EstimationEstimation is the process of rounding a number either up or down to the nearest place value requested. Estimation makes it easier to perform mathematical operations quickly. Read more...iWorksheets: 6Study Guides: 1
GraphsFreeA graph is a diagram that shows information in an organized way. Read more...iWorksheets: 16Study Guides: 1
ProbabilityProbability word problems worksheets. Probability is the possibility that a certain event will occur. An event that is certain to occur has a probability of 1. An event that cannot occur has a probability of 0. Therefore, the probability of an event occurring is always between 0 and 1. The closer a probability is to 1, the more certain that an event will occur. Read more...iWorksheets: 3Study Guides: 1
Commutative/Associative PropertiesThe commutative property allows us to change the order of the numbers without changing the outcome of the problem. The associative property allows us to change the grouping of the numbers. Read more...iWorksheets: 4Study Guides: 1
AreaAn area is the amount of surface a shape covers. <br>An area is measured in inches, feet, meters or centimeters. Read more...iWorksheets: 3Study Guides: 1
Area and Circumference of CirclesFreeThe circumference of a circle is the distance around the outside. The area of a circle is the space contained within the circumference. It is measured in square units. Read more...iWorksheets: 6Study Guides: 1
Area of Triangles and QuadrilateralsThe area is the surface or space within an enclosed region. Area is expressed in square units. Read more...iWorksheets: 9Study Guides: 1Vocabulary Sets: 2
Diameter of CircleThe diameter of a circle is a line segment that passes through the center of a circle connecting one side of the circle to the other. Read more...iWorksheets: 3Study Guides: 1
PerimeterA perimeter is the measurement of the distance around a figure. It is measured in units and can be measured by inches, feet, blocks, meters, centimeters or millimeters. Read more...iWorksheets: 3Study Guides: 1
Add/Subtract FractionsAdding or substracting fractions means to add or subtract the numerators and write the sum over the common denominator. Read more...iWorksheets: 9Study Guides: 1
MultiplicationMultiplication is a mathematical operation in which numbers, called factors, are multiplied together to get a result, called a product. Multiplication can be used with numbers or decimals of any size. Read more...iWorksheets: 3Study Guides: 1
Multiply FractionsMultiplying fractions is the operation of multiplying two or more fractions together to find a product. Read more...iWorksheets: 3Study Guides: 1
Number PatternsA number pattern is a group of numbers that are related to one another in some sort of pattern. Finding a pattern is a simpler way to solve a problem. Read more...iWorksheets: 3Study Guides: 1
Simplify FractionsSimplifying fractions is the process of reducing fractions and putting them into their lowest terms. Read more...iWorksheets: 3Study Guides: 1
TablesTables refer to the different types of diagram used to display data. <br>There are many types of tables such as data table, frequency table, line chart and stern-and-leaf plot. Read more...iWorksheets: 3Study Guides: 1
Mixed NumbersA mixed number has both a whole number and a fraction. Read more...iWorksheets: 4Study Guides: 1
Whole Numbers to TrillionsThe number system we use is based on a place value system. Although there are only 10 different digits in this system, it is possible to order them in so many variations that the numbers represented are infinite. Read more...iWorksheets: 4Study Guides: 1

