OKCPS
OCPS ACADEMIC STANDARDS

Mathematics - Grade 8

Mathematics

The Priority Academic Student Skills (PASS) set forth the basic skills for Oklahoma students. These skills are meant to be used by educators in developing mathematics curriculum appropriate to the needs of their students.

The Process Standards are benchmarked standards. For first through fifth grades, the process standards are included in only the fifth grade curriculum; for sixth through eighth grade, the process standards are included in only the eighth grade curriculum; and for the high school courses, the process standards are included in the curriculum for each course.

The primary goal of the Mathematics tests in the Iowa Tests of Basic Skills (ITBS), Form M is "to measure students' ability to reason and think mathematically."

The Stanford Achievement Test, Ninth Edition (SAT-9) contains two subtests for Mathematics levels Primary 1 through Advanced 2. At the SESAT and Task levels, only one subtest of Mathematics is included.

The Oklahoma Core Curriculum Test (P.A.S.S. Exam) for mathematics offers descriptors of student performance levels for grade 5, grade 8, and Algebra I.

The Mathematics section of the ACT contains sixty multiple-choice questions:
    * Twenty-four questions dealing with pre-algebra and elementary algebra
    * Eighteen questions dealing with intermediate algebra and coordinate geometry
    * Fourteen questions dealing with plane geometry
    * Four questions dealing with trigonometry

Grade 8

The Oklahoma PASS provides learning goals for mathematics that students must meet by the end of eighth grade. The Oklahoma Core Curriculum Test (P.A.S.S. Exam) for mathematics offers descriptors of student performance levels for students in eighth grade.


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.

    1.1 Solids: Drawing/Perspectives
The learner will be able to construct models, sketch (from different perspectives), and classify solid figures such as rectangular solids, prisms, cones, cylinders, pyramids, and combined forms (e.g., draw a figure that could result from making 1, 2, or 3 cuts in a given solid).
Strand Bloom's Scope Hours Source
Three-Dimensional Solids Synthesis Master 0.5 OK: PASS Standard 3.1; PASS Exam
  
    1.2 Pythagorean Theorem: Develop
The learner will be able to develop and apply the Pythagorean Theorem.
Strand Bloom's Scope Hours Source
Pythagorean Theorem Synthesis Master 1.0 OK: PASS Standard 3.5
  
    1.3 Similarity: Solve/Relationships
The learner will be able to apply knowledge of ratio and proportion to solve relationships between similar geometric figures (e.g., build a model of a 3-dimensional object to scale).
Strand Bloom's Scope Hours Source
Similarity Application Master 1.0 OK: PASS Standard 3.3; PASS Exam
  

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.

    2.1 Volume/Surface Area: Estimate
The learner will be able to approximate and determine surface area and volume in real world situations (e.g., unwrap a box to explore surface area, use rice, 1-inch cubes, centimeter cubes, cups...to estimate the volume of boxes, irregular shaped objects, containers).
Strand Bloom's Scope Hours Source
Perimeter/Area/Volume Application Master OK: PASS Standard 3.2; PASS Exam
  
    2.2 Area: Determine/Region
The learner will be able to find the area of a "region of a region" for simple composite figures (e.g., area of a rectangular picture frame).
Strand Bloom's Scope Hours Source
Area Application Master 1.0 OK: PASS Standard 3.4b; PASS Exam
  
    2.3 Formula: Choose/Measurement
The learner will be able to select and apply appropriate formulas for given situation in measurement problems (e.g., p=21+2w, v=lwh).
Strand Bloom's Scope Hours Source
Formulas Application Master 1.0 OK: PASS Standard 3.4a.II; PASS Exam
  

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.

    3.1 Number Forms: Illustrate/Interpret
The learner will be able to represent and interpret large numbers and numbers less than one using exponential and scientific notation.
Strand Bloom's Scope Hours Source
Number Forms Evaluation Master OK: PASS Standard 2.2b; PASS Exam
  
    3.2 Ratio/Proportion: Problem Solving
The learner will be able to apply ratios and proportions to solve problems.
Strand Bloom's Scope Hours Source
Ratio/Proportion Application Master 2.0 OK: PASS Standard 2.1c; PASS Exam
  

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

    4.1 Number Line: Graph
The learner will be able to graph the solution to linear inequalities with one variable on a number line.
Strand Bloom's Scope Hours Source
Number Lines Application Master OK: PASS Standard 1.2b; PASS Exam
  
    4.2 Patterns: Recognize/Continue/Apply
The learner will be able to recognize and continue patterns and apply experiences and observations in order to formulate suppositions.
Strand Bloom's Scope Hours Source
Patterns: Identify/Describe/Continue Application Master OK: PASS Process Standard 3.1
  
    4.3 Magnitude: Describe/Estimation
The learner will be able to use estimation strategies (e.g., rounding) to describe the magnitude of large numbers and numbers less than one.
Strand Bloom's Scope Hours Source
Magnitude Comprehension Master 1.0 OK: PASS Standard 2.2c; PASS Exam
  

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.).

