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8.A
Mathematical Process
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8.A.1
Use reasoning and logic to:
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8.A.1.1
Perceive patterns
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8.A.1.2
Identify relationships
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8.A.1.3
Formulate questions
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8.A.1.4
Pose problems
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8.A.1.5
Make conjectures
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8.A.1.6
Justify strategies
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8.A.1.7
Test reasonableness of results
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8.A.2
Communicate mathematical ideas and logical reasoning using the vocabulary of mathematics in a variety of ways e.g., using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models.
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8.A.3
Connect mathematics to the real world, as well as within mathematics.
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8.A.4
Create and use representations to organize, record, and communicate mathematical ideas.
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8.A.5
Solve and analyze routine and non-routine problems.
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8.B
Number Operations and Relationships
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8.B.a
Concepts
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8.B.a.1
Recognize and apply place-value concepts to numbers less than 100,000,000 with decimals to the thousandths place.
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8.B.a.2
Read, write and represent numbers using words, numerals, number lines, arrays, and expanded form (12.09=10+2+.09) and symbolic renaming (12.09= 13-.91).
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8.B.a.3
Compare and order a set of fractions or decimals (to the hundredths place) and use symbols (<, >, =, "not equal to").
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8.B.a.4
Identify and use number theory concepts:
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8.B.a.4.a
prime and composite numbers
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8.B.a.4.b
divisibility potential of numbers (divisors of 1-10, 25, and multiples of 10).
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8.B.a.4.c
least common multiples
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8.B.a.4.d
greatest common factor of two numbers
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8.B.a.5
Demonstrate understanding of fractions and percents with and without contexts (e.g.,sales tax and discounts, 40 is 25 percent of what number?; What number is 25 percent of 160?)
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8.B.a.6
Apply proportional reasoning to a variety of problem situations. (E.g. comparisons, rates, and similarities).
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8.B.a.7
Identify equivalent forms of fractions, decimals and percents.
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8.B.b
Computation
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8.B.b.1
Use all operations in everyday situations to solve single or multi-step word problems.
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8.B.b.2
Solve problems involving percents with and without context.
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8.B.b.2.a
Add and subtract decimals including thousandths with and without text.
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8.B.b.2.b
Multiply decimals and integers (-100 to 100) including thousandths with and without context. (Ex. interest rates)
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8.B.b.2.c
Divide decimals and integers in problems with and without context.
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8.B.b.3
Demonstrate understanding of the concept of division of fractions in a contextual setting.
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8.B.b.4
Add and subtract mixed numbers and fractions with unlike denominators, multiply mixed numbers.
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8.B.b.5
Estimate the sum, difference and product of whole numbers, common fractions, mixed numbers and decimals to thousandths.
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8.B.b.6
Determine reasonableness of answers.
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8.C
Geometry
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8.C.a
Describing Figures
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8.C.a.1
Name 3-dimensional figures (e.g., rectangular prisms, square pyramids, cones, cylinders and spheres.)
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8.C.a.2
Find the measure of the third angle of a triangle when given the measures of two interior or exterior angles.
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8.C.a.3
Determine the sum of the angles of a polygon using diagonals drawn from one vertex.
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8.C.a.4
Determine the measure of an angle in a drawing of an adjacent and supplementary or adjacent and complementary pair of angles when given the measure of the other angle.
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8.C.b
Spatial Relationships and Transformations
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8.C.b.1
Draw and/or describe a similar figure when given a polygon drawn on graph paper with vertices at lattice points.
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8.C.b.2
Identify figures that are congruent and/or similar.
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8.C.b.3
Demonstrate understanding of similarity by finding the relationship between the sides of two figures.
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8.C.b.4
Draw or identify the image of a figure based on one or more transformations (reflection, rotation and/or translation).
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8.C.b.5
Design symmetrical shapes.
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8.C.b.6
Draw or identify lines of symmetry.
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8.C.b.7
Classify figures possessing line symmetry only; line and rotation symmetry; rotational symmetry only; no symmetry.
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8.C.b.8
Identify and describe 3-dimensional figures from multiple perspectives.
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8.C.c
Coordinate Systems
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8.C.c.1
Identify, locate, plot coordinates in all four quadrants; draw or identify the reflection of a point across the x- or y-axis or the translation of a point at integer coordinates in any of the four quadrants.
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8.C.c.2
Locate or plot coordinates in any of the four quadrants using a geometric figure (e.g., transformations).
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8.D
Measurement
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8.D.a
Measurable Attributes
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8.D.a.1
Select the appropriate unit of measure (U.S. customary and metric) to estimate the length, liquid capacity, volume, time, and weight/mass of everyday objects.