### CO.6.1. Number Sense, Properties, and Operations

#### 6.1.1. Quantities can be expressed and compared using ratios and rates. Students can:

##### 6.1.1.a. Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (CCSS: 6.RP.1)
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioRatios are used to make a comparison between two things. Read more...iWorksheets :9Study Guides :1Vocabulary :1
RatioA ratio is a comparison of two numbers. The two numbers must have the same unit in order to be compared. Read more...iWorksheets :3Study Guides :1
Simple ProportionsA proportion is a statement that two ratios are equal. A ratio is a pair of numbers used to show a comparison. To solve a proportion, calculate equivalent fractions in order to be sure the two fractions (ratios) are equal. Read more...iWorksheets :3Study Guides :1
Numerical ProportionsNumerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1
##### 6.1.1.b. Apply 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. (CCSS: 6.RP.2)
Numerical ProportionsNumerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1
##### 6.1.1.c. Use ratio and rate reasoning to solve real-world and mathematical problems. (CCSS: 6.RP.3)
###### 6.1.1.c.i. 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. (CCSS: 6.RP.3a)
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioRatios are used to make a comparison between two things. Read more...iWorksheets :9Study Guides :1Vocabulary :1
RatioA ratio is a comparison of two numbers. The two numbers must have the same unit in order to be compared. Read more...iWorksheets :3Study Guides :1
Simple ProportionsA proportion is a statement that two ratios are equal. A ratio is a pair of numbers used to show a comparison. To solve a proportion, calculate equivalent fractions in order to be sure the two fractions (ratios) are equal. Read more...iWorksheets :3Study Guides :1
Numerical ProportionsNumerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1
###### 6.1.1.c.ii. Use tables to compare ratios. (CCSS: 6.RP.3a)
Proportions/Equivalent FractionsEquivalent fractions represent the same ratio between two values. Read more...iWorksheets :3Study Guides :1
RatioRatios are used to make a comparison between two things. Read more...iWorksheets :9Study Guides :1Vocabulary :1
RatioA ratio is a comparison of two numbers. The two numbers must have the same unit in order to be compared. Read more...iWorksheets :3Study Guides :1
Simple ProportionsA proportion is a statement that two ratios are equal. A ratio is a pair of numbers used to show a comparison. To solve a proportion, calculate equivalent fractions in order to be sure the two fractions (ratios) are equal. Read more...iWorksheets :3Study Guides :1
Numerical ProportionsNumerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1
###### 6.1.1.c.iii. Solve unit rate problems including those involving unit pricing and constant speed. (CCSS: 6.RP.3b)
FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
Numerical ProportionsNumerical proportions compare two numbers. The numbers can have the same units such as a ratio or the numbers can have different units such as rates. A proportion is usually in the form of a:b or a/b. Ratios are used to compare objects, wins and losses, sides of a figure to its area and many more. Rates are used to compare miles per hour, words per minute, and many others. A unit rate is when the denominator of a proportion is one. Read more...iWorksheets :4Study Guides :1
###### 6.1.1.c.iv. Find a percent of a quantity as a rate per 100. (CCSS: 6.RP.3c)
PercentageThe term percent refers to a fraction in which the denominator is 100. It is a way to compare a number with 100. Read more...iWorksheets :6Study Guides :1
Multiple Representation of Rational NumbersWhat are multiple representations of rational numbers? A rational number represents a value or a part of a value. Rational numbers can be written as integers, fractions, decimals, and percents.The different representations for any given rational number are all equivalent. Read more...iWorksheets :3Study Guides :1
Introduction to PercentWhat Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
###### 6.1.1.c.v. Solve problems involving finding the whole, given a part and the percent. (CCSS: 6.RP.3c)
Percent, Rate, BaseA percent is a way of comparing a number with 100. Percents are usually written with a percent sign. To solve a percent problem, multiply the value by the percent using one of the representations for the percent. Read more...iWorksheets :3Study Guides :1
PercentageThe term percent refers to a fraction in which the denominator is 100. It is a way to compare a number with 100. Read more...iWorksheets :6Study Guides :1
Introduction to PercentWhat Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
Applying PercentsApplying percents is a term that refers to the different ways that percents can be used. The percent of change refers to the percent an amount either increases or decreases based on the previous amounts or numbers. Applying percents also means to calculate simple interest using the interest equation, I = P · r · t, where P is the principal; r is the rate and t is the time. Read more...iWorksheets :3Study Guides :1
###### 6.1.1.c.vi. Use common fractions and percents to calculate parts of whole numbers in problem situations including comparisons of savings rates at different financial institutions (PFL).
Percent, Rate, BaseA percent is a way of comparing a number with 100. Percents are usually written with a percent sign. To solve a percent problem, multiply the value by the percent using one of the representations for the percent. Read more...iWorksheets :3Study Guides :1
FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
Applying PercentsApplying percents is a term that refers to the different ways that percents can be used. The percent of change refers to the percent an amount either increases or decreases based on the previous amounts or numbers. Applying percents also means to calculate simple interest using the interest equation, I = P · r · t, where P is the principal; r is the rate and t is the time. Read more...iWorksheets :3Study Guides :1
###### 6.1.1.c.vii. Express the comparison of two whole number quantities using differences, part-to-part ratios, and part-to-whole ratios in real contexts, including investing and saving (PFL).
Exponential & Scientific NotationExponential notation is shorten way of expressing a large number using exponents. Read more...iWorksheets :6Study Guides :1Vocabulary :1
Compare and Order NumbersComparing two numbers and deciding which one is greater Read more...iWorksheets :3Study Guides :1
###### 6.1.1.c.viii. Use ratio reasoning to convert measurement units. (CCSS: 6.RP.3d)
MeasurementFreeThere are many units of measurement: inches, feet, yards, miles, millimeters, meters, seconds, minutes, hours, cups, pints, quarts, gallons, ounces, pounds, etc Read more...iWorksheets :6Study Guides :1

