## Grade 7 – CA Common Core Standards & IXL Practice

##### 7.7.RP.1     Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Understanding ratios (Seventh grade – J.1)

Unit rates (Seventh grade – J.5)

Unit prices (Seventh grade – M.3)

Unit prices with unit conversions (Seventh grade – M.4)

##### 7.7.RP.2.a     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.

Equivalent ratios (Seventh grade – J.2)

Equivalent ratios: word problems (Seventh grade – J.3)

Do the ratios form a proportion? (Seventh grade – J.6)

Do the ratios form a proportion: word problems (Seventh grade – J.7)

Identify proportional relationships (Seventh grade – K.6)

##### 7.7.RP.2.b     Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Find the constant of proportionality from a table (Seventh grade – K.1)

Find the constant of proportionality from a graph (Seventh grade – K.3)

Find the constant of proportionality: word problems (Seventh grade – K.7)

##### 7.7.RP.2.c     Represent proportional relationships by equations.

Solve proportions: word problems (Seventh grade – J.9)

Write equations for proportional relationships (Seventh grade – K.4)

Write equations for proportional relationships (Eighth grade – I.4)

##### 7.7.RP.3  Use proportional relationships to solve multistep ratio and percent problems.

Estimate population size using proportions (Seventh grade – J.10)

Estimate percents of numbers (Seventh grade – L.4)

Percents of numbers and money amounts (Seventh grade – L.5)

Percents of numbers: word problems (Seventh grade – L.6)

Solve percent equations (Seventh grade – L.7)

Solve percent equations: word problems (Seventh grade – L.8)

Percent of change (Seventh grade – L.9)

Percent of change: word problems (Seventh grade – L.10)

Unit prices with unit conversions (Seventh grade – M.4)

Unit prices: find the total price (Seventh grade – M.5)

Percent of a number: tax, discount, and more (Seventh grade – M.6)

Find the percent: tax, discount, and more (Seventh grade – M.7)

Sale prices: find the original price (Seventh grade – M.8)

Multi-step problems with percents (Seventh grade – M.9)

Estimate tips (Seventh grade – M.10)

Simple interest (Seventh grade – M.11)

Compound interest (Seventh grade – M.12)

Experimental probability (Seventh grade – CC.3)

##### 7.7.NS.1.a     Describe situations in which opposite quantities combine to make 0.

Absolute value and opposite integers (Seventh grade – B.4)

##### 7.7.NS.1.b       Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Integers on number lines (Seventh grade – B.2)

Absolute value and opposite integers (Seventh grade – B.4)

Integer inequalities with absolute values (Seventh grade – B.6)

Decimal number lines (Seventh grade – D.3)

Absolute value of rational numbers (Seventh grade – H.3)

##### 7.7.NS.1.c     Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Understanding integers (Seventh grade – B.1)

Integers on number lines (Seventh grade – B.2)

Decimal number lines (Seventh grade – D.3)

#### 7.7.NS.1.d    Apply properties of operations as strategies to add and subtract rational numbers.

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

##### 7.7.NS.2.a     Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Multiply and divide rational numbers (Seventh grade – H.8)

Distributive property (Seventh grade – S.2)

##### 7.7.NS.2.b     Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Multiplicative inverses (Seventh grade – A.3)

Divisibility rules (Seventh grade – A.4)

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Divide decimals by whole numbers: word problems (Seventh grade – E.6)

Understanding fractions: word problems (Seventh grade – F.3)

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Multiply and divide rational numbers (Seventh grade – H.8)

##### 7.7.NS.2.c     Apply properties of operations as strategies to multiply and divide rational numbers.

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Multiply decimals (Seventh grade – E.3)

Divide decimals (Seventh grade – E.5)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

Multiply fractions and whole numbers (Seventh grade – G.7)

Multiply fractions (Seventh grade – G.9)

Multiply mixed numbers (Seventh grade – G.10)

Divide fractions (Seventh grade – G.12)

Divide mixed numbers (Seventh grade – G.13)

Apply multiplication and division rules (Seventh grade – H.9)

#### 7.7.NS.2.d     Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Classify numbers (Seventh grade – A.10)

Convert between decimals and fractions or mixed numbers (Seventh grade – H.2)

#### 7.7.NS.3     Solve real-world and mathematical problems involving the four operations with rational numbers.

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Multiply decimals (Seventh grade – E.3)

Multiply decimals and whole numbers: word problems (Seventh grade – E.4)

Divide decimals (Seventh grade – E.5)

