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7Grade 7 Standards
Top Mathematicians
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Shape and Space
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7.SS.1
Demonstrate an understanding of circles by
• describing the relationships among radius, diameter, and circumference of circles
• relating circumference to pi (π)
• determining the sum of the central angles
• constructing circles with a given radius or diameter
• solving problems involving the radii, diameters, and circumferences of circles
• Illustrate and explain that the diameter is twice the radius in a circle.
• Illustrate and explain that the circumference is approximately three times the diameter in a circle.
• Explain that, for all circles, pi (π) is the ratio of the circumference to the diameter (c/d), and its value is approximately 3.14.
• Explain, using an illustration, that the sum of the central angles of a circle is 360°.
• Draw a circle with a given radius or diameter with or without a compass.
• Solve a contextual problem involving circles. -
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7.815
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7.825
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7.835
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7.845
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7.SS.2
Develop and apply a formula for determining the area of
• triangles
• parallelograms
• circles
• Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.
• Generalize a rule to create a formula for determining the area of triangles.
• Illustrate and explain how the area of a rectangle can be used to determine the area of a parallelogram.
• Generalize a rule to create a formula for determining the area of parallelograms.
• Illustrate and explain how to estimate the area of a circle without the use of a formula.
• Apply a formula for determining the area of a circle.
• Solve a problem involving the area of triangles, parallelograms, or circles. -
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7.825
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7.835
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7.8510
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7.865
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7.SS.3
Perform geometric constructions, including
• perpendicular line segments
• parallel line segments
• perpendicular bisectors
• angle bisectors
• Describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors, and angle bisectors in the environment.
• Identify line segments on a diagram that are parallel or perpendicular.
• Draw a line segment perpendicular to another line segment, and explain why they are perpendicular.
• Draw a line segment parallel to another line segment, and explain why they are parallel.
• Draw the bisector of an angle using more than one method, and verify that the resulting angles are equal.
• Draw the perpendicular bisector of a line segment using more than one method, and verify the construction. -
7.SS.4
Identify and plot points in the four quadrants of a Cartesian plane using ordered pairs.
• Label the axes of a Cartesian plane and identify the origin.
• Identify the location of a point in any quadrant of a Cartesian plane using an ordered pair.
• Plot the point corresponding to a ordered pair on a Cartesian plane with units of 1, 2, 5, or 10 on its axes.
• Draw shapes and designs, using ordered pairs, in a Cartesian plane.
• Create shapes and designs in a Cartesian plane and identify the points used. -
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7.8810
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7.8915
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7.SS.5
Perform and describe transformations of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral vertices).
(It is intended that the original shape and its image have vertices with integral coordinates.)
• Identify the coordinates of the vertices of a 2-D shape on a Cartesian plane.
• Describe the horizontal and vertical movement required to move from a given point to another point on a Cartesian plane.
• 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 or successive transformations on a Cartesian plane.
• Perform a transformation or consecutive transformations on a 2-D shape, and identify coordinates of the vertices of the image.
• Describe the image resulting from the transformation of a 2-D shape on a Cartesian plane by comparing the coordinates of the vertices of the image. -
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7.905
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7.915
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7.9210
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7.935
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7.9410
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7.9510
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7.9610
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7.SS.1
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Patterns and Relations
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7.PR.1
Demonstrate an understanding of oral and written patterns and their corresponding relations.
• Formulate a relation to represent the relationship in an oral or written pattern.
• Provide a context for a relation that represents a pattern.
• Represent a pattern in the environment using a relation. -
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7.535
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7.545
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7.555
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7.565
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7.5715
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7.5810
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7.PR.2
Construct a table of values from a relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.
• Create a table of values for a relation by substituting values for the variable.
• Create a table of values using a relation, and graph the table of values (limited to discrete elements).
• Sketch the graph from a table of values created for a relation, and describe the patterns found in the graph to draw conclusions (e.g., graph the relationship between n and 2n + 3).
• Describe the relationship shown on a graph using everyday language in spoken or written form to solve problems.
• Match a set of relations to a set of graphs.
• Match a set of graphs to a set of relations. -
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7.5715
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7.5810
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7.595
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7.605
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7.6115
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7.6210
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7.6310
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7.645
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7.655
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7.665
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7.675
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7.6810
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7.6910
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7.PR.3
Demonstrate an understanding of preservation of equality by
• modelling preservation of equality, concretely, pictorially, and symbolically
• applying preservation of equality to solve equations
• Model the preservation of equality for addition, subtraction, multiplication, or division using concrete materials or using pictorial representations, explain the process orally, and record it symbolically.
• Solve a problem by applying preservation of equality. -
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7.2315
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7.2415
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7.2515
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7.7010
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7.7110
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7.725
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7.7415
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7.755
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7.765
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7.7710
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7.785
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7.7910
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7.PR.4
Explain the difference between an expression and an equation.
