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Mathematics

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Introduction
Ordering Info

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Penn-Trafford School District
Penn-Trafford Secondary Mathematics
Mathematics - PreAlgebra

Algebraic Concepts
Order of Operations: Applying Rules
The learner will be able to use the rules of order of operations to obtain the value of expressions.
Scope Activities
Master Home
  
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.
Scope Activities
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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.
Scope Activities
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Equations: Choose/Apply
The learner will be able to choose and apply a method to solve an equation, describe the solution and check the solution for accuracy.
Scope Activities
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Algebraic Concepts: Manipulatives
The learner will be able to use manipulatives to represent algebraic concepts.
Scope Activities
Introduce Home
  
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.
Scope Activities
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Equality/Inequality: Relationships
The learner will be able to demonstrate that an equality/inequality relationship between two quantities stays the same when changes are made as long as the change is made to both quantities.
Scope Activities
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Computation: Proficiency
The learner will be able to exhibit proficiency when performing computational procedures.
Scope Activities
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Computation: Real World Problems
The learner will be able to obtain solutions to real world problems that involve computations.
Scope Activities
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Exponents: Apply Rules
The learner will be able to apply the rules of exponents.
Scope Activities
Introduce Home
  
Inequalities: Concept
The learner will be able to understand the concepts of inequalities by solving for, describing, and checking the solution.
Scope Activities
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Variable/Expression/Equation
The learner will be able to comprehend the concepts of variable, expression,inequality, and equation.
Scope Activities
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Real Life examples
The learner will be able to express real liffe situations using expressions.
Scope Activities
Introduce Home
  