#### 6.1.2. Formulate, represent, and use algorithms with positive rational numbers with flexibility, accuracy, and efficiency. Students can:

##### 6.1.2.a. Fluently divide multi-digit numbers using standard algorithms. (CCSS: 6.NS.2)
DivisionDivision is a mathematical operation is which a number, called a dividend is divided by another number, called a divisor to get a result, called a quotient. Read more...iWorksheets :3Study Guides :1
DivisionDivide three-digit numbers by one- and two-digit numbers. Read more...iWorksheets :6Study Guides :1Vocabulary :1
##### 6.1.2.b. Fluently add, subtract, multiply, and divide multidigit decimals using standard algorithms for each operation. (CCSS: 6.NS.3)
Add/Subtract/Multiply/Divide DecimalsYou add/subtract/multiply/divide decimals the same way you add/subtract/multiply/divide whole numbers BUT you also need to place the decimal in the correct spot. When multiplying decimals, the decimals may or may NOT be lined up in the multiplication problem. Read more...iWorksheets :10Study Guides :1Vocabulary :1
Decimal OperationsDecimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
##### 6.1.2.c. Find the greatest common factor of two whole numbers less than or equal to 100. (CCSS: 6.NS.4)
Common FactorsFactors are two numbers multiplied together to get a product (an answer to a multiplication problem) Read more...iWorksheets :6Study Guides :1Vocabulary :1
##### 6.1.2.e. 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. (CCSS: 6.NS.4)
Distributive PropertyThe distributive property offers a choice in multiplication of two ways to treat the addends in the equation. We are multiplying a sum by a factor which results in the same product as multiplying each addend by the factor and then adding the products. Read more...iWorksheets :3Study Guides :1
Using IntegersIntegers are negative numbers, zero and positive numbers. To compare integers, a number line can be used. On a number line, negative integers are on the left side of zero with the larger a negative number, the farther to the left it is. Positive integers are on the right side of zero on the number line. If a number is to the left of another number it is said to be less than that number. In the coordinate plane, the x-axis is a horizontal line with negative numbers, zero and positive numbers. Read more...iWorksheets :4Study Guides :1
##### 6.1.2.f. Interpret and model quotients of fractions through the creation of story contexts. (CCSS: 6.NS.1)
Multiply / Divide FractionsFreeTo multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this operation. Read more...iWorksheets :6Study Guides :1
Fraction OperationsFraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
##### 6.1.2.g. Compute quotients of fractions. (CCSS: 6.NS.1)
Multiply / Divide FractionsFreeTo multiply two fractions with unlike denominators, multiply the numerators and multiply the denominators. It is unnecessary to change the denominators for this operation. Read more...iWorksheets :6Study Guides :1
Fraction OperationsFraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1

#### 6.1.3. In the real number system, rational numbers have a unique location on the number line and in space. Students can:

