Virginia

6.NS Number and Number Sense

• 6.NS.1 The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.

  • 6.NS.1.a Estimate and determine the percent represented by a given model, including percents greater than 100% and less than 1%.

    • What percentage is illustrated? (6-U.1)
    • Benchmark percents with strip models: multiples of 10, 20, 25, 33, and 50 (6-U.3)

  • 6.NS.1.b Represent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models.

    • Convert between percents and decimals (6)

  • 6.NS.1.c Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models.

    • Convert fractions to percents using grid models (6-U.4)

  • 6.NS.1.d Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models.

    • Write fractions in lowest terms (6-G.1)
    • Convert between improper fractions and mixed numbers (6-G.3)
    • Convert decimals to fractions (6)
    • Convert between fractions and repeating decimals (6-G.6)
    • Convert between percents, fractions, and decimals (6-U.7)
    • Convert between percents, fractions, and decimals: word problems (6-U.8)
    • Equivalent fractions review (6)
    • Convert fractions to decimals (6)
    • Convert between decimals and fractions (6)
    • Convert between decimals and mixed numbers (6)

  • 6.NS.1.e Use multiple strategies to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order.

    • Put a mix of decimals and fractions in order (6-G.9)
    • Put a mix of decimals, fractions, and mixed numbers in order (6-G.10)
    • Compare percents to each other and to fractions (6-U.9)
    • Compare percents and fractions: word problems (6-U.10)
    • Compare percents to fractions and decimals (6)

• 6.NS.2 The student will reason and use multiple strategies to represent, compare, and order integers.

  • 6.NS.2.a Represent integers, including models derived from contextual situations, and identify an integer represented by a point on a number line.

    • Understanding integers (6-O.1)
    • Integers on number lines (6-O.2)
    • Graph integers on horizontal and vertical number lines (6-O.3)
    • Understanding opposite integers (6-O.4)

  • 6.NS.2.b Compare and order integers using a number line.

    • Compare integers (6-O.7)
    • Put integers in order (6-O.8)

  • 6.NS.2.c Compare integers, using mathematical symbols (<, >, =).

    • Compare integers (6-O.7)

  • 6.NS.2.d Identify and describe the absolute value of an integer as the distance from zero on the number line.

    • Understanding absolute value (6-O.5)
    • Absolute value (6-O.6)
    • Absolute value and integers: word problems (6-O.10)

  • Checkpoint opportunity

• 6.NS.3 The student will recognize and represent patterns with whole number exponents and perfect squares.

  • 6.NS.3.a Recognize and represent patterns with bases and exponents that are whole numbers.

    • Write multiplication expressions using exponents (6-D.1)

  • 6.NS.3.b Recognize and represent patterns of perfect squares not to exceed 20², by using concrete and pictorial models.

  • 6.NS.3.c Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.

    • Square numbers (6)

  • 6.NS.3.d Recognize and represent powers of 10 with whole number exponents by examining patterns in place value.

    • Write powers of ten with exponents (6-D.3)

  • Checkpoint opportunity

    • Checkpoint: Exponents (6)

6.CE Computation and Estimation

• 6.CE.1 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.

  • 6.CE.1.a Demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple representations.

    • Multiply a mixed number by a whole number using a model (6)
    • Multiply with mixed numbers using area models (6)
    • Divide unit fractions and whole numbers using area models (6)
    • Multiply two fractions using models (6-L.5)
    • Divide whole numbers by unit fractions using models (6-M.1)
    • Divide whole numbers and fractions using models (6)
    • Divide fractions using models (6)
    • Divide fractions and mixed numbers using models (6)
    • Divide fractions and mixed numbers using models: word problems (6)

  • 6.CE.1.b Multiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

    • Multiply mixed numbers (6)
    • Multiply fractions and whole numbers (6)
    • Estimate products of fractions and whole numbers (6-L.4)
    • Multiply fractions greater than one using models (6-L.6)
    • Multiply two fractions (6)
    • Multiply three or more fractions and whole numbers (6)
    • Estimate products of mixed numbers (6)
    • Multiply a mixed number by a whole number (6)
    • Multiply three or more mixed numbers, fractions, and/or whole numbers (6)
    • Divide whole numbers and unit fractions (6-M.3)
    • Divide fractions (6)
    • Divide fractions and mixed numbers (6)
    • Fractions of a number: word problems (6)
    • Divide fractions and whole numbers (6)

  • 6.CE.1.c Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one.

    • Scaling whole numbers by fractions: justify your answer (6-L.9)
    • Scaling by fractions and mixed numbers (6-L.10)

  • 6.CE.1.d Estimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

    • Add and subtract fractions with like denominators: word problems (6)
    • Maps with fractional distances (6-K.9)
    • Add, subtract, multiply, or divide two fractions: word problems (6)
    • Add and subtract fractions and mixed numbers: word problems (6)
    • Add, subtract, multiply, or divide fractions in recipes (6)

  • 6.CE.1.e Estimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

    • Multiply fractions and whole numbers: word problems (6)
    • Multiply fractions: word problems (6)
    • Multiply mixed numbers: word problems (6)
    • Divide fractions by whole numbers in recipes (6)
    • Divide fractions and mixed numbers using models: word problems (6)
    • Divide fractions and mixed numbers: word problems (6)
    • Add, subtract, multiply, or divide two fractions: word problems (6)
    • Add, subtract, multiply, or divide fractions in recipes (6)

  • Checkpoint opportunity

    • Checkpoint: Multiply and divide fractions (6)

• 6.CE.2 The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.

