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8.1
Number Sense and Operation
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8.1.1
Recognize, model, and compare different forms of integers and rational numbers including percents, fractions, decimals, and numbers using exponents and scientific notation.
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8.1.1.A
Read, write, and compare numbers using integer exponents and scientific notation.
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8.1.1.B
Compare, order, and graph rational numbers on a number line.
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8.1.1.C
Estimate and explain the square root of any whole number from 1-225.
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8.1.2
Select and apply appropriate estimation strategies to judge the reasonableness of solutions to problems including those computed on a calculator. Demonstrate correct use of order of operations.
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8.1.2.A
Use a calculator to evaluate numeric expressions involving order of operations and check reasonableness with appropriate estimation strategies.
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8.1.3
Use number theory concepts such as prime factorization, greatest common factor, and least common multiple in problem situations.
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8.1.3.A
Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems.
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8.1.4
Compute fluently and solve multi-step problems using integers, fractions, decimals, and numbers in exponential form.
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8.1.4.A
Solve multi-step problems containing rational numbers and numbers in exponential form.
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8.1.4.B
Evaluate numeric expressions including nested parentheses, exponents, and other grouping symbols.
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8.1.5
Use metric and standard units of measurement in relevant scientific and cultural situations, including those of Montana American Indians, compare and convert within systems, and use appropriate technology.
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8.1.5.A
Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians.
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8.1.6
Understand and apply proportional relationships to model real world situations and to solve problems involving rates, ratios, proportions, percents, and direct variation.
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8.1.6.A
Use proportions to solve contextual problems including similarity and congruence.
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8.1.6.B
Rewrite a proportion as a direct variation equation to model a real world situation.
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8.1.6.C
Use rates to justify conversions between units of measure (e.g., convert miles/hour to feet/second).
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8.2
Data Analysis Mathematics
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8.2.1
Collect data from a variety of contexts (e.g., science, history, and culture, including Montana American Indians). Organize and represent data in box plots, scatter plots, histograms, and circle graphs using technology when appropriate.
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8.2.1.A
Collect, organize, and represent univariate data in box plots.
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8.2.1.B
Create and justify the appropriate visual representation for given data sets from science, history, and culture, including those of Montana American Indians with and without technology.
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8.2.2
Interpret, analyze, and evaluate data using mean, median, range, and quartiles to identify trends and make decisions and predictions about data within scientific and cultural contexts, including those of Montana American Indians.
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8.2.2.A
Describe and interpret a box plot using the 5 # summary, the interquartile range, and percentiles.
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8.2.2.B
Compare and analyze the data represented in two or more parallel box plots.
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8.2.2.C
Estimate the line of best fit on a scatter plot to make decisions and predictions about data within daily life, scientific, and cultural contexts, including those of Montana American Indians.
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8.2.2.D
Compare and analyze the strengths and limitations of using each descriptive statistical measure and evaluate how changes in data affect those statistics.
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Statistics: Calculate mean, median, mode, and range (Eighth grade - BB.1)
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Statistics: Interpret charts to find mean, median, mode, and range (Eighth grade - BB.2)
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Statistics: Mean, median, mode, and range: find the missing number (Eighth grade - BB.3)
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Statistics: Changes in mean, median, mode, and range (Eighth grade - BB.4)
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8.2.3
Create sample spaces and simulations from events found in different cultures, including those of Montana American Indians, determine experimental and theoretical probabilities, and use probability to make predictions.
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8.2.3.A
Create and test conjectures made from the results of experiments and simulations using experimental and theoretical probabilities from scientific and cultural events, including those of Montana American Indians.
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8.2.3.B
Describe and apply the addition rule for probabilities of events that are mutually exclusive and for events that are not mutually exclusive.
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8.2.3.C
Identify misleading presentations of data found in the media and predict the effects of conclusions drawn.
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8.3
Geometric Reasoning
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8.3.1
Define, classify and compare properties of solids and plane figures, including lines and angles.
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8.3.1.A
Name and describe the basic objects of plane geometry.
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8.3.1.B
Describe and define the angles created by intersecting rays, intersecting lines, and parallel lines cut by transversals.
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8.3.2
Use spatial reasoning to determine congruence, similarity, and symmetry of objects in mathematics, art, science, and culture, including Montana American Indians.
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8.3.2.A
Justify similarity of figures using proportional reasoning and angle relationships.
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8.3.2.B
Justify congruency of figures using sides and angle relationships.
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8.3.3
Define, identify, and execute transformations including translations, rotations, reflections, and dilations with appropriate technology.
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8.3.3.A
Define, identify and execute a dilation with and without technology.
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8.3.4
Measure and compute angles, perimeter, area, surface area, and volume including the use of formulas and choosing appropriate units.
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8.3.4.A
Use attributes of angles created by intersecting lines and parallel lines cut by transversals to solve problems involving missing sides or angles.
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8.3.4.B
Use Pythagorean Theorem to find a missing side of right triangles to calculate perimeter, area, surface area and volume, and label with appropriate units.
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8.3.5
Develop informal arguments to verify geometric relationships and solve problems such as an informal justification of the Pythagorean Theorem in a variety of contexts.
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8.3.5.A
Develop and justify a formula (informal or formal) for area of regular polygons (e.g., decompose a regular polygon into congruent isosceles triangles).
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8.3.5.B
Develop and justify the theorem for the sum of the interior angles of a triangle equaling 180ยบ.
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8.3.5.C
Make a logical argument for the Pythagorean Theorem (e.g., decompose a square in two different ways).
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8.4
Algebraic and Functional Reasoning
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8.4.1
Create and use tables, graphs or diagrams, symbolic expressions, and verbal descriptions to represent, analyze, and generalize a variety of patterns involving numbers and operations.
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8.4.1.A
Create and use multiple representations (tables, graphs, verbal descriptions, symbolic expressions) of data to generalize the patterns and make connections among all representations.
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8.4.2
Identify linear and non-linear functional relationships and contrast their properties using tables, graphs, or equations with appropriate technology.
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8.4.2.A
Identify the properties (slope, intercepts, continuity, and discreteness) of linear relationships using multiple representations.
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8.4.2.B
Determine from a set of ordered pairs, a table, graph, or a rule whether a relation is a function.
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8.4.2.C
Compare and contrast the properties of linear and non-linear relationships using technology when appropriate.
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8.4.2.D
Compare and contrast the properties of functional and non-functional relations using technology when appropriate.
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8.4.3
Use number properties and inverse operations to solve multi-step equations and inequalities involving a single variable.
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8.4.3.A
Solve multi-step linear equations incorporating multiple grouping symbols and check the reasonableness of the solution.
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8.4.3.B
Use properties of numbers and inverse operations to solve multi-step linear inequalities in one variable, graph the solution on a number line and check the reasonableness of the solution.
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8.4.4
Recognize, simplify, and generate equivalent forms of algebraic expressions, justifying each step with properties of operations.
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8.4.4.A
Generate equivalent forms of algebraic expressions including those involving like terms and justify each step with properties of operations.
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8.4.5
Identify and compute rate of change/slope and intercepts from equations, graphs, and tables; model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians.
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8.4.5.A
Determine the slope, x-intercept, and y-intercept of a line given its graph, equation, or two points on the line.
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8.4.5.B
Identify the solution to a system of linear equations by determining whether the lines are parallel, intersecting, or the same line.
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8.4.5.C
Model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians.
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