##### 6.1.3.b. Use number line diagrams and coordinate axes to represent points on the line and in the plane with negative number coordinates. (CCSS: 6.NS.6)
###### 6.1.3.b.iv. Explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (CCSS: 6.NS.6b)
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
Graphs and TablesUsing tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
###### 6.1.3.b.v. Find and position integers and other rational numbers on a horizontal or vertical number line diagram. (CCSS: 6.NS.6c)
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
Graphs and TablesUsing tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
###### 6.1.3.b.vi. Find and position pairs of integers and other rational numbers on a coordinate plane. (CCSS: 6.NS.6c)
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
Graphs and TablesUsing tables and graphs is a way people can interpret data. Data means information. So interpreting data just means working out what information is telling you. Information is sometimes shown in tables, charts and graphs to make the information easier to read. Read more...iWorksheets :3Study Guides :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
##### 6.1.3.c. Order and find absolute value of rational numbers. (CCSS: 6.NS.7)
###### 6.1.3.c.ii. Write, interpret, and explain statements of order for rational numbers in real-world contexts. (CCSS: 6.NS.7b)
Fractions/DecimalsAny fraction can be changed into a decimal and any decimal can be changed into a fraction. Read more...iWorksheets :3Study Guides :1
Ordering DecimalsWhen putting decimals in order from least to greatest, we must look at the highest place value first. Read more...iWorksheets :7Study Guides :1Vocabulary :1
Compare and Order FractionsWhen comparing two fractions that have a common denominator, you can looks at the numerators to decide which fraction is greater Read more...iWorksheets :4Study Guides :1Vocabulary :1
Ordering FractionsThe order of rational numbers depends on their relationship to each other and to zero. Rational numbers can be dispersed along a number line in both directions from zero. Read more...iWorksheets :6Study Guides :1
Positive & Negative IntegersPositive integers are all the whole numbers greater than zero. Negative integers are all the opposites of these whole numbers, numbers that are less than zero. Zero is considered neither positive nor negative Read more...iWorksheets :4Study Guides :1
Ordering FractionsA fraction consists of two numbers separated by a line - numerator and denominator. To order fractions with like numerators, look at the denominators and compare them two at a time. The fraction with the smaller denominator is the larger fraction. Read more...iWorksheets :3Study Guides :1
Fractions/DecimalsHow to convert fractions to decimals: Divide the denominator (the bottom part) into the numerator (the top part). Read more...iWorksheets :3Study Guides :1
Less Than, Greater ThanCompare fractions and decimals using <, >, or =. Read more...iWorksheets :3Study Guides :1
Rational and Irrational NumbersA rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. Read more...iWorksheets :3Study Guides :1
Exponents, Factors and FractionsFreeIn a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :8Study Guides :1
##### 6.1.3.d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane including the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. (CCSS: 6.NS.8)
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
CoordinatesFreeThe use of coordinates pertains to graphing and the quadrants that are formed by the x and y-axis. Read more...iWorksheets :14Study Guides :1
Plotting PointsIn a coordinate pair, the first number indicates the position of the point along the horizontal axis of the grid. The second number indicates the position of the point along the vertical axis. Read more...iWorksheets :4Study Guides :1Vocabulary :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1

### CO.6.2. Patterns, Functions, and Algebraic Structures

#### 6.2.1. Algebraic expressions can be used to generalize properties of arithmetic. Students can:

##### 6.2.1.a. Write and evaluate numerical expressions involving whole number exponents. (CCSS: 6.EE.1)
Exponents to Repeated MultiplicationAn exponent is a smaller-sized number which appears to the right and slightly above a number. Read more...iWorksheets :4Study Guides :1
Order of OperationsA numerical expression is a phrase which represents a number. Read more...iWorksheets :8Study Guides :1
Evaluate ExponentsEvaluating an expression containing a number with an exponent means to write the repeated multiplication form and perform the operation Read more...iWorksheets :3Study Guides :1
Repeated Multiplication to ExponentsThe result of raising a number to a power is the same number that would be obtained by multiplying the base number together the number of times that is equal to the exponent. Read more...iWorksheets :3Study Guides :1
ExponentsThe exponent represents the number of times to multiply the number, or base. When a number is represented in this way it is called a power. Read more...iWorksheets :4Study Guides :1
Exponents, Factors and FractionsFreeIn a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :8Study Guides :1
##### 6.2.1.b. Write, read, and evaluate expressions in which letters stand for numbers. (CCSS: 6.EE.2)
###### 6.2.1.b.i. Write expressions that record operations with numbers and with letters standing for numbers. (CCSS: 6.EE.2a)
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
###### 6.2.1.b.ii. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) and describe one or more parts of an expression as a single entity. (CCSS: 6.EE.2b)
Order of OperationsA numerical expression is a phrase which represents a number. Read more...iWorksheets :8Study Guides :1
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
###### 6.2.1.b.iii. Evaluate expressions at specific values of their variables including expressions that arise from formulas used in real-world problems. (CCSS: 6.EE.2c)
FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Algebraic EquationsFreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
###### 6.2.1.b.iv. 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). (CCSS: 6.EE.2c)
FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Algebraic EquationsFreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
##### 6.2.1.c. Apply the properties of operations to generate equivalent expressions. (CCSS: 6.EE.3)
AlgebraAlgebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :7Study Guides :1Vocabulary :1
Order of OperationsA numerical expression is a phrase which represents a number. Read more...iWorksheets :8Study Guides :1
FormulasThe formulas contain places for inputting numbers. Evaluating a formula requires inputting the correct data and performing the operations. Read more...iWorksheets :3Study Guides :1
One & Two Step EquationsAn algebraic equation is an expression in which a letter represents an unknown number Read more...iWorksheets :5Study Guides :1
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Algebraic EquationsFreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
Equations and InequalitiesAlgebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :6Study Guides :1
Algebraic EquationsWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :5Study Guides :1
Algebraic InequalitiesFreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1
Introduction to FunctionsA function is a rule that is performed on a number, called an input, to produce a result called an output. The rule consists of one or more mathematical operations that are performed on the input. An example of a function is y = 2x + 3, where x is the input and y is the output. The operations of multiplication and addition are performed on the input, x, to produce the output, y. By substituting a number for x, an output can be determined. Read more...iWorksheets :7Study Guides :1
Nonlinear Functions and Set TheoryA function can be in the form of y = mx + b. This is an equation of a line, so it is said to be a linear function. Nonlinear functions are functions that are not straight lines. Some examples of nonlinear functions are exponential functions and parabolic functions. An exponential function, y = aˆx, is a curved line that gets closer to but does not touch the x-axis. A parabolic function, y = ax² + bx +c, is a U-shaped line that can either be facing up or facing down. Read more...iWorksheets :5Study Guides :1

