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Chester Township Public Schools Mathematics The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research on teaching and learning, and professional guidelines. Remedial Math II The Foundations of Learning curriculum provides objectives for ninth grade students. |
| Algebraic Concepts |
| The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. 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. |
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Problem Solving: Evaluating Forms
The learner will be able to solve real-world problems involving whole numbers, fractions, decimals, percents, integers, scientific notation, and exponential notation by determining the operation required (addition, subtraction, multiplication, division), setting up the correct number sentence, solving the problem, and using inverse operations to check the solution.
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Problem Solving: Evaluating Forms
The learner will be able to recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions, decimals, percents, or integers, evaluate the situation, articulate the nature and elements of the problem, and solve the problem, without being cued about the operations required or number form (fractions, decimals, etc.).
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Problem Solving: Evaluating Forms
The learner will be able to recognize a real-world situation which calls for operations (addition, subtraction, multiplication, or division) with fractions, decimals, percents, or integers (without being cued that the calculations involved would require a specific operation or number form), evaluate the situation, articulate the nature and elements of the problem, solve the problem, and use inverse operations to check the solution.
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Translate Problems: Two Variables
The learner will be able to translate a given real-world scenario (delivered orally or in a written prompt) into an equation or inequality with two variables, use order of operations to solve the equation, and apply inverse operations to check the answer.
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Solution Methods: Equation/Inequality
The learner will be able to solve real world situations by using linear equations, inequalities, and multiple representations.
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Missing Elements
The learner will be able to determine how to solve for an unknown variable when given the problem in written form.
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Order of Operations: Determine
The learner will be able to determine the correct order of calculations when more than one operation is to be performed.
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Order of Operations: Fractions
The learner will be able to determine the correct order of operations for an equation containing fractions.
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Order of Operations: Decimals
The learner will be able to determine the correct order of operations for an equation containing decimal numbers.
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Properties: Real Numbers
The learner will be able to identify and use properties of real numbers.
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Multiple Step Problems: Writing
The learner will be able to compose both problems and story problems requiring multiple operations.
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Expressions: Represent
The learner will be able to interpret expressions using models and manipulatives.
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Expressions: Real World
The learner will be able to evaluate expressions (and formulas) when the expressions are presented within the context of a real-world problem.
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Exponents: Multiplying
The learner will be able to multiply two whole numbers with different exponents.
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Exponents: Dividing
The learner will be able to divide 2 whole numbers with different exponents.
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Operations: Relationships
The learner will be able to determine relationships between operations on whole numbers, decimals, fractions, and integers with and without the use of technology (calculators).
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Inverse Operations: Whole/Real Numbers
The learner will be able to use inverse operations to extend the system of whole numbers to the system of real numbers.
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Rates
The learner will be able to compare the prices of several items.
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Variable/Expression/Equation
The learner will be able to comprehend the concepts of variable, expression, and equation.
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Algorithms: Real World Problems
The learner will be able to manipulate algorithms as models in solving real world problems.
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Solution Tools: Analysis
The learner will be able to analyze which solution tool would best solve a problem: calculator, pencil and paper, mental math.
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| Data Interpretation |
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The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving. This unit includes presenting data in graphical forms and interpreting data given in graphical forms. |
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Communicating: Graphical Forms/Creating
The learner will be able to communicate complex ideas effectively by creating graphical forms of data, including collecting data from a variety of sources, consolidating raw data, and selecting appropriate elements of the data to organize and include in a logical graphical form.
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Analyzing: Graphical Forms
The learner will be able to use graphical forms (tables, bar graphs, maps, and information pyramids) to derive information, interpret information, and draw conclusions about real-world phenomena such as population shifts, factors of population shifts, areas of population shifts, etc.
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Analyzing: Graphical Forms
The learner will be able to demonstrate the ability to interpret graphical forms of data by articulating the details, facts, and concepts presented in the forms, and by evaluating the reasonableness of specific graphical forms given the types of information presented in the forms.
