Bloomsburg Area School District
Math 6-8 - with Extended Math

Mathematics - Grade 7- Extended Math

Mathematics

Academic Standards For Mathematics
INTRODUCTION
The Pennsylvania Academic Standards for Mathematics are:

2.1. Numbers, Number Systems and Number Relationships
2.2. Computation and Estimation
2.3. Measurement and Estimation
2.4. Mathematical Reasoning and Connections
2.5. Mathematical Problem Solving and Communication
2.6. Statistics and Data Analysis
2.7. Probability and Predictions
2.8. Algebra and Functions
2.9. Geometry
2.10. Trigonometry
2.11. Concepts of Calculus

This document avoids repetition of learned skills, making an obvious progression across grade levels less explicit. Teachers shall expect that students know and can apply the concepts and skills expressed at the preceding level. Consequently, previous learning is reinforced but not retaught. Students who achieve these mathematical standards will be able to communicate mathematically. Although it is an interesting and enjoyable study for its own sake, mathematics is most appropriately used as a tool to help organize and understand information from other academic disciplines.
Because our capacity to deal with all things mathematical is changing rapidly, students must be able to bring the most modern and effective technology to bear on their learning of mathematical concepts and skills.

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.
Strand Bloom's Scope Hours Source
Analyzing/Evaluating Graphical Forms Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.A
  
    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.
Strand Bloom's Scope Hours Source
Analyzing/Evaluating Graphical Forms Analysis Master 2.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Stem-and-Leaf Plots: Display/Data
The learner will be able to display data in a stem-and-leaf plot.
Strand Bloom's Scope Hours Source
Stem-and-Leaf/Box-and-Whisker Plots Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.E
  
    Stem-and-Leaf Plots: Interpret
The learner will be able to interpret data shown in a stem-and-leaf graph.
Strand Bloom's Scope Hours Source
Stem-and-Leaf/Box-and-Whisker Plots Analysis Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.E
  
    Box-and-Whisker Plots: Display/Data
The learner will be able to display data in a box-and-whisker plot.
Strand Bloom's Scope Hours Source
Stem-and-Leaf/Box-and-Whisker Plots Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.E
  
    Box-and-Whisker Plots: Interpret
The learner will be able to interpret data shown in a box-and-whisker graph.
Strand Bloom's Scope Hours Source
Stem-and-Leaf/Box-and-Whisker Plots Analysis Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.E
  
    Sampling: Design/Follow Through
The learner will be able to design and follow through with a random sampling procedure.
Strand Bloom's Scope Hours Source
Analyzing/Evaluating Graphical Forms Synthesis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.D
  
    Data Analysis: Graphing Calculator
The learner will be able to organize and study data using scientific and graphing calculators and computer spreadsheets.
Strand Bloom's Scope Hours Source
Analyzing/Evaluating Graphical Forms Master 0.8 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.F
  

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.
Strand Bloom's Scope Hours Source
Predictions Master 2.5 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.E
  
    Permutations: Determine
The learner will be able to find the permutations in a given situation.
Strand Bloom's Scope Hours Source
Permutations Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.A
  
    Combinations: Determine
The learner will be able to find the combinations in a given situation.
Strand Bloom's Scope Hours Source
Combinations Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.A
  
    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.
Strand Bloom's Scope Hours Source
Data Analysis Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.B
  
    Probability: Compare
The learner will be able to observe similarities and/or differences that may exist between experimental results and mathematical calculations of probabilities.
Strand Bloom's Scope Hours Source
Probability Analysis Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.D
  

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.
Strand Bloom's Scope Hours Source
Lines Analysis Master 0.8 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Angles: Measuring
The learner will be able to measure angles in degrees.
Strand Bloom's Scope Hours Source
Angles Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.E
  
    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.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Analysis Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Angles: Compare
The learner will be able to compare angles.
Strand Bloom's Scope Hours Source
Angles Analysis Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.E
  
    Angles: Draw/Measure/Label/List
The learner will be able to draw, measure, list, and label the attributes of complementary, supplementary, and vertical angles.
Strand Bloom's Scope Hours Source
Angles Master 0.7 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.B
  
    Lines: Draw/Transversal
The learner will be able to draw a transversal.
Strand Bloom's Scope Hours Source
Lines Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.E
  
    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.
Strand Bloom's Scope Hours Source
Lines/Angles/Polygons Knowledge Master 2.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    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.
Strand Bloom's Scope Hours Source
Properties of Figures Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.D
  
    Polygons: Classify
The learner will be able to classify familiar polygons as regular or irregular(up to a decagon).
Strand Bloom's Scope Hours Source
Polygons Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.C
  
    Congruence/Similarity: Polygons
The learner will be able to explain why polygons may be classified as similar, congruent, or neither.
Strand Bloom's Scope Hours Source
Congruence/Similarity/Symmetry Comprehension Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.F
  
