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## WA.6.1.Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Students have done extensive work with fractions and decimals in previous grades and are now prepared to learn how to multiply and divide fractions and decimals with understanding. They can solve a wide variety of problems that involve the numbers they see every day - whole numbers, fractions, and decimals. By using approximations of fractions and decimals, students estimate computations and verify that their answers make sense.

Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Students have done extensive work with fractions and decimals in previous grades and are now prepared to learn how to multiply and divide fractions and decimals with understanding. They can solve a wide variety of problems that involve the numbers they see every day - whole numbers, fractions, and decimals. By using approximations of fractions and decimals, students estimate computations and verify that their answers make sense.
6.1.A. Compare and order non-negative fractions, decimals, and integers using the number line, lists, and the symbols <, >, or =.
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Vocabulary Terms Ordering Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Positive & Negative Integers

6.1.B. Represent multiplication and division of non-negative fractions and decimals using area models and the number line, and connect each representation to the related equation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions

6.1.C. Estimate products and quotients of fractions and decimals.
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation

6.1.D. Fluently and accurately multiply and divide non-negative fractions and explain the inverse relationship between multiplication and division with fractions.
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions

6.1.E. Multiply and divide whole numbers and decimals by 1000, 100, 10, 1, 0.1, 0.01, and 0.001.

6.1.F. Fluently and accurately multiply and divide non-negative decimals.
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations

6.1.G. Describe the effect of multiplying or dividing a number by one, by zero, by a number between zero and one, and by a number greater than one.

## WA.6.2.Core Content: Mathematical expressions and equations (Operations, Algebra) Students continue to develop their understanding of how letters are used to represent numbers in mathematics - an important foundation for algebraic thinking. Students use tables, words, numbers, graphs, and equations to describe simple linear relationships. They write and evaluate expressions and write and solve equations. By developing these algebraic skills at the middle school level, students will be able to make a smooth transition to high school mathematics.

Core Content: Mathematical expressions and equations (Operations, Algebra) Students continue to develop their understanding of how letters are used to represent numbers in mathematics - an important foundation for algebraic thinking. Students use tables, words, numbers, graphs, and equations to describe simple linear relationships. They write and evaluate expressions and write and solve equations. By developing these algebraic skills at the middle school level, students will be able to make a smooth transition to high school mathematics.
6.2.A. Write a mathematical expression or equation with variables to represent information in a table or given situation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Algebra

6.2.B. Draw a first-quadrant graph in the coordinate plane to represent information in a table or given situation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

6.2.C. Evaluate mathematical expressions when the value for each variable is given.
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Algebra

6.2.D. Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.
Vocabulary Terms Order of Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Distributive Property
Quiz, Flash Cards, Worksheet, Game & Study Guide Order of Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Order of Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

6.2.E. Solve one-step equations and verify solutions.
Flip Charts Solving Equations
Flip Charts Solving Equations
Vocabulary Terms Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

6.2.F. Solve word problems using mathematical expressions and equations and verify solutions.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Algebra

## WA.6.3.Core Content: Ratios, rates, and percents (Numbers, Operations, Geometry/Measurement, Algebra, Data/Statistics/Probability) Students extend their knowledge of fractions to develop an understanding of what a ratio is and how it relates to a rate and a percent. Fractions, ratios, rates, and percents appear daily in the media and in everyday calculations like determining the sale price at a retail store or figuring out gas mileage. Students solve a variety of problems related to such situations. A solid understanding of ratios and rates is important for work involving proportional relationships in grade seven.

Core Content: Ratios, rates, and percents (Numbers, Operations, Geometry/Measurement, Algebra, Data/Statistics/Probability) Students extend their knowledge of fractions to develop an understanding of what a ratio is and how it relates to a rate and a percent. Fractions, ratios, rates, and percents appear daily in the media and in everyday calculations like determining the sale price at a retail store or figuring out gas mileage. Students solve a variety of problems related to such situations. A solid understanding of ratios and rates is important for work involving proportional relationships in grade seven.
6.3.A. Identify and write ratios as comparisons of part-to-part and part-to-whole relationships.
Flip Charts Box It Up
Flip Charts Triangle Tricks
Vocabulary Terms Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Proportions/Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Proportions

