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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 - Grade 6

Algebraic Concepts
Variable
The learner will be able to understand the basic concept of a variable as representing an unknown quantity.
Scope Activities
Introduce Home
  
Symbols: Explain
The learner will be able to explain the application of combinations of symbols and numbers in expressions, equations, and inequalities.
Scope Activities
Introduce Home
  
Expressions: Create
The learner will be able to create expressions that represent mathematical situations using physical objects and combinations of symbols and numbers.
Scope Activities
Introduce Home
  
Number Sentence: Choose/Apply
The learner will be able to choose and apply appropriate methods, including physical materials, to obtain solutions to number sentences and describe the method of solution.
Scope Activities
Reinforce Home
  
Equations: Describe
The learner will be able to use information given in equations inequalities tables of graphs in the description of a realistic scenario.
Scope Activities
Reinforce Home
  
Algorithms: Describe
The learner will be able to describe algorithms for multiplication and division.
Scope Activities
Reinforce Home
  
Computation: Select
The learner will be able to select a suitable computational strategy.
Scope Activities
Introduce Home
  
Rates: Explain Relationship/Time
The learner will be able to explain the relationship between rates of change and time.
Scope Activities
Reinforce 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
Master Home
  
Introduction to Equations
The learner will be able to identify and solve simple one step equations.
Scope Activities
Introduce Home
  
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Data Interpretation
Bar& Line Graphs: Organize/Display/D
The learner will be able to organize and present data in a basic bar and/or line graph.
Scope Activities
Reinforce Home
  
top  

Decimals
Decimal Notation
The learner will be able to identify and use decimal notation.
Scope Activities
Introduce Home
  
Operations with decimals
The learner will be able to apply algorithms to add, subtract , multiply, and divide decimals with and without a calculator.
Scope Activities
Reinforce Home
  
Compare Decimals
The learner will be able to compare and order decimal numbers.
Scope Activities
Master Home
  
Decimals: Expanded Notation
The learner will be able to comprehend the use of decimals with expanded notation.
Scope Activities
Master Home
  
Decimals: Read/Write
The learner will be able to correctly read decimals and/or express them in written form.
Scope Activities
Master Home
  
Divide Decimals: Quotient
The learner will be able to determine the quotient, where the dividend is represented as a decimal number through the thousandths place, and the divisor is a decimal through the thousands place with only one non-zero digit; use calculators and approximation techniques when the divisor has more than one non-zero digit.
Scope Activities
Master Home
  
Estimating
The learner will be able to employ strategies for estimating the range of an answer, or the number of digits in an answer to addition, subtraction, multiplication, or division problems, and articulate these strategies to others.
Scope Activities
Master Home
  
Number Sense: Place Value
The learner will be able to articulate (in terms of place value) the reasoning behind placing the decimal point in the appropriate position when evaluating number sentences involving operations on decimals.
Scope Activities
Master Home
  
Number Sense: Zeros With Decimals
The learner will be able to demonstrate an understanding of zeros with decimals by explaining how a zero to the left of the decimal point or extra zeros to the right do not change the value of the decimal or its corresponding fraction.
Scope Activities
Master Home
  
Multiply Decimal and Whole Numbers
The learner will be able to multiply several decimal and/or whole numbers.
Scope Activities
Master Home
  
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Fractions
Fraction Notation
The learner will be able to evaluate fraction notation in context as part of a whole, in division, or as a ratio and understand the meaning of numerator and denominator.
Scope Activities
Reinforce Home
  
Problem Solving: Fractions
The learner will be able to apply fraction representations to solve real-world problems.
Scope Activities
Master Home
  
Add/Subtract Fractions
The learner will be able to demonstrate an ability to add and/or subtract mixed numbers and fractions with single digit like and unlike denominators.
Scope Activities
Master Home
  
Compare Fractions:
The learner will be able to compare and order fractions.
Scope Activities
Master Home
  
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
Master Home
  
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
Master Home
  
Fractions: Simplest Form
The learner will be able to use many different methods in order to express a fraction in simplest form.
Scope Activities
Master Home
  
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Functions: Generate/Relate
The learner will be able to use tables of data to generate functions and relate data to corresponding graphs and functions.
Scope Activities
Reinforce Home
  
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Figures: Name/Identify
The learner will be able to identify, name, and/or apply properties of geometric figures.
Scope Activities
Master Home
  
