grade6 scopesequence math

6th Grade Mathematics-Quarter 1

Focus Clusters: 6.RP Understand ratio concepts and use ratio reasoning to solve problems.

Unit Clusters:6.RP Understand ratio concepts and use ratio reasoning to solve problems. (Unit 1)6.NS Compute fluently with multi-digit numbers and find common factors and multiples. (Overall)

Foundational: Compute fluently with multi-digit numbers and find common factors and multiples. [Specifically 6.NS.2, 6.NS.3, 6.NS.4 these standards should be taught throughout this quarter to support mathematical fluency and to support instruction of ratios and fractions.]6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. [Connected to TN Standards: SPI 0606.2.3 Solve problems involving the addition, subtraction, multiplication, and division of decimals. SPI 0606.2.4 Solve multistep arithmetic problems using fractions, mixed numbers, and decimals. Reference 5.NBT.6 for 5th grade foundational]6.NS.4 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. For example, express 36 + 8 as 4(9+2). [Second portion of 6.NS.4 to be covered leading up to the cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. Reference 4.OA,4 for foundational skill from previous grade.]5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. [Foundational skill for finding missing values in rate tables.] Fluently multiply and divide with all multiples of 1-12. Multiplication with fractions (5.NF.3, 5.NF.4a, 5.NF.4b, 5.NF.5a, 5.NF.5b, 5.NF.6)

UnitCCSSMLearning Targets(KDE and NC Unpacked Standards)SMP emphasized(NC Unpacked Standards)Corresponding SPIs (Not Addressed by CCSSM)Corresponding EPAS Standards

Unit 0: Fraction Foundations (2 weeks)CC.4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or 1; sums > 1; differences with fractions > 1; sums of more than two fractions. (RNP 8) SMP2 Be able to write an addition or subtraction equation using a story problem, then recontextualize the answer in terms of the problem.

SMP6 Ensure all fractions have common denominators before adding or subtracting, and explain why denominators have to be equivalent in order to perform subtraction or addition operations. SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.

CC.3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. I can represent fractions on a number line. (RNP 15) I can represent the addition and subtraction of fractions on a number line. (RNP 16) SMP4 Represent addition and subtraction using number lines and compare that to representation using fraction circles.

CC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

I can use fraction circles to find the product of a whole number and a fraction. (RNP 17) I can explain that the expression a x b can be read as a groups of b (whole number x fraction). (RNP 17) I can explain the difference between multiplying a whole number of groups and a fractional number of groups. (RNP 20) I can develop a numerical algorithm for the multiplication of a fraction by a fraction. (fraction x fraction) (RNP 22) SMP1 Be able to explain what we mean when we multiply a whole number of groups and when we multiply a fractional number of groups.

SMP8 Be able to recognize a pattern when multiplying a fraction by a fraction and be able to determine that a/b x c/d = ac/bd. SPI 0606.2.1 Solve problems involving the multiplication and division of fractions.

CC.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. I can multiply a whole number and a fraction using fraction circles, drawing pictures, and using mental images. (whole number x fraction) (RNP 18) I can use a number line to multiply a fraction and a whole number. (fraction x whole number) (RNP 19) I can multiply a fraction by a fraction using an area model. (fraction x fraction) (RNP 21) I can multiply a fraction by a fraction using a number line. (fraction x fraction) (RNP 23) I can draw connections between fraction circles, number lines, and numerical algorithms to multiply a fraction by a fraction. (fraction x fraction) (RNP 24)SMP4 Be able to represent multiplication of fractions using an area model, pictures, a number line, and a numerical algorithm.

SMP5 Determine when a mathematical model (area model, picture, number line) is helpful in answering a multiplication problem with fractions. SPI 0606.2.1 Solve problems involving the multiplication and division of fractions.


Unit 1: Ratios and Rates (6 weeks)6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." For every vote candidate A received, candidate C received nearly three votes." I can write and recognize a ratio in three different forms - __:__, __ to __, and __/__. I can simplify a ratio. I can recognize a simplified ratio as being equivalent to an unsimplified ratio. I can recognize that order matters when writing a ratio. I can explain that a ratio compares two quantities. I can determine what type of ratio is given (part-to-part or part-to-whole) by analyzing the context of the situation. I can rewrite a part-to-part ratio as a part-to-whole ratio and vice versa. I can explain the difference between part-to-part ratios and part-to-whole ratios. SMP2 Students contextualize ratios using picture/model to help represent ratio situations, circle groups to reduce ratios, etc. Furthermore students explain ratios in different ways. Explain why a part-to-part is different than a part-to-whole but still can be used to describe the same set of data.

SMP6 Students should use correct format/language when talking about ratios. SPI 0606.2.6 Solve problems involving ratios, rates and percents.

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." I can identify and calculate a unit rate. I can interpret a rate using ratio language. I can take a real-world ratio and put it in the context of a rate. SMP2 Contextualize a ratio as a rate; interpret a rate. SMP6 Students attend to precise language when describing rate as x per 1 (as opposed to a ratio).

