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Index
 
Mathematics

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Introduction
Ordering Info

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Penn-Trafford School District
Penn-Trafford Secondary Mathematics
Mathematics - Algebra 1

Algebraic Concepts
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
Reinforce Home
  
Equations: Solve/Graph
The learner will be able to use scientific and graphing calculators, computers, and pencil and paper to solve and graph equations and inequalities.
Scope Activities
Master Home
  
Inequalities: Interpret
The learner will be able to interpret inequalities using tables and graphs as tools.
Scope Activities
Master Home
  
Operations: Analyzing
The learner will be able to demonstrate an understanding of the effect of operations on real numbers and algebraic expressions by applying operations appropriately in problem solving.
Scope Activities
Master Home
  
Algebraic Concepts: Explain
The learner will be able to explain the idea of unit rate, ratio, and slope in the context of rate of change.
Scope Activities
Master Home
  
Algebraic Concepts: Create/Solve
The learner will be able to create and interpret expressions, equations, or inequalities that illustrate problem scenarios.
Scope Activities
Master Home
  
Algebraic Concepts: Manipulatives
The learner will be able to use manipulatives to represent algebraic concepts.
Scope Activities
Reinforce Home
  
Expressions: Simplify/Exponents
The learner will be able to simplify expressions that involve exponents.
Scope Activities
Master Home
  
Expressions: Expand
The learner will be able to expand expressions that involve exponents.
Scope Activities
Master Home
  
Variable: Solving For
The learner will be able to manipulate a given formula to solve for a specific variable.
Scope Activities
Master Home
  
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.
Scope Activities
Reinforce Home
  
Factorials: Apply
The learner will be able to apply factorial notation.
Scope Activities
Master Home
  
Operations: Polynomials
The learner will be able to perform operations with polynomials to obtain problem solutions.
Scope Activities
Master Home
  
Polynomials: Add/Subtract/Multiply
The learner will be able to perform addition, subtraction, and multiplication of polynomials.
Scope Activities
Master Home
  
Polynomials: Multiply
The learner will be able to multiply two binomials to make a trinomial.
Scope Activities
Master Home
  
Equations: Variables/Distributive
The learner will be able to apply the distributive property to an equation containing variables.
Scope Activities
Master Home
  
Expressions: Distributive Property
The learner will be able to understand and apply the distributive property in expressions that may contain variables.
Scope Activities
Master Home
  
Exponents: Rules
The learner will be able to state rules pertaining to operations with exponents.
Scope Activities
Master Home
  
Exponents: Use/Laws of Exponents
The learner will be able to use the laws of exponents.
Scope Activities
Master Home
  
using formulas
The learner will be able to calculate the solution to a formula given values of all independent variables.
Scope Activities
Master Home
  
using formulas
The learner will be able to calculate the solution to a formula given values of all independent variables.
Scope Activities
Master Home
  
Computation: Develop/Apply
The learner will be able to develop and apply computation ideas, operations and procedures with real numbers in problem-solving situations.
Scope Activities
Master Home
  
Equations: Choose/Apply
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.
Scope Activities
Master Home
  
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
Master Home
  
Graphing/2 Variables
The learner will be able to graph a linear equation in two variables: including equations in slope intercept form and standard form.
Scope Activities
Master Home
  
Inequalities: Algebraic/Solve
The learner will be able to obtain solutions to algebraic inequalities and graph them on a number line.
Scope Activities
Master Home
  
Linear Equations: Solve
The learner will be able to obtain solutions to linear equations.
Scope Activities
Master Home
  
Computation: Error/Estimations
The learner will be able to explain the amount of error that is possible when using estimation in computation.
Scope Activities
Master Home
  
Quadratic Equation: Quadratic Formula
The learner will be able to solve quadratic equations by applying the quadratic formula.
Scope Activities
Introduce Home
  
Absolute Value Problems
The learner will be able to solve absolute value problems.
Scope Activities
Master Home
  
Absolute Value: Solve/Equations
The learner will be able to find the solution to absolute value equations containing one absolute value expression.
Scope Activities
Master Home
  
Absolute Value: Solve/Inequalities
The learner will be able to obtain solutions to absolute value inequalities.
Scope Activities
Master Home
  
top  

Data Interpretation
Data Display: Box-and-Whisker
The learner will be able to display data in a box-and-whisker plot.
Scope Activities
Master Home
  
