-
6Grade 6 Standards
Top Mathematicians
-
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. -
-
6.520
-
6.610
-
6.715
-
6.820
-
6.920
-
-
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. -
-
6.115
-
6.125
-
6.135
-
6.145
-
6.155
-
-
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 -
-
6.1610
-
6.1715
-
6.1815
-
6.195
-
6.205
-
6.215
-
6.2215
-
6.2315
-
6.2420
-
6.255
-
6.2615
-
-
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. -
-
6.275
-
6.285
-
6.3015
-
-
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. -
-
6.3515
-
-
6.N.1
-
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. -
-
6.155
-
6.3615
-
6.3710
-
-
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. -
-
6.3615
-
6.3710
-
6.3815
-
-
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. -
-
6.3915
-
6.405
-
6.415
-
6.4210
-
-
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)].
-
6.PR.1
-
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. -
-
6.5015
-
6.515
-
6.5215
-
6.5315
-
6.5415
-
6.555
-
-
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. -
-
6.565
-
-
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).
-
6.SS.1
-
Statistics & Probability
-
6.SP.1
Create, label, and interpret line graphs to draw conclusions.
• Determine the common attributes (title, axes, and intervals) of line graphs by comparing a set of line graphs.
• Determine whether a set of data can be represented by a line graph (continuous data) or a series of points (discrete data), and explain why.
• Create a line graph from a table of values or set of data.
• Interpret a line graph to draw conclusions. -
-
6.655
-
6.665
-
6.675
-
6.685
-
6.695
-
-
6.SP.2
Select, justify, and use appropriate methods of collecting data, including
• questionnaires
• experiments
• databases
• electronic media
• Select a method for collecting data to answer a question, and justify the choice.
• Design and administer a questionnaire for collecting data to answer a question and record the results.
• Answer a question by performing an experiment, recording the results, and drawing a conclusion.
• Explain when it is appropriate to use a database as a source of data.
• Gather data for a question by using electronic media, including selecting data from databases. -
-
6.SP.3
Graph collected data and analyze the graph to solve problems.
• Select a type of graph for displaying a set of collected data, and justify the choice of graph.
• Solve a problem by graphing data and interpreting the resulting graph. -
-
6.655
-
6.665
-
6.675
-
6.685
-
6.695
-
6.7020
-
6.715
-
6.725
-
6.735
-
6.745
-
6.755
-
6.765
-
6.775
-
6.785
-
6.795
-
6.805
-
6.815
-
6.825
-
6.835
-
6.845
-
-
6.SP.4
Demonstrate an understanding of probability by
• identifying all possible outcomes of a probability experiment
• differentiating between experimental and theoretical probability
• determining the theoretical probability of outcomes in a probability experiment
• determining the experimental probability of outcomes in a probability experiment
• comparing experimental results with the theoretical probability for an experiment
• List the possible outcomes of a probability experiment, such as
- tossing a coin
- rolling a die with any number of sides
- spinning a spinner with any number of sectors
• Determine the theoretical probability of an outcome occurring for a probability experiment.
• Predict the probability of an outcome occurring for a probability experiment by using theoretical probability.
• Conduct a probability experiment, with or without technology, and compare the experimental results to the theoretical probability.
• Explain that as the number of trials in a probability experiment increases, the experimental probability approaches theoretical probability of a particular outcome.
• Distinguish between theoretical probability and experimental probability, and explain the differences.
-
6.SP.1