• 6
    Grade 6 Standards
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  • Patterns and Relations
    • 6.RP.1.1
      Students will be expected to demonstrate an understanding of the relationships within tables of values to solve problems.
      • Performance Indicators
      - PR01.01 Generate values in one column of a table of values, given values in the other column, and a pattern rule.
      - PR01.02 State, using mathematical language, the relationship in a given table of values.
      - PR01.03 Create a concrete or pictorial representation of the relationship shown in a table of values.
      - PR01.04 Predict the value of an unknown term using the relationship in a table of values, and verify the prediction.
      - PR01.05 Formulate a rule to describe the relationship between two columns of numbers in a table of values.
      - PR01.06 Identify missing terms in a given table of values.
      - PR01.07 Identify errors in a given table of values.
      - PR01.08 Describe the pattern within each column of a given table of values.
      - PR01.09 Create a table of values to record and reveal a pattern to solve a given problem.
    • 6.RP.1.2
      Students will be expected to represent and describe patterns and relationships, using graphs and tables.
      • Performance Indicators
      - PR02.01 Translate a pattern to a table of values, and graph the table of values (limited to linear graphs with discrete elements).
      - PR02.02 Create a table of values from a given pattern or a given graph.
      - PR02.03 Describe, using everyday language, orally or in writing, the relationship shown on a graph.
    • 6.RP.1.3
      Students will be expected to represent generalizations arising from number relationships using equations with letter variables.
      • Performance Indicators
      - PR03.01 Write and explain the formula for finding the perimeter of any regular polygon.
      - PR03.02 Write and explain the formula for finding the area of any given rectangle.
      - PR03.03 Develop and justify equations using letter variables that illustrate the commutative property of addition and multiplication (e.g., a + b = b + a or a × b = b × a).
      - PR03.04 Describe the relationship in a given table using a mathematical expression.
      - PR03.05 Represent a pattern rule using a simple mathematical expression, such as 4d or 2n + 1.
    • 6.RP.1.4
      Students will be expected to demonstrate and explain the meaning of preservation of equality concretely, pictorially, and symbolically.
      • Performance Indicators
      - PR04.01 Model the preservation of equality for addition using concrete materials, such as a balance, or using pictorial representations, and orally explain the process.
      - PR04.02 Model the preservation of equality for subtraction using concrete materials, such as a balance, or using pictorial representations, and orally explain the process.
      - PR04.03 Model the preservation of equality for multiplication using concrete materials, such as a balance, or using pictorial representations, and orally explain the process.
      - PR04.04 Model the preservation of equality for division using concrete materials, such as a balance, or using pictorial representations, and orally explain the process.
      - PR04.05 Write equivalent forms of a given equation by applying the preservation of equality and verify using concrete materials (e.g., 3b = 12 is the same as 3b + 5 = 12 + 5 or 2r = 7 is the same as 3(2r) = 3(7)).
  • Geometry
    • 6.G.1.1
      Students will be expected to construct and compare triangles, including scalene, isosceles, equilateral, right, obtuse, or acute in different orientations.
      • Performance Indicators
      - G01.01 Sort a given set of triangles according to the length of the sides.
      - G01.02 Sort a given set of triangles according to the measures of the interior angles.
      - G01.03 Identify the characteristics of a given set of triangles according to their sides and/or their interior angles.
      - G01.04 Sort a given set of triangles and explain the sorting rule.
      - G01.05 Draw a specified triangle.
      - G01.06 Replicate a given triangle in a different orientation and show that the two are congruent.
    • 6.G.1.2
      Students will be expected to describe and compare the sides and angles of regular and irregular polygons.
      • Performance Indicators
      - G02.01 Sort a given set of 2-D shapes into polygons and non-polygons and explain the sorting rule.
      - G02.02 Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing.
      - G02.03 Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by measuring.
      - G02.04 Demonstrate that the sides of a regular polygon are the same length and that the angles of a regular polygon are the same measure.
      - G02.05 Sort a given set of polygons as regular or irregular and justify the sorting.
      - G02.06 Identify and describe regular and irregular polygons in the environment.
    • 6.G.1.3
      Students will be expected to perform a combination of translation(s), rotation(s), and/or reflection(s) on a single 2-D shape, with and without technology, and draw and describe the image.
      • Performance Indicators
      - G03.01 Demonstrate that a 2-D shape and its transformation image are congruent.
      - G03.02 Model a given set of successive translations, successive rotations, or successive reflections of a 2-D shape.
      - G03.03 Model a given combination of two different types of transformations of a 2-D shape.
      - G03.04 Draw and describe a 2-D shape and its image, given a combination of transformations.
      - G03.05 Describe the transformations performed on a 2-D shape to produce a given image.
      - G03.06 Model a given set of successive transformations (translation, rotation, or reflection) of a 2-D shape.
      - G03.07 Perform and record one or more transformations of a 2-D shape that will result in a given image.
    • 6.G.1.4
      Students will be expected to perform a combination of successive transformations of 2-D shapes to create a design and identify and describe the transformations.