  • 6.CE.2.a Demonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or concrete manipulatives.

    • Add integers using counters (6-P.1)
    • Add integers using number lines (6-P.2)
    • Subtract integers using counters (6-P.4)
    • Subtract integers using number lines (6-P.5)
    • Understand multiplying by a negative integer using a number line (6-P.11)

  • 6.CE.2.b Add, subtract, multiply, and divide two integers.

    • Add integers (6-P.3)
    • Subtract integers (6-P.6)
    • Add and subtract integers: find the sign (6-P.7)
    • Add and subtract integers: input/output tables (6-P.9)
    • Multiply integers: find the sign (6-P.12)
    • Multiply integers (6-P.13)
    • Divide integers: find the sign (6-P.14)
    • Divide integers (6-P.15)
    • Add, subtract, multiply, or divide two integers (6-P.16)

  • 6.CE.2.c Simplify an expression that contains absolute value bars | | and an operation with two integers and represent the result on a number line.

  • 6.CE.2.d Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers.

    • Add and subtract integers: word problems (6-P.8)

  • Checkpoint opportunity

6.MG Measurement and Geometry

• 6.MG.1 The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.

  • 6.MG.1.a Identify and describe chord, diameter, radius, circumference, and area of a circle.

    • Parts of a circle (6)

  • 6.MG.1.b Investigate and describe the relationship between: diameter and radius; radius and circumference; and diameter and circumference.

  • 6.MG.1.c Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or technological models.

  • 6.MG.1.d Develop the formula for circumference using the relationship between diameter, radius, and pi.

  • 6.MG.1.e Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.

    • Circumference of circles (6)
    • Area of circles (6)
    • Circles: word problems (6)
    • Area between two circles (6)

• 6.MG.2 The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.

  • 6.MG.2.a Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives.

    • Understanding area of a parallelogram (6-GG.3)
    • Understanding area of a triangle (6-GG.5)

  • 6.MG.2.b Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.

    • Area of parallelograms (6-GG.4)
    • Area of triangles (6-GG.6)
    • Area between two triangles (6-GG.14)
    • Area and perimeter of rectangles and squares: word problems (6)
    • Perimeter of triangles and parallelograms (6)
    • Area of squares, rectangles, and triangles: word problems (6)

  • Checkpoint opportunity

• 6.MG.3 The student will describe the characteristics of the coordinate plane and graph ordered pairs.

  • 6.MG.3.a Identify and label the axes, origin, and quadrants of a coordinate plane.

    • Describe the coordinate plane (6-R.1)

  • 6.MG.3.b Identify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be limited to coordinates expressed as integers.

    • Describe the coordinate plane (6-R.1)
    • Quadrants (6-R.4)

  • 6.MG.3.c Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

    • Graph points on a coordinate plane: integers only (6)

  • 6.MG.3.d Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

    • Objects on a coordinate plane (6)

  • 6.MG.3.e Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers.

    • Coordinate planes as maps (6-R.6)
    • Distance between two points: integers only (6)

  • 6.MG.3.f Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving contextual and mathematical problems.

    • Area and perimeter of squares and rectangles on the coordinate plane (6-R.9)
    • Graph triangles and quadrilaterals (6-EE.6)

  • Checkpoint opportunity

• 6.MG.4 The student will determine congruence of segments, angles, and polygons.

  • 6.MG.4.a Identify regular polygons.

    • Identify and classify polygons (6-EE.1)

  • 6.MG.4.b Draw lines of symmetry to divide regular polygons into two congruent parts.

    • Line symmetry (6-EE.11)

  • 6.MG.4.c Determine the congruence of segments, angles, and polygons given their properties.

  • 6.MG.4.d Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.

    • Identify congruent figures (6)

6.PS Probability and Statistics

• 6.PS.1 The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs.

  • 6.PS.1.a Formulate questions that require the collection or acquisition of data with a focus on circle graphs.

    • Identify statistical questions (6-JJ.1)

  • 6.PS.1.b Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods.

  • 6.PS.1.c Determine the factors that will ensure that the data collected is a sample that is representative of a larger population.

    • Identify representative and random samples (6)

  • 6.PS.1.d Organize and represent data using circle graphs, with and without the use of technology tools. The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100.

  • 6.PS.1.e Analyze data represented in a circle graph by making observations and drawing conclusions.

    • Interpret circle graphs (6-II.14)

  • 6.PS.1.f Compare data represented in a circle graph with the same data represented in other graphs, including but not limited to bar graphs, pictographs, and line plots (dot plots), and justify which graphical representation best represents the data.

• 6.PS.2 The student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed.