SMP7 Students identify the structural elements of ratio and use that to determine the structural elements of rate. SPI 0606.2.6 Solve problems involving ratios, rates and percents. Basic Operations & Applications. 20-23. Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average. 24-27. Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour

6.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 6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot pairs of values on the coordinate plane. Use tables to compare ratios. I can create a table of equivalent ratios using whole numbers. I can find the missing values in a table of equivalent ratios. I can create a table of equivalent ratios given a real-world problem. I can use two different tables to compare ratios given a real-world mathematical problem. I can plot pairs of values that represent equivalent ratios on the coordinate plane. may need to save for after 6.EE.4SMP1 Given a real-world problem like At Books Unlimited, 3 paperback books cost $18. What would 7 books cost? How many books could be purchased with $54 use different representations (table, graph, equivalent ratios) to determine the solution.

SMP2 Students interpret situations, decontextualize ratio in order to operation and perform computations, then recontextualize in order to explain their solution.

SMP4 Students use graphs to model rate of change with ratios in a table.

SMP6 - Students use rate and percentage terminology accurately. Attend to precision in unit conversions (canceling units, etc.).

SMP8 - Students seek out patterns and explain patterns as ratios/rates. SPI 0606.2.1 Solve problems involving the multiplication and division of fractions.

SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.

SPI 0606.2.5 Transform numbers from one form to another (fractions, decimals, percents, and mixed numbers).Comment by Susie Phadke: Should I add learning targets that specifically address this SPI? Comment by Amy English: Can we add them to the Unit 0??? It seems like they would make more sense there. Then we can add an instructional note that this SPI should be embedded in Ratio instruction?

SPI 0606.2.6 Solve problems involving ratios, rates and percents.

Numbers: Concepts and Properties 13-15. (6.RP.3a) Recognize equivalent fractions and fractions in lowest terms

Basic Operations & Applications 13-15. (6.RP.3d) Perform common conversions (e.g., inches to feet or hours to minutes) 16-19. (6.RP.3c) Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single step percent 16-19. (6.RP.3c) Solve some routine two-step arithmetic problems 20-23. Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, and computing with a given average. 24-27. Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)

6.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. 6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? I can solve real world problems involving unit pricing by using tables of ratios, calculations of unit rates, multiplication, double-number line diagrams, or other methods. I can solve real world problems involving constant speed by using tables of ratios, calculations of unit rates, multiplication, double-number line diagrams, or other methods.

6.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. 6.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. I can explain that a percent is a ratio of a number to 100. I can use various rate/ratio strategies (tables, finding unit rate, diagrams, etc.) to find the percent of a given number. I can find a whole amount given a part and a percent in a mathematical problem. I can find a while amount given a part and a percent in a real-world problem.

6.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. 6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. I can write a ratio for a unit conversion. I can apply ratio reasoning to convert measurement units in mathematical problems. I can apply ratio reasoning to convert measurement units in real-world problems. I can determine when to use a unit conversion or its inverse when solving a problem using measurement conversion.

Instructional Notes: General Notes: An additional week of time in Quarter 1 has been left for remediation and MAP testing. Concepts from 6.NS.2, 6.NS.3, and 6.NS.4 should be integrated throughout the quarter to develop fluency. Unit 0 Notes:The first two weeks of instruction should focus on fraction foundations. Use lessons 1-8 and 15-24 from the Rational Number Project to build conceptual understanding of fractions, as well as multiplication of fractions. With a shift in CCSSM, multiplication of fractions has moved from 6th grade to 5th grade, meaning that the incoming class of 6th graders needs to have focused time on multiplication of fractions. The scope of fractional understanding in middle grades can be found in the linked document. RNP lessons can be used as-is, combined, or modified to add other tasks. With 100-minute blocks, two lessons can be taught in one class period. RNP lessons connected to 5.NF.6 with modeling multiplication of fractions will be a useful precursor to the modeling of volume using fractional unit cubes (6.G.2). Consider introducing the concept here in an exploratory way. The Pizza with Friends lesson can be used to support instruction related to the lessons RNP 5/6/7. This lesson focuses on the following practices: SMP1, SMP3, SMP4, and SMP7. Where are the Cookies? is a formative assessment related to foundational fraction concepts (4.NF, 5.NF, and 6.NS), which can be used to introduce students to a problem-based assessment. This assessment focuses on SMP1, SMP4, and SMP7. The Representing Fractions on a Number Line lesson is a lower-level fraction lesson that can be used as a resource for RTI with students who struggle to place fractions on a number line in lesson RNP 15.

Unit 1 Notes: When teaching equivalent ratios (6.RP.3a), cross multiplication is a strategy for 7th grade rigor repeated addition, multiplication, diagrams, etc. are appropriate for 6th grade. When teaching unit conversions (6.RP.3d), students will be given most conversions but will be expected to convert across English/metric and make multiple conversions. The Sharing Gasoline task can be used to teach 6.RP, while emphasizing SMP1, SMP2, and SMP4.

