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

Mathematics - Grade 7

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

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 the order of operations, including rules for exponents, to make number and/or variable expressions less complex.
Strand Bloom's Scope Hours Source
Order of Operations Comprehension Develop 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.B
  
    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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.G
  
    Algebraic Concepts: Create/Interpret
The learner will be able to create and interpret expressions, equations, or inequalities that illustrate problem scenarios.
Strand Bloom's Scope Hours Source
Algebraic Concepts Master PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.C
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- New Progress in Mathematics, Sadlier-Oxford, 1998, Workbook [Textbook].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
  
    Equality/Inequality: Solution Methods
The learner will be able to choose and apply a method to solve an equation or inequality, describe the solution and check the solution for accuracy.
Strand Bloom's Scope Hours Source
Equality/Inequality Master PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.E
  
    Algorithms: Create/Use/Describe
The learner will be able to create, use, and describe algorithmic procedures for computing and approximating with whole numbers, fractions, decimals and integers.
Strand Bloom's Scope Hours Source
Algorithms Master PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.D
  
    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 Master 0.5 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.A
  
    Equality: Relationships
The learner will be able to demonstrate that an equality relationship between two quantities stays the same when changes are made as long as the change is made to both quantities.
Strand Bloom's Scope Hours Source
Equations Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.J
  
    Inequalities: Interpret
The learner will be able to interpret inequalities using tables and graphs as tools.
Strand Bloom's Scope Hours Source
Inequalities Analysis Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    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 1.0 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 1.0 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    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 Master 1.0 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 Application Master 1.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Texbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
  

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 Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
  
    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
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Worook [Work Books].  
Assessment Resources
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  

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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.J
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  

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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.C
  
    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 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.D
  
    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 Master PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
  
    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.
  
    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
  
    Congruent/Similar: Exploring Figures
The learner will be able to explore concepts of both congruent and similar 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 and/or similarity.
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
  
    Lines: Draw/Transversal
The learner will be able to draw a transversal.
Strand Bloom's Scope Hours Source
Lines Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.16,2.9.8.E
  
    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
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
  
    Tessellations: Representations
The learner will be able to study objects to identify whether they represent tessellations.
Strand Bloom's Scope Hours Source
Tessellations Analysis Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.K
  
    Inductive/Deductive Reasoning: Identify
The learner will be able to identify the difference between inductive and deductive reasoning.
Strand Bloom's Scope Hours Source
Reasoning Knowledge Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.E
  
    Symmetry
The learner will be able to determine if a given shape is symmetrical.
Strand Bloom's Scope Hours Source
Symmetry Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.17,2.9.8.K
Instructional Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  
    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 2.0 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 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#3 week tested: 26.
Instructional Resources
- Strategies for Math..., Options Inc, 1997, Handouts [Textbook].  
- The Problem Solver, Creative Pub, 1998, Workbook [Work Books].  
  

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 Master PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Workbook and Textbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Workbook and Textbook [Textbook].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  
    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
  

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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.7,2.4.8.A
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Workbook and Textbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Workbook and Textbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Workbook and Textbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Workbook and Textbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
  
    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
  

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 Master PA: System of School Assessment, 1997, Grade 8, p.11,#2 week tested: 26.
  
    Scale Models: Construct/Apply
The learner will be able to construct and apply scale models.
Strand Bloom's Scope Hours Source
Scale Drawings Master PA: Academic Standards, January 16, 1999, Grade 8, p.6,2.3.8.G
  
    Measurement: Approximate/Use/Explain
The learner will be able to approximate, use, and explain measures of distance, rate, perimeter, area, volume, capacity, weight, mass, and angles.
Strand Bloom's Scope Hours Source
Measurement: Estimation Master 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 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
  
    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.
  
    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
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Strategies for Math..., Options Inc, 1997, Workbook [Textbook].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
  
    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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.A
  
    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
Ratio/Proportion Master PA: Academic Standards, January 16, 1999, Grade 8, p.2,2.1.8.D
  
    Factors: Understand/Use
The learner will be able to understand and use factors.
Strand Bloom's Scope Hours Source
Factors Master 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 1.0 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 2.0 PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Strategies for Math..., Options Inc, 1997, Workbook [Textbook].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
  

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 Master PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
Instructional Resources
- Classroom Quickies, Critical Thinking Press, 1982, With Software [Work Books].  
  
