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

Mathematics - Grade 6

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

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.


Algebraic Concepts
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.

    Order of Operations: Simplify
The learner will be able to apply rules of order of operations, including rules for exponents, to make numerical expressions less complex.
Strand Bloom's Scope Hours Source
Order of Operations Knowledge Introduce 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.B
Instructional Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
- Merrill Algebra One, 1990, text [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
  
    Equations: Unknown Quantities
The learner will be able to apply the inverse relationship that exists between addition and subtraction and between multiplication and division, and exponentiation and root extraction to find unknown quantities in equations.
Strand Bloom's Scope Hours Source
Equations Application Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.G
Instructional Resources
- Heath Math Connections, 1992, text [misc].  
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Algebraic Concepts: Create/Interpret
The learner will be able to create and interpret expressions and equations that illustrate problem scenarios.
Strand Bloom's Scope Hours Source
Algebraic Concepts Synthesis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.C
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Equality/Inequality: Solution Methods
The learner will be able to choose and apply a method to solve an equation, describe the solution and check the solution for accuracy.
Strand Bloom's Scope Hours Source
Equality/Inequality Application Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.E
Instructional Resources
- Merrill Algebra One, 1990, text [Textbook].  
- Algebra With Pizzazz A, Creative Pub, 1989, misc [Work Books].  
Assessment Resources
- Algebra With Pizzazz A, Creative Pub, 1989, misc [Work Books].  
  
    Algorithms: Create/Use/Describe
The learner will be able to describe, use,apply algorithmic procedures for computing and approximating with whole numbers,fractions and decimals.
Strand Bloom's Scope Hours Source
Algorithms Application Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.D
Instructional Resources
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
  
    Order of Operations: Applying Rules
The learner will be able to use the rules of order of operations to obtain the value of expressions.
Strand Bloom's Scope Hours Source
Order of Operations Application, Synthesis Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.A
  
    Expressions: Expand
The learner will be able to expand expressions that involve exponents.
Strand Bloom's Scope Hours Source
Expressions Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.E
  
    Algebraic Concepts: Manipulatives
The learner will be able to use manipulatives to represent algebraic concepts.
Strand Bloom's Scope Hours Source
Algebraic Concepts Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.D
  
    Variable
The learner will be able to understand the basic concept of a variable as representing an unknown quantity.
Strand Bloom's Scope Hours Source
Variable Comprehension Master 0.3 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
Instructional Resources
- Assessment Strategies For Math, Walch Publishing, 2003, misc [Textbook].  
  
    Variable: Solving For
The learner will be able to manipulate a given formula to solve for a specific variable.
Strand Bloom's Scope Hours Source
Variable Application, Synthesis Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    Simplify Expressions: Exponents
The learner will be able to simplify expressions that involve exponents.
Strand Bloom's Scope Hours Source
Simplify Expressions Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.E
  

Decimals
The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. Students compare and compute decimals, study money, estimate decimals, problem solve using decimals, and reason using decimals.

    Decimal Notation: Identify/Use
The learner will be able to identify and use decimal notation.
Strand Bloom's Scope Hours Source
Decimals Comprehension, Synthesis Develop 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Heath Math Connections, 1992, text [misc].  
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
- Graph Paper Masters, Dale Seymour, 1989, worksheets [worksheets].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  

Fractions
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. Students compare and order fractions, study fraction parts, estimate with fractions, reason using fractions, and problem solve using fractions.

    Fraction Notation: Evaluate
The learner will be able to evaluate fraction notation in context as part of a whole, in division, or as a ratio.
Strand Bloom's Scope Hours Source
Fractions Evaluation Master 1.5 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Heath Math Connections, 1992, text [misc].  
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
- Understanding Fractions - Book 2, Dale Seymour, 1981, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Problem Solving: Represent/Real World
The learner will be able to apply fraction representations to solve real world problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Math Yellow Pages For Students and Teachers, Incentive Publications, 2002, misc [Textbook].  
- Assessment Strategies For Math, Walch Publishing, 2003, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  

Functions
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.