Sample Tasks for each CCSSM can be found on the following sites:http://map.mathshell.org/materials/index.phphttp://www.turnonccmath.net/?p=maphttp://www.illustrativemathematics.org/illustrations/330http://www.parcconline.org/samples/item-task-prototypeshttp://www.smarterbalanced.org/sample-items-and-performance-tasks/http://www.turnonccmath.net/?p=mapSample Tasks for TCAP can be found at:http://www.tn.gov/education/assessment/ach_samplers.shtml


Focus Clusters: 6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS Apply and extend previous understandings of numbers to the system of rational numbers. 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions. (Continues into Quarter 3)

Unit Clusters:6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. (Unit 2)6.NS Apply and extend previous understandings of numbers to the system of rational numbers. (Unit 2)6.G Solve real-world and mathematical problems involving area, surface area, and volume. (Unit 2)6.NS Compute fluently with multi-digit numbers and find common factors and multiples. (Unit 3)6.EE Apply and extend previous understandings of arithmetic to algebraic expressions. (Unit 3)

Foundational: 6.NS.4 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. For example, express 36 + 8 as 4(9+2). [First portion of 6.NS.4 covered during Quarter 1]5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)3.OA.5 Distributive propertyPerform operations with variables (add like terms, multiply a constant with a variable, etc.)5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [Order of operations]


Unit 2: Rational Numbers and the Coordinate Plane (6 weeks)6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fractions models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) - ad/bc). How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? I can compute the quotient of a fraction divided by a fraction. I can interpret the quotient of a fraction. I can solve word problems involving division of fractions by fractions by using multiple representations.

SMP2 Student reason abstractly by first evaluating an expression representing division of fraction by fractions. Next they contextualize their symbolic work by representing the computation using models and creating a story context for the expression.

SMP4 Use visual models and symbolic expressions and equations to represent division of a fraction by a fraction.

SMP8 After repeatedly calculating quotients, students look for structure in their calculation and use that structure to generalize (a/b)(c/d) as ad/bc. SPI 0606.2.1 Solve problems involving the multiplication and division of fractions.

SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.

6.NS.5 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. I can identify an integer and its opposite. I can use integers to represent quantities in real world situations. I can explain where zero fits into a situation represented by integers. SMP2 Contextualize negative numbers, positive numbers, and zero in real-world situations.

SMP4 Be able to draw a diagram that represents a positive integer vs. a negative integer.

SPI 0606.1.3 Use concrete, pictorial, and symbolic representation for integers.

6.NS.6 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 number coordinates. 6.NS.6a 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. I can identify a negative number as being to the left of zero and a positive number as being to the right on a horizontal number line. I can identify a negative number as being below zero and a positive number as being above zero on a vertical number line. I can identify a number and its opposite on a number line. I can recognize that the opposite of the opposite of a number is itself. I can recognize that zero is its own opposite. SMP3 Be able to explain why 3 is the opposite of -3; be able to reason why the opposite of the opposite of a number is itself.

SMP4 Be able to model a number on the number line based on its sign.

SMP6 When graphing points, be able to place them on the number line or coordinate plane correctly.

SMP7 Observe patterns in graph when changing the sign of the coordinate, then create a rule that applies to the changing sign.

Graphical Representations 16-19. Locate points on the number line and in the first quadrant. 20-23. Locate points in the coordinate plane.

6.NS.6 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 number coordinates. 6.NS.6b 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. I can recognize that the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located. I can reason that when only the x value in a set of ordered pairs are opposites, it creates a reflection over the y axis, e.g., (x, y) and (-x, y). I can recognize that when only the y value in a set of ordered pairs are opposites, it creates a reflection over the x axis, e.g., (x, y) and (x, -y). I can reason that when two ordered pairs differ only by signs, the locations of the points are related by reflections across both axes, e.g. (-x, -y) and (x, y).

6.NS.6 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 number coordinates. 6.NS.6c 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. I can find and position rational numbers on a horizontal or vertical number line diagram. I can find and position pairs of integers and other rational numbers on a coordinate plane. SPI 0606.1.3 Use concrete, pictorial, and symbolic representation for integers.

SPI 0606.2.7 Locate positive rational numbers on the number line.

SPI 0606.2.8 Locate integers on the number line.

6.NS.7 Understand ordering and absolute value of rational numbers. 6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right. I can order rational numbers on a number line. I can interpret statements of inequality as statements about relative position of two numbers on a number line diagram. SMP2 Be able to contextualize that a balance of -$57 is less than a balance of -$48, but using absolute value, a person who has a balance of -$57 owes more money.

SMP4 Be able to use the placement of numbers on a number line to create an inequality statement. Be able to use the number line to demonstrate absolute value as the distance of a number from zero.

SMP7 Be able to recognize patterns when writing inequalities to compare positive/positive numbers, positive/negative numbers, and negative/negative numbers. Numbers: Concepts and Properties 20-23. Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor.