#### 6.2.2. Variables are used to represent unknown quantities within equations and inequalities. Students can:

##### 6.2.2.a. Describe 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? (CCSS: 6.EE.5)
AlgebraAlgebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :7Study Guides :1Vocabulary :1
One & Two Step EquationsAn algebraic equation is an expression in which a letter represents an unknown number Read more...iWorksheets :5Study Guides :1
Algebraic EquationsFreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
Equations and InequalitiesAlgebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :6Study Guides :1
Using IntegersIntegers are negative numbers, zero and positive numbers. To compare integers, a number line can be used. On a number line, negative integers are on the left side of zero with the larger a negative number, the farther to the left it is. Positive integers are on the right side of zero on the number line. If a number is to the left of another number it is said to be less than that number. In the coordinate plane, the x-axis is a horizontal line with negative numbers, zero and positive numbers. Read more...iWorksheets :4Study Guides :1
Decimal OperationsDecimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
Fraction OperationsFraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
Introduction to PercentWhat Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
Algebraic EquationsWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :5Study Guides :1
Algebraic InequalitiesFreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1
##### 6.2.2.c. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. (CCSS: 6.EE.6)
###### 6.2.2.c.i. Recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. (CCSS: 6.EE.6)
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
##### 6.2.2.d. 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. (CCSS: 6.EE.7)
AlgebraAlgebra is the study of mathematical symbols and the rules for manipulating these symbols Read more...iWorksheets :7Study Guides :1Vocabulary :1
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Algebraic EquationsFreeWhat are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. Read more...iWorksheets :6Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
Equations and InequalitiesAlgebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :6Study Guides :1
##### 6.2.2.e. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. (CCSS: 6.EE.8)
Equations and InequalitiesAlgebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :6Study Guides :1
Algebraic InequalitiesFreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1
##### 6.2.2.f. Show that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (CCSS: 6.EE.8)
Equations and InequalitiesAlgebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :6Study Guides :1
Algebraic InequalitiesFreeAlgebraic inequalities are mathematical equations that compare two quantities using these criteria: greater than, less than, less than or equal to, greater than or equal to. The only rule of inequalities that must be remembered is that when a variable is multiplied or divided by a negative number the sign is reversed. Read more...iWorksheets :3Study Guides :1
##### 6.2.2.g. Represent and analyze quantitative relationships between dependent and independent variables. (CCSS: 6.EE)
###### 6.2.2.g.i. Use variables to represent two quantities in a real-world problem that change in relationship to one another. (CCSS: 6.EE.9)
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
###### 6.2.2.g.ii. 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. (CCSS: 6.EE.9)
Simple AlgebraSimple algebra is the term used when using expressions with letters or variables that represent numbers. Read more...iWorksheets :3Study Guides :1
Introduction to AlgebraAlgebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :4Study Guides :1
###### 6.2.2.g.iii. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (CCSS: 6.EE.9)
Introduction to FunctionsA function is a rule that is performed on a number, called an input, to produce a result called an output. The rule consists of one or more mathematical operations that are performed on the input. An example of a function is y = 2x + 3, where x is the input and y is the output. The operations of multiplication and addition are performed on the input, x, to produce the output, y. By substituting a number for x, an output can be determined. Read more...iWorksheets :7Study Guides :1

