NUMBER AND OPERATIONS - FRACTIONS 4.NF.a: Understand a fraction a/b with a > as a sum of fractions /b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Accumulating unit fractions (/b) results in a fraction (a/b), where a is greater than. From the Introduction: Students extend previous understandings about how fractions are built from unit fractions, composing (joining) fractions from unit fractions, and decomposing (separating) fractions into unit fractions... I can add fractions that result in a fraction that is greater than one. I can understand that adding and subtracting fractions is the result of composing/joining and decomposing/separating the whole. *Improper fractions composing *decomposing *(Decomposition) Using fraction models, reason that addition of fractions is joining parts that are referring to the same whole. I can use fraction models to illustrate the addition of fractions. Using fraction models, reason that subtraction of fractions is separating parts that are referring to the same whole. I can use fraction models to illustrate the subtraction of fractions. NUMBER AND OPERATIONS - FRACTIONS 4.NF.b: Understand a fraction a/b with a > as a sum of fractions /b. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: /8 = /8 + /8 + /8 ; /8 = /8 + /8 ; /8 = + + /8 = 8/8 + 8/8 + /8. Add and subtract fractions with like denominators. Recognize multiple representations of one whole using fractions with the same denominator. Using visual fraction models, decompose a fraction into the sum of fractions with the same denominator in more than one way. Record decompositions of fractions as an equation and explain the equation using visual fraction models. I can add and subtract fractions with like denominators. I can identify many ways to make one whole using fractions with the same denominator. I can use models to decompose a fraction with the same denominator. I can record and demonstrate decompositions of fractions as equation and explain the equation using visual fraction models.
NUMBER AND OPERATIONS - FRACTIONS 4.NF.c: Understand a fraction a/b with a > as a sum of fractions /b. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Add and subtract mixed numbers with like denominators by using properties of operations and the relationship between addition and subtraction. Replace mixed numbers with equivalent fractions, using visual fraction models. Replace improper fractions with a mixed number, using visual fraction models. Add and subtract mixed numbers by replacing each mixed number with an equivalent fraction. I can add and subtract mixed numbers with like denominators. I can replace mixed numbers with equivalent fractions, using visual fraction models. I can replace improper fractions with mixed number, using visual fraction models. I can add and subtract mixed numbers by replacing each mixed number with an equivalent fraction. *Mixed number *Improper fraction NUMBER AND OPERATIONS - FRACTIONS 4.NF.d: Understand a fraction a/b with a > as a sum of fractions /b. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Add and subtract fractions with like denominators. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, by using visual fraction models and equations to represent the problem. I can add and subtract fractions with like denominators. I can solve word problems with addition and subtraction of fractions having like denominators visual models and equations. LCM-least common multiple GCF-greatest common factor NUMBER AND OPERATIONS - FRACTIONS 5.NF.: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with Solve addition and subtraction problems involving equivalent fractions in such a way as to produce an equivalent sum fractions (including mixed numbers) with like and or difference of fractions with like denominators. For example, / unlike denominators using an equivalent fraction + 5/4 = 8/ + 5/ = /. (In general, a/b + c/d = (ad + bc)/bd.) strategy Generate equivalent fractions to find the like denominator I can generate equivalent fractions to find the like denominator I can solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy equivalent equivalent fractions denominator numerator mixed-number improper fraction * unlike denominator * Least common multiple (LCM) * Greatest common factor (GCF)