    Patterns: Explain/Generalize
The learner will be able to explain, generalize, and gain knowledge of patterns, including linear, exponential and simple quadratic relationships.
Strand Bloom's Scope Hours Source
Patterns Master PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.B
Instructional Resources
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
  
    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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.C
  
    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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.E
  
    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
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- Strategies for Math..., Options Inc, 1997, Workbook [Textbook].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  
    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.
Instructional Resources
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
  
    Patterns: Apply/Basic Number Theory
The learner will be able to apply simple algebraic patterns to basic number theory.
Strand Bloom's Scope Hours Source
Patterns Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.A
  
    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
  
    Number Lines: Plotting Points
The learner will be able to plot points using a given number line.
Strand Bloom's Scope Hours Source
Number Lines Application Master 0.5 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    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
  
    Number Lines: Problem Solving
The learner will be able to solve real world problems using number lines.
Strand Bloom's Scope Hours Source
Number Lines Application Master 2.0 PA: System of School Assessment, 1997, Grade 8, p.12,#5 week tested: 26.
  
    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 Master PA: System of School Assessment, 1997, Grade 8, p.11,#1 week tested: 26.
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Milliken Beginning Algebra, 1989, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Pre-Algebra With Pizzazz AA, Creative Pub, 1989, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
- Strategies for Math..., Options Inc, 1997, Workbook [Textbook].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
- The Problem Solver, Creative Pub, 1998, Activities [Work Books].  
- Middle School Math Challenge, The Learning Works Inc, 1995, Workbook [Work Books].  
- Classroom Quickies, Critical Thinking Press, 1982, With Software [Work Books].  
- Holt Algebra 1, 1992, Textbook [Textbook].  
Assessment Resources
- Merrill Pre-Algebra, A Problem Solving Approach, 1982, Workbook [Work Books].  
- Nasco's Pre-Algebra, 2003, Workbook [Work Books].  
- Algebra With Pizzazz A, Creative Pub, 1989, Workbook [Work Books].  
  

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.).

    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 Master PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.E
  
    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 Master 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 PA: Academic Standards, January 16, 1999, Grade 8, p.11,2.7.8.B
Instructional Resources
- New Progress in Mathematics, Sadlier-Oxford, 1998, Textbook and Workbook [Textbook].  
- Heath Mathematics Connections, Heath, 1992, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 7, 1982, Textbook and Workbook [Textbook].  
- Holt School Mathematics, Grade 8, 1982, Textbook and Workbook [Textbook].  
- Middle School Math with Pizzazz, Creative Pub, 1989, Workbook [Work Books].  
- Strategies for Math..., Options Inc, 1997, Workbook [Textbook].  
- The Problem Solver, Creative Pub, 1998, Activtites [Work Books].  
- Teaching Problem Solving Strategies, Addison Wesley, 1983, Workbook [Work Books].  
  
    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 Master PA: System of School Assessment, 1997, Grade 8, p.12,#4 week tested: 26.
  
    Sampling: Validity/Newspapers
The learner will be able to determine if the sampling strategy described in studies published in local or national newspapers is valid.
Strand Bloom's Scope Hours Source
Sampling Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.9,2.6.8.G
  

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 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 PA: Academic Standards, January 16, 1999, Grade 8, p.8,2.5.8.A
  
    Strategies: Invent
The learner will be able to invent methods, materials, and strategies used to obtain solutions to problems.
Strand Bloom's Scope Hours Source
Strategies Master 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 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
  
    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 2.0 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 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 numbers.
Strand Bloom's Scope Hours Source
Operations Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.4,2.2.8.A
  
    Rational Numbers: Ordering
The learner will be able to order a group of rational numbers in the appropriate sequence.
Strand Bloom's Scope Hours Source
Rational Numbers Analysis Master 1.0 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 rational number concepts and operations.
Strand Bloom's Scope Hours Source
Problem Solving Application Master 1.0 PA: Academic Standards, January 16, 1999, Grade 8, p.14,2.8.8.H
  

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.

    Graphing: Illustrate Relationships
The learner will be able to illustrate relationships with tables or graphs in the coordinate plane, and verbal or symbolic rules.
Strand Bloom's Scope Hours Source
Graphing Master PA: Academic Standards, January 16, 1999, Grade 8, p.13,2.8.8.G
  

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.
  

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