• 6
    Grade 6 Standards
Top Mathematicians
  • Patterns and Relations
    • 6.PR.1
      Demonstrate an understanding of the relationships within tables of values to solve problems.
      • Generate values in one column of a table of values, values in the other column, and a pattern rule.
      • State, using mathematical language, the relationship in a table of values.
      • Create a concrete or pictorial representation of the relationship shown in a table of values.
      • Predict the value of an unknown term using the relationship in a table of values and verify the prediction.
      • Formulate a rule to describe the relationship between two columns of numbers in a table of values.
      • Identify missing elements in a table of values.
      • Identify and correct errors in a table of values.
      • Describe the pattern within each column of a table of values.
      • Create a table of values to record and reveal a pattern to solve a problem.
    • 6.PR.2
      Represent and describe patterns and relationships using graphs and tables.
      • Translate a pattern to a table of values and graph the table of values (limit to linear graphs with discrete elements).
      • Create a table of values from a pattern or a graph.
      • Describe, using everyday language, orally or in writing, the relationship shown on a graph.
    • 6.PR.3
      Represent generalizations arising from number relationships using equations with letter variables.
      • Write and explain the formula for finding the perimeter of any rectangle.
      • Write and explain the formula for finding the area of any rectangle.
      • 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).
      • Describe the relationship in a table using a mathematical expression.
      • Represent a pattern rule using a simple mathematical expression, such as 4d or 2n + 1.
    • 6.PR.4
      Demonstrate and explain the meaning of preservation of equality, concretely, pictorially, and symbolically.
      • Model the preservation of equality for addition using concrete materials, such as a balance or using pictorial representations, and orally explain the process.
      • Model the preservation of equality for subtraction using concrete materials, such as a balance or using pictorial representations, and orally explain the process.
      • Model the preservation of equality for multiplication using concrete materials, such as a balance or using pictorial representations, and orally explain the process.
      • Model the preservation of equality for division using concrete materials, such as a balance or using pictorial representations, and orally explain the process.
      • Write equivalent forms of an 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)].
  • Number
    • 6.N.1
      Demonstrate an understanding of place value for numbers
      • greater than one million
      • less than one-thousandth

      • 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.
      • Provide examples of where large numbers and small decimals are used (e.g., media, science, medicine, technology).
    • 6.N.2
      Solve problems involving large numbers, using technology.
      • Identify which operation is necessary to solve a problem and solve it.
      • Determine the reasonableness of an answer.
      • Estimate the answer and solve a problem.
      • Identify and correct errors in a solution to a problem that involves large numbers.
    • 6.N.3
      Demonstrate an understanding of factors and multiples by
      • determining multiples and factors of numbers less than 100
      • identifying prime and composite numbers
      • solving problems involving factors or multiples

      • Identify multiples for a number and explain the strategy used to identify them.
      • Determine all the whole-number factors of a number using arrays.
      • Identify the factors for a number and explain the strategy used (e.g., concrete or visual representations, repeated division by prime numbers or factor trees).
      • Identify common factors and common multiples for 2 or 3 numbers.
      • Provide an example of a prime number and explain why it is a prime number.
      • Provide an example of a composite number and explain why it is a composite number.
      • Sort a set of numbers as prime and composite.
      • Solve a problem involving factors, multiples, the largest common factor or the lowest common multiple.
      • Explain why 0 and 1 are neither prime nor composite.
    • 6.N.4
      Relate improper fractions to mixed numbers.
      • Demonstrate using models that an improper fraction represents a number greater than 1.
      • Express improper fractions as mixed numbers.
      • Express mixed numbers as improper fractions.
      • Place a set of fractions, including mixed numbers and improper fractions, on a horizontal or vertical number line, and explain strategies used to determine position.
    • 6.N.5
      Demonstrate an understanding of ratio, concretely, pictorially, and symbolically.
      • Provide a concrete or pictorial representation for a ratio.
      • Write a ratio from a concrete or pictorial representation.
      • Express a ratio in multiple forms, such as 3:5, 3/5 , or 3 to 5.
      • Identify and describe ratios from real-life contexts and record them symbolically.
      • Explain the part/whole and part/part ratios of a set (e.g., for a group of 3 girls and 5 boys, explain the ratios 3:5, 3:8, and 5:8).
      • Solve a problem involving ratio.
    • 6.N.6
      Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially, and symbolically.
      • Explain that “percent” means “out of 100.”
      • Explain that percent is the ratio of a certain number of units to 100 units.
      • Use concrete materials and pictorial representations to illustrate a percent.
      • Record the percent displayed in a concrete or pictorial representation.
      • Express a percent as a fraction and a decimal.
      • Identify and describe percents from real-life contexts and record them symbolically.
      • Solve a problem involving percents
    • 6.N.7
      Demonstrate an understanding of integers, concretely, pictorially, and symbolically.
      • Extend a horizontal or vertical number line by adding numbers less than zero and explain the pattern on each side of zero.
      • Place a set of integers on a horizontal or vertical number line and explain how integers are ordered.
      • Describe contexts in which integers are used (e.g., on a thermometer).
      • Compare two integers, represent their relationship using the symbols <, >, and =, and verify using a horizontal or vertical number line.
      • Order a set of integers in ascending or descending order.
    • 6.N.8
      Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by
      • using personal strategies
      • using the standard algorithms
      • using estimation
      • solving problems

