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Robein School District 85
CURRICULUM GUIDE
Mathematics - Grade 8

Goal 6: Numeration

Standard 6.A
The learner will be able to demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings.
Strand Bloom's Scope Source Activities
Standard 6.A Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 6.A Classroom
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Rational Numbers: Order/Compare
The learner will be able to represent, order, and compare rational numbers.
Strand Bloom's Scope Source Activities
Standard 6.A Comprehension, Analysis Master IL Performance Descriptors: 6A. Stage H. Classroom
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Notation: Exponential/Scientific/Calcula
The learner will be able to recognize and use exponential, scientific, and calculator notation.
Strand Bloom's Scope Source Activities
Standard 6.A Knowledge, Application Master IL Performance Descriptors: 6A. Stage H. Classroom
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Rational Numbers: Number Lines
The learner will be able to place rational numbers on a number line.
Strand Bloom's Scope Source Activities
Standard 6.A Application Master IL Performance Descriptors: 6A. Stage H. Classroom
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Standard 6.B
The learner will be able to investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
Strand Bloom's Scope Source Activities
Standard 6.B Analysis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 6.B Classroom
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Operations: Integers/Decimals
The learner will be able to determine and describe the effects of arithmetic operations with decimals and integers (e.g., multiply by a decimal between zero and one, divide by a negative integer).
Strand Bloom's Scope Source Activities
Standard 6.B Analysis Master IL Performance Descriptors: 6B. Stage H. Classroom
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Operations: Inverse Relationships
The learner will be able to describe and use the inverse relationships of squaring and finding square roots to simplify computations and solve problems.
Strand Bloom's Scope Source Activities
Standard 6.B Application Master IL Performance Descriptors: 6B. Stage H. Classroom
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Divisibility: Justify/Rules/Problem Solv
The learner will be able to justify divisibility rules for 3, 4, 6, 8, and 9.
Strand Bloom's Scope Source Activities
Standard 6.B Application, Evaluation Master IL Performance Descriptors: 6B. Stage H. Classroom
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Order of Operations: Field Properties
The learner will be able to simplify arithmetic expressions containing integers using the field properties and order of operations.
Strand Bloom's Scope Source Activities
Standard 6.B Synthesis Master IL Performance Descriptors: 6B. Stage H. Classroom
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Factorization: Prime/Least/Greatest
The learner will be able to determine the least common multiple and greatest common factor of a set of numbers using prime factorization containing exponents.
Strand Bloom's Scope Source Activities
Standard 6.B Analysis Master IL Performance Descriptors: 6B. Stage H. Classroom
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Standard 6.C
The learner will be able to compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
Strand Bloom's Scope Source Activities
Standard 6.C Comprehension Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 6.C Classroom
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Real Numbers: Operations/Estimate
The learner will be able to select, use, and justify appropriate operations, methods, and tools to compute or estimate with real numbers.
Strand Bloom's Scope Source Activities
Standard 6.C Analysis, Evaluation Master IL Performance Descriptors: 6C. Stage H. Classroom
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Real Numbers: Analyze Algorithms
The learner will be able to analyze algorithms for computing with real numbers and develop fluency in their use.
Strand Bloom's Scope Source Activities
Standard 6.C Analysis Master IL Performance Descriptors: 6C. Stage H. Classroom
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Standard 6.D
The learner will be able to solve problems using comparison of quantities, ratios, proportions and percents.
Strand Bloom's Scope Source Activities
Standard 6.D Analysis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 6.D Classroom
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Problem Solving: Rational Numbers
The learner will be able to develop, use, analyze, and explain methods for solving number sentences or word problems involving proportions with rational numbers.
Strand Bloom's Scope Source Activities
Standard 6.D Analysis Master IL Performance Descriptors: 6D. Stage H. Classroom
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Problem Solving: Percent
The learner will be able to solve problems that involve percents, including percent increase and decrease, regardless of the piece of information that is missing.
Strand Bloom's Scope Source Activities
Standard 6.D Application Master IL Performance Descriptors: 6D. Stage H. Classroom
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Goal 7: Measurement

Standard 7.A
The learner will be able to measure and compare quantities using appropriate units, instruments and methods.
Strand Bloom's Scope Source Activities
Standard 7.A Analysis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 7.A Classroom
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Exploring: Derived Measurement
The learner will be able to determine derived measurements.
Strand Bloom's Scope Source Activities
Standard 7.A Analysis Master IL Performance Descriptors: 7A. Stage H. Classroom
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Surface Area: Three-Dimensional Solid
The learner will be able to determine the surface area of three-dimensional figures.