Divide decimals by whole numbers: word problems (Seventh grade – E.6)

Add, subtract, multiply, and divide decimals: word problems (Seventh grade – E.8)

Inequalities with addition and subtraction of fractions and mixed numbers (Seventh grade – G.5)

Multiply fractions and whole numbers (Seventh grade – G.7)

Multiply fractions (Seventh grade – G.9)

Multiply mixed numbers (Seventh grade – G.10)

Multiply fractions and mixed numbers: word problems (Seventh grade – G.11)

Divide fractions (Seventh grade – G.12)

Divide mixed numbers (Seventh grade – G.13)

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Seventh grade – G.16)

Multiply and divide rational numbers (Seventh grade – H.8)

Add, subtract, multiply, and divide money amounts: word problems (Seventh grade – M.1)

Price lists (Seventh grade – M.2)

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

Factor linear expressions (Seventh grade – R.10)

Identify equivalent linear expressions (Seventh grade – R.11)

Distributive property (Seventh grade – S.2)

Write equivalent expressions using properties (Seventh grade – S.3)

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

Scientific notation (Seventh grade – A.8)

Compare numbers written in scientific notation (Seventh grade – A.9)

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Round decimals (Seventh grade – D.4)

Estimate sums, differences, and products of decimals (Seventh grade – E.7)

Multi-step inequalities with decimals (Seventh grade – E.9)

Maps with decimal distances (Seventh grade – E.10)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

Equivalent fractions (Seventh grade – F.1)

Simplify fractions (Seventh grade – F.2)

Compare and order fractions (Seventh grade – F.5)

Compare fractions: word problems (Seventh grade – F.6)

Convert between mixed numbers and improper fractions (Seventh grade – F.7)

Compare mixed numbers and improper fractions (Seventh grade – F.8)

Round mixed numbers (Seventh grade – F.9)

Estimate sums and differences of mixed numbers (Seventh grade – G.6)

Estimate products and quotients of fractions and mixed numbers (Seventh grade – G.15)

Maps with fractional distances (Seventh grade – G.17)

Convert between decimals and fractions or mixed numbers (Seventh grade – H.2)

Compare ratios: word problems (Seventh grade – J.4)

Convert between percents, fractions, and decimals (Seventh grade – L.2)

Compare percents to fractions and decimals (Seventh grade – L.3)

Unit prices with unit conversions (Seventh grade – M.4)

Unit prices: find the total price (Seventh grade – M.5)

Estimate to solve word problems (Seventh grade – N.1)

Multi-step word problems (Seventh grade – N.2)

Guess-and-check word problems (Seventh grade – N.3)

Use Venn diagrams to solve problems (Seventh grade – N.4)

Find the number of each type of coin (Seventh grade – N.5)

Elapsed time word problems (Seventh grade – N.6)

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

Solve proportions: word problems (Seventh grade – J.9)

Solve equations using properties (Seventh grade – S.4)

Model and solve equations using algebra tiles (Seventh grade – T.3)

Solve one-step equations (Seventh grade – T.5)

Solve two-step equations (Seventh grade – T.6)

Solve equations: word problems (Seventh grade – T.7)

Solve equations involving like terms (Seventh grade – T.8)

Solve word problems involving two-variable equations (Seventh grade – V.4)

##### 7.7.EE.4.b     Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Solutions to inequalities (Seventh grade – U.1)

Write inequalities from number lines (Seventh grade – U.2)

Graph inequalities on number lines (Seventh grade – U.3)

Solve one-step inequalities (Seventh grade – U.4)

Graph solutions to one-step inequalities (Seventh grade – U.5)

Solve two-step inequalities (Seventh grade – U.6)

Graph solutions to two-step inequalities (Seventh grade – U.7)

#### 7.7.G.     Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Scale drawings and scale factors (Seventh grade – J.13)

Similar and congruent figures (Seventh grade – X.12)

Similar figures: side lengths and angle measures (Seventh grade – X.13)

Similar figures and indirect measurement (Seventh grade – X.14)

Congruent figures: side lengths and angle measures (Seventh grade – X.15)

Congruence statements and corresponding parts (Seventh grade – X.16)

Perimeter, area, and volume: changes in scale (Seventh grade – X.30)

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

Front, side, and top view (Seventh grade – X.25)

Names and bases of 3-dimensional figures (Seventh grade – X.26)

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

Parts of a circle (Seventh grade – X.21)

Circles: word problems (Seventh grade – X.23)

