin and theequation y = mx + b for a line interceptingthe vertical axis at b.Use functions to model relationshipsbetween quantities.MCC8.F.4 Construct a function to model alinear relationship between two quantities.Determine the rate of change and initial valueof the function from a description of arelationship or from two (x , y) values,including reading these from a table or from agraph. Interpret the rate of change and initialvalue of a linear function in terms of thesituation it models, and in terms of its graphor a table of values.MCC8.F.5 Describe qualitatively thefunctional relationship between twoquantities by analyzing a graph (e.g., wherethe function is increasing or decreasing, linearor nonlinear). Sketch a graph that exhibits thequalitative features of a function that hasbeen described verbally.Investigate patterns of association in bivariate data.MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit astraight line, and informally assess the modelfit by judging the closeness of the data points to the line.MCC8.SP.3 Use the equation of a linearmodel to solve problems in the context ofbivariate measurement data, interpreting theslope and intercept.MCC8.SP.4 Understand that patterns ofassociation can also be seen in bivariatecategorical data by displaying frequencies andrelative frequencies in a two‐way table.Construct and interpret a two‐way tablesummarizing data on two categoricalvariables collected from the same subjects.Use relative frequencies calculated for rowsor columns to describe possible association between the two variables.

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 7 Introduction to Linear FunctionsCCGPS Standards:

Define, evaluate, and compare functions. MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions Use functions to model relationships between quantities.MCC8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x , y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.MCC8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.Investigate patterns of association in bivariate data.MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.MCC8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.MCC8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two‐way table. Construct and interpret a two‐way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.Understand the connections between proportional relationships, lines, and linear equations.MCC8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.MCC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.Define, evaluate, and compare functions. MCC8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Prerequisite Skills: identifying and calculating slope identifying the y-intercept creating graphs using given data analyzing graphs making predictions from a graph determining unit rate applying proportional relationships recognizing a function in various forms plotting points on a coordinate plane understanding of writing rules for sequences and number

patterns differences in graphing of discrete and continuous data attributes of similar figures computation with whole numbers and decimals,

including application of order of operations plotting points in a four quadrant coordinate plan understanding of independent and dependent variables characteristics of a proportional relationship

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 7 Introduction to Linear Functions

Key Vocabulary: Model Interpret Initial Value Qualitative

Variables Linear Non-linear Slope Rate of Change Bivariate Data Quantitative

Variables Scatter Plot Line of Best Fit Clustering Outlier Intersecting lines Origin Proportional

Relationships Slope Domain Function Graph of a

Function Range of a

Function

Enduring Understandings: Collecting and examining data can sometimes help one

discover patterns in the way in which two quantities vary. Changes in varying quantities are often related by patterns

which, once discovered, can be used to predict outcomes and solve problems.

Written descriptions, tables, graphs, and equations are useful in representing and investigating relationships between varying quantities.

Different representations (written descriptions, tables, graphs, and equations) of the relationships between varying quantities may have different strengths and weaknesses.

Linear functions may be used to represent and generalize real situations.

Slope and y-intercept are keys to solving real problems involving linear relationships.

Patterns and relationships can be represented graphically, numerically, and symbolically.

Several ways of reasoning, all grounded in sense making, can be generalized into algorithms for solving proportion problems

A function is a specific type of relationship in which each input has a unique output.

A function can be represented in an input-output table. A function can be represented graphically using ordered

pairs that consist of the input and the output of the function in the form (input, output).

A function can be represented with an algebraic rule.

Suggested Learning Resources:https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_8_8thGrade_Unit6SE.pdf

Task Winter Is Over Heartbeats Walk the Graph Forget the Formula Heartbeats Too Mineral Samples Walking Race and Making Money Mini-Problems My Cotton Boll Data Outdoor Theater How Long Should Shoe Laces Really Be? Culminating Task: Is the Data Linear? By the Book What’s My Line? Culminating Task: Filling the Tank

CMP2F4 CMP: Thinking With Mathematical Models (Inv. 1-3) CMP: The Shapes of Algebra (Inv. 4) CMP: Say It With Symbols (Inv. 4)F5 CMP: Thinking With Mathematical Models (Inv. 2) CMP: Growing, Growing, Growing (Inv. 1-4) CMP: Frogs, Fleas, and Painted Cubes (Inv. 1-4) CMP: Say It With Symbols (Inv. 4)SP1 CMP: Samples and Populations (Inv. 4)SP2 CMP: Moving Straight Ahead (Inv. 1-4) CMP: Thinking With Mathematical Models (Inv. 2) CMP: Samples and Populations (Inv. 4)SP3 CMP: Moving Straight Ahead (Inv. 1-4)CMP: Thinking with Mathematical Models (Inv. 2-3)CMP: The Shapes of Algebra (Inv. 2-3)SP4CMP: Data About Us (Inv. 2)