      • Performance Indicators
      - G04.01 Analyze a given design created by transforming one or more 2-D shapes, and identify the original shape and the transformations used to create the design.
      - G04.02 Create a design using one or more 2-D shapes and describe the transformations used.
      - G04.03 Describe why a shape may or may not tessellate.
      - G04.04 Create a tessellation and describe how tessellations are used in the real world.
    • 6.G.1.5
      Students will be expected to identify and plot points in the first quadrant of a Cartesian plane using whole number ordered pairs.
      • Performance Indicators
      - G05.01 Label the axes of the first quadrant of a Cartesian plane and identify the origin.
      - G05.02 Plot a point in the first quadrant of a Cartesian plane given its ordered pair.
      - G05.03 Match points in the first quadrant of a Cartesian plane with their corresponding ordered pair.
      - G05.04 Plot points in the first quadrant of a Cartesian plane with intervals of 1, 2, 5, or 10 on its axes, given whole number ordered pairs.
      - G05.05 Draw shapes or designs in the first quadrant of a Cartesian plane, using given ordered pairs.
      - G05.06 Determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane.
      - G05.07 Draw shapes or designs in the first quadrant of a Cartesian plane, and identify the points used to produce them.
    • 6.G.1.6
      Students will be expected to perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).
      • Performance Indicators
      - G06.01 Identify the coordinates of the vertices of a given 2-D shape (limited to the first quadrant of a Cartesian plane).
      - G06.02 Perform a transformation on a given 2-D shape, and identify the coordinates of the vertices of the image (limited to the first quadrant).
      - G06.03 Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation (limited to first quadrant).
  • Measurement and Data
    • 6.MD.1.1
      Students will be expected to demonstrate an understanding of angles by
      • identifying examples of angles in the environment
      • classifying angles according to their measure
      • estimating the measure of angles using 45°, 90°, and 180° as reference angles
      • determining angle measures in degrees
      • drawing and labelling angles when the measure is specified

      • Performance Indicators
      - M01.01 Identify examples of angles found in the environment.
      - M01.02 Classify a given set of angles according to their measure (e.g., acute, right, obtuse, straight, reflex).
      - M01.03 Sketch 45°, 90°, and 180° angles without the use of a protractor, and describe the relationship among them.
      - M01.04 Estimate the measure of an angle using 45°, 90°, and 180° as reference angles.
      - M01.05 Measure, using a protractor, given angles in various orientations.
      - M01.06 Draw and label a specified angle in various orientations using a protractor.
      - M01.07 Describe the measure of an angle as the measure of rotation of one of its sides.
      - M01.08 Describe the measure of angles as the measure of an interior angle of a polygon.
    • 6.MD.1.2
      Students will be expected to demonstrate that the sum of interior angles is 180° in a triangle and 360° in a quadrilateral.
      • Performance Indicators
      - M02.01 Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles.
      - M02.02 Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals.
    • 6.MD.1.3
      Students will be expected to develop and apply a formula for determining the
      • perimeter of polygons
      • area of rectangles
      • volume of right rectangular prisms

      • Performance Indicators
      - M03.01 Explain, using models, how the perimeter of any polygon can be determined.
      - M03.02 Generalize a rule (formula) for determining the perimeter of polygons.
      - M03.03 Explain, using models, how the area of any rectangle can be determined.
      - M03.04 Generalize a rule (formula) for determining the area of rectangles.
      - M03.05 Explain, using models, how the volume of any rectangular prism can be determined.
      - M03.06 Generalize a rule (formula) for determining the volume of rectangular prisms.
      - M03.07 Solve a given problem involving the perimeter of polygons, the area of rectangles, and/or the volume of right rectangular prisms.
  • The Number System
    • 6.NS.1.1
      Students will be expected to demonstrate an understanding of place value for numbers greater than one million and less than one-thousandth.
      • Performance Indicators
      - N01.01 Explain how the pattern of the place-value system (e.g., the repetition of ones, tens, and hundreds) makes it possible to read and write numerals for numbers of any magnitude.
      - N01.02 Describe the pattern of adjacent place positions moving from right to left and from left to right.
      - N01.03 Represent a given numeral using a place-value chart.
      - N01.04 Explain the meaning of each digit in a given numeral.
      - N01.05 Read a given numeral in several ways.
      - N01.06 Record, in standard form, numbers expressed orally, concretely, pictorially, or symbolically as expressions, in decimal notation, and in expanded notation, using proper spacing without commas.
      - N01.07 Express a given numeral in expanded notation and/or in decimal notation.
      - N01.08 Represent a given number using expressions.
      - N01.09 Represent a given number in a variety of ways, and explain how they are equivalent.
      - N01.10 Read and write given numerals in words.
      - N01.11 Compare and order numbers in a variety of ways.
      - N01.12 Establish personal referents for large numbers.
      - N01.13 Provide examples of where large whole numbers and small decimal numbers are used.
    • 6.NS.1.2
      Students will be expected to solve problems involving whole numbers and decimal numbers.