NUMBER AND OPERATIONS - FRACTIONS 5.NF.: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result /5 + / = /7, by observing that /7 < /. Solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem) Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. I can solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem) I can evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction. * reasonable unlike denominators benchmark fraction equation * evaluate NUMBER AND OPERATIONS - FRACTIONS 5.NF.: Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret /4 as the result of dividing by 4, noting that /4 multiplied by 4 equals, and that when wholes are shared equally among 4 people each person has a share of size /4. If 9 people want to share a 50- pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer l Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (e.g. using visual fraction models or equations to represent the problem.) Interpret the remainder as a fractional part of the problem. I can interpret a fraction as division of the numerator by the denominator (a/b = a b). I can solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (e.g. using visual fraction models or equations to represent the problem.) I can interpret the remainder as a fractional part of the problem. interpret remainder fractional part numerator denominator
4 NUMBER AND OPERATIONS - FRACTIONS 5.NF.4a: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (/) 4 = 8/, and create a story context for this equation. Do the same with (/) (4/5) = 8/5. (In general, (a/b) (c/d) = ac/bd.) Multiply fractions by whole numbers. Multiply fractions by fractions Interpret the product of a fraction times a whole number as total number of parts of the whole. (for example ¾ x = ¾ + ¾ + ¾ = 9/4) Determine the sequence of operations that result in the total number of parts of the whole. (for example ¾ x = ( x )/4 = 9/4) I can multiply fractions by whole numbers. I can multiply fractions by fractions I can Interpret the product of a fraction times a whole number as total number of parts of the whole. (for example ¾ x = ¾ + ¾ + ¾ = 9/4) I can determine the sequence of operations that result in the total number of parts of the whole. (for example ¾ x = ( x )/4 = 9/4) whole number product operations Interpret the product of a fraction times a fraction as the total number of parts of the whole I can interpret the product of a fraction times a fraction as the total number of parts of the whole NUMBER SYSTEM 6.NS.: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (/) (/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (/) (/4) = 8/9 because /4 of 8/9 is /. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if people share / lb of chocolate equally? How many /4-cup servings are in / of a cup of yogurt? How wide is a rectangular strip of land with length /4 mi and area / square mi? Compute quotients of fractions divided by fractions (including mixed numbers). Interpret quotients of fractions Solving word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. I can divide fractions by fractions (including mixed numbers) to find a quotient. I can interpret the quotient of fractions. I can solve word problems (involving division of fractions by fractions) using visual representations. Fractions Mixed Numbers Quotient
5 NUMBER SYSTEM 6.NS.: Fluently divide multi-digit numbers using the standard algorithm. Fluently divide multi-digit numbers using the standard algorithm with speed and accuracy. I can divide multi-digit numbers with speed and accuracy. Accuracy Speed NUMBER SYSTEM RATIO & PROPORTIONAL RELATIONSHIPS 6.NS.: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation with speed and accuracy. I can add multi-digit decimals with speed and accuracy. I can subtract multi-digit decimals with speed and accuracy. I can multiply multi-digit decimals with speed and accuracy. Decimals I can divide multi-digit decimals with speed and accuracy. NUMBER SYSTEM 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 00 and the least common multiple of two whole numbers less than or equal to. Use the distributive property to express a sum of two whole numbers 00 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 6 + 8 as 4 (9 + ). Identify the factors of two whole numbers less than or equal to 00 and determine the Greatest Common Factor. Identify the multiples of two whole numbers less than or equal to and determine the Least Common Multiple. I can identify the factors of two whole numbers less than or equal to 00. I can determine the GCF of two whole numbers less than or equal to 00. I can identify the multiples of two whole number less than or equal to. I can determine the LMC of two whole numbers less than or equal to. Distributive Property Factors Greatest Common Factor (GCF) Least Common Multiple (LCM) Multiples Apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor I can use the Distributive Property to write addition problems by factoring out the GCF.