Figures: Identify/Properties
The learner will be able to recognize geometric shapes and/or know the properties they may possess.
Scope Activities
Master Home
  
Figures: Constructed/Changed
The learner will be able to create a mental image of constructed and/or altered shapes.
Scope Activities
Master Home
  
Circle: Radius/Diameter
The learner will be able to recognize the radius and diameter of a circle and measure them.
Scope Activities
Master Home
  
Logic: Interpret Statements
The learner will be able to analyze and/or understand statements that are constructed with the specific language of logic, including the terms all, every, none, some, and/or many.
Scope Activities
Reinforce Home
  
Properties: Define
The learner will be able to define the elementary properties of two and three dimensional figures.
Scope Activities
Reinforce Home
  
Figures: Describe/Constructing
The learner will be able to give word descriptions of how geometric shapes are constructed.
Scope Activities
Master Home
  
Triangles: Compare
The learner will be able to make comparisons of triangles based upon their sides or angles.
Scope Activities
Master Home
  
Triangles: Classify
The learner will be able to classify triangles according to their side lengths and angle measures.
Scope Activities
Master Home
  
Tessellations: Recognize
The learner will be able to recognize tessellations.
Scope Activities
Introduce Home
  
Point/Line/Plane: Represent
The learner will be able to draw representations of the undefined terms (point, line, and plane) of geometry.
Scope Activities
Master Home
  
Rotation: Analyze/Line Segments
The learner will be able to study the rotations of line segments at 90, 180, 270, and 360 degree increments.
Scope Activities
Introduce Home
  
Constructions: 2-D
The learner will be able to construct two-dimensional shapes through the use of physical materials.
Scope Activities
Master Home
  
Quadrilaterals: Classify
The learner will be able to classify quadrilaterals based upon their sides or angles.
Scope Activities
Master Home
  
Angles: Measure
The learner will be able to measure angles in plane figures.
Scope Activities
Master Home
  
Lines of Symmetry
The learner will be able to identify lines of symmetry in two dimensional figures.
Scope Activities
Master Home
  
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Integers: Computing
The learner will be able to perform computations involving integers through the use of models, manipulatives, and/or rules.
Scope Activities
Master Home
  
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Mathematics Processes
Modeling: Multiplication
The learner will be able to illustrate the idea of multiplication as area, volume, array, change in size, rate factor, and/or repeated addition through the use of concrete models as well as pictorial and algebraic representations.
Scope Activities
Master Home
  
Models: Fractions/Decimals
The learner will be able to illustrate fractions and decimals using models.
Scope Activities
Master Home
  
Relationships: Conclusion
The learner will be able to arrive at a conclusion by combining numeric relationships.
Scope Activities
Introduce Home
  
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Units
The learner will be able to obtain solutions to and approximate suitable answers for problems that use metric and/or customary measurement units.
Scope Activities
Master Home
  
Measurement Concepts: Add/Subtract
The learner will be able to perform addition and/or subtraction with measurement values, including weight and/or length.
Scope Activities
Master Home
  
Accuracy: Apply Concept
The learner will be able to apply the related concepts of accuracy, precision, and error of measurement.
Scope Activities
Master Home
  
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Number Forms: Negative Numbers
The learner will be able to apply the simple concepts of negative numbers.
Scope Activities
Master Home
  
Number Theory Concepts: Develop/Apply
The learner will be able to develop and apply number theory concepts to illustrate numbers in many different ways.
Scope Activities
Master Home
  
Expanded Notation: Whole Numbers
The learner will be able to write whole numbers in expanded notation.
Scope Activities
Master Home
  
Primes/Composites: Describe
The learner will be able to describe the idea of prime and composite numbers.
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
Master Home
  
Number Theory: Renaming
The learner will be able to use number theory concepts to rename a number quantity.
Scope Activities
Master Home
  
Place Value: Whole Numbers/Decimals
The learner will be able to identify place value in whole numbers and decimals through decillions and millionths.
Scope Activities
Master Home
  
Place Value: Whole Numbers/Decimals
The learner will be able to comprehend place value concepts related to whole numbers and decimals (to two decimal places) as well as the manner in which they relate to simple fractions, and apply concepts of negative numbers.
Scope Activities
Master Home
  
Place Value: Whole Numbers/Decimals
The learner will be able to explain properties of, give a definition of, produce examples of, and/or apply the place value of whole numbers and decimals to both real world and mathematical situations.
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
Master Home
  