6.NS.7 Understand ordering and absolute value of rational numbers. 6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3C > -7C to express the fact that -3C is warmer than -7C. I can write statements of order for rational numbers in real-world contexts. I can interpret statements of order for rational numbers in real-world contexts. I can explain statements of order for rational numbers in real-world contexts.

6.NS.7 Understand ordering and absolute value of rational numbers. 6.NS.7c 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. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars. I can find the absolute value of a rational number and interpret it as distance from 0 on a number line. I can interpret absolute value as a magnitude for a positive or negative quantity in a real-world situation.

6.NS.7 Understand ordering and absolute value of rational numbers. 6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars. I can tell the difference between of absolute value and statements of order and apply to real-world contexts.

6.NS.8 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. I can solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. I can use the coordinates and absolute value to find the distance between points that have the same first or second coordinate. SMP1 Find distances using coordinates, and check answers using a diagram. Be able to reason why an answer is wrong (achieved by a wrong operation) after checking with a diagram.

SMP2 Be able to use absolute value to calculate side length, then put calculations in context of the problem.

SMP4 Use the graphed coordinates to model the shape and find distances.

SMP6 Use mathematical algorithms accurately when adding or subtracting numbers (especially fractions). Accurately graph on a variety of scales. SPI 0606.3.9 Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.

Graphical Representations 16-19. Locate points on the number line and in the first quadrant. 20-23. Locate points in the coordinate plane.

6.G.3 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. I can draw polygons in the coordinate plane given the coordinates of the vertices. I can use coordinates (with the same first or coordinate or the same second coordinate) to find the length of a side of the polygon. I can find the coordinates of a missing vertex using the properties of a shape. I can apply the techniques of finding side lengths with coordinates to solve real-world problems like finding area and perimeter. may need to save for after 6.G.1.SMP1 Use mathematical algorithm to find the area of a shape, then make sense of the answer by approximating/ checking the number of squares. When asked to find area, be able to make sense of the information given in the problem (e.g., coordinates), create a logical series of steps (find side lengths, then put in formula), and calculate the answer.

SMP4 Draw out the sketch of a shape to help determine where the missing vertex should be.

SMP7 Use known properties of triangles/rectangles to find the missing vertex. SPI 0606.2.2 Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers. Foundational SPI for this standard.Graphical Representations 20-23. Locate points in the coordinate plane.


Unit 3: Expressions and Equivalence (4 weeks)6.NS.4 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. For example, express 36 + 8 as 4(9+2). I can apply the distributive property to rewrite addition problems by factoring out the Greatest Common Factor of two whole numbers 1-100 and multiplying the Greatest Common Factor by the sum of the two remaining factors. SMP2 Apply skills of finding GCF of a pair of numbers to rewrite as a product of a sum. Attend to precision. Be diligent in finding the GCF, not just any factor of a pair of numbers.

SMP5 Find GCF of numbers without use of a calculator (or use a calculator only to check an initial guess for GCF).

SMP7 Use patterns of pairs of numbers to find factors. (ex., a pair of even numbers will be divisible by the number 2, etc.)Numbers: Concepts and Properties 20-23. Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor. 24-27. Find and use the least common multiple. 24-27. Work with numerical factors.

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. I can write numerical expressions involving whole number exponents. I can evaluate numerical expressions involving whole number exponents (as repeated multiplication). I can solve order of operations problems that contain exponents. SMP7 Recognize the pattern of exponents as repeated multiplication, and be able to solve. Expressions, Equations, & Inequalities 16-19. Substitute whole numbers for unknown quantities to evaluate expressions. 20-23. Evaluate algebraic expressions by substituting integers for unknown qualities. 20-23. Add and subtract simple algebraic expressions. 24-27. Identify solutions to simple quadratic equations.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "subtract y from 5" as 5 - y. I can use numbers and variables to write an algebraic expression. I can translate an algebraic expression into a written phrase. SMP6 Ensure accuracy in the order of numbers and variables when writing an algebraic expression.

SMP7 Use consistency in phrases to determine when words stand for a certain mathematical symbol. SPI 0606.3.5 Translate between verbal expressions/sentences and algebraic expressions/equations.

Expressions, Equations, & Inequalities 16-19. (6.EE.2c) Substitute whole numbers for unknown quantities to evaluate expressions. 20-23. (6.EE.2c) Evaluate algebraic expressions by substituting integers for unknown quantities. 20-23. Add and subtract simple algebraic expressions.

Measurement 20-23. (6.EE.2c) Use geometric formulas when al necessary information is given.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2b 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. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. I can identify parts of an expression using mathematical terms (sum, difference, product, factor, quotient, term, constant, variable, coefficient). I can identify parts of an expression as a single entity. I can model algebraic expressions using algebra tiles. SMP2 Be able to reason why the numerator of a fraction or a quantity in parentheses could be considered a single entity. Be able to reason why the coefficient of a variable x is 1, not 0.

