• 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Generate values in one column of a table of values, given values in the other column and a pattern rule.
      - State, using mathematical language, the relationship in a given 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 given table of values.
      - Identify errors in a given table of values.
      - Describe the pattern within each column of a given table of values.
      - Create a table of values to record and reveal a pattern to solve a given problem.
    • 6.PR.2
      Represent and describe patterns and relationships using graphs and tables.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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 given pattern or a given 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Write and explain the formula for finding the perimeter of any regular polygon.
      - Write and explain the formula for finding the area of any given 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 given 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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 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).
  • 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.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Provide examples of angles found in the environment.
      - Classify a given 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, given angles in various orientations.
      - Draw and label a specified 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.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Explain, using models, how the perimeter of any polygon can be determined.
      - Generalize a rule (formula) for determining the perimeter of polygons, including rectangles and squares.
      - Explain, using models, how the area of any rectangle can be determined.
      - Generalize a rule (formula) for determining the area of rectangles.
      - Explain, using models, how the volume of any right rectangular prism can be determined.
      - Generalize a rule (formula) for determining the volume of right rectangular prisms.
      - Solve a given problem involving the perimeter of polygons, the area of rectangles and/or the volume of right rectangular prisms.
    • 6.SS.4
      Construct and compare triangles, including:
      • scalene
      • isosceles
      • equilateral
      • right
      • obtuse
      • acute
      in different orientations.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Sort a given set of triangles according to the length of the sides.
      - Sort a given set of triangles according to the measures of the interior angles.
      - Identify the characteristics of a given set of triangles according to their sides and/or their interior angles.
      - Sort a given set of triangles and explain the sorting rule.
      - Draw a specified triangle, e.g., scalene.
      - Replicate a given 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Sort a given 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 given 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 translation(s), rotation(s) and/or reflection(s) on a single 2-D shape, with and without technology, and draw and describe the image.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Demonstrate that a 2-D shape and its transformation image are congruent.
      - Model a given set of successive translations, successive rotations or successive reflections of a 2-D shape.
      - Model a given 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 given set of successive transformations (translation, rotation and/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 given 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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).
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Identify the coordinates of the vertices of a given 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 given 2-D shape to the corresponding vertices of its image as a result of a transformation (limited to first quadrant).
  • Number
    • 6.N.1
      Demonstrate an understanding of place value for numbers:
      • greater than one million
      • less than one thousandth.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Identify which operation is necessary to solve a given problem and solve it.
      - Determine the reasonableness of an answer.
      - Estimate the solution and solve a given problem.
    • 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 multiples.

      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Identify multiples for a given number and explain the strategy used to identify them.
      - Determine all the whole number factors of a given number using arrays.
      - 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.
      - 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 given set of numbers as prime and composite.
      - Solve a given problem involving factors or multiples.
      - Explain why 0 and 1 are neither prime nor composite.
    • 6.N.4
      Relate improper fractions to mixed numbers.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Demonstrate using models that a given improper fraction represents a number greater than 1.
      - Express improper fractions as mixed numbers.
      - Express mixed numbers as improper fractions.
      - Place a given set of fractions, including mixed numbers and improper fractions, on a number line and explain strategies used to determine position.
    • 6.N.5
      Demonstrate an understanding of ratio, concretely, pictorially and symbolically.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Provide a concrete or pictorial representation for a given ratio.
      - Write a ratio from a given concrete or pictorial representation.
      - Express a given ratio in multiple forms, such as “three to five”, 3:5, 3 to 5, or 3/5.
      - 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 given problem involving ratio.
    • 6.N.6
      Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolically.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Explain that “percent” means “out of 100.”
      - Explain that percent is a ratio out of 100.
      - Use concrete materials and pictorial representations to illustrate a given percent.
      - Record the percent displayed in a given concrete or pictorial representation.
      - Express a given percent as a fraction and a decimal.
      - Identify and describe percents from real-life contexts, and record them symbolically.
      - Solve a given problem involving percents.
    • 6.N.7
      Demonstrate an understanding of integers, concretely, pictorially and symbolically.
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Extend a given number line by adding numbers less than zero and explain the pattern on each side of zero.
      - Place given integers on a 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 number line.
      - Order given integers in ascending or descending order.
    • 6.N.8
      Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural number divisors).
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - Place the decimal point in a product using front-end estimation, e.g., for 15.205 m × 4, think 15 m × 4, so the product is greater than 60 m.
      - 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.
      - Correct errors of decimal point placement in a given product or quotient without using paper and pencil.
      - Predict products and quotients of decimals using estimation strategies.
      - Solve a given problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9.
    • 6.N.9
      Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).
      • Achievement Indicators
      • Students who have achieved this outcome(s) should be able to:
      - 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, e.g., computer, calculator.
  • Statistics & Probability