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Evaluating: Graphical Forms
The learner will be able to evaluate a given graph to determine if the information is reasonable, if the graph format is the most effective one for the type of information presented, and to find possible inconsistencies in the information contained in the graph.
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Scatterplots: Story Problems
The learner will be able to solve real world problems using scatterplots as models.
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Bar Graphs: Analyze
The learner will be able to analyze data on a bar graph to make judgments about the graph.
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Bar Graphs: Proportional Relationships
The learner will be able to use proportional relationships to extrapolate values on a bar graph.
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Pictographs
The learner will be able to identify, compare, and add or subtract amounts read from pictographs.
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Chart/Graph: Scale/Interpret
The learner will be able to understand scales given on graphs, tables, and charts.
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Table: Classification
The learner will be able to determine the method by which information is classified within a table to determine where new information should be placed.
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Table: Rearrange
The learner will be able to rearrange and read information from a table using a new criteria.
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Table: Predict
The learner will be able to make predictions and decisions based on real-world data presented in the form of a table.
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Logical Reasoning: Making Predictions
The learner will be able to use real world data to make predictions from data presented in scatterplots, diagrams of frequency distributions, histograms, and stem-and-leaf plots.
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Graphs: Construct
The learner will be able to construct graphs recording information in tables, bar graphs, line graphs, and pictographs.
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Diagram: Problem Solving
The learner will be able to solve real-world problems using diagrams.
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Graphs: Data/Story Problems
The learner will be able to interpret graphical data to solve story problems.
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Evaluate Graphical Forms: Select Display
The learner will be able to choose the most suitable form and/or method of data display.
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Graphs: Summarize Data
The learner will be able to make appropriate summaries about data presented in charts, tables, and graphs.
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Graphs: Evaluate Data Analysis
The learner will be able to determine the validity of an argument based on a given set of data.
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| Decimals |
| This unit includes comparing decimals, performing operations with decimals, converting decimals to other number forms, using manipulatives to demonstrate decimals, and solving problems with decimals in real-world contexts. |
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Problem Solving: Application
The learner will be able to evaluate, solve, and justify solutions for real-world mathematical problems which include ambiguous circumstances.
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Problem Solving: Application
The learner will be able to use manipulatives, calculators, symbols, mental math, and diagrams to solve real-world scenario problems which call for the rounding, addition, subtraction, multiplication, and division of decimals. This process includes evaluating a given problem scenario, identifying the problem, determining the relevant elements and the required operation (without being cued about the operation the problem would require), setting up a number sentence, solving the problem, using inverse operations to check the solution, and articulating to others the solution and the reasoning behind the solution.
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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.
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Reasoning: Using Decimals
The learner will be able to incorporate a variety of estimation techniques such as front-ending, clustering, averaging, rounding compatible numbers, and special cases, to check the reasonableness of solutions, and articulate responses in either oral or written form.
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Addition Story Problems
The learner will be able to solve story problems involving adding 3 numbers with decimals.
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Subtraction Story Problems
The learner will be able to solve story problems involving subtracting decimals.
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Addition/Subtraction Decimals
The learner will be able to add, subtract, and compare decimals using the correct order of operations when necessary.
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Multiplication Story Problems
The learner will be able to solve real-world story problems by determining that multiplication is required, by regrouping the numbers, and by multiplying the appropriate decimals up to the hundredths position.
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Multiplication/Division Decimals
The learner will be able to multiply, divide, and compare decimals using the correct order of operations when necessary.
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Decimals: Rounding
The learner will be able to round decimal numbers to the nearest whole number, tenths, and hundredths place, in the context of a problem involving money amounts.
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Decimals and Equivalent Fractions
The learner will be able to determine equivalent fractions and decimals.
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Division Story Problems
The learner will be able to solve story problems by dividing decimals up to the hundredths position.
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Compare Decimals: Up to 0.000001
The learner will be able to compare decimal numbers up to the millionths place (0.000001) using the order symbols (<, >, =).