Variable
The learner will be able to understand the basic concept of a variable as representing an unknown quantity.
Scope Activities
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Graphing in one dimension
The learner will be able to graph inequality solutions on a number line.
Scope Activities
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Data Interpretation
Analyze/Produce Output
The learner will be able to analyze and create graphic output in the form of bar, line, and pie graphs.
Scope Activities
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Data Display: Stem-and-Leaf
The learner will be able to display data in a stem-and-leaf plot.
Scope Activities
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Graphs: Stem-and-Leaf Graphs
The learner will be able to interpret data shown in a stem-and-leaf graph.
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Decimals
Compare Decimals: Terminating/Repeating
The learner will be able to comprehend the relationship between terminating and repeating decimals.
Scope Activities
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Computing: Decimal Numbers
The learner will be able to become proficient in the addition, subtraction, multiplication, and division of decimal numbers with and without a calculator.
Scope Activities
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Decimals: Non-Terminating
The learner will be able to explore, represent and apply concepts of non-terminating decimals.
Scope Activities
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Decimals: Word Names/Fractions
The learner will be able to discover and understand fractional names for decimals through the use of decimal and fraction models.
Scope Activities
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Problem Solving: Operations
The learner will be able to solve problems by applying basic operations with decimals, using the appropriate solution method.
Scope Activities
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Computing: Decimals/Real-World
The learner will be able to perform the basic operations with decimals in real-world situations with and without the use of a calculator.
Scope Activities
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Decimal Point Alignment: Multiplication
The learner will be able to identify the resulting decimal place of the product of 2 decimals.
Scope Activities
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Decimals: Estimate/Common Fractions
The learner will be able to estimate decimal amounts using the values of common fractions.
Scope Activities
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Decimals: Estimate/Solve
The learner will be able to estimate solution and apply appropriate operations to solve problems with decimals.
Scope Activities
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Decimals: Ordering
The learner will be able to place a series of decimal numbers, up to thousandths, in order.
Scope Activities
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Decimals: Use
The learner will be able to apply decimals.
Scope Activities
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Multiply/Divide: Equivalent Expressions
The learner will be able to identify equivalent expressions for the multiplication and division of decimals.
Scope Activities
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Problem Solving: Equivalent Decimals
The learner will be able to solve real-world problems by identifying equivalent decimals.
Scope Activities
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Word Names: Hundred-Thousandth
The learner will be able to read and write word forms of decimal numbers to the hundred-thousandths place.
Scope Activities
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Equivalent Froms: Dec, Fracs, %'s
The learner will be able to convert between equivalent forms of fractions, decimals, and percents.
Scope Activities
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Divide Decimals
The learner will be able to divide a decimal or integer by a decimal or integer.
Scope Activities
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Estimate Quotients
The learner will be able to estimate a quotient by rounding when the quotient has more than 4 decimal places to a predetermined placevalue.
Scope Activities
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Fractions
Add/Subtract Fractions
The learner will be able to demonstrate an ability to add and/or subtract mixed numbers and fractions with like and unlike denominators.
Scope Activities
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Division: Fractions/Mixed Numbers
The learner will be able to use models, pictures, and manipulatives to demonstrate division of fractions and mixed numbers, and be able to record and explain the results.
Scope Activities
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Multiply Fractions
The learner will be able to perform multiplication of proper fractions and mixed numbers and state the answer in simplest form.
Scope Activities
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Addition/Subtraction Fractions
The learner will be able to solve story problems requiring the addition or subtraction of fractions and reduce answers to lowest terms.
Scope Activities
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Compare Fractions: Common Denominator
The learner will be able to compare fractions by determining their equivalent fractions with a common denominator.
Scope Activities
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Compare Fractions: Cross Product
The learner will be able to compare fractions by determining their cross product.
Scope Activities
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Compare Fractions: Decimal/Common
The learner will be able to use decimal fractions to compare common fractions.
Scope Activities
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Division Story Problems
The learner will be able to solve real-world scenario problems where the division of fractions, mixed fractions, and whole numbers is involved.
Scope Activities
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Equivalent Fractions: Identify/Forms
The learner will be able to identify equivalent forms of fractions by appropriate methods.
Scope Activities
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Fraction Terms: Numerator/Identify
The learner will be able to identify both the numerator and denominator and what they stand for in the context of a fraction.
Scope Activities
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Fractions: Change/Mixed Number
The learner will be able to make an improper fraction into a mixed number and vice versa.
Scope Activities
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Fractions: Convert Proper/Improper
The learner will be able to identify the proper form of an improper fraction.
Scope Activities
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Fractions: Estimation/Operations
The learner will be able to use estimation to perform the basic operations with fractions.
Scope Activities
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Fractions: Ordering
The learner will be able to identify a fraction that is greater than or less than a given fraction or order three of more from least to greatest.
Scope Activities
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Fractions: Use
The learner will be able to apply fractions in real life situations.
Scope Activities
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Divide Fractions, Mixed Nos., Whole Nos.
The learner will be able to divide a fraction, mixed number, or whole number by a fraction, mixed number, or whole number.
Scope Activities
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Problem Solving
The learner will be able to recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions (without being cued that the calculations involved would require a specific operation), evaluate the situation, articulate the nature and elements of the problem, solve the problem, and use inverse operations to check the solution.