6 NUMBER SYSTEM Identify an integer and its opposite I can identify an integer. * Integer 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. Use integers to represent quantities in real world situations (above/below sea level, etc) Explain where zero fits into a situation represented by integers I can identify the opposite of an integer. I can use integers to represent quantities in real world situations (above/below sea level, temperature, etc ). I can explain the meaning of zero in real-world situations. Opposite Zero NUMBER SYSTEM 6.NS.6abc: 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. 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., ( ) =, 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. Identify a rational number as a point on the number line. Identify the location of zero on a number line in relation to positive and negative numbers Recognize opposite signs of numbers as locations on opposite sides of 0 on the number line Recognize the signs of both numbers in an ordered pair indicate which quadrant of the coordinate plane the ordered pair will be located 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 Reason that the opposite of the opposite of a number is the number itself. I can identify a rational number as a point on a number line. I can identify the location of zero on a number line in relation to positive and negative numbers. I can determine a number's location and its opposite in relation to zero. I can use the signs of both numbers in an ordered pair to determine the quadrant where the ordered pair is located. I can locate all rational numbers (fractions, integers) on a horizontal or vertical number line. I can graph ordered pairs (including fractions and mixed numbers) on a coordinate plane. I can explain that the opposite of the opposite of a number is the number itself. Negative Numbers Number Line Ordered Pairs Positive Numbers * Quadrants * Rational Numbers
7 NUMBER SYSTEM 6.NS.6abc: Standard (Continued) 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 apply the rule for reflecting ordered pairs across the x-axis. Reflection X-Axis 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 apply the rule for reflecting ordered pairs across the y-axis. Y-Axis 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) I can apply the rule for reflecting ordered pairs across both the x and y- axes NUMBER SYSTEM 6.NS.7abcd: 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. For example, interpret > 7 as a statement that is located to the right of 7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write C > 7 C to express the fact that C is warmer than 7 C. 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. For example, for an account balance of 0 dollars, write 0 = 0 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 0 dollars represents a debt greater than 0 dollars. Order rational numbers on a number line Identify absolute value of rational numbers Interpret statements of inequality as statements about relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation Distinguish comparisons of absolute value from statements about order and apply to real world contexts I can order rational numbers on a number line. I can identify absolute value of rational numbers. I can compare rational numbers. I can use absolute value to explain situations in the real-world.
8 NUMBER SYSTEM Calculate absolute value. I can calculate absolute value. * Absolute Value 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. Graph points in all four quadrants of the coordinate plane. Solve real-world problems by graphing points in all four quadrants of a coordinate plane. I can graph points in all four quadrants of the coordinate plane. Coordinate Plane Coordinates Distance Given only coordinates, calculate the distances between two points with the same first coordinate or the same second coordinate using absolute value. I can calculate the distance between two points on the same vertical line or the same horizontal line. Horizontal Line Vertical Line 6.EE.: Write and evaluate numerical expressions involving wholenumber exponents. Write numerical expressions involving whole number exponents Ex. 4 = xxx Evaluate numerical expressions involving whole number exponents Ex. 4 = xxx = 8 Solve order of operation problems that contain exponents Ex. + ( + ) = I can write numerical expressions involving whole number exponents. I can evaluate numerical expressions involving whole number exponents. I can solve order of operation problems that contain exponents. Exponents Numerical Expression Order of Operations 6.EE.a: 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. For example, express the calculation Subtract y from 5 as 5 y. Use numbers and variables to represent desired operations Translating written phrases into algebraic expressions. Translating algebraic expressions into written phrases. I can translate written phrases into algebraic expressions. I can translate algebraic expressions into written phrases. * Algebraic Expressions
