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Yearly Math Plans

Scope and Sequence Map

Domains, Content Clusters, & Standard Numbers

Units of Study (expected proficiency)

1st nwks 2ndnwks 3rdnwks 4thnwks

Ratios and Proportional Relationships (RP)

Understand ratio concepts and use ratio reasoning to solve problems: 1, 2, 3

3

The Number System (NS)

Apply and extend previous understandings of multiplication and division to divide by fractions: 4

Compute fluently with multi-digit numbers and find common factors and multiples: 5, 6, 7

Apply and extend previous understandings of numbers to the system of rational numbers: 8, 9, 10, 11

1, 2 4

Expressions and Equations (EE)

Apply and extend previous understandings of arithmetic to algebraic expressions: 12, 13, 14, 15

Reason about and solve one-variable equations and inequalities: 16, 17, 18, 19

Represent and analyze quantitative relationships between dependent and independent variables: 20

6 7

Geometry (G)

Solve real-world and mathematical problems involving area, surface area, and volume: 21, 22, 23, 24

5

Statistics and Probability (SP)

Develop understanding of statistical variability: 25, 26, 27

Summarize and describe distributions: 28, 29

8

Units of Study

Unit 1- The Number System Indicators of Proficiency

Standards COS #

CCSS #

Basic Proficient Advanced

Fluently divide multi-digit numbers using the standard algorithm

5 6-NS2

Divide single digit divisors with friendly numbers

Divide whole numbers Divide whole numbers with 2-digit divisors & 3+ dividends

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6 6-NS3

Add/subtract decimals

Add/subtract/multiply decimals

Add/subtract

Multiply/divide decimals

Instructional Recommendations / Resources:

Include basic mean, median, mode vocabulary and computation

Unit 2- Fractions Indicators of Proficiency

Standards COS #

CCSS #


Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

7 6-NS4

Find GCF or LCM Find GCF and LCM Find GCF and LCM

Apply distributive property

Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem.

4 6-NS1

Divide fractions Divide fractions with word problems

Divide fractions with word problems and model


Unit 3- Ratios and Proportional Reasoning Indicators of Proficiency

Standards COS #

CCSS #


Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities.

1 6-RP1

Define and write ratios

Understand ratios Apply ratios

Understand the concept of a unit rate associated with a ratio a:b withb 0, and use rate language in the context of a ratio relationship.

2 6-RP2

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.

a) 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.

b) Solve unit rate problems including those involving unit pricing and constant speed.

c) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means times the quantity); solve problems involving finding the whole, given a part and the percent.

d) Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

3 6-RP3 Define and write unit rates. Solves simple rate problems.

Knows different units within a measurement system.

Understand unit rates and can use them to solve problems.

Can solve a proportion. using percent.

Knows and converts between different units within a measurement

Develop unit rates to solve mathematical situations.

Write and solve a proportion using percent.

Applies ratio reasoning with

Unit 3- Ratios and Proportional Reasoning Indicators of Proficiency

Standards COS #

CCSS #


system. measurements to real world situations.


Unit 4- The Number System - Integers Indicators of Proficiency

Standards COS #

CCSS #


Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts explaining the meaning of 0 in each situation.

8 6-NS5

Understand positive / negative numbers

Use positive / negative numbers in the real world

Provide examples of positive / negative numbers.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative coordinates.

a) Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the

9 6-NS6 Identify which quadrant ordered pairs are located

Graph ordered pairs in all quadrants

Recognize reflections without graphing


Standards COS #

CCSS #


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.

b) Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

c) Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.Understand ordering and absolute value of rational numbers.

a) Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

b) Write, interpret, and explain statements of order for rational numbers in real-world contexts.

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

d) Distinguish comparisons of absolute value from statements about order.

10 6-NS7

Understand ordering and absolute value of rational numbers

Write and interpret ordering of rational numbers

Explain ordering of rational numbers in real-world contexts


Standards COS #

CCSS #


Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

11 6-NS8

Calculate distance with visual representation

Calculate distance abstractly

Create a real-world situation


Unit 5- Geometry Indicators of Proficiency

Standards COS #

CCSS #


Find the 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

21 6-G1

Determine area of regular polygons using manipulatives / drawings

Calculate the area of regular and irregular polygons using manipulatives / drawings

Use strategies to determine areas in real-world problems

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 prism with fractional edge lengths in the context of solving real-world and mathematical problems.

22 6-G2

Determine volume of rectangular prisms using manipulatives / drawings

Calculate the volume of rectangular prisms using side lengths

Use strategies to determine volume in real-world problems

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find

23 6-G3 Draw polygon based on given vertices

Find the length of a side using the coordinates

Apply strategies in real-world contexts

Unit 5- Geometry Indicators of Proficiency

Standards COS #

CCSS #


the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.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.

24 6-G4

Recognize the net shape of each 3-D figure

Find surface area using nets

Apply use of 3-D nets to develop formulas


Unit 6- Algebraic Expression & Inequalities Indicators of Proficiency

Standards COS #

CCSS #


Write and evaluate numerical expressions involving whole-number exponents.

12 6-EE1Write and evaluate expressions

Use PEMDAS with exponents

Use PEMDAS with more operators

Write, read, and evaluate expressions in which letters stand for numbers.

a) Write expressions that record operations with numbers and with letters standing for numbers.

b) Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

c) Evaluate expressions at

13 6-EE2 Know vocabulary; evaluate simple expressions

Know vocabulary; write, identify and evaluate expressions

Solve expressions with parentheses and expoents

Unit 6- Algebraic Expression & Inequalities Indicators of Proficiency

Standards COS #

CCSS #


specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).Apply the properties of operations to generate equivalent expressions.