#### 7.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Identify complementary, supplementary, vertical, adjacent, and congruent angles (Seventh grade – X.4)

Find measures of complementary, supplementary, vertical, and adjacent angles (Seventh grade – X.5)

#### 7.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Area of rectangles and parallelograms (Seventh grade – X.18)

Area of triangles and trapezoids (Seventh grade – X.19)

Area and perimeter: word problems (Seventh grade – X.20)

Nets of 3-dimensional figures (Seventh grade – X.27)

Surface area (Seventh grade – X.28)

### 7.7.SP Statistics and Probability

#### 7.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Identify representative, random, and biased samples (Seventh grade – BB.5)

#### 7.7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Estimate population size using proportions (Seventh grade – J.10)

#### 7.7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Calculate mean, median, mode, and range (Seventh grade – BB.1)

Interpret charts to find mean, median, mode, and range (Seventh grade – BB.2)

Mean, median, mode, and range: find the missing number (Seventh grade – BB.3)

Changes in mean, median, mode, and range (Seventh grade – BB.4)

##### 7.7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

Experimental probability (Seventh grade – CC.3)

Make predictions (Seventh grade – CC.4)

#### 7.7.SP.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Probability of simple events (Seventh grade – CC.1)

#### 7.7.SP.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Experimental probability (Seventh grade – CC.3)

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

Probability of opposite, mutually exclusive, and overlapping events (Seventh grade – CC.2)

Identify independent and dependent events (Seventh grade – CC.6)

Probability of independent and dependent events (Seventh grade – CC.7)

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

Compound events: find the number of outcomes (Seventh grade – CC.5)

Counting principle (Seventh grade – CC.10)

Combination and permutation notation (Seventh grade – CC.11)

## Grade 6 CA Common Core – Standards with Learning Objectives

### 6.6.RP Ratios and Proportional Relationships

6 Understand ratio concepts and use ratio reasoning to solve problems.

#### 6.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Interpret ratios of two quantities  Write a ratio to describe objects in a picture (Sixth grade – R.1)

Use ratios to solve  word problems (Sixth grade – R.3)

#### 6.6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.

Interpret and calculate nit rates and equivalent rates (Sixth grade – R.8)

Calculate unit rates.  Unit rates: word problems (Sixth grade – R.9)

#### 6.6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Determine ratio tables (Sixth grade – R.2)

Equivalent ratios (Sixth grade – R.4)

Equivalent ratios: word problems (Sixth grade – R.5)

Compare ratios using tables: word problems (Sixth grade – R.6)

Coordinate graphs review (Sixth grade – W.1)

#### 6.6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed.

Unit rates and equivalent rates (Sixth grade – R.8)

Unit rates: word problems (Sixth grade – R.9)

Unit prices with fractions and decimals (Sixth grade – U.3)

Unit prices with customary unit conversions (Sixth grade – U.4)

#### 6.6.RP.3.c 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.

Percents of numbers and money amounts (Sixth grade – R.14)

Percents of numbers: word problems (Sixth grade – R.15)

Which is the better coupon? (Sixth grade – U.1)

Sale prices (Sixth grade – U.5)

Sale prices: find the original price (Sixth grade – U.6)

Percents – calculate tax, tip, mark-up, and more (Sixth grade – U.7)

#### 6.6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Convert and compare customary units (Sixth grade – S.3)

Convert, compare, add, and subtract mixed customary units (Sixth grade – S.4)

Multiply and divide mixed customary units (Sixth grade – S.5)

Customary unit conversions involving fractions and mixed numbers (Sixth grade – S.6)

Convert and compare metric units (Sixth grade – S.7)

Convert between customary and metric systems (Sixth grade – S.8)

Unit prices with customary unit conversions (Sixth grade – U.4)

### 6.6.NS The Number System

#### 6.6.NS.1 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.

Divide whole numbers by unit fractions using models (Sixth grade – L.1)

Divide whole numbers and unit fractions (Sixth grade – L.3)

Divide fractions (Sixth grade – L.5)

Estimate quotients when dividing mixed numbers (Sixth grade – L.6)

Divide fractions and mixed numbers (Sixth grade – L.7)

Divide fractions and mixed numbers: word problems (Sixth grade – L.8)

Add, subtract, multiply, or divide two fractions: word problems (Sixth grade – O.8)

#### 6.6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

Divisibility rules (Sixth grade – C.1)

Division patterns with zeroes (Sixth grade – C.2)

Divide numbers ending in zeroes: word problems (Sixth grade – C.3)