Graphs: Box and Whisker Graphs/Interpret
The learner will be able to interpret data shown in a box and whisker graph.
Scope Activities
Master Home
  
top  

Decimals
Decimal Operations
The learner will be able to add, subtract, multiply, and divide decimal numbers within the context of numerical problems.
Scope Activities
Reinforce Home
  
top  

Fractions
Problem Solving: Fractions
The learner will be able to apply fraction representations to solve real-world problems.
Scope Activities
Reinforce Home
  
Add and Subt.: Algebraic Fractions/Unlik
The learner will be able to find the sum or difference of algebraic fractions with unlike denominators.
Scope Activities
Master Home
  
Add and Subt: Algebraic Fraction/Like
The learner will be able to find the sum or difference of algebraic fractions with like denominators.
Scope Activities
Master Home
  
Equivalent Fractions: Calculate
The learner will be able to calculate equivalent fractions.
Scope Activities
Reinforce Home
  
Mult. and Dividing Fractions
The learner will be able to multiply and divide numeric and algebraic fractions.
Scope Activities
Master Home
  
top  

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.
Scope Activities
Reinforce Home
  
Functions: Graph
The learner will be able to create graphs of functions.
Scope Activities
Master Home
  
Graping Functions: Table
The learner will be able to create a table from a function.
Scope Activities
Master Home
  
Graphing: Study/Maximum/Minimum
The learner will be able to study graphs of related quantities for maximum and minimum values and give justification for the findings.
Scope Activities
Master Home
  
Exponential Functions: Graph
The learner will be able to graph exponential functions.
Scope Activities
Master Home
  
Exponential Functions: Investigate
The learner will be able to apply exponential growth or decay to investigate exponential functions.
Scope Activities
Master Home
  
Exponential Functions: Real World
The learner will be able to solve real world problems involving exponential functions.
Scope Activities
Master Home
  
Absolute Value Function: Graph
The learner will be able to graph an absolute value function in one dimension.
Scope Activities
Master Home
  
Functional Relationships: Represent
The learner will be able to use tables, charts or graphs to represent a functional relationship.
Scope Activities
Master Home
  
Relations: Domain/Range
The learner will be able to identify the domain and range for a given relation given as a set of ordered pairs.
Scope Activities
Master Home
  
top  

Geometry
Angles: Draw/Measure/Label/List
The learner will be able to draw, measure, list, and label the attributes of complementary and supplementary angles.
Scope Activities
Reinforce Home
  
Figures: Comparison
The learner will be able to compare the properties of two and three dimensional shapes.
Scope Activities
Master Home
  
Congruence/Similarity: Polygons
The learner will be able to explain why polygons may be classified as similar, congruent, or neither.
Scope Activities
Master Home
  
Congruence/Similarity: Classification
The learner will be able to classify figures by congruence and/or similarity.
Scope Activities
Master Home
  
Circles: Pi
The learner will be able to use experimentation to estimate the value of pi.
Scope Activities
Master Home
  
Inductive/Deductive Reasoning: Identify
The learner will be able to identify the difference between inductive and deductive reasoning.
Scope Activities
Master Home
  
Triangle Inequality
The learner will be able to apply the Triangle Inequality in determining the length of the third side of a triangle given the lengths of the other two sides.
Scope Activities
Master Home
  
Triangle Inequality: Apply
The learner will be able to apply triangle inequality properties to determine if a triangle exists.
Scope Activities
Master Home
  
Figures: Know/Similarities/Differences
The learner will be able to display knowledge of how two shapes or two solids are similar.
Scope Activities
Master Home
  
Figures: 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.
Scope Activities
Introduce Home
  
Logic: Create Arguments
The learner will be able to apply if...then statements in the creation of elementary valid arguments.
Scope Activities
Master Home
  
Angles: Compare
The learner will be able to compare angles.
Scope Activities
Reinforce Home
  
Angles: Measuring
The learner will be able to measure angles.
Scope Activities
Reinforce Home
  
Pythagorean Relationships: Apply
The learner will be able to apply Pythagorean relationships to obtain solutions to problems in real world and mathematical situations.
Scope Activities
Master Home
  
top  

Integers
Problem Solving: Integers
The learner will be able to solve both mathematical and real-world problems by applying concepts of and operations with integer numbers.
Scope Activities
Master Home
  
