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7Grade 7 Standards
Top Mathematicians
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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.
• Achievement Indicators
- Determine mean, median and mode for a given set of data, and explain why these values may be the same or different.
- Determine the range of given sets 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 given 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.
• Achievement Indicators
- Analyze a given set of data to identify any outliers.
- Explain the effect of outliers on the measures of central tendency for a given data set.
- Identify outliers in a given 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 and would not be used in reporting 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.
• Achievement Indicators
- 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 and without technology, to display a given 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 given problem.
- Interpret a given 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.
• Achievement Indicators
- Determine the probability of a given outcome occurring for a given probability experiment, and express it as a ratio, fraction and 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.
• Achievement Indicators
- 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 each of 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.
• Achievement Indicators
- Determine the theoretical probability of a given outcome involving two independent events.
- Conduct a probability experiment for an outcome involving two independent events, with and without technology, to compare the experimental probability to the theoretical probability.
- Solve a given 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
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Patterns and Relations
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7.PR.1
Demonstrate an understanding of oral and written patterns and their equivalent linear relations.
• Achievement Indicators
- Formulate a linear relation to represent the relationship in a given oral or written pattern.
- Provide a context for a given linear relation that represents a pattern.
- Represent a pattern in the environment using a linear 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
Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.
• Achievement Indicators
- Create a table of values for a given linear relation by substituting values for the variable.
- Create a table of values using a linear relation and graph the table of values (limited to discrete elements).
- Sketch the graph from a table of values created for a given linear 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 given set of linear relations to a given set of graphs.
- Match a given set of graphs to a given set of linear 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.
• Achievement Indicators
- Model the preservation of equality for each of the four operations using concrete materials or using pictorial representations, explain the process orally and record it symbolically.
- Solve a given 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.
• Achievement Indicators
- 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 a given 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).
• Achievement Indicators
- Substitute a value for an unknown in a given 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.
• Achievement Indicators
- Represent a given problem with a linear equation and solve the equation using concrete models, e.g., counters, integer tiles.
- Draw a visual representation of the steps required to solve a given linear equation.
- Solve a given problem using a linear equation.
- Verify the solution to a given linear equation using concrete materials and diagrams.
- Substitute a possible solution for the variable in a given linear equation into the original 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.
• Achievement Indicators
- Model a given problem with a linear equation and solve the equation using concrete models, e.g., counters, integer tiles.
- Draw a visual representation of the steps used to solve a given linear equation.
- Solve a given problem using a linear equation and record the process.
- Verify the solution to a given linear equation using concrete materials and diagrams.
- Substitute a possible solution for the variable in a given linear equation into the original 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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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
• 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.
• Achievement Indicators
- Illustrate and explain that the diameter is twice the radius in a given circle.
- Illustrate and explain that the circumference is approximately three times the diameter in a given circle.
- Explain that, for all circles, pi 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 and without a compass.
- Solve a given 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.
• Achievement Indicators
- 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 given circle.
- Solve a given problem involving the area of triangles, parallelograms and/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.
• Achievement Indicators
- Describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors and angle bisectors in the environment.
- Identify line segments on a given 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 a given 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 integral ordered pairs.
• Achievement Indicators
- Label the axes of a four quadrant Cartesian plane and identify the origin.
- Identify the location of a given point in any quadrant of a Cartesian plane using an integral ordered pair.
- Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes.
- Draw shapes and designs, using given integral ordered pairs, in a Cartesian plane.
- Create shapes and designs, and identify the points used to produce the shapes and designs in any quadrant of a Cartesian plane. -
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7.8810
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7.8915
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7.SS.5
Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).
• Achievement Indicators
(It is intended that the original shape and its image have vertices with integral coordinates.)
- Identify the coordinates of the vertices of a given 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 given 2-D shape to the corresponding vertices of its image as a result of a transformation or successive transformations on a Cartesian plane.
- Determine the distance between points along horizontal and vertical lines in a Cartesian plane.
- Perform a transformation or consecutive transformations on a given 2-D shape and identify coordinates of the vertices of the image.
- 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 a combination of successive transformations.
- Describe the image resulting from the transformation of a given 2-D shape on a Cartesian plane by identifying 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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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.
• Achievement Indicators
- Determine if a given number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10 and explain why.
- Sort a given set of numbers based upon their divisibility using organizers, such as Venn and Carroll diagrams.
- Determine the factors of a given 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 (for more than 1-digit divisors or 2-digit multipliers, the use of technology is expected) to solve problems.
• Achievement Indicators
- Solve a given problem involving the addition of two or more decimal numbers.
- Solve a given problem involving the subtraction of decimal numbers.
- Solve a given problem involving the multiplication of decimal numbers.
- Solve a given problem involving the multiplication or division of decimal numbers with 2- digit multipliers or 1-digit divisors (whole numbers or decimals) without the use of technology.
- Solve a given problem involving the multiplication or division of decimal numbers with more than a 2-digit multiplier or 1-digit divisor (whole number or decimal), with the use of technology.
- 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 solutions using estimation.
- Solve a given problem that involves operations on decimals (limited to thousandths) taking into consideration the order of operations. -
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7.415
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7.515
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7.615
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7.720
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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%.
• Achievement Indicators
- Express a given percent as a decimal or fraction.
- Solve a given problem that involves finding a percent.
- Determine the answer to a given 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 positive repeating decimals and positive fractions, and positive terminating decimals and positive fractions.
• Achievement Indicators
- Predict the decimal representation of a given fraction using patterns, e.g., 1/11 = 0.09, 2/11 = 0.18, 3/11 = ? ...
- Match a given set of fractions to their decimal representations.
- Sort a given set of fractions as repeating or terminating decimals.
- Express a given fraction as a terminating or repeating decimal.
- Express a given repeating decimal as a fraction.
- Express a given 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).
• Achievement Indicators
- Model addition and subtraction of a given positive fraction or a given mixed number using concrete representations, and record symbolically.
- Determine the sum of two given positive fractions or mixed numbers with like denominators.
- Determine the difference of two given positive fractions or mixed numbers with like denominators.
- Determine a common denominator for a given set of positive fractions or mixed numbers.
- Determine the sum of two given positive fractions or mixed numbers with unlike denominators.
- Determine the difference of two given positive fractions or mixed numbers with unlike denominators.
- Simplify a given positive fraction or mixed number by identifying the common factor between the numerator and denominator.
- Simplify the solution to a given problem involving the sum or difference of two positive fractions or mixed numbers.
- Solve a given 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.
• Achievement Indicators
- Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero.
- Illustrate, using a 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 given integers using concrete materials or pictorial representations and record the process symbolically.
- Subtract two given integers using concrete materials or pictorial representations and record the process symbolically.
- Solve a given problem involving the addition and subtraction of integers. -
7.N.7
Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using:
• benchmarks
• place value
• equivalent fractions and/or decimals.
• Achievement Indicators
- Order the numbers of a given set that includes positive fractions, positive decimals and/or whole numbers in ascending or descending order, and verify the result using a variety of strategies.
- Identify a number that would be between two given numbers in an ordered sequence or on a number line.
- Identify incorrectly placed numbers in an ordered sequence or on a number line.
- Position fractions with like and unlike denominators from a given set on a number line and explain strategies used to determine order.
- Order the numbers of a given set by placing them on a number line that contains benchmarks, such as 0 and 1 or 0 and 5.
- Position a given set of positive fractions, including mixed numbers and improper fractions, on a 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