Bloomsburg Area School District Mathematics Academic Standards For Mathematics Grade 7- Extended Math The Mathematics Standards describe what students should know and be able to do at the eighth grade level. They reflect the increasing complexity and sophistication that students are expected to achieve as they progress through school. |
Data Interpretation |
The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. |
Mean/Median/Mode/Range/Quartiles
The learner will be able to compare and contrast various plots of data by applying values of mean, median, mode, quartiles, and range.
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Analyzing Graphs: Tables/Charts/Graphs
The learner will be able to create and analyze tables, charts, and graphs (bar graphs, line graphs, circle graphs, and scatterplots) and be able to determine mean, median, mode, and range from the graphs.
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Stem-and-Leaf Plots: Display/Data
The learner will be able to display data in a stem-and-leaf plot.
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Stem-and-Leaf Plots: Interpret
The learner will be able to interpret data shown in a stem-and-leaf graph.
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Box-and-Whisker Plots: Display/Data
The learner will be able to display data in a box-and-whisker plot.
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Box-and-Whisker Plots: Interpret
The learner will be able to interpret data shown in a box-and-whisker graph.
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Sampling: Design/Follow Through
The learner will be able to design and follow through with a random sampling procedure.
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Data Analysis: Graphing Calculator
The learner will be able to organize and study data using scientific and graphing calculators and computer spreadsheets.
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Probability/Statistics |
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.). |
Predictions: Probability
The learner will be able to apply probability (simple and compound) methods in the prediction of given event outcomes.
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Permutations: Determine
The learner will be able to find the permutations in a given situation.
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Combinations: Determine
The learner will be able to find the combinations in a given situation.
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Data Analysis: Representation
The learner will be able to study and/or illustrate data through the use of tables, charts, and graphs of many different types.
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Probability: Compare
The learner will be able to observe similarities and/or differences that may exist between experimental results and mathematical calculations of probabilities.
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Geometry |
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
Lines/Segments/Rays/Points/Angles
The learner will be able to explore the interrelationships between point, lines, segments, rays, and angles in a plane region.
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Angles: Measuring
The learner will be able to measure angles in degrees.
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Acute/Right/Obtuse Angles: Classify
The learner will be able to make classifications and drawings of various angles, determining if they are acute, right, obtuse, or straight.
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Angles: Compare
The learner will be able to compare angles.
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Angles: Draw/Measure/Label/List
The learner will be able to draw, measure, list, and label the attributes of complementary, supplementary, and vertical angles.
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Lines: Draw/Transversal
The learner will be able to draw a transversal.
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Angles: Parallel/Transversal
The learner will be able to identify angle relationships created by parallel and transversal lines, including corresponding, adjacent, alternate interior, alternate exterior, and vertical as well as understanding congruence, complementary, and supplementary qualities.
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Properties: Recognize/Name/Draw/List
The learner will be able to recognize, name, draw, and list all the properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms, and cylinders.
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Polygons: Classify
The learner will be able to classify familiar polygons as regular or irregular(up to a decagon).
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Congruence/Similarity: Polygons
The learner will be able to explain why polygons may be classified as similar, congruent, or neither.
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Triangles: Apply/Properties
The learner will be able to apply the properties of triangles.
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Triangles: Classify
The learner will be able to classify triangles using multiple criteria.
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Triangles: Problem Solving/Sum of Angles
The learner will be able to apply the property that the sum of the interior angles of a triangle is 180 degrees in order to obtain problem solutions.
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Trigonometric Concepts
The learner will be able to calculate measures of sides and angles by applying proportions, the Pythagorean Theorem, and right triangle relationships.
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Triangles: Congruence
The learner will be able to determine the conditions necessary for the congruence of triangles.
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Triangles: Determine/Corresponding Sides
The learner will be able to determine corresponding sides in similar or congruent triangles.
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Ratio/Proportion: Apply/Math Problems
The learner will be able to use ratio and proportion in mathematical problem scenarios involving distance, rate, time, and similar triangles.
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Triangles: Similar/Proportion
The learner will be able to find missing measures in similar triangles by applying proportions.
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Quadrilaterals: Identify/Special
The learner will be able to identify special quadrilaterals including squares, rectangles, rhombuses, trapezoids, and parallelograms.
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Circle: Parts
The learner will be able to identify and define circle parts.
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Circles: Pi
The learner will be able to use experimentation to estimate the value of pi.
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Circles: Problems/Area/Circumference
The learner will be able to obtain solutions to problems that involve the circumference or area of a circle when presented with the diameter or radius of the circle.
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Symmetry
The learner will be able to determine if a given shape is symmetrical.
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Measurement |
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving. |
Measurement: Approximate/Use/Explain
The learner will be able to approximate, use, and explain measures of distance, rate, perimeter, area (including triangles and quadrilaterals), volume, and angles using formulas.
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Real Numbers and the Coordinate Plane |
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
Coordinate Plane: Identify Components
The learner will be able to recognize the various components of the Cartesian plane.
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Coordinate Geometry: Find/Points
The learner will be able to find and plot points in each of the four quadrants on a coordinate plane.
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Coordinate Plane: Graph/Linear Equation
The learner will be able to create ordered pairs to graph a linear equation with and without a calculator.
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Coordinate Geometry: Graphing
The learner will be able to graph similar figures, reflections, and translations on a coordinate plane.
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Coordinate System: Apply/Transformations
The learner will be able to apply the rectangular coordinate system to study connections between stretching, shrinking, and transforming figures.
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Reflections: Coordinate Plane
The learner will be able to perform reflections of plane figures in the coordinate plane over the x- and y-axis.
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Rotation: Illustrate
The learner will be able to illustrate rotations using physical or pictorial models.
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Rotation: Finding Points
The learner will be able to find the coordinate points of the vertices of an illustrated figure after a given rotation is performed.
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Rotations: Recognize/Point
The learner will be able to recognize the point of rotation given the figure and the rotated figure.
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Translation: Illustrate
The learner will be able to illustrate a translation using physical or pictorial models.
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Functions |
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
Graphing Functions: Table
The learner will be able to create a table from a function.
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Functions: Graph
The learner will be able to create graphs of functions.
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Analyzing: Functions
The learner will be able to analyze and graph functions using graphing calculators and computer spreadsheets.
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Problem Solving |
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
Solutions: Verify/Interpret
The learner will be able to verify and interpret results by applying accurate mathematical language, notation, and illustrations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams.
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Strategies: Choose/Apply/Justify
The learner will be able to choose, apply, and justify the methods, materials, and strategies used to obtain solutions to problems.
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Irrelevant Information: Identify
The learner will be able to identify irrelevant information given in a story problem.
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Necessary Information: Solution
The learner will be able to determine if further information is necessary in order to obtain problem solutions.
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Solutions: Justifying
The learner will be able to justify a solution within a problem solving situation.
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Strategies: Justify Reasoning
The learner will be able to justify the reasoning behind using a specific problem solving strategy.
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