9 6.EE.b: Write, read, and evaluate expressions in which letters stand 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. For example, describe the expression (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) Identify parts of an expression as a single entity, even if not a monomial. I can identify parts of an algebraic or numerical expression using mathematical terms (sum, term, product, factor, quotient, coefficient). *Coefficient Product Sum Term 6.EE.c: Write, read, and evaluate expressions in which letters stand for numbers. 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 conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s and A = 6 s to find the volume and surface area of a cube with sides of length s = /. Substitute specific values for variables. Evaluate algebraic expressions including those that arise from real-world problems. Apply order of operations when there are no parentheses for expressions that include whole number exponents I can substitute specific values for variables. I can evaluate algebraic expressions. I can apply order of operations. Order of Operations Variables 6.EE.: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression ( + x) to produce the equivalent expression 6 + x; apply the distributive property to the expression 4x + 8y to produce the equivalent expression 6 (4x + y); apply properties of operations to y + y + y to produce the equivalent expression y. Generate equivalent expressions using the properties of operations. (e.g. distributive property, associative property, adding like terms with the addition property of equality, etc.) Apply the properties of operations to generate equivalent expressions. I can write equivalent expressions using the distributive property. I can write equivalent expressions by combining like terms. Equivalent Expressions * Like Terms 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 y are equivalent because they name the same number regardless of which number y stands for. Recognize when two expressions are equivalent. Prove (using various strategies) that two expressions are equivalent no matter what number is substituted. I can determine if two expressions are equivalent. I can prove that two expressions are equivalent no matter what number is substituted. Substitute
0 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. Recognize solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true? Know that the solutions of an equation or inequality are the values that make the equation or inequality true. I can determine from a set of numbers, which value makes an equation true. I can determine from a set of numbers, which values make an inequality true. * Variable Equation * Inequality Use substitution to determine whether a given number in a specified set makes an equation or inequality true. I can substitute a given number for a variable in an equation to determine if it is a solution. 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. Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Relate variables to a context. Write expressions when solving a real-world or mathematical problem I can substitute given numbers for a variable in an inequality to determine if it is a solution. I can write an expression using a variable for an unknown. Unknown Define inverse operation. I can define inverse operations. Inverse Operations 6.EE.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. Know how inverse operations can be used in solving one-variable equations. Apply rules of the form x + p = q and px = q, for cases in which p, q and x are all nonnegative rational numbers, to solve real world and mathematical problems. (There is only one unknown quantity.) I can solve one-variable equations using inverse operations. I can write equations for real-world mathematical problems containing one unknown. Develop a rule for solving one-step equations using inverse operations with nonnegative rational coefficients. Solve and write equations for real-world mathematical problems containing one unknown.
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. Identify the constraint or condition in a real-world or mathematical problem in order to set up an inequality. Recognize that inequalities of the form x > c or x < c have infinitely many solutions. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Represent solutions to inequalities or the form x > c or x < c, with infinitely many solutions, on number line diagrams. I can write an inequality. I can graph solutions to an inequality on a number line. Solution 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. 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. Define independent and dependent variables. Use variables to represent two quantities in a realworld problem that change in relationship to one another. Write an equation to express one quantity (dependent) in terms of the other quantity (independent). Analyze the relationship between the dependent variable and independent variable using tables and graphs Relate the data in a graph and table to the corresponding equation. I can define and give examples of independent variables. I can define and give examples of dependent variables. I can write an equation to express one quantity (dependent) in terms of the other quantity (independent). I can analyze the relationship between dependent and independent variables using tables and graphs. I can identify the equation being represented in a table or graph. * Independent Variable * Dependent Variable
RATIO & PROPORTIONAL RELATIONSHIPS 6.RP.: 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 :, because for every wings there was beak. For every vote candidate A received, candidate C received nearly three votes. Write ratio notation- :, to, / Know order matters when writing a ratio Know ratios can be simplified Know ratios compare two quantities; the quantities do not have to be the same unit of measure Recognize that ratios appear in a variety of different contexts; part-to-whole, part-to-part, and rates Generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship. I can write a ratio in three different forms. I can write a ratio in the correct order. I can simplify ratios. I can compare two quantities using ratios. I can identify types of ratios: part-towhole, part-to-part, or rates. I can determine which type of ratio is represented. Compare Quantities * Rate * Ratio Ratio Notation Simplify Unit of Measure Analyze your context to determine which kind of ratio is represented RATIO & PROPORTIONAL RELATIONSHIPS Identify and calculate a unit rate. I can identify a unit rate. Convert 6.RP.: Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of cups of flour to 4 cups of sugar, so there is /4 cup of flour for each cup of sugar. We paid $75 for 5 hamburgers, which is a rate of $5 per hamburger. (Note: Expectations for unit rates in this grade are limited to non-complex fractions.) Use appropriate math terminology as related to rate. Analyze the relationship between a ratio a:b and a unit rate a/b where b 0. I can calculate a unit rate. I can use appropriate math vocabulary to explain rates. (per, each, unit, etc ) I can convert a ratio into a unit rate. * Unit Rate