    Triangles: Apply/Properties
The learner will be able to apply the properties of triangles.
Strand Bloom's Scope Hours Source
Triangles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Triangles: Classify
The learner will be able to classify triangles using multiple criteria.
Strand Bloom's Scope Hours Source
Triangles Analysis Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    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.
Strand Bloom's Scope Hours Source
Triangles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Trigonometric Concepts
The learner will be able to calculate measures of sides and angles by applying proportions, the Pythagorean Theorem, and right triangle relationships.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.18,2.10.8.A
  
    Triangles: Congruence
The learner will be able to determine the conditions necessary for the congruence of triangles.
Strand Bloom's Scope Hours Source
Triangles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Triangles: Determine/Corresponding Sides
The learner will be able to determine corresponding sides in similar or congruent triangles.
Strand Bloom's Scope Hours Source
Triangles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    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.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.D
  
    Triangles: Similar/Proportion
The learner will be able to find missing measures in similar triangles by applying proportions.
Strand Bloom's Scope Hours Source
Triangles Application Master 1.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Quadrilaterals: Identify/Special
The learner will be able to identify special quadrilaterals including squares, rectangles, rhombuses, trapezoids, and parallelograms.
Strand Bloom's Scope Hours Source
Quadrilaterals Knowledge Master 1.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Circle: Parts
The learner will be able to identify and define circle parts.
Strand Bloom's Scope Hours Source
Circles Knowledge Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Circles: Pi
The learner will be able to use experimentation to estimate the value of pi.
Strand Bloom's Scope Hours Source
Circles Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.G
  
    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.
Strand Bloom's Scope Hours Source
Circles Application Master 2.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Symmetry
The learner will be able to determine if a given shape is symmetrical.
Strand Bloom's Scope Hours Source
Symmetry Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.K
  

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.
Strand Bloom's Scope Hours Source
Measurement: Estimation Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.D
  

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.
Strand Bloom's Scope Hours Source
Coordinate Geometry Knowledge Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Coordinate Geometry: Find/Points
The learner will be able to find and plot points in each of the four quadrants on a coordinate plane.
Strand Bloom's Scope Hours Source
Coordinate Geometry Application Master 0.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Coordinate Plane: Graph/Linear Equation
The learner will be able to create ordered pairs to graph a linear equation with and without a calculator.
Strand Bloom's Scope Hours Source
Coordinate Geometry Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Coordinate Geometry: Graphing
The learner will be able to graph similar figures, reflections, and translations on a coordinate plane.
Strand Bloom's Scope Hours Source
Coordinate Geometry Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Coordinate System: Apply/Transformations
The learner will be able to apply the rectangular coordinate system to study connections between stretching, shrinking, and transforming figures.
Strand Bloom's Scope Hours Source
Coordinate Geometry Analysis Master 1.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Reflections: Coordinate Plane
The learner will be able to perform reflections of plane figures in the coordinate plane over the x- and y-axis.
Strand Bloom's Scope Hours Source
Connecting Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Rotation: Illustrate
The learner will be able to illustrate rotations using physical or pictorial models.
Strand Bloom's Scope Hours Source
Connecting Application Master 0.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    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.
Strand Bloom's Scope Hours Source
Connecting Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Rotations: Recognize/Point
The learner will be able to recognize the point of rotation given the figure and the rotated figure.
Strand Bloom's Scope Hours Source
Connecting Knowledge Master 0.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Translation: Illustrate
The learner will be able to illustrate a translation using physical or pictorial models.
Strand Bloom's Scope Hours Source
Connecting Application Master 0.5 BLOOMSBURG AREA SCHOOL DISTRICT
  

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.
Strand Bloom's Scope Hours Source
Graphing Functions Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.I
  
    Functions: Graph
The learner will be able to create graphs of functions.
Strand Bloom's Scope Hours Source
Graphing Functions Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.I
  
    Analyzing: Functions
The learner will be able to analyze and graph functions using graphing calculators and computer spreadsheets.
Strand Bloom's Scope Hours Source
Absolute Value/Quadratic Functions Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.I
  

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.
Strand Bloom's Scope Hours Source
Solution Master 0.6 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.B
  
    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.
Strand Bloom's Scope Hours Source
Strategies Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.A
  
    Irrelevant Information: Identify
The learner will be able to identify irrelevant information given in a story problem.
Strand Bloom's Scope Hours Source
Irrelevant/Necessary Information Knowledge Master 0.4 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.D
  
    Necessary Information: Solution
The learner will be able to determine if further information is necessary in order to obtain problem solutions.
Strand Bloom's Scope Hours Source
Irrelevant/Necessary Information Application Master 0.4 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.D
  
    Solutions: Justifying
The learner will be able to justify a solution within a problem solving situation.
Strand Bloom's Scope Hours Source
Solution Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.C
  
    Strategies: Justify Reasoning
The learner will be able to justify the reasoning behind using a specific problem solving strategy.
Strand Bloom's Scope Hours Source
Strategies Evaluation Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.C
  

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