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6Grade 6 Standards
Top Mathematicians
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Number & Operations
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6.N.1.1
Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.
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6.N.1.2
Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.
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6.N.1.3
Explain that a percent represents parts "out of 100" and ratios "to 100."
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6.N.1.4
Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.
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6.6Convert Between Percents, Fractions and Decimals15
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6.7Compare Percents to Fractions and Decimals15
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6.8Compare Ratios5
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6.9Percents of Numbers and Money Amounts5
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6.10Percents of Numbers5
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6.11Constant of Variation15
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6.N.1.5
Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents.
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6.12Prime and Composite Numbers10
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6.13Identify Factors20
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6.N.1.6
Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.
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6.14Greatest Common Factors (GCF)15
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6.15Least Common Multiples (LCM)20
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6.16GCF and LCM20
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6.17Make Equivalent Fractions20
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6.18Reducing Fractions to Lowest Terms15
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6.19Reduce to Lowest Terms20
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6.20Subtract Fractions with Unlike Denominators5
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6.21Add Fractions with Unlike Denominators5
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6.22Add and Subtract Mixed Numbers15
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6.N.2.1
Estimate solutions to addition and subtraction of integers problems in order to assess the reasonableness of results.
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6.23Estimate Mixed Equations20
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6.N.2.2
Illustrate addition and subtraction of integers using a variety of representations.
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6.N.2.3
Add and subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms.
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6.N.3.1
Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different.
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6.24Describe Pictures as Ratios5
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6.25Equivalent Ratios5
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6.26Ratio Tables5
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6.27Equivalent Ratios15
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6.28Ratios and Proportions15
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6.29Scale Drawings and Scale Factors15
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6.8Compare Ratios5
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6.N.3.2
Determine the unit rate for ratios.
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6.30Unit Rates and Equivalent Rates10
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6.31Unit Rates10
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6.N.3.3
Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.
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6.8Compare Ratios5
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6.10Percents of Numbers5
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6.N.3.4
Use multiplicative reasoning and representations to solve ratio and unit rate problems.
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6.27Equivalent Ratios15
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6.32Ratios5
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6.33Equivalent Ratios5
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6.8Compare Ratios5
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6.N.4.1
Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.
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6.34Estimate Products Up to 100020
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6.35Estimate Quotients20
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6.36Estimate Quotients Up to 100020
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6.37Estimate Quotients Up to 10,00020
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6.38Estimate Products of Decimal Numbers15
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6.N.4.2
Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.
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6.39Multiply Fractions with Models15
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6.40Divide by Fractions with Models15
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6.N.4.3
Multiply and divide fractions and decimals using efficient and generalizable procedures.
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6.41Multiply Decimals with Numbers Up to 10015
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6.42Multiply Decimals5
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6.43Divide Decimals by Whole Numbers15
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6.44Divide Decimals by Whole Numbers15
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6.45Multiply and Divide Decimals by Powers of Ten15
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6.46Division with Decimals15
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6.47Division with Decimal Quotients15
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6.48Multiply Fractions15
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6.49Multiply Fractions by Whole Numbers15
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6.50Divide and Multiply Mixed Numbers15
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6.51Multiply Mixed Numbers15
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6.52Reciprocals15
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6.53Divide Unit Fractions by Whole Numbers Up to 20 I15
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6.54Divide Fractions Up to 1/5, 1/7, 1/915
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6.55Divide Fractions with Mixed Numbers Up to 2015
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6.56Estimate Quotients When Dividing Mixed Numbers20
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6.57Divide Fractions and Mixed Numbers Up to 1/16, 1/3210
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6.58Divide Fractions and Mixed Numbers Up to 1/325
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6.59Divide Fractions and Mixed Numbers15
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6.60Divide Fractions and Mixed Numbers Up to 1/1610
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6.61Mixed Equations with Decimals15
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6.62Evaluate Expressions with Decimals15
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6.63Mixed Fraction Equations with Mixed Numbers Up to 50015
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6.64Multiply and Divide Rational Numbers15
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6.N.4.4
Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.
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6.65Add and Subtract Decimals15
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6.66Add and Subtract Decimals Up to 1020
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6.67Add and Subtract Decimal Up to 10015
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6.68Mixed Decimal Equations20
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6.69Mixed Fraction Equations Up to 50015
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6.70Customary Unit Conversions Involving Fractions and Mixed10
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6.71Find the Number of Each Type of Coin5
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6.72Add and Subtract Money: Up to $10,0005
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6.73Multiply Money Amounts10
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6.74Divide Money Amounts10
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6.75Unit Prices: Which Is the Better Buy?20
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6.76Which Is the Better Coupon?5
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6.77Consumer Math: Unit Prices20
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6.78Unit Prices with Customary Unit Conversions and Fractions10
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6.79Consumer Math: Unit Prices20
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6.80Unit Prices with Metric Unit Conversions10
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6.81Unit Prices with Customary Unit Conversions Up to 10010
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6.82Sale Prices15
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6.83Sale Prices: Find the Original Price15
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6.84Calculate Tip, Markup and Commission15
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6.85Simple Interest15
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6.N.1.1
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Geometry & Measurement
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6.GM.1.1
Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm.
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6.138Area of Rectangles and Parallelograms5
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6.139Area of Triangles and Trapezoids5
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6.140Area of Complex Figures10
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6.GM.1.2
Develop and use formulas to determine the area of triangles.
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6.139Area of Triangles and Trapezoids5
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6.141Area of Right Triangles10
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6.GM.1.3
Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.
