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

Mathematics - Grade 6- Entended 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 6- Entended 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.


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. 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.

    Units of Measurement: Appropriateness
The learner will be able to determine what unit of measure would be appropriate if measuring a given object.
Strand Bloom's Scope Hours Source
Units Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Time: Elapsed/Practical Problems
The learner will be able to solve practical problems using elapsed time.
Strand Bloom's Scope Hours Source
Time Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Time: Problem Solving/Zones
The learner will be able to solve real world problem situations where time zones are involved.
Strand Bloom's Scope Hours Source
Time Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Scale Maps: Interpret/Measurements
The learner will be able to interpret maps or drawings using scale measurements.
Strand Bloom's Scope Hours Source
Scale Drawings Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.F
  
    Converting: Solve/Time
The learner will be able to obtain solutions to problems involving the conversion of units of measure, including time.
Strand Bloom's Scope Hours Source
Converting Synthesis Master 2.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Distance/Rate/Time
The learner will be able to apply the distance formula to solve story problems.
Strand Bloom's Scope Hours Source
Distance/Rate/Time/Acceleration Application Master 1.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Problem Solving: Rates
The learner will be able to obtain solutions to problems by applying rates.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.B
  
    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
  
    Formulas: Develop
The learner will be able to develop and/or apply formulas and methods for finding measurement values.
Strand Bloom's Scope Hours Source
Formulas Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.A
  

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 1.0 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 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.B
  
    Properties: Recognize/Name/Draw/List
The learner will be able to recognize, name, draw, and list all the properties of squares, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, and triangles.
Strand Bloom's Scope Hours Source
Properties of Figures Master 1.5 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
  
    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
  
    Perimeter/Area: Measurement Solution
The learner will be able to determine whether a problem requires a solution of length or area.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Area of a Square: Formula/Apply
The learner will be able to apply the area formula for a square.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Area of a Rectangle: Formula/Understand
The learner will be able to understand the area formula for a rectangle.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Comprehension Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Area of a Triangle: Compute
The learner will be able to compute the area of a triangle.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Formula: Surface Area/Volume
The learner will be able to apply formulas for the surface area and volume of basic three-dimensional figures.
Strand Bloom's Scope Hours Source
Acute/Right/Obtuse Angles Application Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  

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 3.0 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 3.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    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 1.5 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 1.5 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 simple probability 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
  
    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
  

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 Plane: Identify/Ordered Pairs
The learner will be able to recognize the coordinates of a specific point in the first quadrant.
Strand Bloom's Scope Hours Source
Coordinate Geometry Knowledge Master 1.0 BLOOMSBURG AREA SCHOOL DISTRICT
  

Integers
The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. Students compare integers, perform operations with integers, convert integers to other number forms, use manipulatives to demonstrate integers, and solve problems with integers in real world contexts.

    Integers: Recognize
The learner will be able to identify integers.
Strand Bloom's Scope Hours Source
Integers Knowledge Master 0.5 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Integers: Number Lines
The learner will be able to interpret real world scenarios involving integers presented on number lines.
Strand Bloom's Scope Hours Source
Integers Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.F
  
    Add/Subtract: Understand/Manipulatives
The learner will be able to use manipulatives and number lines to understand addition and subtraction of integers.
Strand Bloom's Scope Hours Source
Add/Subtract Integers Comprehension Master 2.0 BLOOMSBURG AREA SCHOOL DISTRICT
  
    Addition/Subtraction Integers
The learner will be able to add and subtract integer numbers.
Strand Bloom's Scope Hours Source
Add/Subtract Integers Application Master 2.0 BLOOMSBURG AREA SCHOOL DISTRICT
  

Problem Solving
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems.

    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 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.D
  
    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 0.4 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
  

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