Bloomsburg Area School District Mathematics Academic Standards For Mathematics 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.
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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.
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Algebraic Concepts: Create/Interpret
The learner will be able to create and interpret expressions and equations that illustrate problem scenarios.
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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.
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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.
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Order of Operations: Applying Rules
The learner will be able to use the rules of order of operations to obtain the value of expressions.
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Expressions: Expand
The learner will be able to expand expressions that involve exponents.
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Algebraic Concepts: Manipulatives
The learner will be able to use manipulatives to represent algebraic concepts.
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Variable
The learner will be able to understand the basic concept of a variable as representing an unknown quantity.
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Variable: Solving For
The learner will be able to manipulate a given formula to solve for a specific variable.
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Simplify Expressions: Exponents
The learner will be able to simplify expressions that involve exponents.
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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.
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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.
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Problem Solving: Represent/Real World
The learner will be able to apply fraction representations to solve real world problems.
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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.
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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.
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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.
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Problem Solving: Relationships
The learner will be able to make connections and determine relationships between geometry concepts in order to solve problems.
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Figures: Classify/Criterion
The learner will be able to use a given criterion to classify figures.
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Figures: Describing
The learner will be able to describe object shapes.
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Congruence/Similarity: Polygons
The learner will be able to explain why polygons may be classified as congruent or not congruent.
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Congruent/Similar: Exploring Figures
The learner will be able to explore concepts of congruent figures.
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Congruence/Similarity: Classification
The learner will be able to classify figures by congruence.
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Angles: Congruent
The learner will be able to identify congruent angles.
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Angles: Compare
The learner will be able to compare angles.
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Symmetry
The learner will be able to determine if a given shape is symmetrical.
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Properties: Comparison
The learner will be able to compare the properties of two- and three-dimensional shapes.
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Problem Solving: Geometric Properties
The learner will be able to apply geometric properties to solve problems.
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Polygons: Classify
The learner will be able to classify familiar polygons as regular or irregular(up to a decagon).
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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.
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Integers: Number Lines
The learner will be able to interpret real world scenarios involving integers presented on number lines.
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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.
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Relationships: Conclusion
The learner will be able to arrive at a conclusion by combining numeric relationships.
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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.
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Scale Models: Construct/Apply
The learner will be able to construct and apply scale models.
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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.
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Formulas: Develop
The learner will be able to develop and/or apply formulas and methods for finding measurement values.
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Problem Solving: Rates
The learner will be able to obtain solutions to problems by applying rates.
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Perimeter: Application
The learner will be able to solve real world application problems involving perimeter measurements.
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Area/Volume: Combine/Separate
The learner will be able to solve for the area of the combination or separation of figures.
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Circumference: Application
The learner will be able to solve real world application problems involving circumference measurements.
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Measurement: Quantify Issues
The learner will be able to quantify issues using measurement.
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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.
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Ratio/Proportion: Apply/Math Problems
The learner will be able to use ratio and proportion in mathematical problem scenarios involving distance, rate,and time.
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Factors: Understand/Use
The learner will be able to understand and use factors.
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Ratio/Proportion: Solve/Story Problems
The learner will be able to obtain solutions to story problems using ratio and proportion.
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Ratio/Proportion: Apply/Real World
The learner will be able to apply ratio and proportion concepts to solve real world scenario problems.
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Multiples: Understand
The learner will be able to demonstrate an understanding of multiples.
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Divisibility: Determine/Divide Evenly
The learner will be able to determine which number is evenly divisible by a given number.
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Scientific Notation: Simplify/Expression
The learner will be able to simplify numerical expressions involving scientific notation.
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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.
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Patterns: Explain/Generalize
The learner will be able to explain, generalize, and gain knowledge of patterns, including linear, exponential and simple relationships.
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Estimation: Tips/Discount
The learner will be able to approximate the amount of tips and discounts applying ratios, proportions and percents.
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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.
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Estimate/Problems: Use
The learner will be able to use estimation in solving problems.
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Patterns: Analyze/Sequence/Series
The learner will be able to analyze mathematical patterns such as sequences, series, and recursive patterns.
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Patterns: Extend/Infinitely
The learner will be able to extend number or object patterns that can be infinitely continued.
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Estimation: Appropriateness
The learner will be able to identify the appropriateness of overestimating or underestimating in computation.
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Number Line: Represent Integers
The learner will be able to illustrate integers on a number line.
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Rounding: Estimation
The learner will be able to relate rounding skills to estimating possible outcomes of equations and estimations of size.
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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.
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Communicating: Write/Percents
The learner will be able to write percents.
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Decimal Percent of a Whole Number
The learner will be able to determine the decimal percent of a whole number.
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Fractional Percent of a Whole Number
The learner will be able to determine the fractional percent of a whole number.
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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 (%).
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Percent: Mental Math
The learner will be able to calculate percents using mental math.
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Percent: Recognize Equivalent
The learner will be able to identify the equivalent percent of a specific decimal or fraction.
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Percents: Compare/Fractions
The learner will be able to convert a given percentage to a fraction (or vice versa) in order to compare them.
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Problem Solving: Solution Strategies
The learner will be able to develop strategies for solving problems involving percents.
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Percents: Convert to Decimals
The learner will be able to convert from a percent to decimal representation of a number.
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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.
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Probability: Conjectures
The learner will be able to formulate conjectures that have a basis in theoretical or experimental probability.
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Predictions: Probability
The learner will be able to apply probability methods in the prediction of given event outcomes.
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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.
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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.
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Sampling: Design/Follow Through
The learner will be able to design and follow through with a random sampling procedure.
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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.
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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.
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Strategies: Invent
The learner will be able to formulate methods, materials, and strategies used to obtain solutions to problems.
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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.
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Irrelevant Information: Identify
The learner will be able to identify irrelevant information given in a story problem.
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Necessary Information: Solution
The learner will be able to determine if further information is necessary in order to obtain problem solutions.
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Solutions: Justifying
The learner will be able to justify a solution within a problem solving situation.
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Strategies: Justify Reasoning
The learner will be able to justify the reasoning behind using a specific problem solving strategy.
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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.
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Rational Numbers: Ordering
The learner will be able to order a group of ( positive) rational numbers in the appropriate sequence.
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Problem Solving: Rational
The learner will be able to obtain solutions to real world problems applying (positive) rational number concepts and operations.
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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.
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Add Multi-Digit Numbers
The learner will be able to perform the addition of multi-digit numbers.
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Divide Multi-Digit Numbers
The learner will be able to perform division of multi-digit numbers.
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Multiply: Multiple Digit Numbers
The learner will be able to perform multiplication of multiple digit numbers.
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Subtraction: Regrouping Whole Numbers
The learner will be able to identify a situation where regrouping is required.
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