RATIO & PROPORTIONAL RELATIONSHIPS 6.RP.abcd: 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 wholenumber 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. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 5 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 00 (e.g., 0% of a quantity means 0/00 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. Make a table of equivalent ratios using whole numbers. Find the missing values in a table of equivalent ratios. Plot pairs of values that represent equivalent ratios on the coordinate plane. Know that a percent is a ratio of a number to 00. Find a % of a number as a rate per 00. Use tables to compare proportional quantities Solve real-world and mathematical problems involving ratio and rate, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. I can create a table of equivalent ratios using whole numbers. I can use multiplication / division to find the missing values in a table of equivalent ratios. I can plot pairs of values that represent equivalent ratios on the coordinate plane. I can write a percent as a ratio of a number to 00. I can calculate the % of a number as a rate per 00. I can use tables to compare equivalent ratios. I can solve mathematical problems involving ratio and rate. Equivalent Ratios Plot Coordinate Plane * Percent Unit Pricing Apply the concept of unit rate to solve real-world problems involving unit pricing. I can use unit rates to solve problems involving unit pricing. RATIO & PROPORTIONAL RELATIONSHIPS 6.RP.abcd: Standard (Continued) Apply the concept of unit rate to solve real-world problems involving constant speed. I can use unit rates to solve problems using constant speed. Convert Constant Speed Solve real-world problems involving finding the whole, given a part and a percent. Apply ratio reasoning to convert measurement units in real-world and mathematical problems. I can calculate the "whole" when given a part and a percent. I can convert measurement units using ratios (multiplying or dividing). Part Whole Apply ratio reasoning to convert measurement units by multiplying or dividing in real-world and mathematical problems.
4 GEOMETRY.G.: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Identify and define rhombuses, rectangles, and squares as examples of quadrilaterals based on their attributes. Describe, analyze, and compare properties of twodimensional shapes. Compare and classify shapes by attributes, sides and angles. Group shapes with shared attributes to define a larger category (e.g., quadrilaterals) Draw examples of quadrilaterals that do and do not belong to any of the subcategories. (Product) I can identify and define rhombuses, rectangles, and squares. I can describe, analyze, and compare properties of two-dimensional shapes. I can compare and classify shapes by attributes, sides and angles. I can group shapes with shared attributes to define a larger category. I can draw examples of unusual quadrilaterals. * Rhombus * Quadrilaterals GEOMETRY Graph points in the first quadrant I can graph points in the first quadrant quadrant 5.G.: 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. Represent real world and mathematical problems by graphing points in the first quadrant Interpret coordinate values of points in real world context and mathematical problems I can represent real world and mathematical problems by graphing points in the first quadrant I can interpret coordinate values of points in real world context and mathematical problems
5 GEOMETRY 6.G.: 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. Recognize and know how to compose and decompose polygons into triangles and rectangles. Compare the area of a triangle to the area of the composted rectangle. (Decomposition addressed in previous grade.) Apply the techniques of composing and/or decomposing to find the area of triangles, special quadrilaterals and polygons to solve mathematical and real world problems. I can find the area of a triangle. I can find the area of a special quadrilateral. I can find the area of irregular figures (composed of triangles and Discuss, develop and justify formulas for triangles and quadrilaterals). parallelograms (6th grade introduction) I can justify the area formulas for triangles and parallelograms. Area Triangle Quadrilateral Irregular Figures GEOMETRY 6.G.: 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. Know how to calculate the volume of a right rectangular prism. Apply volume formulas for right rectangular prisms to solve real-world and mathematical problems involving rectangular prisms with fractional edge lengths. 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. (Performance) I can find the volume of a right rectangular prism using unit cubes. I can calculate the volume of a right rectangular prism using the volume formula. Volume Right rectangular prism GEOMETRY 6.G.: 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 realworld and mathematical problems. Draw polygons in the coordinate plane. Use coordinates (with the same x-coordinate or the same y-coordinate) to find the length of a side of a polygon. Apply the technique of using coordinates to find the length of a side of a polygon drawn in the coordinate plane to solve real-world and mathematical problems. I can draw polygons on a coordinate plane given the vertices. I can find the length of a side of a polygon using coordinate plane. Polygon Vertex