    6.1 Sampling: Select/Generalize
The learner will be able to determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population (e.g., is the average height of a men's college basketball team a good representative sample for height predictions?).
Strand Bloom's Scope Hours Source
Theoretical Probability Application, Evaluation Master OK: PASS Standard 4.3
  
    6.2 Central Tendency: Determine
The learner will be able to find the range and measures of central tendency (mean, median and mode) of a set of data.
Strand Bloom's Scope Hours Source
Measures of Central Tendency Application Master 1.0 OK: PASS Standard 4.2; PASS Exam
  
    6.3 Data Display: Select/Use
The learner will be able to select and apply appropriate formats (e.g., line plots, bar graphs, stem-and-leaf plots, scatter plots, histograms, circle graphs) to display collected data.
Strand Bloom's Scope Hours Source
Data Display Application Master 1.0 OK: PASS Standard 4.1; PASS Exam
  

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.

    8.1 Linear Equations: Create/Solve
The learner will be able to model, write, and solve one- and two-step linear inequalities with one variable.
Strand Bloom's Scope Hours Source
Linear Equations Evaluation Master OK: PASS Standard 1.2a; PASS Exam
  
    8.2 Linear Equations:Model/Write/2-Step
The learner will be able to model, write, and solve two-step linear equations using many different methods.
Strand Bloom's Scope Hours Source
Linear Equations Evaluation Master OK: PASS Standard 1.1a; PASS Exam
  
    8.3 Linear Equations: Graph/Interpret
The learner will be able to graph and interpret the solution to linear equations with one variable on a number line.
Strand Bloom's Scope Hours Source
Linear Equations Evaluation Master OK: PASS Standard 1.1b; PASS Exam
  
    8.4 Equations: Use/Formula/Suitable
The learner will be able to select and apply appropriate formulas for given situations for an equation (e.g., d=rt, i=prt).
Strand Bloom's Scope Hours Source
Equations Application Master 0.5 OK: PASS Standard 3.4a.I; PASS Exam
  
    8.5 Exponents: Use Rules/ Solve
The learner will be able to use the rules of exponents to solve problems.
Strand Bloom's Scope Hours Source
Exponents Application Master 1.0 OK: PASS Standard 2.2a; PASS Exam
  

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

    10.1 Strategies: Create/Test
The learner will be able to create and test methods to obtain solutions to practical, daily problems which may have one or more answers.
Strand Bloom's Scope Hours Source
Strategies Synthesis Master OK: PASS Process Standard 1.1
  
    10.2 Strategies: Multi-Step/Non-Routine
The learner will be able to use many different strategies to obtain problem solutions, focusing on problems that are non-routine or require multiple steps.
Strand Bloom's Scope Hours Source
Strategies Application Master OK: PASS Process Standard 1.5
  
    10.3 Strategies: Other Disciplines/Real
The learner will be able to apply mathematical problem solving strategies to other disciplines as well as real world scenarios.
Strand Bloom's Scope Hours Source
Strategies Application Master OK: PASS Process Standard 4.1
  
    10.4 Problems: Create/Generalize
The learner will be able to create problems from scenarios within and outside of mathematics and generalize answers and strategies to new problem scenarios.
Strand Bloom's Scope Hours Source
Problems Synthesis Master OK: PASS Process Standard 1.3
  
    10.5 Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
Strand Bloom's Scope Hours Source
Solution Evaluation Master 1.5 OK: PASS Process Standard 1.4
  

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.