      • Performance Indicators
      - N02.01 Determine whether technology, mental mathematics, or paper-and-pencil calculation is appropriate to solve a given problem and explain why.
      - N02.02 Identify which operation is necessary to solve a given problem and solve it.
      - N02.03 Determine the reasonableness of an answer.
      - N02.04 Estimate the solution and solve a given problem using an appropriate method (technology, mental mathematics, or paper-and-pencil calculation).
      - N02.05 Create problems involving large numbers and decimal numbers.
      - N02.06 Use technology, mental mathematics, or paper-and-pencil calculation to solve problems involving the addition, subtraction, multiplication, and division of whole numbers.
      - N02.07 Use technology, mental mathematics, or paper-and-pencil calculation to solve problems involving the addition and subtraction of decimal numbers.
    • 6.NS.1.3
      Students will be expected to demonstrate an understanding of factors and multiples by
      • determining multiples and factors of numbers less than 100
      • identifying prime and composite numbers
      • solving problems using multiples and factors

      • Performance Indicators
      - N03.01 Identify multiples for a given number and explain the strategy used to identify them.
      - N03.02 Determine all the whole number factors of a given number using arrays.
      - N03.03 Identify the factors for a given number and explain the strategy used (e.g., concrete or visual representations, repeated division by prime numbers, or factor trees).
      - N03.04 Provide an example of a prime number, and explain why it is a prime number.
      - N03.05 Provide an example of a composite number, and explain why it is a composite number.
      - N03.06 Sort a given set of numbers as prime and composite.
      - N03.07 Solve a given problem involving factors or multiples.
      - N03.08 Explain why 0 and 1 are neither prime nor composite.
    • 6.NS.1.4
      Students will be expected to relate improper fractions to mixed numbers and mixed numbers to improper fractions.
      • Performance Indicators
      - N04.01 Demonstrate, using models, that a given improper fraction represents a number greater than 1.
      - N04.02 Express improper fractions as mixed numbers.
      - N04.03 Express mixed numbers as improper fractions.
      - N04.04 Place a given set of fractions, including mixed numbers and improper fractions, on a number line, and explain strategies used to determine position.
      - N04.05 Represent a given improper fraction using concrete, pictorial, and symbolic forms.
      - N04.06 Represent a given mixed number using concrete, pictorial, and symbolic forms.
    • 6.NS.1.5
      Students will be expected to demonstrate an understanding of ratio, concretely, pictorially, and symbolically.
      • Performance Indicators
      - N05.01 Represent a given ratio concretely and pictorially.
      - N05.02 Write a ratio from a given concrete or pictorial representation.
      - N05.03 Express a given ratio in multiple forms, such as 'three to five,' 3:5, 3 to 5, or 3/5 .
      - N05.04 Identify and describe ratios from real-life contexts and record them symbolically.
      - N05.05 Explain the part-whole and part-part ratios of a set (e.g., For a group of three girls and five boys, explain the ratios 3:5, 3:8, and 5:8.).
      - N05.06 Solve a given problem involving ratio.
      - N05.07 Verify that two ratios are or are not equivalent using concrete materials.
    • 6.NS.1.6
      Students will be expected to demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially, and symbolically.
      • Performance Indicators
      - N06.01 Explain that “percentâ€
    • 6.NS.1.7
      Students will be expected to demonstrate an understanding of integers contextually, concretely, pictorially, and symbolically.
      • Performance Indicators
      - N07.01 Extend a given number line by adding numbers less than 0 and explain the pattern on each side of 0.
      - N07.02 Place given integers on a number line and explain how integers are ordered.
      - N07.03 Describe contexts in which integers are used (e.g., on a thermometer).
      - N07.04 Compare two integers; represent their relationship using the symbols <, >, and =; and verify using a number line.
      - N07.05 Order given integers in ascending or descending order.
    • 6.NS.1.8
      Students will be expected to demonstrate an understanding of multiplication and division of decimals (one-digit whole number multipliers and one-digit natural number divisors).
      • Performance Indicators
      - N08.01 Model the multiplication and division of decimals using concrete and visual representations.
      - N08.02 Predict products and quotients of decimals using estimation strategies.
      - N08.03 Place the decimal point in a product using front-end estimation (e.g., For 15.205 × 4, think 15 × 4, so the product is greater than 60.).
      - N08.04 Place the decimal point in a quotient using front-end estimation (e.g., For $25.83 ÷ 4, think $24 ÷ 4, so the quotient is greater than $6.).
      - N08.05 Use estimation to correct errors of decimal point placement in a given product or quotient without using paper and pencil.
      - N08.06 Create and solve story problems that involve multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9.
      - N08.07 Solve a given problem, using a personal strategy, and record the process symbolically.
    • 6.NS.1.9
      Students will be expected to explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).
      • Performance Indicators
      - N09.01 Demonstrate and explain, with examples, why there is a need to have a standardized order of operations.
      - N09.02 Apply the order of operations to solve multi-step problems with or without technology (e.g., computer, calculator).
  • Statistics & Probability
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