6 GEOMETRY 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. Know that -D figures can be represented by nets. Represent three-dimensional figures using nets made up of rectangles and triangles. Apply knowledge of calculating the area of rectangles and triangles to a net, and combine the areas for each shape into one answer representing the surface area of a -dimensional figure. I can represent a three-dimensional figure using nets made up of rectangles and triangles. I can use the net of a figure to find surface area. Three dimensional figure * Net * Surface Area Solve real-world and mathematical problems involving surface area using nets. MEASUREMENT AND DATA.MD.7a: Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Find the area of a rectangle by tiling it in unit squares Find the side lengths of a rectangle in units Compare the area found by tiling a rectangle to the area found by multiplying the side lengths I can find the area of a rectangle by tiling it in unit squares. I can find the side lengths of a rectangle in units. I can compare area using models and multiplication. * Tiling
7 MEASUREMENT AND DATA.MD.: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and twostep how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Explain the scale of a graph with a scale greater than one. Identify the scale of a graph with a scale greater than one. Analyze a graph with a scale greater than one. Choose a proper scale for a bar graph or picture graph. Interpret a bar/picture graph to solve one or two step problems asking how many more and how many less. Create a scaled picture graph to show data. (Product) I can identify and explain the scale of a graph with a scale greater than one. I can analyze a graph with a scale greater than one. I can choose a scale for a bar graph or picture graph. I can interpret a bar/picture graph to determine "how many more" and "how many less." I can create a scaled picture graph to show data. * Scale * Bar Graph * Picture Graph Create a scaled bar graph to show data. (Product) I can create a scaled bar graph to show data. 4 STATISTICS & PROBABILITY 6.SP.: 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. Recognize that data can have variability. Recognize a statistical question (examples versus nonexamples) I can identify which data has statistical variability. I can give examples and non-examples of a statistical question. * Statistical Variability * Statistical Question 4 STATISTICS & PROBABILITY 6.SP.: 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. Know that a set of data has a distribution. Describe a set of data by its center, e.g., mean and median. Describe a set of data by its spread and overall shape, e.g. by identifying data clusters, peaks, gaps and symmetry I can identify the distribution of a data set (range) I can describe a set of data by its center spread and overall shape using a visual representation of data. distribution
8 STATISTICS & PROBABILITY 6.SP.: 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. Recognize there are measures of central tendency for a data set, e.g., mean, median, mode. Recognize there are measures of variances for a data set, e.g., range, interquartile range, mean absolute deviation. I can describe the measures of central tendency (mean, median, and mode). I can describe the measures of variance (range, interquartile range, and mean absolute deviation). *Measures of Central Tendency * Mean * Median 4 Recognize measures of central tendency for a data set summarizes the data with a single number. Recognize measures of variation for a data set describes how its values vary with a single number. I can explain the difference between measures of central tendency and measures of variation. * Mode * Measures of Variation * Range * Interquartile Range * Mean Absolute Deviation STATISTICS & PROBABILITY 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots Identify the components of dot plots, histograms, and box plots. Find the median, quartile and interquartile range of a set of data. Analyze a set of data to determine its variance. I can create a dot plot. I can create a histogram. I can create a box plot on a number line. * Dot Plot (Scatterplot) * Histogram * Box Plots (Box and Whisker Plot) 4 Create a dot plot to display a set of numerical data. (Product) Create a histogram to display a set of numerical data. (Product) Create a box plot to display a set of numerical data (Product)
9 4 STATISTICS & PROBABILITY 6.SP.5abcd : 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. Organize and display data in tables and graphs. Report the number of observations in a data set or display. Describe the data being collected, including how it was measured and its units of measurement. Calculate quantitative measures of center, e.g., mean, median, mode. Calculate quantitative measures of variance, e.g., range, interquartile range, mean absolute deviation. I can collect and organize data to display in tables and graphs. I can describe the data being collected, including how it was measured and its units of measurement. I can calculate quantitative measures of center (mean, median, mode). I can calculate quantitative measures of variance (range, interquartile range, mean absolute deviation). I can identify outliers. * Outlier Identify outliers Determine the effect of outliers on quantitative measures of a set of data, e.g., mean, median, mode, range, interquartile range, mean absolute deviation. I can determine the effect of outliers on a data set. STATISTICS & PROBABILITY 6.SP.5abcd Standard (Continued) Choose the appropriate measure of central tendency to represent the data. I can choose and justify the appropriate measure of central tendency to represent the data. 4 Analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context