Strand Bloom's Scope Source Activities
Standard 7.A Analysis Master IL Performance Descriptors: 7A. Stage H. Classroom
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Formulas: Volume/Sphere
The learner will be able to determine the volume of a sphere.
Strand Bloom's Scope Source Activities
Standard 7.A Analysis Master IL Performance Descriptors: 7A. Stage H. Classroom
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Standard 7.B
The learner will be able to estimate measurements and determine acceptable levels of accuracy.
Strand Bloom's Scope Source Activities
Standard 7.B Analysis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 7.B Classroom
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Data Analysis: Measurement Error
The learner will be able to determine the maximum error in measurements.
Strand Bloom's Scope Source Activities
Standard 7.B Analysis Master IL Performance Descriptors: 7B. Stage H. Classroom
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Measurement: Accuracy of tool
The learner will be able to measure any quantity to the greatest degree of accuracy determined by the tool.
Strand Bloom's Scope Source Activities
Standard 7.B Application Master IL Performance Descriptors: 7B. Stage H. Classroom
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Standard 7.C
The learner will be able to select and use appropriate technology, instruments and formulas to solve problems, interpret results and communicate findings.
Strand Bloom's Scope Source Activities
Standard 7.C Comprehension Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 7.C Classroom
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Measurement: Derived/Rates
The learner will be able to solve simple problems involving rates and other derived measurements such as velocity and density.
Strand Bloom's Scope Source Activities
Standard 7.C Application Master IL Performance Descriptors: 7C. Stage H. Classroom
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Surface Area/Volume: Develop/Describe
The learner will be able to develop and describe surface area and volume formulas for cones and cylinders by relating pyramids to cones and prisms to cylinders.
Strand Bloom's Scope Source Activities
Standard 7.C Comprehension Master IL Performance Descriptors: 7C. Stage H. Classroom
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Angle Measurements: Polygons/Circles
The learner will be able to solve problems involving angle measurements in polygons and circles.
Strand Bloom's Scope Source Activities
Standard 7.C Application Master IL Performance Descriptors: 7C. Stage H. Classroom
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Goal 8: Algebraic Concepts

Standard 8.A
The learner will be able to describe numerical relationships using variables and patterns.
Strand Bloom's Scope Source Activities
Standard 8.A Knowledge Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 8.A Classroom
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Pattern: Recursive Form
The learner will be able to investigate and describe linear, quadratic, and exponential patterns recursively.
Strand Bloom's Scope Source Activities
Standard 8.A Analysis Master IL Performance Descriptors: 8A. Stage H. Classroom
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Sequence: Describe Rule/Nth Term
The learner will be able to investigate and write algebraic expressions to describe the nth term of a simple linear, power, or exponential sequence.
Strand Bloom's Scope Source Activities
Standard 8.A Analysis Master IL Performance Descriptors: 8A. Stage H. Classroom
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Pattern: Number Theory
The learner will be able to determine the given term of a pattern of numbers or drawings.
Strand Bloom's Scope Source Activities
Standard 8.A Analysis Master IL Performance Descriptors: 8A. Stage H. Classroom
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Sequences: Arithmetic/Geometric
The learner will be able to create arithmetic and geometric sequences to fit a given set of conditions.
Strand Bloom's Scope Source Activities
Standard 8.A Synthesis Master IL Performance Descriptors: 8A. Stage H. Classroom
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Linear Equations: Slope-Intercept
The learner will be able to recognize and generate equivalent forms for linear equations, including transforming linear equations into standard and slope-intercept form.
Strand Bloom's Scope Source Activities
Standard 8.A Synthesis Master IL Performance Descriptors: 8A. Stage H. Classroom
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Standard 8.B
The learner will be able to interpret and describe numerical relationships using tables, graphs and symbols.
Strand Bloom's Scope Source Activities
Standard 8.B Comprehension Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 8.B Classroom
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Expressions: Symbolic/Graphs of lines
The learner will be able to describe the relationships between symbolic expressions and graphs of lines using the appropriate vocabulary for the intercepts and slope of the line.
Strand Bloom's Scope Source Activities
Standard 8.B Comprehension, Application Master IL Performance Descriptors: 8B. Stage H. Classroom
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Absolute Value: Graph on Number Line
The learner will be able to graph absolute values on a number line.
Strand Bloom's Scope Source Activities
Standard 8.B Application Master IL Performance Descriptors: 8B. Stage H. Classroom
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Linear Relationships: Describe
The learner will be able to graph a set of points and describe the relationship as linear or nonlinear.