Scope Activities
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Multiply Fraction within Story Problems
The learner will be able to solve real-world scenario problems where the multiplication of fractions, mixed nos., and whole nos. is invovled.
Scope Activities
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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.
Scope Activities
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Angles: Draw/Measure/Label/List
The learner will be able to draw, measure, list, and label the attributes of complementary, supplementary, and vertical angles.
Scope Activities
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Logic: Create Arguments
The learner will be able to apply if...then statements in the creation of elementary valid arguments.
Scope Activities
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Angles: Compare
The learner will be able to compare angles.
Scope Activities
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Angles: Measuring
The learner will be able to measure angles.
Scope Activities
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Tesselations: Representations
The learner will be able to study objects to identify whether they represent tessellations.
Scope Activities
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Inductive/Deductive Reasoning: Identify
The learner will be able to identify the difference between inductive and deductive reasoning.
Scope Activities
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Symmetry
The learner will be able to determine if a given shape is symmetrical and if so draw lines of symmetry.
Scope Activities
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Polygons: Classify
The learner will be able to identify familiar polygons as regular or irregular(up to a decagon).
Scope Activities
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Spatial Sense: Demonstrate
The learner will be able to use written and oral communication to demonstrate spatial sense.
Scope Activities
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Lines formed by // lines and transversal
The learner will be able to identify corresponding, alternate interior, and vertical angles and apply properties.
Scope Activities
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Parts
The learner will be able to identify center, radius, diameter, circumference, and area.
Scope Activities
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Constructions: 3-D
The learner will be able to construct two and three-dimensional shapes through the use of physical materials.
Scope Activities
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Quadrilaterals: Compare
The learner will be able to make comparisons of quadrilaterals based upon their sides or angles.
Scope Activities
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Congruence/Similarity: Classification
The learner will be able to classify figures by congruence and/or similarity.
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Integers: Number Lines
The learner will be able to interpret real-world scenarios involving integers presented on number lines.
Scope Activities
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Perform operations with Integers
The learner will be able to add, subtract, multiply, and divde integers with and without a calculator.
Scope Activities
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Mathematics Processes
Reasoning: Conjecture
The learner will be able to formulate conjectures based on logical reasoning and use counterexamples to test conjectures.
Scope Activities
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Relationships: Conclusion
The learner will be able to arrive at a conclusion by combining numeric relationships.
Scope Activities
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Mathematical Modeling: Problem/Represent
The learner will be able to represent problem situations by applying the following models: diagrams, flowcharts, or pictures.
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Formulas: Develop
The learner will be able to develop and/or apply formulas and methods for finding measurement values.
Scope Activities
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Problem Solving: Rates
The learner will be able to obtain solutions to problems by applying rates.
Scope Activities
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Scale Maps: Interpret/Measurements
The learner will be able to interpret maps or drawings using scale measurements.
Scope Activities
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Scale Models: Construct/Apply
The learner will be able to construct and apply scale models.
Scope Activities
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Scale: Analyze
The learner will be able to analyze objects to determine whether they illustrate scale.
Scope Activities
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Angle Measure: Degrees
The learner will be able to measure angles in degrees.
Scope Activities
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Angle Measure: Relations
The learner will be able to determine relations of angles.
Scope Activities
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Accuracy: Choose/Apply Tools
The learner will be able to choose and use suitable tools and units to measure to the degree of accuracy required in a particular scenario.
Scope Activities
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Measurement Concepts: Understanding
The learner will be able to show a comprehension of the concepts of perimeter, area, surface area, volume, capacity, weight (mass), and temperature.
Scope Activities
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Perimeter/Area/Volume
The learner will be able to find the perimeter, area, and/or volume of a given figure.
Scope Activities
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Conversion: Between Systems
The learner will be able to solve problems which require converting units of measurement between and within systems.
Scope Activities
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Equivalent Forms: Represent/Use
The learner will be able to display and/or apply numbers in many different equivalent forms.
Scope Activities
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Ratio/Proportion: Apply
The learner will be able to use ratio and proportion in mathematical problem scenarios involving distance, rate, time, and similar triangles.
Scope Activities
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Ratio/Proportion: Story Problems
The learner will be able to obtain solutions to story problems using ratio and proportion.
Scope Activities
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Scientific Notation: Convert
The learner will be able to convert between scientific and decimal notation.
Scope Activities
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Divisibility/Multiples/Factors
The learner will be able to determine the divisibility of whole numbers, determine the multiples of whole numbers, and identify prime and composite numbers.
Scope Activities
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Place Value: Applications
The learner will be able to understand and apply place value concepts when reading, writing, calculating, and estimating numbers.
Scope Activities
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Multiples
The learner will be able to demonstrate an understanding of multiples.
Scope Activities
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Factors: Applications
The learner will be able to understand and use factors.
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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.
Scope Activities
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