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| Fractions |
| This unit includes comparing fractions, performing computations with fractions, converting fractions to other number forms, using manipulatives to demonstrate fractions, and solving problems with fractions in real-world contexts. |
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Reasoning: Using Fractions
The learner will be able to incorporate a variety of estimation techniques such as front-ending, clustering, averaging, rounding compatible numbers, and considering special cases, to check the reasonableness of solutions to problems involving fractions.
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Adding: Mixed Fractions
The learner will be able to add mixed fractions.
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Addition Story Problems
The learner will be able to add two fractions, either mixed fractions or with different denominators, in the context of a story problem.
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Subtraction Story Problems
The learner will be able to solve story problems involving subtracting two fractions with the same or different denominators.
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Subtracting Mixed Fractions
The learner will be able to subtract two mixed fractions.
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Addition/Subtraction Fractions
The learner will be able to add or subtract fractions and mixed fractions, including finding a lowest common denominator and reducing the answer to its lowest terms.
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Multiplication: Mixed Fractions
The learner will be able to multiply either two mixed fractions or a fraction and a whole number.
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Multiplication Story Problems
The learner will be able to multiply two fractions, a fraction and a whole number, or a mixed fraction and a whole number in the context of a story problem.
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Division: Mixed Fractions
The learner will be able to divide two mixed fractions or divide a whole number by a fraction.
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Division Story Problems
The learner will be able to divide a fraction by a whole number or a mixed fraction by a whole number.
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Fraction Parts: Part of a Set
The learner will be able to show an understanding of fractions by matching fractions with the appropriate diagrams of partially shaded figures.
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Fractions: Understanding
The learner will be able to compare a fraction with its reduced form, find lowest common denominators, identify reciprocals, and compare a fraction with its lowest term, whole numbers, fractions, and improper fractions.
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Fractions: Multiple Step Story Problems
The learner will be able to solve story problems involving multiple operations with fractions.
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Compare Fractions: Equivalent/Mixed
The learner will be able to compare 2 equivalent fractions and equivalent and mixed fractions.
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| Geometry |
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The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. This unit includes exploring geometric concepts from multiple perspectives. |
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Figures: Unseen Faces
The learner will be able to describe, explore, and compare the unseen faces of various three dimensional figures.
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Transformations: Explaining
The learner will be able to explain transformations in writing, and construct diagrams and graphs which illustrate the process.
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Line Segments: Properties
The learner will be able to apply the basic properties of line segments.
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Triangles: Sum Theorem/Finding Angle
The learner will be able to determine the unknown angle of a given triangle by using the measures of the other 2 angles and the triangle sum theorem.
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Logic: Conditional Statements
The learner will be able to analyze a conditional statement and determine whether it is true or false.
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Reasoning: Terms
The learner will be able to draw logical conclusions about situations with concrete materials using the following terms: and, or, if...then, all, some, none, not, and out of.
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Reasoning: Syllogisms
The learner will be able to compose syllogisms using "if...then" types of hypotheses.
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Logic: Conditional Statement
The learner will be able to compose conditional statements when making logical arguments.
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Logic: Verify Conclusion/Indirect Reason
The learner will be able to apply indirect reasoning and other laws of logic to evaluate the validity of a conclusion.
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Logic: Applying/Proofs
The learner will be able to use logic to prove a statement using a given premise.
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Logic: Arguments/Conjectures
The learner will be able to identify various points of view by making arguments and conjectures.
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Congruency: Congruent Figures/Apply
The learner will be able to analyze how geometric principles related to congruency are applied in real-world problem solving.
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Congruency: Proving Theorems
The learner will be able to use properties of congruent polygons in proving theorems.
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Congruence: Quadratic Congruence
The learner will be able to determine quadratic congruence.
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| Integers |
| This unit includes comparing integers, performing operations with integers, converting integers to other number forms, using manipulatives to demonstrate integers, and solving problems with integers in real-world contexts. |
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Addition/Subtraction: Order
The learner will be able to add and subtract positive and negative numbers using the correct order of operations when parentheses are involved.
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Reasoning: Using Integers
The learner will be able to incorporate a variety of estimation techniques such as front-ending, clustering, averaging, rounding compatible numbers, and considering special cases, to check the reasonableness of solutions to problems involving integers.
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