SMP6 Use correct terminology consistently when referring to different parts of mathematical terms.

SMP7 Recognize the pattern between a term and the symbol used to represent it. SPI 0606.1.5 Model algebraic expressions using algebra tiles.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2c 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 conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V=s and A= 6s to find the volume and surface area of a cube with sides of length s=1/2. I can substitute specific values for variables in an algebraic expression and evaluate the expression. I can apply the order of operations when there are no parentheses for expressions that include whole number exponents. I can evaluate algebraic expressions in formulas from real-world problems. Emphasis with order of operations in 6th grade is exponents. SMP2 Be able to explain where there are single entities within an expression, and evaluate the expression accordingly.

SMP5 Use calculators in conjunction with order of operations to ensure answers are accurate. (Calculators should be used strategically with specific types of numbers, and work should be shown to support understanding of order of operations.)

SMP7 Make use of order of operations when evaluating expressions. SPI 0606.3.2 Use order of operations and parentheses to simplify expressions and solve problems.

SPI 0606.2.4 Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. I can generate equivalent expressions using the distributive property. I can generate equivalent expressions using the associative property. I can generate equivalent expressions using other properties of operations (addition property of equality, commutative properties of addition/multiplication, multiplicative property of identity, etc.)SMP1 Be able to make sense of why variables cannot be subtracted from constants.

SMP2 Be able to expand upon previous knowledge of finding GCF to find GCF in terms with variables.

SMP8 Be able to create rules for repeated addition of variables or multiplication of variables by a constant.

SPI 0606.1.4 Select the representation that models one of the arithmetic properties (commutative, associative, or distributive).

SPI 0606.3.4 Rewrite expressions to represent quantities in different ways.

Numbers: Concepts and Properties 24-27. Work with numerical factors. Expressions, Equations, & Inequalities 24-27. Add and subtract simple algebraic expressions.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. I can recognize when two expressions are equivalent. I can prove (using various strategies) that two equations are equivalent no matter what number is substituted. SMP3 Use substitution to show that two expressions are equivalent and be able to refute a false argument.

SMP4 Use algebra tiles to model equivalent expressions and prove that they are equivalent. SPI 0606.1.5 Model algebraic expressions using algebra tiles.

Expressions, Equations, & Inequalities 16-19. Combine like terms (e.g., 2x + 5x). 20-23. Add and subtract simple algebraic expressions.

Instructional Notes: General Notes:Unit 3 should be split over Quarters 2 and 3. Teach and assess 6.NS.4, 6.EE.1 and 6.EE.2 before winter break, then teach and assess 6.EE.3 and 6.EE.4 after the break.

Unit 2 Notes:When teaching division of a fraction by another fraction (6.NS.1), students should model first, then compute, in order to develop conceptual reasoning. Lessons 25-28 from the Rational Number Project can be used to help teach division of a fraction by a fraction.

Unit 3 Notes: SPI 0606.3.2 is a dropped SPI, but seems to be relevant in this objective as foundational knowledge. When teaching 6.NS.4, focus on the second half of the objective in preparation for teaching 6.EE.3When teaching 6.EE.1, note that the NC Unpacking Curriculum document expresses that students should be able to write expressions with variables as well as with numbers.The Laws of Arithmetic activity is a good formative assessment to determine whether students understand how to identify equivalent expressions, and whether they can apply properties of operations to create those equivalent expressions. This activity applies to SMP1, SMP5, and SMP7. It requires students to have the basic skill of finding the area of a rectangle, which is addressed in 6.G.1, but is also learned in previous grades. Algebra tiles are an effect way to help students make sense of how to manipulate algebraic expressions and equations. Note SPI 0606.1.5 Model algebraic expressions using algebra tiles.



Focus Clusters: 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions. (Continued from Quarter 2)6.EE Reason about and solve one-variable equations and inequalities. 6.EE Represent and analyze quantitative relationships between dependent and independent variables.

Unit Clusters:6.G Solve real-world and mathematical problems involving area, surface area, and volume. 6.EE Reason about and solve one-variable equations and inequalities. 6.EE Represent and analyze quantitative relationships between dependent and independent variables.

Foundational: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.6.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. 6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot pairs of values on the coordinate plane. Use tables to compare ratios.5.MD.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent three-fold whole-number products as volumes, e.g., to represent the associative property of multiplication.Be able to define an equation as two sides having equal value.


Unit 4: Geometry Area, Surface Area, and Modeled Volume (3 weeks)6.G.1 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. I can compose and decompose special quadrilaterals and polygons using triangles and rectangles. I can find the area of special quadrilaterals and polygons by composing and decomposing them with triangles and rectangles. I can compare the area of a triangle to the area of a composed rectangle. I can discuss, develop, and justify formulas for triangles and parallelograms. Note: 6th grade is an introduction to justifying/proving these formulas.SMP2 Be able to reason how to divide polygons into easy-to-find areas, but then realize that the separate areas are just a tool to find the entire sum.