Strand Bloom's Scope Source Activities
Standard 8.B Application Master IL Performance Descriptors: 8B. Stage H. Classroom
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Slope: Determine From Graph
The learner will be able to determine the slope of a line from a graph.
Strand Bloom's Scope Source Activities
Standard 8.B Analysis Master IL Performance Descriptors: 8B. Stage H. Classroom
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Graphing: Linear Equations/Cartesian
The learner will be able to graph linear equations and inequalities on the Cartesian plane.
Strand Bloom's Scope Source Activities
Standard 8.B Application Master IL Performance Descriptors: 8B. Stage H. Classroom
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Standard 8.C
The learner will be able to solve problems using systems of numbers and their properties.
Strand Bloom's Scope Source Activities
Standard 8.C Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 8.C Classroom
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Inverse: Solve/Equations/Equations
The learner will be able to solve simple algebraic equations for a given variable using inverse operations.
Strand Bloom's Scope Source Activities
Standard 8.C Application Master IL Performance Descriptors: 8C. Stage H. Classroom
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Properties: Real Numbers/Equations
The learner will be able to solve arithmetic and simple algebraic equations using properties of real numbers, equality, and inequality, and justify the procedures.
Strand Bloom's Scope Source Activities
Standard 8.C Application Master IL Performance Descriptors: 8C. Stage H. Classroom
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Standard 8.D
The learner will be able to use algebraic concepts and procedures to represent and solve problems.
Strand Bloom's Scope Source Activities
Standard 8.D Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 8.D Classroom
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Absolute Value: Equations/Inequalities
The learner will be able to solve absolute value equations or inequalities in one variable using algebraic or graphical representations.
Strand Bloom's Scope Source Activities
Standard 8.D Application Master IL Performance Descriptors: 8D. Stage H. Classroom
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Equations: Inequalities/Linear
The learner will be able to solve algebraic equations or word problems that involve linear equations or inequalities using algebraic or graphical representations.
Strand Bloom's Scope Source Activities
Standard 8.D Application Master IL Performance Descriptors: 8D. Stage H. Classroom
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Linear Relationships: Word Problems
The learner will be able to create word problems that meet given conditions and represent linear relationships.
Strand Bloom's Scope Source Activities
Standard 8.D Synthesis Master IL Performance Descriptors: 8D. Stage H. Classroom
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Goal 9: Geometry

Standard 9.A
The learner will be able to demonstrate and apply geometric concepts involving points, lines, planes and space.
Strand Bloom's Scope Source Activities
Standard 9.A Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 9.A Classroom
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Geometric Concepts
The learner will be able to analyze the results of a combination of reflections, rotations, and translations of a figure and determine alternate notions that could produce the same results.
Strand Bloom's Scope Source Activities
Standard 9.A Analysis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Congruence: Transformations
The learner will be able to examine the congruence or similarity of objects using transformations.
Strand Bloom's Scope Source Activities
Standard 9.A Application Master IL Performance Descriptors: 9A. Stage H. Classroom
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Shapes: Identify View/2 and 3 Dimension
The learner will be able to identify possible types of two- or three- dimensional figures that would match a set of given conditions.
Strand Bloom's Scope Source Activities
Standard 9.A Knowledge Master IL Performance Descriptors: 9A. Stage H. Classroom
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Geometric Concepts: Shape/Relationships
The learner will be able to solve pictorial or word problems that involve geometric relationships within a single geometric shape or figure, including the Pythagorean theorem.
Strand Bloom's Scope Source Activities
Standard 9.A Application Master IL Performance Descriptors: 9A. Stage H. Classroom
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Coordinate Geometry: Analyze
The learner will be able to represent and analyze the properties of geometric shapes using coordinate geometry.
Strand Bloom's Scope Source Activities
Standard 9.A Analysis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Central Tendency: Determine
The learner will be able to determine the best measure of central tendency from mean, median, or mode.
Strand Bloom's Scope Source Activities
Standard 9.A Analysis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Shapes: Understand Properties
The learner will be able to analyze properties of a shape or a combination of shapes that enable it to tesselate the plane.
Strand Bloom's Scope Source Activities
Standard 9.A Analysis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Proofs: Triangle Inequality
The learner will be able to determine if a triangle is possible using side lengths and the triangle inequality.
Strand Bloom's Scope Source Activities
Standard 9.A Analysis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Shapes: Construct/Combining Shapes
The learner will be able to combine simple construction techniques to construct squares, equilateral triangles, or other simple combinations of equal segments, angles, etd.