      • Estimate a product using front-end estimation (e.g., for 15.205 m x 4, think 15 m x 4, so the product is greater than 60 m), and place the decimal in the appropriate place.
      • Estimate a quotient using front-end estimation (e.g., for $26.83 ÷ 4, think 24 ÷ 4, so the quotient is greater than $6), and place the decimal in the appropriate place.
      • Predict products and quotients of decimals using estimation strategies.
      • Identify and correct errors of decimal point placement in a product or quotient by estimating.
      • Solve a problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9.
      • Use mental math to determine products or quotients involving decimals when the multiplier or divisor is a multiple of 10 (e.g., 2.47 × 10 = 24.7; 31.9 ÷ 100 = 0.319).
      • Model and explain the relationship that exists between an algorithm, place value, and number properties.
      • Determine products and quotients using the standard algorithms of vertical multiplication (numbers arranged vertically and multiplied using single digits which are added to form a final product) and long division (the multiples of the divisor are subtracted from the dividend).
      • Solve multiplication and division problems in context using personal strategies, and record the process.
      • Refine personal strategies, such as mental math, to increase their efficiency when appropriate (e.g., 4.46 ÷ 2 think 446 ÷ 2 = 223, and then use front-end estimation to determine the placement of the decimal 2.23).
    • 6.N.9
      Explain and apply the order of operations, excluding exponents (limited to whole numbers).
      • Demonstrate and explain with examples why there is a need to have a standardized order of operations.
      • Apply the order of operations to solve multi-step problems with or without technology.
  • Shape and Space
    • 6.SS.1
      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

      • Provide examples of angles found in the environment.
      • Classify a set of angles according to their measure (e.g., acute, right, obtuse, straight, reflex).
      • Sketch 45°, 90°, and 180° angles without the use of a protractor, and describe the relationship among them.
      • Estimate the measure of an angle using 45°, 90°, and 180° as reference angles.
      • Measure, using a protractor, angles in various orientations.
      • Draw and label an angle in various orientations using a protractor.
      • Describe the measure of an angle as the measure of rotation of one of its sides.
      • Describe the measure of angles as the measure of an interior angle of a polygon.
    • 6.SS.2
      Demonstrate that the sum of interior angles is
      • 180° in a triangle
      • 360° in a quadrilateral

      • Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles.
      • Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals.
    • 6.SS.3
      Develop and apply a formula for determining the
      • perimeter of polygons
      • area of rectangles
      • volume of right rectangular prisms

      • Explain, using models, how the perimeter of any polygon can be determined.
      • Generalize a rule for determining the perimeter of polygons.
      • Explain, using models, how the area of any rectangle can be determined.
      • Generalize a rule for determining the area of rectangles.
      • Explain, using models, how the volume of any right rectangular prism can be determined.
      • Generalize a rule for determining the volume of right rectangular prisms.
      • Solve a problem involving the perimeter of polygons, the area of rectangles, or the volume of right rectangular prisms.
    • 6.SS.4
      Construct and compare triangles, including
      • scalene
      • isosceles
      • equilateral
      • right
      • obtuse
      • acute
      in different orientations.

      • Sort a set of triangles according to the length of the sides.
      • Sort a set of triangles according to the measures of the interior angles.
      • Identify the characteristics of a set of triangles according to their sides or their interior angles.
      • Sort a set of triangles and explain the sorting rule.
      • Draw a triangle (e.g., scalene).
      • Replicate a triangle in a different orientation and show that the two are congruent.
    • 6.SS.5
      Describe and compare the sides and angles of regular and irregular polygons.
      • Sort a set of 2-D shapes into polygons and non-polygons, and explain the sorting rule.
      • Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by superimposing.
      • Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by measuring.
      • Demonstrate that the sides of a regular polygon are of the same length and that the angles of a regular polygon are of the same measure.
      • Sort a set of polygons as regular or irregular and justify the sorting.
      • Identify and describe regular and irregular polygons in the environment.
    • 6.SS.6
      Perform a combination of transformations (translations, rotations, or reflections) on a single 2-D shape, and draw and describe the image.
      • Demonstrate that a 2-D shape and its transformation image are congruent.
      • Model a set of successive translations, successive rotations, or successive reflections of a 2-D shape.
      • Model a combination of two different types of transformations of a 2-D shape.
      • Draw and describe a 2-D shape and its image, given a combination of transformations.
      • Describe the transformations performed on a 2-D shape to produce a given image.
      • Model a set of successive transformations (translation, rotation, or reflection) of a 2-D shape.
      • Perform and record one or more transformations of a 2-D shape that will result in a given image.
    • 6.SS.7
      Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.
      • Analyze a design created by transforming one or more 2-D shapes, and identify the original shape and the transformations used to create the design.
      • Create a design using one or more 2-D shapes and describe the transformations used.
    • 6.SS.8
      Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs.
      • Label the axes of the first quadrant of a Cartesian plane and identify the origin.
      • Plot a point in the first quadrant of a Cartesian plane given its ordered pair.
      • Match points in the first quadrant of a Cartesian plane with their corresponding ordered pair.
      • 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.
      • Draw shapes or designs, given ordered pairs in the first quadrant of a Cartesian plane.
      • Determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane.
      • Draw shapes or designs in the first quadrant of a Cartesian plane and identify the points used to produce them.
    • 6.SS.9
      Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole-number vertices).
      • Identify the coordinates of the vertices of a 2-D shape (limited to the first quadrant of a Cartesian plane).
      • Perform a transformation on a given 2-D shape and identify the coordinates of the vertices of the image (limited to the first quadrant).
      • Describe the positional change of the vertices of a 2-D shape to the corresponding vertices of its image as a result of a transformation (limited to first quadrant).
  • Statistics & Probability