SMP3 Be able to create a viable argument for the area of a triangle based on the formula for area of a rectangle.

SMP4 Use diagrams to explore formulas for triangles and parallelograms. Measurement 24-27. Compute the area of triangles and rectangles when one or more additional simple steps are required.

6.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 = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. I can calculate the volume of a right rectangular prism. I can apply volume formulas for right rectangular prisms to solve real-world and mathematical problems involving rectangular prisms with fractional edge lengths. I can model the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths. SMP2 Be able to make comparisons between a unit cube of 1 x 1 x 1 and a unit cube that is x x . Apply comparisons to finding volume of prisms with fractional side lengths.

SMP4 Use unit cubes in a model to support the mathematical calculation volume in a rectangular prism with fractional edge lengths.

SMP7 Be able to recognize a pattern in calculating volume of a rectangular prism with fractional edge lengths and use that pattern to make calculations. SPI 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.

SPI 0606.2.1 Solve problems involving the multiplication and division of fractions.

6.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. I can represent three-dimensional figures using nets made up of rectangles and triangles. I can use nets to find the surface area of three-dimensional figures. I can solve real-world and mathematical problems involving surface area using nets. SMP1 Be able to find surface area using formulas and compare to surface area as found by nets.

SMP4 Be able to draw/visualize a net for any pyramid or prism.

SMP5 Use a net as a tool to find surface area of a prism or pyramid. SPI 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders.

CCSSMLearning Targets(KDE and NC Unpacked Standards)SMP emphasized(NC Unpacked Standards)Corresponding SPIs (Not Addressed by CCSSM)Corresponding EPAS Standards

Unit 5: Expressions, Equations and Inequalities Writing, Solving, Proving (4 weeks)6.EE.6 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. I can recognize that a variable can represent an unknown number, or, depending on the purpose, any number in a specified set. I can relate variables to a context in a real-world problem. I can write expressions when solving a real-world or mathematical problem. SMP2 Write a mathematical equation or expression for a real-world scenario, then be able to explain the meaning of the variable and the equation in context of the scenario. SPI 0606.3.5 Translate between verbal expressions/sentences and algebraic expressions/equations.

Expressions, Equations, & Inequalities 13-15. Solve equations in the form of x + a = b, where a and b are whole numbers or decimals. 16-19. Solve one-step equations having integer or decimal answers. 20-23. Solve routine first-degree equations. 20-23. Perform straightforward word-to-symbol translations. 24-27. Solve real-world problems using first-degree equations.

6.EE.5 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. I can recognize solving an equation or inequality as a process of answering the question: which values from a specified set, if any, make the equation or inequality true? I can show that the solution set of an equation or inequality is the set of values that makes the equation/inequality true. I can use substitution to determine whether a given number in a specified set makes an equation or inequality true. SMP3 Be able to use substitution to prove that a solution makes an equation or inequality true. Be able to use counterexamples to disprove any solutions.

Expressions, Equations, & Inequalities 13-15. Solve equations in the form of x + a = b, where a and b are whole numbers or decimals. 16-19. Solve one-step equations having integer or decimal answers. 20-23. Solve routine first-degree equations. 24-27. Solve real-world problems using first-degree equations.

6.EE.7 Solve real-world or 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 numbers. I can define an inverse operation. I can show how inverse operations can be used in solving one-variable equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. I can develop a rule for solving one-step equations using inverse operations with non-negative rational coefficients. I can write and solve equations for real-world mathematical problems containing one unknown. SMP1 Use inverse operations to solve a mathematical problem, then be able to reason that the answer is correct (or possibly incorrect if an error is made) using substitution. Be able to persevere and recheck answers if a solution is not correct after checking.

SMP4 Use pictures to model solutions to equations. For example, when solving x + 3 = 12, model that x must be 9 objects in order to create an equal number of objects on both sides of an equal sign. For 3x = 18, each of the three groups on the right side must have 6 objects in order to total 18 objects.

SMP8 Be able to make a rule or generalization about using inverse operations to solve an equation. SPI 0606.3.3 Write equations that correspond to given situations or represent a given mathematical relationship.

Expressions, Equations, & Inequalities 13-15. Solve equations in the form of x + a = b, where a and b are whole numbers or decimals. 16-19. Solve one-step equations having integer or decimal answers. 20-23. Solve routine first-degree equations. 24-27. Solve real-world problems using first-degree equations.

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. I can identify the constraint or condition in a real-world or mathematical problem in order to set up an inequality. I can write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. I can recognize that inequalities of the form x > c or x < c have infinitely many solutions. I can represent solutions to inequalities of the form x > c or x < c with infinitely many solutions on a number line diagram. SMP2 Be able to explain why an inequality fits the constraints of a real-world problem.

SMP4 Be able to model an inequality on a number line and explain how that model accounts for an infinite number of solutions. Expressions, Equations, & Inequalities 20-23. Perform straightforward word-to-symbol translations.