    13.1 Linear Equations: Predict/Effects
The learner will be able to predict the effect on the graph of a linear equation when the slope changes (e.g., make predictions from graphs, identify the slope in the equation y=mx+b and relate to a graph).
Strand Bloom's Scope Hours Source
Linear Equations Application Master 1.0 OK: PASS Standard 1.1c; PASS Exam
  

Rational and Irrational Numbers

    14.1 Rational Numbers: Compare/Order
The learner will be able to compare and order rational numbers (positive and negative integers, fractions and decimals) in real world situations.
Strand Bloom's Scope Hours Source
Rational Numbers Evaluation Master 1.0 OK: PASS Standard 2.1a; PASS Exam
  

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

    16.1 Modeling: Organize/Record Data
The learner will be able to use many different representations to organize and record data.
Strand Bloom's Scope Hours Source
Mathematical Modeling Knowledge, Application Master OK: PASS Process Standard 5.1
  
    16.2 Modeling: Communication
The learner will be able to apply representations to aid in the communication of mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Modeling Application Master OK: PASS Process Standard 5.2
  
    16.3 Modeling: Create/Representations
The learner will be able to create many different mathematical representations that can be used flexibly and suitably.
Strand Bloom's Scope Hours Source
Mathematical Modeling Synthesis Master OK: PASS Process Standard 5.3
  
    16.4 Modeling: Solve/Problems
The learner will be able to apply many different representations to model and obtain solutions to physical, social, and mathematical problems.
Strand Bloom's Scope Hours Source
Mathematical Modeling Evaluation Master OK: PASS Process Standard 5.4
  
    16.5 Mathematical Concepts: Discuss
The learner will be able to discuss mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Concepts Comprehension Master 1.0 OK: PASS Process Standard 2.1
  
    16.6 Math Concepts: Apply
The learner will be able to apply counterexamples to disprove suppositions.
Strand Bloom's Scope Hours Source
Mathematical Concepts Application Master 0.5 OK: PASS Process Standard 3.2
  
    16.7 Mathematical Concepts: Interpret
The learner will be able to interpret mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Concepts Evaluation Master 1.0 OK: PASS Process Standard 2.1
  
    16.8 Mathematical Concepts: Translate
The learner will be able to translate (from one to another) mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Concepts Comprehension Master 1.0 OK: PASS Process Standard 2.1
  
    16.9 Mathematical Concepts: Evaluate
The learner will be able to evaluate mathematical concepts.
Strand Bloom's Scope Hours Source
Mathematical Concepts Evaluation Master 1.0 OK: PASS Process Standard 2.1
  
    16.10 Reasoning: Choose/Strategies
The learner will be able to choose various types of reasoning strategies.
Strand Bloom's Scope Hours Source
Reasoning Application Master 1.0 OK: PASS Process Standard 3.4
  
    16.11 Reasoning:Reflect/Problem Solving
The learner will be able to reflect on the reasoning used in mathematical problem solving.
Strand Bloom's Scope Hours Source
Reasoning Analysis Master 1.0 OK: PASS Process Standard 2.2
  
    16.12 Reasoning: Use/Strategies
The learner will be able to use many different reasoning strategies.
Strand Bloom's Scope Hours Source
Reasoning Application Master 2.0 OK: PASS Process Standard 3.4
  
    16.13 Reasoning:Justify/Problem Solving
The learner will be able to justify the reasoning used in mathematical problem solving.
Strand Bloom's Scope Hours Source
Reasoning Evaluation Master 1.0 OK: PASS Process Standard 2.2
  
    16.14 Communication: Choose/Terminology
The learner will be able to choose appropriate mathematical terminology when discussing mathematical concepts.
Strand Bloom's Scope Hours Source
Communication Application Master 1.0 OK: PASS Process Standard 2.3
  
    16.15 Arguments: Create/Mathematical
The learner will be able to create mathematical arguments.
Strand Bloom's Scope Hours Source
Conjecture/Argument Synthesis Master 2.0 OK: PASS Process Standard 3.3
  
    16.16 Arguments: Evaluate/Mathematical
The learner will be able to evaluate mathematical arguments.
Strand Bloom's Scope Hours Source
Conjecture/Argument Evaluation Master 2.0 OK: PASS Process Standard 3.3
  

Perspective/Role in Society
The Perspective/Role in Society Unit includes Competencies/Objectives which focus on real world mathematics. Students study the mathematics of society and the role of mathematics in personal finance and careers.

    19.1 Mathematical Situations: Model
The learner will be able to apply verbal, written, physical, pictorial, graphical and/or algebraic methods to model mathematical situations.
Strand Bloom's Scope Hours Source
Mathematical Situations Application Master OK: PASS Process Standard 1.6
  

Technology
The Technology Unit includes Competencies/Objectives which focus on studying computer hardware and software, uses for calculators, and applications of technology in problem solving.

    21.1 Problem Solving: Technology/Data
The learner will be able to appropriately use technology to solve problems by both generating and analyzing data.
Strand Bloom's Scope Hours Source
Problem Solving Application Master OK: PASS Process Standard 1.2
  

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