• Identify and provide an example of a constant term, a numerical coefficient, and a variable in an expression and an equation.
• Explain what a variable is and how it is used in an expression.
• Provide an example of an expression and an equation, and explain how they are similar and different. -
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7.PR.5
Evaluate an expression given the value of the variable(s).
• Substitute a value for each unknown in an expression and evaluate the expression. -
7.PR.6
Model and solve problems that can be represented by one-step linear equations of the form x + a = b, concretely, pictorially, and symbolically, where a and b are integers.
• Represent a problem with a linear equation and solve the equation using concrete models.
• Draw a visual representation of the steps required to solve a linear equation.
• Solve a problem using a linear equation.
• Verify the solution to a linear equation using concrete materials or diagrams.
• Substitute a possible solution for the variable in a linear equation to verify the equality. -
7.PR.7
Model and solve problems that can be represented by linear equations of the form:
• ax + b = c
• ax = b
• x/a = b, a ≠ 0
concretely, pictorially, and symbolically, where a, b, and c, are whole numbers.
• Model a problem with a linear equation and solve the equation using concrete models.
• Draw a visual representation of the steps used to solve a linear equation.
• Solve a problem using a linear equation and record the process.
• Verify the solution to a linear equation using concrete materials or diagrams.
• Substitute a possible solution for the variable in a linear equation to verify the equality. -
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7.595
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7.605
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7.725
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7.755
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7.765
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7.7710
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7.PR.1
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Number
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7.N.1
Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and why a number cannot be divided by 0.
• Determine if a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and explain why.
• Sort a set of numbers based upon their divisibility using organizers, such as Venn or Carroll diagrams.
• Determine the factors of a number using the divisibility rules.
• Explain, using an example, why numbers cannot be divided by 0. -
7.N.2
Demonstrate an understanding of the addition, subtraction, multiplication, and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, technology could be used).
• Solve a problem involving the addition of two or more decimal numbers.
• Solve a problem involving the subtraction of decimal numbers.
• Solve a problem involving the multiplication or division of decimal numbers (for more than 1-digit divisors or 2-digit multipliers, technology could be used).
• Place the decimal in a sum or difference using front-end estimation (e.g., for 4.5 + 0.73 + 256.458, think 4 + 256, so the sum is greater than 260).
• Place the decimal in a product using front-end estimation (e.g., for $12.33 × 2.4, think $12 × 2, so the product is greater than $24).
• Place the decimal in a quotient using front-end estimation (e.g., for 51.50 m ÷ 2.1, think 50 m ÷ 2, so the quotient is approximately 25 m).
• Check the reasonableness of answers using estimation.
• Solve a problem that involves operations on decimals (limited to thousandths), taking into consideration the order of operations.
• Explain, using an example, how to use mental math for products or quotients when the multiplier or the divisor is 0.1 or 0.5 or 0.25. -
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7.415
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7.515
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7.620
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7.715
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7.815
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7.95
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7.1015
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7.1120
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7.1215
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7.1315
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7.1420
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7.1515
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7.165
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7.N.3
Solve problems involving percents from 1% to 100%.
• Express a percent as a decimal or fraction.
• Solve a problem that involves finding a percent.
• Determine the answer to a percent problem where the answer requires rounding, and explain why an approximate answer is needed (e.g., total cost including taxes). -
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7.1710
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7.1815
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7.1915
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7.2015
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7.215
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7.225
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7.2315
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7.2415
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7.2515
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7.N.4
Demonstrate an understanding of the relationship between repeating decimals and fractions, and terminating decimals and fractions.
• Predict the decimal representation of a fraction using patterns (e.g., 1/11 = 0.09, 2/11 = 0.18, 3/11 = ? ...).
• Match a set of fractions to their decimal representations.
• Sort a set of fractions as repeating or terminating decimals.
• Express a fraction as a terminating or repeating decimal.
• Express a repeating decimal as a fraction.
• Express a terminating decimal as a fraction.
• Provide an example where the decimal representation of a fraction is an approximation of its exact value. -
7.N.5
Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences).
• Model addition and subtraction of positive fractions or mixed numbers using concrete representations, and record symbolically.
• Determine the sum of two positive fractions or mixed numbers with like denominators.
• Determine the difference of two positive fractions or mixed numbers with like denominators.
• Determine a common denominator for a set of positive fractions or mixed numbers.
• Determine the sum of two positive fractions or mixed numbers with unlike denominators.
• Determine the difference of two positive fractions or mixed numbers with unlike denominators.
• Simplify a positive fraction or mixed number by identifying the common factor between the numerator and denominator.