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6.138Area of Rectangles and Parallelograms5
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6.139Area of Triangles and Trapezoids5
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6.140Area of Complex Figures10
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6.141Area of Right Triangles10
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6.GM.2.1
Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.
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6.GM.2.2
Develop and use the fact that the sum of the interior angles of a triangle is 180° to determine missing angle measures in a triangle.
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6.GM.3.1
Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.
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6.GM.3.2
Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.
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6.147Compare and Convert Customary Units with Numbers Up to 205
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6.148Convert, Compare and Subtract Mixed Customary Units5
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6.149Multiply and Divide Mixed Metric Units5
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6.150Multiply and Divide Mixed Customary Units5
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6.151Metric Unit Conversions Involving Fractions and Mixed5
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6.152Compare and Convert Metric Units5
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6.153Convert Between Metric and Customary Units5
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6.154Find the Change in Time I20
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6.155Change in Time Review20
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6.156Find Start and End Times5
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6.70Customary Unit Conversions Involving Fractions and Mixed10
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6.GM.4.1
Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure.
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6.157Identify Reflections, Rotations and Translations5
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6.158Translations: Graph the Image5
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6.159Reflections: Graph the Image5
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6.160Rotations: Graph the Image10
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6.GM.4.2
Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent.
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6.GM.4.3
Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures.
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6.91Relative Coordinates15
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6.161Maps with Decimal Distances5
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6.162Maps with Fractional Distances5
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6.163Distance Between Two Points15
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6.GM.4.4
Identify and describe the line(s) of symmetry in two-dimensional shapes.
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6.164Symmetry5
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6.GM.1.1
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Algebraic Reasoning & Algebra
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6.A.1.1
Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.
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6.86Coordinate Graphs Review10
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6.87Coordinate Graphs with Decimals and Negative Numbers15
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6.88Coordinate Graphs Review with Whole Numbers10
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6.89Graph Points on a Coordinate Plane15
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6.90Coordinate Graphs as Maps5
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6.91Relative Coordinates15
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6.A.1.2
Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.
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6.92Evaluate Multi-Variable Expressions15
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6.93Linear Function5
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6.94Two-Variable Equations5
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6.95Function Tables15
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6.96Write Linear Functions10
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6.97Graph Linear Functions15
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6.98Graph a Line from a Function Table10
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6.99Graph a Line from an Equation10
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6.100Interpret Double Bar Graphs5
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6.101Interpret Line Graphs5
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6.102Interpret Bar Graphs5
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6.103Interpret Double Line Graphs5
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6.104Complete a Function Table10
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6.105Write a Rule for a Function Table10
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6.A.1.3
Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.
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6.92Evaluate Multi-Variable Expressions15
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6.106Write Variable Expressions5
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6.107Write Variable Expressions5
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6.108Linear Function10
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6.109Write Variable Equations to Represent5
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6.110Evaluate Variable Expressions with Whole Numbers5
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6.111Identify Terms, Coefficients, and Monomials5
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6.112Properties of Addition5
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6.113Choose Properties of Multiplication15
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6.114Factors of Multiplication5
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6.115Properties of Multiplication with Factors Up to 1215
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6.116Simplify Variable Expressions10
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6.117Distributive Property5
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6.118Add and Subtract Like Terms10
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6.A.2.1
Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.
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6.119Write Multiplication Expressions Using Exponents10
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6.120Evaluate Exponents15
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6.121Exponents with Decimal Bases15
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6.122Exponents with Fractional Bases15
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6.123Simplify Expressions15
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6.92Evaluate Multi-Variable Expressions15
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6.62Evaluate Expressions with Decimals15
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6.A.3.1
Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
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6.124Model and Solve Equations Using Algebra Tiles5
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6.126Multi-Step20
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6.127Solve Two-Step Linear Equations5
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6.128Solve Equations Involving Like Terms10
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6.129Solve Mixed Equations5
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6.130Solve One-Step Linear Inequalities5
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6.131Solve One-Step Linear Equations5
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6.107Write Variable Expressions5
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6.108Linear Function10
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6.109Write Variable Equations to Represent5
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6.110Evaluate Variable Expressions with Whole Numbers5
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6.A.3.2
Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = q and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.
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6.A.1.1
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Data & Probability
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6.D.1.1
Calculate the mean, median, and mode for a set of real-world data.
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6.165Calculate Mean10
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6.166Calculate Range10
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6.167Calculate Mode10
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6.168Calculate Median10
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6.169Calculate Mean, Median, Mode and Range10
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6.170Interpret Charts to Find Mean, Median, Mode, and Range5
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6.171Interpret Charts to Find Median5
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6.172Interpret Charts to Find Mode5
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6.173Interpret Charts to Find Mean5
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6.174Interpret Charts to Find Range5
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6.175Mean, Median, Mode, and Range: Find the Missing Number10
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6.176Mode: Find the Missing Number10
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6.177Median: Find the Missing Number10
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6.178Mean: Find the Missing Number10
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6.179Range: Find the Missing Number10
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6.D.1.2
Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.
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6.D.1.3
Create and analyze box and whisker plots observing how each segment contains one quarter of the data.
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6.180Interpret Box-And-Whisker Plots5
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6.D.2.1
Represent possible outcomes using a probability continuum from impossible to certain.
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6.D.2.2
Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.
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6.181Probability of Simple Events5
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6.182Making Predictions5
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6.183Prediction Problems5
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6.184Probability of Opposite and Overlapping Events5
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6.185Compound Events: Find the Number of Outcomes5
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6.D.2.3
Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.
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6.D.1.1