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8.D.a.2
Convert units within a system e.g., feet to yards; ounces to pounds; inches to feet; pints to quarts.
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8.D.a.3
Approximate conversions of units between metric and U.S. customary systems using a model or in context (quart/liter; yard/meter).
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8.D.b
Direct Measurement
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8.D.b.1
Apply appropriate tools techniques to measure down to the nearest 1/4-, 1/8- or 1/16-inch or nearest centimeter or millimeter.
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8.D.b.2
Determine and compare elapsed time in problem-solving situations.
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8.D.b.3
Measure and/or draw angles up to 360 degrees.
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8.D.c
Indirect Measurement
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8.D.c.1
Estimate area given a reference.
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8.D.c.2
Determine perimeter/circumference and area of polygons and circles with and without context.
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8.D.c.3
Determine the distance between points using a scale.
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8.D.c.4
Determine volume and surface area of cylinders, rectangular prisms and pyramids with base shapes of triangle, square, regular pentagon and regular hexagon in real-world context.
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8.D.c.5
Draw similar figures in any shape using a scale factor (e.g., enlarge/shrink).
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8.D.c.6
Use ratio and proportion in context.
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8.D.c.7
Use d = r*t formula in simple contexts.
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8.E
Statistics and Probability
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8.E.a
Data Analysis and Statistics
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8.E.a.1
Compare two sets of data to generate or confirm/deny hypotheses.
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8.E.a.2
Extract, interpret and analyze data including multiple representations of the same data from tables, double back-to-back stem-and-leaf plots, double bar graphs, simple circle graphs, line plots, line graphs, charts and diagrams with and without context.
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8.E.a.3
Create graph with one-variable data sets using back-to-back stem-and-leaf plots, double bar graphs, circle graphs, line plots and line graphs; discuss appropriateness of graph selected.
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8.E.a.4
Find mean, median (with odd or even number of data), mode and range of a set of data with and without context.
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8.E.a.5
Evaluate sources of data in context and multiple representations of a given data set.
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8.E.b
Probability
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8.E.b.1
Determine the likelihood of an event and probability based on one or two dependent or independent events.
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8.E.b.2
Use probabilities to estimate outcomes and evaluate fair and unfair simple events.
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8.E.b.3
Use data from simulations provided in charts/tables to solve and interpret probability problems.
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8.E.b.4
Determine the number of arrangements from a set of 5 or less. Ex: How many different ways could 5 students stand in line?
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8.E.b.5
Solve problems involving sample spaces or diagrams.
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8.E.b.6
Analyze outcomes based on an understanding of theoretical and experimental probability.
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8.F
Algebraic Relationships
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8.F.a
Patterns, Relations and Functions
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8.F.a.1
Use two concurrent numeric patterns to describe and analyze functional relationships between two variables.
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8.F.a.2
Describe and analyze in words functional relationships in two concurrent numeric patterns using multiplication and exponents and describe the relationship in words.
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8.F.a.3
Extend an increasing or decreasing arithmetic or geometric pattern.
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8.F.a.4
Describe and interpret linear patterns in tables and graphs.
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8.F.a.5
Identify the rule to complete or extend a function table or any combination of the two using one or two operations (+, -, x, ¡Ò) and numbers (-100 through 100) in the function table..
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8.F.a.6
Describe real-world phenomena represented by a graph. Describe real-world phenomena that a given graph might represent.
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8.F.a.7
Justify the accuracy of the chosen item in a sequence.
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8.F.b
Expressions, Equations and Inequalities
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8.F.b.1
Solve single-variable inequalities using symbols.
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8.F.b.2
Solve single-variable one- and two-step equations with whole number, whole number integer, or rational, coefficients with and without context.
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8.F.b.3
Find values of expressions with one variable and up to two operations including basic operations and exponents.
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8.F.b.4
Solve two-step multi-operation equations with letter variables and whole number or integer coefficients with and without context. Ex: -3x +1 =.
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8.F.b.5
Write an algebraic expression (with one or two operations) which generalizes a linear pattern.
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8.F.b.6
Create a corresponding algebraic expression when given an arithmetic operation/relationship expressed in words.
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8.F.b.7
Evaluate formulas with and without context by solving for a specified variable.
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8.F.c
Properties
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8.F.c.1
Identify a pair of equivalent numerical or one-variable expressions when using commutative or associative properties with addition and multiplication.
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8.F.c.2
Demonstrate understanding of up to four-step order of operations expression using parentheses, exponents and fraction symbol.
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8.F.c.3
Demonstrate understanding of distributive property without variables.
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8.F.c.4
Solve order of operations problems with one variable to demonstrate understanding of commutativity and associativity.
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