• Simplify the solution to a problem involving the sum or difference of two positive fractions or mixed numbers.
• Solve a problem involving the addition or subtraction of positive fractions or mixed numbers, and determine if the solution is reasonable. -
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7.2720
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7.2815
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7.2920
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7.3020
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7.3120
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7.3220
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7.3315
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7.3415
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7.3515
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7.3615
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7.3715
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7.N.6
Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically.
• Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is equal to zero.
• Illustrate, using a horizontal or vertical number line, the results of adding or subtracting negative and positive integers (e.g., a move in one direction followed by an equivalent move in the opposite direction results in no net change in position).
• Add two integers using concrete materials or pictorial representations, and record the process symbolically.
• Subtract two integers using concrete materials or pictorial representations, and record the process symbolically.
• Solve a problem involving the addition and subtraction of integers. -
7.N.7
Compare and order fractions, decimals (to thousandths), and integers by using
• benchmarks
• place value
• equivalent fractions and/or decimals
• Order the numbers of a set that includes fractions, decimals, or integers in ascending or descending order, and verify the result using a variety of strategies.
• Identify a number that would be between two numbers in an ordered sequence or on a horizontal or vertical number line.
• Identify incorrectly placed numbers in an ordered sequence or on a horizontal or vertical number line.
• Position fractions with like and unlike denominators from a set on a horizontal or vertical number line, and explain strategies used to determine order.
• Order the numbers of a set by placing them on a horizontal or vertical number line that contains benchmarks, such as 0 and 1 or 0 and 5.
• Position a set of fractions, including mixed numbers and improper fractions, on a horizontal or vertical number line, and explain strategies used to determine position. -
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7.4320
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7.4410
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7.4520
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7.4615
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7.4720
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7.4815
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7.4915
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7.5015
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7.5115
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7.5215
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7.N.1
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Statistics & Probability
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7.SP.1
Demonstrate an understanding of central tendency and range by
• determining the measures of central tendency (mean, median, mode) and range
• determining the most appropriate measures of central tendency to report findings
• Determine mean, median, and mode for a set of data, and explain why these values may be the same or different.
• Determine the range of a set of data.
• Provide a context in which the mean, median, or mode is the most appropriate measure of central tendency to use when reporting findings.
• Solve a problem involving the measures of central tendency. -
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7.9710
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7.9810
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7.9910
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7.10010
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7.10110
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7.1025
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7.1035
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7.1045
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7.1055
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7.1065
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7.10710
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7.10810
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7.10910
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7.11010
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7.11110
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7.1125
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7.1135
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7.1145
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7.1155
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7.1165
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7.SP.2
Determine the effect on the mean, median, and mode when an outlier is included in a data set.
• Analyze a set of data to identify any outliers.
• Explain the effect of outliers on the measures of central tendency for a data set.
• Identify outliers in a set of data and justify whether or not they are to be included in the reporting of the measures of central tendency.
• Provide examples of situations in which outliers would or would not be used in determining the measures of central tendency. -
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7.1125
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7.1135
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7.1145
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7.1155
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7.1165
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7.SP.3
Construct, label, and interpret circle graphs to solve problems.
• Identify common attributes of circle graphs, such as
- title, label, or legend
- the sum of the central angles is 360°
- the data is reported as a percent of the total and the sum of the percents is equal to 100%
• Create and label a circle graph, with or without technology, to display a set of data.
• Find and compare circle graphs in a variety of print and electronic media, such as newspapers, magazines, and the Internet.
• Translate percentages displayed in a circle graph into quantities to solve a problem.
• Interpret a circle graph to answer questions. -
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7.1175
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7.1185
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7.SP.4
Express probabilities as ratios, fractions, and percents.
• Determine the probability of an outcome occurring for a probability experiment, and express it as a ratio, fraction, or percent.
• Provide an example of an event with a probability of 0 or 0% (impossible) and an event with a probability of 1 or 100% (certain). -
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7.1195
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7.1205
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7.1215
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7.12215
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7.SP.5
Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.
• Provide an example of two independent events, such as
- spinning a four-section spinner and an eight-sided die
- tossing a coin and rolling a twelve-sided die
- tossing two coins
- rolling two dice
and explain why they are independent.
• Identify the sample space (all possible outcomes) for an experiment involving two
independent events using a tree diagram, table, or another graphic organizer. -
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7.1235
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7.12415
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7.SP.6
Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or another graphic organizer) and experimental probability of two independent events.
• Determine the theoretical probability of an outcome for an experiment involving two independent events.
• Conduct a probability experiment for an outcome involving two independent events, with or without technology, to compare the experimental probability to the theoretical probability.
• Solve a probability problem involving two independent events. -
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7.1195
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7.1205
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7.1215
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7.12215
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7.SP.1