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 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. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. I can define independent and dependent variables (in an equation, a graph, and a table). I can use variables to represent two quantities in a real-world problem that change in relationship to one another. I can write an equation to express one quantity (dependent) in terms of the other quantity (independent). I can analyze the relationship between the dependent variable and independent variable using tables and graphs. I can relate the data in a graph or table to the corresponding equation (ex. by writing an equation based on a table. SMP2 Be able to explain how a change in the graph relates to the context of a real-world problem.

SMP4 Use a graph or table to model change as shown in an equation with two variables.

SMP6 Be able to accurately describe/identify independent and dependent variables. Accurately graph quantities on a variety of scales.

Expressions, Equations, & Inequalities 24-27. Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions).

Instructional Notes: General Notes:Unit 3 should be split over Quarters 2 and 3. Teach and assess 6.NS.4, 6.EE.1 and 6.EE.2 before winter break, then teach and assess 6.EE.3 and 6.EE.4 after the break.

Unit 4 Notes:The Optimizing: Security Cameras activity can be used to teach 6.G.1 and to reinforce 6.RP.1. This activity emphasizes SMP1, SMP2, SMP3, and SMP4. 6.G.2 can be used to reinforce 6.EE.1 with exponent concepts. The Candy Carton activity can be used to teach 6.G.4, and it emphasizes SMP1, SMP2, and SMP4

Unit 5 Notes: SPI 0606.4.5 is a dropped SPI, but has relevance to the CCSSM standards 6.G.2 and 6.G.4. Notation differences between > and should be taught in 6.EE.8. Sample Tasks for each CCSSM can be found on the following sites:http://map.mathshell.org/materials/index.phphttp://www.turnonccmath.net/?p=maphttp://www.illustrativemathematics.org/illustrations/330http://www.parcconline.org/samples/item-task-prototypeshttp://www.smarterbalanced.org/sample-items-and-performance-tasks/http://www.turnonccmath.net/?p=mapSample Tasks for TCAP can be found at:http://www.tn.gov/education/assessment/ach_samplers.shtml


Focus Clusters: 6.RP Understand ratio concepts and use ratio reasoning to solve problems. 6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS Apply and extend previous understandings of numbers to the system of rational numbers. 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions.6.EE Reason about and solve one-variable equations and inequalities. 6.EE Represent and analyze quantitative relationships between dependent and independent variables.

Unit Clusters:6.SP Develop understanding of statistical variability. 6.SP Summarize and describe distributions.

Foundational: Calculating averages reinforce long division from 6.NS.2


Unit 6: Statistical Questions, Displays, and Measures (2 weeks)6.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. I can recognize that data has variability. I can recognize a statistical question (vs. a non-statistical question) by checking for variability in the answer to the question. SMP3 Be able to explain why a question is statistical or non-statistical. Be able to change a non-statistical question into a statistical question.

6.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. I can recognize that a set of data has a distribution. I can describe a set of data by its center (e.g., mean and median). Note: mode does not need to be addressed based on CCSS. I can describe a set of data by its spread and overall shape (e.g. by identifying data clusters, peaks, gaps, symmetry, and range). SMP4 Be able to describe the center and shape of a representation of data

SMP6 Use accurate vocabulary to describe different measures of center. Probability, Statistics, & Data Analysis 13-15. Calculate the average, given the frequency counts of all the data values. 16-19. Calculate the average of a list of numbers. 16-19. Calculate the average, given the number of data values and the sum of the data values. 20-23. Calculate the missing data value, given the average and all data values but one. 24-27. Calculate the average, given the frequency counts of all the data values.

6.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. I can recognize that measures of center for a data set summarize its values with a single number. I can recognize that measures of variance for a data set (e.g., range, interquartile range, mean absolute deviation) describe how its values vary with a single number. SMP2 Be able to explain the difference between the two types of measure, and relate each type of measure to a graphical representation of a set of data.

SMP6 Use correct terminology for each type of measure of center or variance and be able to calculate it accurately. Probability, Statistics, & Data Analysis 13-15. Calculate the average, given the frequency counts of all the data values. 16-19. Calculate the average of a list of numbers. 16-19. Calculate the average, given the number of data values and the sum of the data values. 20-23. Calculate the missing data value, given the average and all data values but one. 24-27. Calculate the average, given the frequency counts of all the data values.

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. I can identify the components of a dot plot and display a set of numerical data using a dot plot. I can identify the components of a histogram and display a set of numerical data using a histogram. I can find the median, quartile, and interquartile range of a set of data and display it with a box plot. SMP4 Convert a table of data into a visual display using a variety of plots.

SMP6 Use correct terminology for each component and be able to calculate each measure accurately. Be able to represent data accurately on a variety of scales.Probability, Statistics, & Data Analysis 13-15. Manipulate data from tables and graphs. 20-23. Translate from one representation of data to another (e.g., a bar graph to a circle graph). 24-27. Manipulate data from tables and graphs.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:6.SP.5a Reporting the number of observations. I can report the number of observations in a data set or display. SMP2 Be able to reason the effect that an outlier can have on a measure of center or variability. (An outlier can make the range greater. A high outlier can make an average higher than it is supposed to be.)