Integers: Number Lines
The learner will be able to interpret real-world scenarios involving integers presented on number lines.
Scope Activities
Master Home
  
top  

Mathematics Processes
Reasoning: Conjecture
The learner will be able to formulate conjectures based on logical reasoning and use counterexamples to test conjectures.
Scope Activities
Master Home
  
Relationships: Conclusion
The learner will be able to arrive at a conclusion by combining numeric relationships.
Scope Activities
Master Home
  
Mathematical Concepts: Communication
The learner will be able to apply symbols, mathematical terminology, standard notation, rules, graphing and other mathematical illustrations to communicate observations, predictions, ideas procedures, generalizations, and results.
Scope Activities
Master Home
  
Communication: Clearly
The learner will be able to communicate mathematical procedures and results clearly, systematically, succinctly and accurately.
Scope Activities
Master Home
  
Mathematical Modeling: Problem/Represent
The learner will be able to represent problem situations by applying the following models: diagrams, flowcharts, or pictures.
Scope Activities
Master Home
  
Line of best fit
The learner will be able to from a scatter plot determine a line of best fit if possible.
Scope Activities
Master Home
  
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Measurement
Perimeter/Area/Volume: Describe
The learner will be able to relate how changing an object's linear dimensions alter its perimeter, area, and/or volume.
Scope Activities
Master Home
  
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.
Scope Activities
Master Home
  
Formulas: Develop
The learner will be able to develop and/or apply formulas and methods for finding measurement values.
Scope Activities
Master Home
  
Problem Solving: Rates
The learner will be able to obtain solutions to problems by applying rates.
Scope Activities
Master Home
  
Perimeter: Application
The learner will be able to solve real-world application problems involving perimeter measurements.
Scope Activities
Master Home
  
Area/Volume: Combine/Separate
The learner will be able to solve for the area or volume of the combination or separation of figures.
Scope Activities
Master Home
  
Circumference: Application
The learner will be able to solve real-world application problems involving circumference measurements.
Scope Activities
Master Home
  
Scale Maps: Interpret/Measurements
The learner will be able to interpret maps or drawings using scale measurements.
Scope Activities
Master Home
  
Scale Drawing
The learner will be able to use proportional relationships to determine actual measurements from a diagram or map drawn to scale.
Scope Activities
Master Home
  
Measurement: Quantify Issues
The learner will be able to quantify issues using measurement.
Scope Activities
Reinforce Home
  
Accuracy: Apply Concept
The learner will be able to apply the related concepts of accuracy, error, and degree of precision.
Scope Activities
Introduce Home
  
top  

Number Theory
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
Reinforce Home
  
Ratio/Proportion: Applying
The learner will be able to apply ratio and proportion concepts to solve real-world scenario problems.
Scope Activities
Master Home
  
Multiples
The learner will be able to demonstrate an understanding of multiples.
Scope Activities
Master Home
  
Factors: Applications
The learner will be able to understand and use factors.
Scope Activities
Reinforce Home
  
Scientific Notation: Simplify Expression
The learner will be able to simplify numerical expressions involving scientific notation.
Scope Activities
Master Home
  
Equivalent Forms: Represent/Use
The learner will be able to display and/or apply numbers in many different equivalent forms.
Scope Activities
Reinforce Home
  
top  

Numeration
Patterns: Explain/Generalize
The learner will be able to explain, generalize, and gain knowledge of patterns, including linear, exponential and simple quadratic relationships.
Scope Activities
Master Home
  
Estimation: Tips/Discount
The learner will be able to approximate the amount of tips and discounts applying ratios, proportions and percents.
Scope Activities
Master Home
  
Patterns: Apply
The learner will be able to apply simple algebraic patterns to basic number theory.
Scope Activities
Master Home
  
Patterns: Apply
The learner will be able to apply simple algebraic patterns to spatial relations.
Scope Activities
Master Home
  
Pattern: Extend
The learner will be able to extend number or object patterns that can be infinitely continued.
Scope Activities
Master Home
  
Rounding: Estimation
The learner will be able to relate rounding skills to estimating possible outcomes of equations and estimations of size.
Scope Activities
Master Home
  
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
Master Home
  
Estimation: Appropriateness
The learner will be able to identify the appropriateness of overestimating or underestimating in computation.
Scope Activities
Master Home