### CO.6.3. Data Analysis, Statistics, and Probability

#### 6.3.1. Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge. Students can:

##### 6.3.1.c. Explain 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. (CCSS: 6.SP.3)
StatisticsA statistic is a collection of numbers related to a specific topic. Read more...iWorksheets :6Study Guides :1
StatisticsThe statistical mode is the number that occurs most frequently in a set of numbers. Read more...iWorksheets :3Study Guides :1
Data AnalysisCollecting Data. Data = information. You can collect data from other people using polls and surveys. Recording Data. You can record the numerical data you collected on a chart or graph: bar graphs, pictographs, line graphs, pie charts, column charts. Read more...iWorksheets :6Study Guides :1
Organizing DataThe data can be organized into groups, and evaluated. Mean, mode, median and range are different ways to evaluate data. The mean is the average of the data. The mode refers to the number that occurs the most often in the data. The median is the middle number when the data is arranged in order from lowest to highest. The range is the difference in numbers when the lowest number is subtracted from the highest number. Data can be organized into a table, such as a frequency table. Read more...iWorksheets :3Study Guides :1
##### 6.3.1.d. Summarize and describe distributions. (CCSS: 6.SP)
###### 6.3.1.d.ii.3. Give 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. (CCSS: 6.SP.5c)
StatisticsA statistic is a collection of numbers related to a specific topic. Read more...iWorksheets :6Study Guides :1
StatisticsThe statistical mode is the number that occurs most frequently in a set of numbers. Read more...iWorksheets :3Study Guides :1
Data AnalysisCollecting Data. Data = information. You can collect data from other people using polls and surveys. Recording Data. You can record the numerical data you collected on a chart or graph: bar graphs, pictographs, line graphs, pie charts, column charts. Read more...iWorksheets :6Study Guides :1
Organizing DataThe data can be organized into groups, and evaluated. Mean, mode, median and range are different ways to evaluate data. The mean is the average of the data. The mode refers to the number that occurs the most often in the data. The median is the middle number when the data is arranged in order from lowest to highest. The range is the difference in numbers when the lowest number is subtracted from the highest number. Data can be organized into a table, such as a frequency table. Read more...iWorksheets :3Study Guides :1

### CO.6.4. Shape, Dimension, and Geometric Relationships

#### 6.4.1. Objects in space and their parts and attributes can be measured and analyzed. Students can:

##### 6.4.1.b. Develop and apply formulas and procedures for volume of regular prisms.
###### 6.4.1.b.i. 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. (CCSS: 6.G.2)
VolumeVolume measures the amount a solid figure can hold. Read more...iWorksheets :3Study Guides :1
Finding VolumeVolume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1
###### 6.4.1.b.iii. 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. (CCSS: 6.G.2)
VolumeVolume measures the amount a solid figure can hold. Read more...iWorksheets :3Study Guides :1
Finding VolumeVolume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1
##### 6.4.1.c. Draw polygons in the coordinate plan to solve real-world and mathematical problems. (CCSS: 6.G.3)
###### 6.4.1.c.i. Draw polygons in the coordinate plane given coordinates for the vertices.
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
###### 6.4.1.c.ii. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. (CCSS: 6.G.3)
Plot PointsYou use plot points to place a point on a coordinate plane by using X and Y coordinates to draw on a coordinate grid. Read more...iWorksheets :5Study Guides :1Vocabulary :1
Area of Coordinate PolygonsCalculate the area of basic polygons drawn on a coordinate plane. Coordinate plane is a grid on which points can be plotted. The horizontal axis is labeled with positive numbers to the right of the vertical axis and negative numbers to the left of the vertical axis. Read more...iWorksheets :3Study Guides :1
##### 6.4.1.d. Develop and apply formulas and procedures for the surface area.
###### 6.4.1.d.ii. Use nets to find the surface area of figures. (CCSS: 6.G.4)
Exploring Area and Surface AreaArea is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1
###### 6.4.1.d.iii. Apply techniques for finding surface area in the context of solving real-world and mathematical problems. (CCSS: 6.G.4)
Exploring Area and Surface AreaArea is the amount of surface a shape covers. Area is measured in square units, whether the units are inches, feet, meters or centimeters. The area formula for a triangle is: A = 1/2 · b · h, where b is the base and h is the height. The area formula for a circle is: A = π · r², where π is usually 3.14 and r is the radius of the circle. The area formula for a parallelogram is: A = b · h, where b is the base and h is the height. Read more...iWorksheets :4Study Guides :1