Strand Bloom's Scope Source Activities
Standard 9.A Synthesis Master IL Performance Descriptors: 9A. Stage H. Classroom
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Transformations: Draw/Combination of
The learner will be able to draw the image of an object after a combination of transformations.
Strand Bloom's Scope Source Activities
Standard 9.A Knowledge Master IL Performance Descriptors: 9A. Stage H. Classroom
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Standard 9.B
The learner will be able to identify, describe, classify and compare relationships using points, lines, planes and solids.
Strand Bloom's Scope Source Activities
Standard 9.B Analysis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 9.B Classroom
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Pattern: Geometric Shapes/Solve
The learner will be able to solve problems involving similar figures.
Strand Bloom's Scope Source Activities
Standard 9.B Application Master IL Performance Descriptors: 9B. Stage H. Classroom
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Reasoning: Proportionally
The learner will be able to create and analyze scale models using proportional reasoning.
Strand Bloom's Scope Source Activities
Standard 9.B Analysis, Synthesis Master IL Performance Descriptors: 9B. Stage H. Classroom
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Standard 9.C
The learner will be able to construct convincing arguments and proofs to solve problems.
Strand Bloom's Scope Source Activities
Standard 9.C Synthesis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 9.C Classroom
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Geometric Concepts: Critique Arguments
The learner will be able to create and critique arguments concerning geometric ideas and relationships, such as congruence, similarity, the Pythagorean relationship, or formulas for surface areas or volume of simple three-dimensional objects.
Strand Bloom's Scope Source Activities
Standard 9.C Synthesis Master IL Performance Descriptors: 9C. Stage H. Classroom
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Constructions: Geometric/Methods
The learner will be able to justify the simple construction methods used to produce angle bisectors, perpendicular lines, and equilateral triangles.
Strand Bloom's Scope Source Activities
Standard 9.C Evaluation Master IL Performance Descriptors: 9C. Stage H. Classroom
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Geometric Concepts: Relationships
The learner will be able to represent, solve, and explain numerical and algebraic relationships using geometric concepts.
Strand Bloom's Scope Source Activities
Standard 9.C Comprehension, Application Master IL Performance Descriptors: 9C. Stage H. Classroom
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Geometric Concepts: Conjectures
The learner will be able to provide examples or counter-examples to either illustrate or disprove conjectures about geometric characteristics.
Strand Bloom's Scope Source Activities
Standard 9.C Evaluation Master IL Performance Descriptors: 9C. Stage H. Classroom
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Standard 9.D
The learner will be able to use trigonometric ratios and circular functions to solve problems.
Strand Bloom's Scope Source Activities
Standard 9.D Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 9.D Classroom
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Trig. Ratios: Unknown Length
The learner will be able to solve for missing side lengths using the trigonometric ratios in right triangles.
Strand Bloom's Scope Source Activities
Standard 9.D Application Master IL Performance Descriptors: 9D. Stage H. Classroom
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Problem Solving: Trigonometric Ratios
The learner will be able to identify the basic trigonometric ratios in terms of lengths of the sides of a right triangle and an acute angle.
Strand Bloom's Scope Source Activities
Standard 9.D Knowledge Master IL Performance Descriptors: 9D. Stage H. Classroom
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Pythagorean Theorem: Triples
The learner will be able to recognize Pythagorean triples.
Strand Bloom's Scope Source Activities
Standard 9.D Knowledge Master IL Performance Descriptors: 9D. Stage H. Classroom
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Triangles: 45-45-90/30-60-90
The learner will be able to determine and justify the side length relationships present in 45-45-90 triangles and 30-60-90 triangles.
Strand Bloom's Scope Source Activities
Standard 9.D Evaluation Master IL Performance Descriptors: 9D. Stage H. Classroom
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Angles: Acute/ratio of length of sides
The learner will be able to determine the ratio of lengths of sides of a right triangle with given measures for its acute angles using appropriate technologies.
Strand Bloom's Scope Source Activities
Standard 9.D Analysis Master IL Performance Descriptors: 9D. Stage H. Classroom
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Goal 10: Probability/Statistics

Standard 10.A
The learner will be able to organize, describe and make predictions from existing data.
Strand Bloom's Scope Source Activities
Standard 10.A Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 10.A Classroom
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Data: Explain/Interpret/Evaluate
The learner will be able to construct, read, interpret, infer, predict, draw conclusions, and evaluate data from various displays, including histograms and scatter plots.