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Updated 7/16/2014

Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 7 Introduction to Linear Functions

Essential Question: How can I find the rate of change from a table, graph, equation, or verbal description? How can I find the initial value from a table, graph, equations, or verbal description? How can I write a function to model a linear relationship? How can I sketch a graph given a verbal description? How can I describe a situation given a graph? How can I analyze a scatter plot? How can I create a linear model given a scatter plot? How can I use a linear model to solve problems? How can I use bivariate data to solve problems? What strategies can I use to help me understand and represent real situations involving linear relationships? How can the properties of lines help me to understand graphing linear functions? What can I infer from the data? How can functions be used to model real-world situations? How does a change in one variable affect the other variable in a given situation? Which tells me more about the relationship I am investigating – a table, a graph or an equation? Why?

How can patterns, relations, and functions be used as tools to best describe and help explain real-life relationships? How can the same mathematical idea be represented in a different way? Why would that be useful? What is the significance of the patterns that exist between the triangles created on the graph of a linear function? When two functions share the same rate of change, what might be different about their tables, graphs and equations? What might be the same?

What does the slope of the function line tell me about the unit rate? What does the unit rate tell me about the slope of the function line?

What is a function? What are the characteristics of a function? How do you determine if relations are functions? How is a function different from a relation? Why is it important to know which variable is the independent variable? How can a function be recognized in any form? What is the best way to represent a function? How do you represent relations and functions using tables, graphs, words, and algebraic equations? What strategies can I use to identify patterns? How does looking at patterns relate to functions? How are sets of numbers related to each other? How can you use functions to model real-world situations? How can graphs and equations of functions help us to interpret real-world problems?

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Updated 7/16/2014Course: Advanced 7th Grade YEAR A (6th grade) YEAR A UNIT 7 Introduction to Linear Functions

Day 1 Day 2 Day 3 Day 4 Day 5April 27 April 28 April 29 April 30 May 1

Task: Secret Codes and Number Rules

(F.1-2)

Task: Secret Codes and Number Rules

(F.1-2)

Task: *Foxes and Rabbits(Spotlight Task)

(F.1-2)

Task: Vending Machines(F.1-2) Finish Vending Machines Tasks

Day 6 Day 7 Day 8 Day 9 Day 10May 4 May 5 May 6 May 7 May 8

Task: Order Matters(F.1-2)

Task:*Battery Charging(Spotlight Task)

(F.1-2)

Task: Which is Which?(F.1-2)

Task: Which is Which?(F.1-2)

FAL: Modeling Situations with Linear Equations

Day 11 Day 12 Day 13 Day 14 Day 15May 11 May 12 May 13 May 14 May 15

FAL: Modeling Situations with Linear Equations

(F.1-2)

Assign Culminating TaskSorting Functions

(Due Friday 12/12/14)(F.1-2)

ReviewPractice/Quiz

(F.1-2)Task: Creating Matching

Function Cards(F.1-2)

Task:By the Book(EE.5-6. F.3)

Review(EE.5-6. F.3)

Assessment

Day 16 Day 17 Day 18 Day 19 Day 20May 18 May 19 May 20 May 21 May 22

Assign Culminating Task: Filling the Tank

Task: *UP(Spotlight Task)

(EE.5-6. F.3)

Task: *Starburst Wrapper Dress(Spotlight Task)

(EE.5-6. F.3)

Direct Instruction: Slope, Finding the rate of change from a

pattern(EE.5-6. F.3)

Task: *UP(Spotlight Task)

(EE.5-6. F.3)

MEMORIAL DAY Day 21 Day 22 Day 23 Day 24May 25 May 26 May 27 May 28 May 29

NO SCHOOL

Review(EE.5-6. F.3)

Assign Culminating Task: Filling the Tank

Review(EE.5-6. F.3)

Work independently on culminating task

Culminating Task Presentations

Final Exam Project Presentations

LAST DAY of SCHOOL

Final Exam Project PresentationsAdditional Summer assignment will be assigned and assessed.

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