Estimate quotients (Sixth grade – C.4)

Divide whole numbers – 2-digit divisors (Sixth grade – C.5)

Divide whole numbers – 3-digit divisors (Sixth grade – C.6)

Add, subtract, multiply, or divide two whole numbers (Sixth grade – O.1)

Add, subtract, multiply, or divide two whole numbers: word problems (Sixth grade – O.2)

#### 6.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Estimate sums and differences of decimals (Sixth grade – G.3)

Maps with decimal distances (Sixth grade – G.4)

Multiply decimals (Sixth grade – H.1)

Estimate products of decimal numbers (Sixth grade – H.2)

Inequalities with decimal multiplication (Sixth grade – H.3)

Divide decimals by whole numbers (Sixth grade – H.4)

Divide decimals by whole numbers: word problems (Sixth grade – H.5)

Multiply and divide decimals by powers of ten (Sixth grade – H.6)

Division with decimal quotients (Sixth grade – H.7)

Inequalities with decimal division (Sixth grade – H.8)

Add, subtract, multiply, or divide two decimals: word problems (Sixth grade – O.5)

Perform multiple operations with decimals (Sixth grade – O.6)

#### 6.6.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.

Identify factors (Sixth grade – E.4)

Greatest common factor (Sixth grade – E.7)

Least common multiple (Sixth grade – E.8)

GCF and LCM: word problems (Sixth grade – E.9)

#### 6.6.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.

Understanding integers (Sixth grade – M.1)

Working with temperatures above and below zero (Sixth grade – S.9)

#### 6.6.NS.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

Absolute value and opposite integers (Sixth grade – M.2)

Integers on number lines (Sixth grade – M.3)

#### 6.6.NS.6.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.

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Reflections: graph the image (Sixth grade – BB.18)

#### 6.6.NS.6.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.

Decimal number lines (Sixth grade – F.9)

Integers on number lines (Sixth grade – M.3)

Graph integers on horizontal and vertical number lines (Sixth grade – M.4)

Rational numbers: find the sign (Sixth grade – P.6)

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Coordinate graphs as maps (Sixth grade – W.3)

Translations: graph the image (Sixth grade – BB.17)

#### 6.6.NS.7.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write inequalities from number lines (Sixth grade – Z.2)

#### 6.6.NS.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Compare rational numbers (Sixth grade – P.1)

Put rational numbers in order (Sixth grade – P.2)

#### 6.6.NS.7.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.

Absolute value and opposite integers (Sixth grade – M.2)

Absolute value of rational numbers (Sixth grade – P.3)

#### 6.6.NS.7.d Distinguish comparisons of absolute value from statements about order.

Put rational numbers in order (Sixth grade – P.2)

Absolute value of rational numbers (Sixth grade – P.3)

#### 6.6.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.

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Coordinate graphs as maps (Sixth grade – W.3)

Distance between two points (Sixth grade – W.4)

Relative coordinates (Sixth grade – W.5)

### 6.6.EE Expressions and Equations

#### 6.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

Write multiplication expressions using exponents (Sixth grade – D.1)

Evaluate exponents (Sixth grade – D.2)

Find the missing exponent or base (Sixth grade – D.3)

Exponents with decimal bases (Sixth grade – D.4)

Exponents with fractional bases (Sixth grade – D.5)

#### 6.6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers.

Write variable expressions (Sixth grade – X.1)

Write variable expressions: word problems (Sixth grade – X.2)

Write a two-variable equation (Sixth grade – AA.6)

#### 6.6.EE.2.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.

Identify terms and coefficients (Sixth grade – X.6)

#### 6.6.EE.2.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).

Perform multiple operations with whole numbers (Sixth grade – O.3)

Convert between Celsius and Fahrenheit (Sixth grade – S.10)

Evaluate variable expressions with whole numbers (Sixth grade – X.3)

Evaluate multi-variable expressions (Sixth grade – X.4)

Evaluate variable expressions with decimals, fractions, and mixed numbers (Sixth grade – X.5)

Complete a table for a two-variable relationship (Sixth grade – AA.5)

#### 6.6.EE.3 Apply the properties of operations to generate equivalent expressions.

Properties of multiplication (Sixth grade – X.8)

Distributive property (Sixth grade – X.9)

Write equivalent expressions using properties (Sixth grade – X.11)

#### 6.6.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).

Identify equivalent expressions (Sixth grade – X.13)

#### 6.6.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.

Does x satisfy an equation? (Sixth grade – Y.1)