  • 6.PS.2.a Represent the mean of a set of data graphically as the balance point represented in a line plot (dot plot).

    • Calculate mean (6)

  • 6.PS.2.b Determine the effect on measures of center when a single value of a data set is added, removed, or changed.

    • Changes in mean, median, and mode (6)

  • 6.PS.2.c Observe patterns in data to identify outliers and determine their effect on mean, median, mode, or range.

    • Identify an outlier (6-JJ.8)
    • Identify an outlier and describe the effect of removing it (6-JJ.9)

6.PFA Patterns, Functions, and Algebra

• 6.PFA.1 The student will use ratios to represent relationships between quantities, including those in context.

  • 6.PFA.1.a Represent a relationship between two quantities using ratios.

    • Write a ratio using a colon (6-S.2)
    • Write a ratio using a fraction (6-S.3)
    • Which model represents the ratio? (6-S.6)

  • 6.PFA.1.b Represent a relationship in context that makes a comparison by using the notations ^a/_b, a:b, and a to b.

    • Write a ratio: word problems (6)

  • 6.PFA.1.c Represent different comparisons within the same quantity or between different quantities.

  • 6.PFA.1.d Create a relationship in words for a given ratio expressed symbolically.

  • 6.PFA.1.e Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a ratio.

    • Identify equivalent ratios (6-S.7)
    • Write an equivalent ratio (6-S.8)
    • Ratio tables (6-S.9)

  • 6.PFA.1.f Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contextual situation.

    • Equivalent ratios: word problems (6-S.10)

• 6.PFA.2 The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).

  • 6.PFA.2.a Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph.

    • Unit rates (6-S.11)

  • 6.PFA.2.b Determine a missing value in a ratio table that represents a proportional relationship between two quantities using a unit rate.

    • Ratio tables (6-S.9)

  • 6.PFA.2.c Determine whether a proportional relationship exists between two quantities, when given a table of values, context, or graph.

    • Do the ratios form a proportion? (6-S.19)
    • Identify proportional relationships from graphs (6-T.1)
    • Identify proportional relationships from tables (6-T.2)

  • 6.PFA.2.d When given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph.

  • 6.PFA.2.e Make connections between and among multiple representations of the same proportional relationship using verbal descriptions, ratio tables, and graphs.

    • Ratios and rates: complete a table and make a graph (6-S.14)
    • Identify proportional relationships by graphing (6-T.3)
    • Interpret graphs of proportional relationships (6-T.4)

  • Checkpoint opportunity

    • Checkpoint: Ratio concepts (6-S.22)
    • Checkpoint: Unit rates (6-S.23)

• 6.PFA.3 The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable.

  • 6.PFA.3.a Identify and develop examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficient.

    • Identify terms and coefficients (6-Y.8)
    • Identify expressions and equations (6-AA.4)

  • 6.PFA.3.b Represent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial representations.

    • Model and solve equations using algebra tiles (6-AA.5)
    • Model and solve equations using diagrams (6-AA.6)
    • Write and solve equations that represent diagrams (6-AA.7)

  • 6.PFA.3.c Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fractions. Numeric terms are limited to integers.

    • Solve one-step addition and subtraction equations with whole numbers (6-AA.8)
    • Solve one-step multiplication and division equations with whole numbers (6-AA.9)
    • Solve one-step equations with whole numbers (6-AA.10)
    • Solve one-step equations involving integers (6-AA.19)

  • 6.PFA.3.d Confirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial representations.

    • Does x satisfy an equation? (6)
    • Which x satisfies an equation? (6)

  • 6.PFA.3.e Write a one-step linear equation in one variable to represent a verbal situation, including those in context.

    • Write an equation from words (6-AA.3)
    • Solve one-step addition and subtraction equations: word problems (6-AA.14)
    • Solve one-step multiplication and division equations: word problems (6-AA.15)
    • Write a one-step equation: word problems (6-AA.16)
    • Solve one-step equations: word problems (6-AA.17)

  • 6.PFA.3.f Create a verbal situation in context given a one-step linear equation in one variable.

    • Which word problem matches the one-step equation? (6-AA.18)

  • Checkpoint opportunity

    • Checkpoint: Understand and solve equations (6)

• 6.PFA.4 The student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a number line.

  • 6.PFA.4.a Given the graph of a linear inequality in one variable on a number line, represent the inequality in two equivalent ways using symbols. Symbols include <, >, ≤, ≥.

    • Write inequalities from number lines (6-BB.3)

  • 6.PFA.4.b Write a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a number line.

    • Write inequalities from number lines (6-BB.3)
    • Write and graph inequalities: word problems (6-BB.4)

  • 6.PFA.4.c Given a linear inequality in one variable, create a corresponding contextual situation or create a number line graph.

    • Graph inequalities on number lines (6-BB.2)
    • Write and graph inequalities: word problems (6-BB.4)

  • 6.PFA.4.d Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true.

    • Solutions to inequalities (6-BB.1)

  • 6.PFA.4.e Identify a numerical value(s) that is part of the solution set of a given inequality in one variable.

    • Solutions to inequalities (6-BB.1)

  • Checkpoint opportunity