Strand Bloom's Scope Source Activities
Standard 10.A Evaluation Master IL Performance Descriptors: 10A. Stage H. Classroom
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Logic: Arguments/Conjectures
The learner will be able to make conjectures about the possible correlation between two characteristics of a sample on the basis of scatter plots of the data and approximate lines of fit.
Strand Bloom's Scope Source Activities
Standard 10.A Application Master IL Performance Descriptors: 10A. Stage H. Classroom
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Central Tendency: Points of View
The learner will be able to discuss how data can be manipulated to represent different points of view based on the use of different measures of central tendency and based on different graphical displays.
Strand Bloom's Scope Source Activities
Standard 10.A Comprehension Master IL Performance Descriptors: 10A. Stage H. Classroom
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Analyze Graphical Forms: Display
The learner will be able to analyze graphical displays of data for possible misleading characteristics.
Strand Bloom's Scope Source Activities
Standard 10.A Analysis Master IL Performance Descriptors: 10A. Stage H. Classroom
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Data Analysis: Bias/Reporting
The learner will be able to discuss biased reporting of data and questions that should be asked when data is viewed.
Strand Bloom's Scope Source Activities
Standard 10.A Comprehension, Analysis Master IL Performance Descriptors: 10A. Stage H. Classroom
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Standard 10.B
The learner will be able to formulate questions, design data collection methods, gather and analyze data and communicate findings.
Strand Bloom's Scope Source Activities
Standard 10.B Synthesis Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 10.B Classroom
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Data: Collecting/Analyzing/Information
The learner will be able to analyze potential methods of collecting information and decide which methods would produce the most reliable and accurate data.
Strand Bloom's Scope Source Activities
Standard 10.B Analysis Master IL Performance Descriptors: 10B. Stage H. Classroom
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Survey: Analyze for error and bias
The learner will be able to analyze instruments used for surveys for errors and bias.
Strand Bloom's Scope Source Activities
Standard 10.B Analysis Master IL Performance Descriptors: 10B. Stage H. Classroom
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Experiments/Simulations/bias/error
The learner will be able to analyze potential experiments or simulations for errors and bias.
Strand Bloom's Scope Source Activities
Standard 10.B Analysis Master IL Performance Descriptors: 10B. Stage H. Classroom
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Real World Math: Formulate Questions
The learner will be able to formulate questions, design studies, and collect data.
Strand Bloom's Scope Source Activities
Standard 10.B Synthesis Master IL Performance Descriptors: 10B. Stage H. Classroom
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Standard 10.C
The learner will be able to determine, describe and apply the probabilities of events.
Strand Bloom's Scope Source Activities
Standard 10.C Application Master IL. Learning Standards, 1997, Middle/Junior High School, Standard 10.C Classroom
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Complementary/Mutually Exclusive:
The learner will be able to describe and explain complementary and mutually exclusive events using appropriate terminology.
Strand Bloom's Scope Source Activities
Standard 10.C Analysis Master IL Performance Descriptors: 10C. Stage H. Classroom
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Experiments: Probability/
The learner will be able to design and conduct experiments or simulations for probability, including the possible use of technology to simulate events.
Strand Bloom's Scope Source Activities
Standard 10.C Synthesis Master IL Performance Descriptors: 10C. Stage H. Classroom
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Probability: Theoretical/Empirical
The learner will be able to discuss the difference in empirical and theoretical probability.
Strand Bloom's Scope Source Activities
Standard 10.C Analysis Master IL Performance Descriptors: 10C. Stage H. Classroom
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Probability: Simple Compound Events
The learner will be able to compute probabilities for simple compound events using a variety of methods, including area models.
Strand Bloom's Scope Source Activities
Standard 10.C Application Master IL Performance Descriptors: 10C. Stage H. Classroom
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Independent/Dependent Events
The learner will be able to identify situations where dependent and independent events occur.
Strand Bloom's Scope Source Activities
Standard 10.C Knowledge Master IL Performance Descriptors: 10C. Stage H. Classroom
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Probability/Counting Principles
The learner will be able to determine probabilities using simple counting techniques.
Strand Bloom's Scope Source Activities
Standard 10.C Analysis Master IL Performance Descriptors: 10C. Stage H. Classroom
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Counting: Permutations/Combinations
The learner will be able to discuss situations where permutations and combinations should be used in counting outcomes.
Strand Bloom's Scope Source Activities
Standard 10.C Comprehension Master IL Performance Descriptors: 10C. Stage H. Classroom
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