    Functional Relationships: Analyze
The learner will be able to analyze functional relationships to describe how a change in one quantity results in a change in another.
Strand Bloom's Scope Hours Source
Functional Relationships Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.J
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
  

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.

    Logic: Create Arguments
The learner will be able to apply if...then statements in the creation of elementary valid arguments.
Strand Bloom's Scope Hours Source
Logic Application Master 0.8 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.C
Instructional Resources
- If You're Trying to Get Better Grades . . . This Book, Incentive Publications, 2003, misc [Textbook].  
- Measuring Up to the Pennsylvania Academic Standards, Publishing Group, Inc., 2001, misc [Textbook].  
  
    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 Knowledge Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.D
Instructional Resources
- Heath Math Connections, 1992, text [misc].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Problem Solving: Relationships
The learner will be able to make connections and determine relationships between geometry concepts in order to solve problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Figures: Classify/Criterion
The learner will be able to use a given criterion to classify figures.
Strand Bloom's Scope Hours Source
Figures: Classify Analysis Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    Figures: Describing
The learner will be able to describe object shapes.
Strand Bloom's Scope Hours Source
Figures: Describe Comprehension Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
Instructional Resources
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
  
    Congruence/Similarity: Polygons
The learner will be able to explain why polygons may be classified as congruent or not congruent.
Strand Bloom's Scope Hours Source
Congruence/Similarity/Symmetry Comprehension Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.F
  
    Congruent/Similar: Exploring Figures
The learner will be able to explore concepts of congruent figures.
Strand Bloom's Scope Hours Source
Congruence/Similarity/Symmetry Analysis Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    Congruence/Similarity: Classification
The learner will be able to classify figures by congruence.
Strand Bloom's Scope Hours Source
Congruence/Similarity/Symmetry Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.K
  
    Angles: Congruent
The learner will be able to identify congruent angles.
Strand Bloom's Scope Hours Source
Angles Knowledge Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    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
  
    Symmetry
The learner will be able to determine if a given shape is symmetrical.
Strand Bloom's Scope Hours Source
Symmetry Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.K
  
    Properties: Comparison
The learner will be able to compare the properties of two- and three-dimensional shapes.
Strand Bloom's Scope Hours Source
Properties of Figures Analysis Master 0.5 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    Problem Solving: Geometric Properties
The learner will be able to apply geometric properties to solve problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.5 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    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
Instructional Resources
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
  

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.

    Problem Solving: Mathematical/Real World
The learner will be able to solve both mathematical and real world problems by applying concepts of and operations with integer numbers.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Heath Math Connections, 1992, text [misc].  
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    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
Instructional Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
- Merrill Algebra One, 1990, text [Textbook].  
- Algebra With Pizzazz A, Creative Pub, 1989, misc [Work Books].  
- Pre-Algebra With Pizzazz BB, Creative Pub, 1978, misc [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, misc [Work Books].  
  

Mathematics Processes
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures.

    Reasoning: Conjecture
The learner will be able to formulate conjectures based on logical reasoning and use counterexamples to test conjectures.
Strand Bloom's Scope Hours Source
Reasoning Synthesis Master 0.8 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.A
Instructional Resources
- Measuring Up to the Pennsylvania Academic Standards, Publishing Group, Inc., 2001, misc [Textbook].  
  
    Relationships: Conclusion
The learner will be able to arrive at a conclusion by combining numeric relationships.
Strand Bloom's Scope Hours Source
Relationships Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.B
Instructional Resources
- If You're Trying to Get Better Grades . . . This Book, Incentive Publications, 2003, misc [Textbook].  
  

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.

    Units: Tools
The learner will be able to choose the most suitable tools and units in problem solving situations that may require estimation and measurement, and relate methods used in problem solving using technology as appropriate.
Strand Bloom's Scope Hours Source
Units Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#2 week tested: 26.
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
  
    Scale Models: Construct/Apply
The learner will be able to construct and apply scale models.
Strand Bloom's Scope Hours Source
Scale Drawings Application Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.G
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Measurement: Approximate/Use/Explain
The learner will be able to approximate, use, and explain measures of distance, rate, perimeter, area, capacity, weight, mass, and angles.
Strand Bloom's Scope Hours Source
Measurement: Estimation Application Master 2.5 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.D
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
  
    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 Synthesis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.A
  
    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 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.B
Instructional Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
  
    Perimeter: Application
The learner will be able to solve real world application problems involving perimeter measurements.
Strand Bloom's Scope Hours Source
Perimeter Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#2 week tested: 26.
Instructional Resources
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
  
    Area/Volume: Combine/Separate
The learner will be able to solve for the area of the combination or separation of figures.
Strand Bloom's Scope Hours Source
Perimeter/Area/Volume Application Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#2 week tested: 26.
  