Find the solution from a set (Sixth grade – Y.2)

Solve one-step equations with whole numbers (Sixth grade – Y.6)

Solutions to inequalities (Sixth grade – Z.1)

Solve one-step inequalities (Sixth grade – Z.4)

#### 6.6.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.

Convert between Celsius and Fahrenheit (Sixth grade – S.10)

Write variable expressions: word problems (Sixth grade – X.2)

Write an equation from words (Sixth grade – Y.3)

Solve word problems involving two-variable equations (Sixth grade – AA.4)

#### 6.6.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.

Model and solve equations using algebra tiles (Sixth grade – Y.4)

Write and solve equations that represent diagrams (Sixth grade – Y.5)

Solve one-step equations with whole numbers (Sixth grade – Y.6)

Solve one-step equations with decimals, fractions, and mixed numbers (Sixth grade – Y.7)

Solve one-step equations: word problems (Sixth grade – Y.8)

#### 6.6.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.

Write inequalities from number lines (Sixth grade – Z.2)

Graph inequalities on number lines (Sixth grade – Z.3)

#### 6.6.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.

Solve one-step equations: word problems (Sixth grade – Y.8)

Identify independent and dependent variables (Sixth grade – AA.2)

Find a value using two-variable equations (Sixth grade – AA.3)

Solve word problems involving two-variable equations (Sixth grade – AA.4)

Complete a table for a two-variable relationship (Sixth grade – AA.5)

Write a two-variable equation (Sixth grade – AA.6)

Identify the graph of an equation (Sixth grade – AA.7)

Graph a two-variable equation (Sixth grade – AA.8)

Interpret a graph: word problems (Sixth grade – AA.9)

Write an equation from a graph using a table (Sixth grade – AA.10)

### 6.6.G Geometry

#### 6.6.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.

Area of compound figures (Sixth grade – BB.24)

Compare area and perimeter of two figures (Sixth grade – BB.28)

#### 6.6.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.

Volume of cubes and rectangular prisms (Sixth grade – BB.36)

#### 6.6.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.

Coordinate graphs review (Sixth grade – W.1)

Distance between two points (Sixth grade – W.4)

#### 6.6.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.

Nets of 3-dimensional figures (Sixth grade – BB.35)

Surface area of cubes and rectangular prisms (Sixth grade – BB.37)

Volume and surface area of triangular prisms (Sixth grade – BB.38)

### 6.6.SP Statistics and Probability

#### 6.6.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.

Identify representative, random, and biased samples (Sixth grade – DD.4)

#### 6.6.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.

Stem-and-leaf plots (Sixth grade – CC.3)

Create line plots (Sixth grade – CC.5)

Interpret box-and-whisker plots (Sixth grade – CC.19)

#### 6.6.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.

Calculate mean, median, mode, and range (Sixth grade – DD.1)

Interpret charts to find mean, median, mode, and range (Sixth grade – DD.2)

Mean, median, mode, and range: find the missing number (Sixth grade – DD.3)

#### 6.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Interpret pictographs (Sixth grade – CC.1)

Create pictographs (Sixth grade – CC.2)

Stem-and-leaf plots (Sixth grade – CC.3)

Interpret line plots (Sixth grade – CC.4)

Create line plots (Sixth grade – CC.5)

Create frequency tables (Sixth grade – CC.7)

Interpret bar graphs (Sixth grade – CC.8)

Create bar graphs (Sixth grade – CC.9)

Interpret double bar graphs (Sixth grade – CC.10)

Create double bar graphs (Sixth grade – CC.11)

Create histograms (Sixth grade – CC.13)

Circle graphs with fractions (Sixth grade – CC.14)

Interpret line graphs (Sixth grade – CC.15)

Create line graphs (Sixth grade – CC.16)

Interpret double line graphs (Sixth grade – CC.17)

Create double line graphs (Sixth grade – CC.18)

Interpret box-and-whisker plots (Sixth grade – CC.19)

Choose the best type of graph (Sixth grade – CC.20)

#### 6.6.SP.5.a Reporting the number of observations.

Create frequency tables (Sixth grade – CC.7)

Create histograms (Sixth grade – CC.13)

#### 6.6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Identify representative, random, and biased samples (Sixth grade – DD.4)

#### 6.6.SP.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Calculate mean, median, mode, and range (Sixth grade – DD.1)

Interpret charts to find mean, median, mode, and range (Sixth grade – DD.2)

Mean, median, mode, and range: find the missing number (Sixth grade – DD.3)