Other number systems
The learner will be able to use base 2 and 5 number systems to reinforce place value and exponents (optional).
Scope Activities
Introduce Home
  
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Rounding: Whole Number/Decimals
The learner will be able to display, write, name, make comparisons, order, and round off whole numbers (up to 1 trillion), decimals (though ten-thousandth), fractions, and mixed numbers then extend these ideas to the real-world, and use tools and technology as necessary.
Scope Activities
Master Home
  
Pattern Concepts: Applying
The learner will be able to apply an understanding of mathematical patterns to deal with number systems, operations, and forms.
Scope Activities
Master Home
  
Estimation: Apply/Problems
The learner will be able to apply estimation methods to many different problems including time and money problems.
Scope Activities
Master Home
  
Mental Math: Computations
The learner will be able to perform mental computations through the use of various strategies that may include multiples of ten, powers of ten, compensation, breaking apart numbers, or compatible numbers.
Scope Activities
Master Home
  
Pattern: Identify/Duplicate/Continue
The learner will be able to identify, duplicate, continue, create, and describe patterns, sequences and relationships orally, numerically, symbolically and graphically, using many different materials.
Scope Activities
Master Home
  
Pattern: Rules
The learner will be able to identify and describe rules for given patterns.
Scope Activities
Master Home
  
Comparison: Numbers
The learner will be able to compare and order numbers.
Scope Activities
Master Home
  
Estimation: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of sums, differences, products, and quotients of whole number operations by using a variety of estimation strategies.
Scope Activities
Master Home
  
Estimation
The learner will be able to use estimation in solving problems.
Scope Activities
Master Home
  
Rounding: Demonstrate Skills
The learner will be able to demonstrate the skills necessary to round numbers.
Scope Activities
Master Home
  
Magnitude: Compare
The learner will be able to make comparisons of the magnitudes of numbers.
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
  
Roman Numerals
The learner will be able to read and write Roman Numerals up to 3000 (optional).
Scope Activities
Introduce Home
  
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Probability/Statistics
Mean/Median/Mode:
The learner will be able to apply the concepts of mean, median, and mode.
Scope Activities
Introduce Home
  
Probability of Events: Analyzing
The learner will be able to analyze the probability of events to determine their dependence or independence.
Scope Activities
Master Home
  
Probability
The learner will be able to illustrate and/or display probability measures as rational numbers.
Scope Activities
Master Home
  
Data: Organize/Display
The learner will be able to organize and illustrate data using pictures, tallies, tables, charts, bar graphs, and circle graphs.
Scope Activities
Master Home
  
Predictions: Check/Confirm
The learner will be able to apply models, number facts, properties and relationships to check and confirm predictions and explain reasoning.
Scope Activities
Master Home
  
Venn Diagram: Sort
The learner will be able to use Venn diagrams to sort data.
Scope Activities
Introduce Home
  
Probability: Determine
The learner will be able to identify the probability of an event involving "and", "or" or "not".
Scope Activities
Master Home
  
Probability: Simple Event
The learner will be able to determine the probability of a simple event.
Scope Activities
Master Home
  
Probability: Predict
The learner will be able to predict the probability a situation will occur based on the analysis of data.
Scope Activities
Master Home
  
Data: Create/Defend Conclusions
The learner will be able to create and defend simple conclusions that are based on data.
Scope Activities
Master Home
  
Predictions: Simulations
The learner will be able to perform simulations with physical devices to predict the probability of the occurring of an event.
Scope Activities
Master Home
  
Statistics: Quantify Issues
The learner will be able to quantify issues using statistics such as mean, mode, and median.
Scope Activities
Introduce Home
  
Tree Diagrams
The learner will be able to use tree diagrams to represent possible outcomes.
Scope Activities
Master Home
  
Combinations: Find All
The learner will be able to determine all combinations and arrangements that have a limited number of variables.
Scope Activities
Master Home
  
Experiments: Pattern
The learner will be able to identify patterns formed as a result of an experiment.
Scope Activities
Master Home
  
Impossible/Certain Events: Predict
The learner will be able to predict and identify why some outcomes are certain, more likely, less likely, equally likely or impossible.
Scope Activities
Master Home
  
Probability Concepts: Spinners
The learner will be able to identify the fairness of the design of a spinner.
Scope Activities
Master