    Circumference: Application
The learner will be able to solve real world application problems involving circumference measurements.
Strand Bloom's Scope Hours Source
Circumference Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#2 week tested: 26.
Instructional Resources
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Measurement: Quantify Issues
The learner will be able to quantify issues using measurement.
Strand Bloom's Scope Hours Source
Measurement: Application Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.F
  

Number Theory
The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications.

    Equivalent Forms: Represent/Use
The learner will be able to display and/or apply numbers in many different equivalent forms.
Strand Bloom's Scope Hours Source
Equivalent Forms Application Master 2.5 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.A
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Ratio/Proportion: Apply/Math Problems
The learner will be able to use ratio and proportion in mathematical problem scenarios involving distance, rate,and time.
Strand Bloom's Scope Hours Source
Ratio/Proportion Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.D
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Factors: Understand/Use
The learner will be able to understand and use factors.
Strand Bloom's Scope Hours Source
Factors Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
  
    Ratio/Proportion: Solve/Story Problems
The learner will be able to obtain solutions to story problems using ratio and proportion.
Strand Bloom's Scope Hours Source
Ratio/Proportion Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.B
  
    Ratio/Proportion: Apply/Real World
The learner will be able to apply ratio and proportion concepts to solve real world scenario problems.
Strand Bloom's Scope Hours Source
Ratio/Proportion Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
  
    Multiples: Understand
The learner will be able to demonstrate an understanding of multiples.
Strand Bloom's Scope Hours Source
Multiples Comprehension Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
  
    Divisibility: Determine/Divide Evenly
The learner will be able to determine which number is evenly divisible by a given number.
Strand Bloom's Scope Hours Source
Divisibility Application Master 2.5 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
- Merrill Algebra One, 1990, text [Textbook].  
  
    Scientific Notation: Simplify/Expression
The learner will be able to simplify numerical expressions involving scientific notation.
Strand Bloom's Scope Hours Source
Scientific Notation Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.B
  

Numeration
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.

    Sequences: Reproduce/Extend/Create
The learner will be able to reproduce, extend, and create sequences.
Strand Bloom's Scope Hours Source
Sequences Synthesis Master 0.8 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
Instructional Resources
- If You're Trying to Get Better Grades . . . This Book, Incentive Publications, 2003, misc [Textbook].  
- Measuring Up to the Pennsylvania Academic Standards, Publishing Group, Inc., 2001, misc [Textbook].  
  
    Patterns: Explain/Generalize
The learner will be able to explain, generalize, and gain knowledge of patterns, including linear, exponential and simple relationships.
Strand Bloom's Scope Hours Source
Patterns Synthesis Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.B
  
    Estimation: Tips/Discount
The learner will be able to approximate the amount of tips and discounts applying ratios, proportions and percents.
Strand Bloom's Scope Hours Source
Estimation Application Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.C
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Estimation: Appropriate Uses
The learner will be able to identify when estimation is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.
Strand Bloom's Scope Hours Source
Estimation Comprehension Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.E
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
  
    Estimate/Problems: Use
The learner will be able to use estimation in solving problems.
Strand Bloom's Scope Hours Source
Estimate/Problems Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Patterns: Analyze/Sequence/Series
The learner will be able to analyze mathematical patterns such as sequences, series, and recursive patterns.
Strand Bloom's Scope Hours Source
Patterns: Interpret/Analyze Analysis Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    Patterns: Extend/Infinitely
The learner will be able to extend number or object patterns that can be infinitely continued.
Strand Bloom's Scope Hours Source
Patterns Synthesis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.19,2.11.8.C
  
    Estimation: Appropriateness
The learner will be able to identify the appropriateness of overestimating or underestimating in computation.
Strand Bloom's Scope Hours Source
Estimation Knowledge Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.D
Instructional Resources
- Assessment Strategies For Math, Walch Publishing, 2003, assessment [Textbook].  
  