SMP3 Justify why a particular measure of center or variability was chosen to represent a set of data. Discuss why a particular outlier could have occurred based on data collection methods.

SMP5 Choose the appropriate plot for a set of data. Decide which measure of center and measure of variability best fit a set of data.

Probability, Statistics, & Data Analysis 13-15. (6.SP.5c) Calculate the average, given the frequency counts of all the data values. 13-15. Manipulate data from tables and graphs. 16-19. (6.SP.5c) Calculate the average of a list of numbers. 16-19. (6.SP.5c) Calculate the average, given the number of data values and the sum of the data values. 20-23. (6.SP.5c) Calculate the missing data value, given the average and all data values but one. 20-23. Translate from one representation of data to another (e.g., a bar graph to a circle graph). 24-27. (6.SP.5c) Calculate the average, given the frequency counts of all the data values. 24-27. Manipulate data from tables and graphs.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. I can describe a set of data being collected, including how it was measured and its units of measurement. SPI 0606.5.3 Determine whether or not a sample is biased.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:6.SP.5c 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. I can calculate measures of center for a set of data. I can calculate measures of variance for a set of data. I can identify outliers in a set of data. I can determine the effect of an outlier on measures of center and variance on a set of data. SPI 0606.1.1 Make conjectures and predictions based on data.SPI 0606.5.2 Identify features of graphs that may be misleading.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:6SP.5d 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. I can choose the appropriate measure of center to represent data. I can analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of center and variability and justify why this measure is appropriate in terms of the context.


Unit 7: TCAP Review (3 weeks)Data-driven TCAP review should happen during these three weeks. Instruction should focus on the following clusters:Primary:6.RP Understand ratio concepts and use ratio reasoning to solve problems. 6.NS Apply and extend previous understandings of numbers to the system of rational numbers. 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions.6.EE Reason about and solve one-variable equations and inequalities. Secondary: 6.NS Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.EE Represent and analyze quantitative relationships between dependent and independent variables.


Unit 8: Introduction to 7th Grade Ratios and Proportions (3 weeks)7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. I can define a complex fraction as a fraction divided by another fraction. I can write a rate as a complex fraction. I can multiply or divide a fraction by an appropriate number to create an equivalent fraction with a denominator of 1. I can calculate a unit rate from a rate that is a complex fraction. SMP6 Be able to identify the difference between a regular fraction and a complex fraction.

SMP7 Be able to recognize a pattern of how to turn a complex fraction into a unit rate. Basic Operations & Applications. 24-27. Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour)

7.RP.2 Recognize and represent proportional relationships between quantities. 7.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. I can determine whether a pair of ratios is equivalent by creating a table with one ratio and comparing the values of the table to the second ratio. I can decide whether two quantities are in a proportional relationship by graphing the ratios on a coordinate plane and observing the line. SMP3 Use the graphs to defend your reasoning of whether a pair of ratios are equivalent.

SMP8 Graph various pairs of equivalent ratios and non-equivalent ratios (as determined using the tables), and draw a conclusion about the properties of equivalent ratios in the coordinate plane based on these tests.

7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. I can calculate a unit rate given a table of data and identify it as a constant of proportionality. I can calculate a unit rate given a graph identify it as a constant of proportionality. I can find a unit rate given an equation in the form of y = mx, and identify it as a constant of proportionality. SMP6 Be able to use the terms of unit rate and constant of proportionality correctly.

SMP7 Be able to use the structure of an equation in y=mx form to find a constant of proportionality.

7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. I can use a graph or table to identify a constant of proportionality and write an equation relating values. I can create a graph or table to represent the proportional relationship of an equation. I can use an equation to find an unknown value in a proportional relationship. SMP1 If given a real-world situation that describes a proportional relationship, be able to write an equation based on that proportional relationship, then use that equation to find a missing value in a proportional relationship.

SMP4 Model an equation with a graph or with a table.

Instructional Notes: General Notes:An additional week has been left for MAP testing, IAs, and college trips.

Unit 6 Notes:6.SP.5b is an appropriate point for cross-curricular connection to science.The Mean, Median, Mode, and Range activity can be used as a lesson or formative assessment to determine students understandings of how to calculate those statistics. This activity emphasizes SMP1, SMP2, and SMP4.

Unit 7 Notes:Unit 7 has been left open intentionally to allow teachers to use individual classroom and student data to inform which standards need to be reviewed before TCAP testing.

Unit 8 Notes:Unit 8 has been developed to introduce one of the primary concepts of 7th grade mathematics. The intent is to increase the depth of knowledge of 6th grade ratios and proportions in preparation for 7th grade. 7.RP.2c connects concepts taught in 6.RP and 6.EE.7


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