14 6-EE3Identify the properties

Identify and use the properties

Apply properties

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

15 6-EE4

Recognize that two expressions can be equivalent

Understand that two expressions can be equivalent

Give example of equivalent expressions


Includes Order of Operations

Unit 7- Equations, Inequalities, Basic Functions Indicators of Proficiency

Standards COS #

CCSS #


Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

16 6-EE5

Understand the difference b/n equalities and inequalities

Substitute whole numbers

Understand equality /inequality

Substitute integers

Substitute rational numbers

Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can

17 6-EE6 Variable represents an unknown number

Use and write variables to represent unknowns

Apply to real-world situations

Unit 7- Equations, Inequalities, Basic Functions Indicators of Proficiency

Standards COS #

CCSS #


represent an unknown number or, depending on the purpose at hand, any number in a specified set.Solve real-world and mathematical problems by writing and solving equations of the form x + p = q andpx = q for cases in which p, q, and xare all nonnegative rational numbers.

18 6-EE7 Solve one-step equations using addition / subtraction

Write and solve addition / subtraction/ multiplication one step equations

Write and solve addition / subtraction and multiplication /division one step equations

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

19 6-EE8

Recognize that inequalities have multiple solutions

Write and graph inequalities

Be able to explain the concept of inequalities and apply to real life situations

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.

20 6-EE9

Understand that the output depends on the input

Make input / output table; express relationship as an equation

Demonstrate a situation where dependent and independent variables interact


Unit 8- Statistics & Probability Indicators of Proficiency

Standards COS #

CCSS #


Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the

25 6-SP1 Brainstorm statistical questions

Recognize statistical questions

Create question

Unit 8- Statistics & Probability Indicators of Proficiency

Standards COS #

CCSS #


answers.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.

26 6-SP2

Understand that data collected has variability

Data has a center spread, overall shape

Analyze or predict graph

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.

27 6-SP3

Understand / identify measures of center and variation

Calculate measures of center and variation

Apply measures of center and variation

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

28 6-SP4Display data on a number line and dot plot

Number line, dot plot, histograms; investigate box plots

Create box plots

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 were 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 were gathered.

29 6-SP5

Collect data; use one type of plot

Collect data; describe and represent with plots and graphs

Describe in more detail the outcomes of investigations


Correlation of Standards

Standards Key AL COS #

CCSS # HCS Unit #

Ratios and Proportional Relationships

Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. 1 6-RP1 3

Understand the concept of a unit rate associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. 2 6-RP2 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.

a) 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.

b) Solve unit rate problems including those involving unit pricing and constant speed.

c) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means times the quantity); solve problems involving finding the whole, given a part and the percent.

d) Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

3 6-RP3 3

The Number System

Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem.

4 6-NS1 2

Fluently divide multi-digit numbers using the standard algorithm 5 6-NS2 1Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 6 6-NS3 1

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

7 6-NS4 2

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts explaining the meaning of 0 in each situation.

8 6-NS5 4


CCSS # HCS Unit #

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative coordinates.

a) Recognize opposite signs of numbers as indicating 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.

b) Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

c) Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

9 6-NS6 4

Understand ordering and absolute value of rational numbers.

a) Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

b) Write, interpret, and explain statements of order for rational numbers in real-world contexts.

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

d) Distinguish comparisons of absolute value from statements about order.

10 6-NS7 4

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

11 6-NS8 4

Expressions and Equations

Write and evaluate numerical expressions involving whole-number exponents. 12 6-EE1 6Write, read, and evaluate expressions in which letters stand for numbers.

a) Write expressions that record operations with numbers and with letters standing for numbers.

b) Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

c) Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the

13 6-EE2 6


CCSS # HCS Unit #

conventional order when there are no parentheses to specify a particular order (Order of Operations).Apply the properties of operations to generate equivalent expressions. 14 6-EE3 6Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 15 6-EE4 6

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

16 6-EE5 7

Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set.

17 6-EE6 7

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers.

18 6-EE77

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 chave infinitely many solutions; represent solutions of such inequalities on number line diagrams.

19 6-EE8 7

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.

20 6-EE9 7

Geometry

Find the 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

21 6-G1 5

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 prism with fractional edge lengths in the context of solving real-world and mathematical problems.

22 6-G2 5

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

23 6-G3 5

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.

24 6-G4 5

Statistics and Probability


CCSS # HCS Unit #

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 25 6-SP1 8

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. 26 6-SP2 8

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.

27 6-SP3 8

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 28 6-SP4 8

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 were 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 were gathered.

29 6-SP5 8

Special Notes

The 6th grade Advanced Math curriculum will follow all of the 6th grade Math curriculum as well as standards 1-16, 20-22, and 30 from the 7th grade Math curriculum. See the 7th grade Math curriculum document for further details regarding those standards.

This local curriculum document was developed from the 2010 Alabama Course of Study for Mathematics which was itself based on the newly adopted Common Core State Standards for Mathematics. State COS standards are keyed to CCSS (i.e. Common Core) standards using the lettering and number system employed by the CCSS so that instructional resources which are subsequently designed to support the CCSS can be easily matched back to lessons based on state and local requirements.

The Standards for Mathematical Practice describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students. These standards were developed with input from the National Council of Teachers of Mathematics and the National Research Council, and math teachers should reinforce these process skills when designing daily instructional lessons for students at all grade levels in the Hoover school system:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

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