    Number Line: Represent Integers
The learner will be able to illustrate integers on a number line.
Strand Bloom's Scope Hours Source
Number Lines Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.F
Instructional Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
- Merrill Algebra One, 1990, text [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, text [Work Books].  
  
    Rounding: Estimation
The learner will be able to relate rounding skills to estimating possible outcomes of equations and estimations of size.
Strand Bloom's Scope Hours Source
Rounding Analysis Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
  

Percents
The Percent Unit includes Competencies/Objectives which focus on the concepts of percent. Students perform operations with percents, convert percents to other number forms, use manipulatives to demonstrate percents, and solve problems with percents in real world contexts.

    Number Sense: Applying
The learner will be able to show an intuitive sense of what a percent is, and how percents are used in real world scenarios by completing sentences involving percentages with appropriate and reasonable choices.
Strand Bloom's Scope Hours Source
Number Sense Application Master PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Communicating: Write/Percents
The learner will be able to write percents.
Strand Bloom's Scope Hours Source
Communicating Comprehension Master 0.5 Bloomsburg Area School District
Instructional Resources
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
  
    Decimal Percent of a Whole Number
The learner will be able to determine the decimal percent of a whole number.
Strand Bloom's Scope Hours Source
Calculate Percentages Application Master 0.5 Bloomsburg Area School District
  
    Fractional Percent of a Whole Number
The learner will be able to determine the fractional percent of a whole number.
Strand Bloom's Scope Hours Source
Calculate Percentages Application Master 0.5 Bloomsburg Area School District
  
    Percent/Percentage/Symbol
The learner will be able to identify the definition of percent (one out of a hundred), percentage (part of a whole), and the percent symbol (%).
Strand Bloom's Scope Hours Source
Percent Representations Knowledge Master 0.8 Bloomsburg Area School District
  
    Percent: Mental Math
The learner will be able to calculate percents using mental math.
Strand Bloom's Scope Hours Source
Calculate Percentages Application Master 1.0 Bloomsburg Area School District
  
    Percent: Recognize Equivalent
The learner will be able to identify the equivalent percent of a specific decimal or fraction.
Strand Bloom's Scope Hours Source
Calculate Percentages Knowledge Master 0.5 Bloomsburg Area School District
  
    Percents: Compare/Fractions
The learner will be able to convert a given percentage to a fraction (or vice versa) in order to compare them.
Strand Bloom's Scope Hours Source
Percent Representations Analysis Master 1.0 Bloomsburg Area School District
  
    Problem Solving: Solution Strategies
The learner will be able to develop strategies for solving problems involving percents.
Strand Bloom's Scope Hours Source
Problem Solving Synthesis Master 1.5 Bloomsburg Area School District
Instructional Resources
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Percents: Convert to Decimals
The learner will be able to convert from a percent to decimal representation of a number.
Strand Bloom's Scope Hours Source
Percent Representations Synthesis Master 0.5 Bloomsburg Area School District
  

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.).

    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 and range.
Strand Bloom's Scope Hours Source
Average/Median/Mode/Range Analysis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.A
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Math Yellow Pages For Students and Teachers, Incentive Publications, 2002, misc [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
- Measuring Up to the Pennsylvania Academic Standards, Publishing Group, Inc., 2001, misc [Textbook].  
  
    Probability: Conjectures
The learner will be able to formulate conjectures that have a basis in theoretical or experimental probability.
Strand Bloom's Scope Hours Source
Probability Analysis Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.E
Instructional Resources
- Middle Grades Assessments, Dale Seymour, 1999, assessment [Textbook].  
  
    Predictions: Probability
The learner will be able to apply probability methods in the prediction of given event outcomes.
Strand Bloom's Scope Hours Source
Predictions Application Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.E
Instructional Resources
- Encyclopedia Of Math Topics And References, Dale Seymour, 1996, misc [Textbook].  
- If You're Trying to Get Better Grades . . . This Book, Incentive Publications, 2003, misc [Textbook].  
  
