 • 6
Top Mathematicians
• 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 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.
• 6.SS.2
Demonstrate that the sum of interior angles is:
180° in a triangle.
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 (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 in different orientations.
isosceles in different orientations.
equilateral in different orientations.
right in different orientations.
obtuse in different orientations.
acute in different orientations.
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.
Identify a specified triangle from a given set of triangles; e.g., isosceles.
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.
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 given 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 translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.
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 (translations, rotations and/or reflections) 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(s) 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 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 the first quadrant).
• Number
• Patterns and Relations
• 6.PR.1
Represent and describe patterns and relationships, using graphs and tables.
Translate a pattern to a table of values, and graph the table of values (limited 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.2
Demonstrate an understanding of the relationships within tables of values to solve problems.
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.3
Represent generalizations arising from number relationships, using equations with letter variables.
Write and explain the formula for finding the perimeter of any given rectangle.
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
Express a given problem as an equation in which a letter variable is used to represent an unknown number.
Identify the unknown in a problem where the unknown could have more than one value, and represent the problem with an equation.
Create a problem for a given equation with one unknown.
Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically.
• 6.PR.5
Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.
Model the preservation of equality for addition, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
Model the preservation of equality for subtraction, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
Model the preservation of equality for multiplication, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
Model the preservation of equality for division, using concrete materials (e.g., a balance, pictorial representations), and explain and record the process.
• Statistics & Probability