6.3.B. Write ratios to represent a variety of rates.
Flip Charts Box It Up
Flip Charts Triangle Tricks
Vocabulary Terms Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Proportions/Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratio
Quiz, Flash Cards, Worksheet, Game & Study Guide Simple Proportions

6.3.C. Represent percents visually and numerically, and convert between the fractional, decimal, and percent representations of a number.
Vocabulary Terms Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiple Representation of Rational Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Percent, Rate, Base
Quiz, Flash Cards, Worksheet, Game & Study Guide Percentage
Quiz, Flash Cards, Worksheet, Game & Study Guide Percents

6.3.D. Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions.
Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

6.3.E. Identify the ratio of the circumference to the diameter of a circle as the constant pi, and recognize 22/7 and 3.14 as common approximations of pi.
Flip Charts Dot to Dot
Flip Charts Finding Volume
Flip Charts Shape Up
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Circumference of Circles
Quiz, Flash Cards, Worksheet, Game & Study Guide Diameter of Circle
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference

6.3.F. Determine the experimental probability of a simple event using data collected in an experiment.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability

6.3.G. Determine the theoretical probability of an event and its complement and represent the probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability

## WA.6.4.Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Students extend what they know about area and perimeter to more complex two-dimensional figures, including circles. They find the surface area and volume of simple three-dimensional figures. As they learn about these important concepts, students can solve problems involving more complex figures than in earlier grades and use geometry to deal with a wider range of situations. These fundamental skills of geometry and measurement are increasingly called for in the workplace and they lead to a more formal study of geometry in high school.

Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Students extend what they know about area and perimeter to more complex two-dimensional figures, including circles. They find the surface area and volume of simple three-dimensional figures. As they learn about these important concepts, students can solve problems involving more complex figures than in earlier grades and use geometry to deal with a wider range of situations. These fundamental skills of geometry and measurement are increasingly called for in the workplace and they lead to a more formal study of geometry in high school.
6.4.A. Determine the circumference and area of circles.
Flip Charts Dot to Dot
Flip Charts Shape Up
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Circumference of Circles
Quiz, Flash Cards, Worksheet, Game & Study Guide Diameter of Circle
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference

6.4.C. Solve single- and multi-step word problems involving the relationships among radius, diameter, circumference, and area of circles, and verify the solutions.
Flip Charts Dot to Dot
Flip Charts Shape Up
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Circumference of Circles
Quiz, Flash Cards, Worksheet, Game & Study Guide Diameter of Circle
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Formulas
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference

6.4.E. Determine the surface area and volume of rectangular prisms using appropriate formulas and explain why the formulas work.
Flip Charts Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Volume

6.4.F. Determine the surface area of a pyramid.

6.4.G. Describe and sort polyhedra by their attributes: parallel faces, types of faces, number of faces, edges, and vertices.
Flip Charts Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume

## WA.6.5.Additional Key Content (Numbers, Operations) Students extend their mental math skills now that they have learned all of the operations - addition, subtraction, multiplication, and division - with whole numbers, fractions, and decimals. Students continue to expand their understanding of our number system as they are introduced to negative numbers for describing positions or quantities below zero. These numbers are a critical foundation for algebra, and students will learn how to add, subtract, multiply, and divide positive and negative numbers in seventh grade as further preparation for algebraic study.

Additional Key Content (Numbers, Operations) Students extend their mental math skills now that they have learned all of the operations - addition, subtraction, multiplication, and division - with whole numbers, fractions, and decimals. Students continue to expand their understanding of our number system as they are introduced to negative numbers for describing positions or quantities below zero. These numbers are a critical foundation for algebra, and students will learn how to add, subtract, multiply, and divide positive and negative numbers in seventh grade as further preparation for algebraic study.
6.5.A. Use strategies for mental computations with non-negative whole numbers, fractions, and decimals.
Vocabulary Terms Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Distributive Property
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiply/Divide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

6.5.B. Locate positive and negative integers on the number line and use integers to represent quantities in various contexts.

6.5.C. Compare and order positive and negative integers using the number line, lists, and the symbols <, >, or =.
Quiz, Flash Cards, Worksheet, Game & Study Guide Positive & Negative Integers

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