    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 Application Master 0.1 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.B
  
    Probability/Statistics: Problem Solving
The learner will be able to understand and use basic probability and statistics concepts to solve both real world and theoretical problems.
Strand Bloom's Scope Hours Source
Probability/Statistics Application Master 0.1 PA: System of School Assessment, 1997, Grade 8, p.12,#4 week tested: 26.
  
    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
Sampling Synthesis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.D
  

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 Analysis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.B
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
- Assessment Strategies For Math, Walch Publishing, 2003, assessment [Textbook].  
- Measuring Up to the Pennsylvania Academic Standards, Publishing Group, Inc., 2001, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    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 Evaluation Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.A
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  
    Strategies: Invent
The learner will be able to formulate methods, materials, and strategies used to obtain solutions to problems.
Strand Bloom's Scope Hours Source
Strategies Synthesis Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.A
  
    Problem Solving: Complex/Non-Routine
The learner will be able to apply organization methods and a variety of strategies to solve complex and non-routine problems.
Strand Bloom's Scope Hours Source
Problem Solving Application Master PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    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
Instructional Resources
- Preparing for Math Tests, AGS, 1999, misc [Textbook].  
- Preparing for the Terra Nova, AGS, 1999, misc [Textbook].  
  
    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 1.0 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 1.5 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 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.C
  

Rational and Irrational Numbers
The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers.

    Operations: Rational Numbers
The learner will be able to apply the four basic operations on rational (positive) numbers.
Strand Bloom's Scope Hours Source
Operations Application Master 7.0 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.A
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
- Pre-Algebra With Pizzazz BB, Creative Pub, 1978, misc [Textbook].  
  
    Rational Numbers: Ordering
The learner will be able to order a group of ( positive) rational numbers in the appropriate sequence.
Strand Bloom's Scope Hours Source
Rational Numbers Analysis Master 1.5 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.C
  
    Problem Solving: Rational
The learner will be able to obtain solutions to real world problems applying (positive) rational number concepts and operations.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 2.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.H
Instructional Resources
- When Are We Ever Gonna Have To Use This?, Dale Seymour, Third Edition, 1988, misc [Textbook].  
- Techniques of Problem Solving, Dale Seymour, misc [Textbook].  
  

Whole Numbers
The Whole Numbers Unit includes Competencies/Objectives which focus on whole number concepts. Students perform operations with whole numbers, use manipulatives to demonstrate whole number concepts, and solve problems with whole numbers in real world contexts.

    Operations: Add/Subtract/Multiply/Divide
The learner will be able to add, subtract, multiply, and divide whole numbers within the context of numerical problems.
Strand Bloom's Scope Hours Source
Operations Application Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- Heath Mathematics Connections, Heath, 1992, text [Textbook].  
- Mathimagition Series A-F, Creative Publications, 1983, misc [Textbook].  
- Graph Paper Masters, Dale Seymour, 1989, worksheets [worksheets].  
- Standards-Based Math, McGraw-Hill Children's Publishing, 2002, misc [Textbook].  
- Holt Mathematics, Grade 6, 1978, text [Textbook].  
  
    Add Multi-Digit Numbers
The learner will be able to perform the addition of multi-digit numbers.
Strand Bloom's Scope Hours Source
Add Whole Numbers Application Master 1.0 Bloomsburg Area School District
  
    Divide Multi-Digit Numbers
The learner will be able to perform division of multi-digit numbers.
Strand Bloom's Scope Hours Source
Divide Whole Numbers Application Master 1.0 Bloomsburg Area School District
  
    Multiply: Multiple Digit Numbers
The learner will be able to perform multiplication of multiple digit numbers.
Strand Bloom's Scope Hours Source
Multiply Whole Numbers Application Master 1.0 Bloomsburg Area School District
  
    Subtraction: Regrouping Whole Numbers
The learner will be able to identify a situation where regrouping is required.
Strand Bloom's Scope Hours Source
Subtract Whole Numbers Knowledge Master 1.0 Bloomsburg Area School District
  

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