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6.A
Algebraic Reasoning: Patterns and Functions
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6.A.1
Analyze, describe in writing and extend a variety of patterns to justify predictions and identify trends.
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6.A.2
Create tables of values and scatterplots from mathematical relationships and equations and vice versa to solve problems.
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6.A.3
Examine tables, graphs and equations to determine patterns of change in linear relationships.
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6.A.4
Write expressions, formulas, equations or inequalities using symbols or variables to denote a pattern or represent a contextual situation.
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6.A.5
Evaluate algebraic expressions and formulas using substitution.
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6.A.6
Write, model and solve one-step equations using mental math, tables, substitution and concrete models that demonstrate equivalence and justify the solution.
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6.N
Numerical and Proportional Reasoning
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6.N.1
Locate and label whole numbers, fractions, decimals and positive and negative integers on number lines, scales, coordinate grids (all four quadrants) and measurement tools.
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6.N.2
Compare and order whole numbers, fractions, decimals and positive and negative integers in context using number lines and scales.
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6.N.3
Represent and compare whole numbers (to a billion) and decimals (to thousandths) in expanded notation, e.g., 75.654 = (7 × 10) + (5 × 1) + (6 × 0.1) + (5 × 0.01) + (4 × 0.001).
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6.N.4
Represent chain multiplication, including powers of 10 in exponential and standard form, e.g., 5 × 5 × 5³ = 53 = 125.
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6.N.5
Factor composite numbers and express them as a product of primes using exponents.
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6.N.6
Determine equivalent fraction, decimal, and percentage representations and choose among these forms to solve problems.
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6.N.7
Use ratios and rates (involving different units) to compare quantities.
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6.N.8
Understand place value and patterns in place value when multiplying and dividing decimals by powers of 10.
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6.N.9
Develop, describe and use strategies for solving, simplifying and estimating multiplication and division problems involving large numbers, decimals and powers of 10, e.g., 4.25 × 100 = 425 and 365,000 ÷ 6,000 = 365 ÷ 6 ; 365 ÷ 6= 360 ÷ 6 = 60.
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6.N.10
Estimate and find percentages of a number in context using benchmarks and number patterns and ratios to 100.
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6.N.11
Solve practical problems involving rates, ratios, percentages and proportionality.
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6.N.12
Add, subtract, multiply and divide by fractions and decimals in context.
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6.N.13
Describe situations in writing that connect multiplying fractions to determining the fractional part of a set.
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6.N.14
Examine the relationships between multiplication by a unit fraction and dividing by the fraction's denominator, e.g., 1/2 of $6 is the same as $6 ÷ 2, and use this to solve problems.
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6.N.15
Use the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions.
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6.N.16
Understand and defend in writing the magnitude of the result of multiplication or division problems involving fractions or decimals.
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6.N.17
Determine when an estimate is sufficient or when an exact answer is needed.
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6.N.18
Estimate solutions to problems and justify the reasonableness of estimates in writing.
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6.N.19
Write and solve multistep problems in context involving addition, subtraction, multiplication and division with whole numbers, fractions, decimals, money and simple percentages.
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6.N.20
Understand and use divisibility rules, factors of composite numbers and powers of 10 to find products and quotients.
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6.N.21
Apply the order of operations and algebraic properties; i.e., commutative, associative, distributive, inverse operations, and the additive and multiplicative identities; to compute and solve multistep problems and explain solutions in writing.
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6.N.22
Use concrete models to develop strategies to add and subtract integers.
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6.G
Geometry and Measurement
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6.G.1
Classify sets and subsets of polygons using the relationship of the sides (length, parallel and perpendicular) and angles (types and measure).
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6.G.2
Make and test conjectures about polygons and congruence using side and angle relationships and describe the results in writing.
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6.G.3
Identify lines of symmetry and reflections, rotations and translations of geometric figures.
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6.G.4
Use rectangles as basic shapes to model and develop formulas for finding the area of triangles, parallelograms and trapezoids.
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6.G.5
Recognize the relationships among radius, diameter, circumference and area of circles and develop formulas for finding circumference and area based on these relationships.
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6.G.6
Use and describe concrete strategies for finding the volume of rectangular solids and cylinders.
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6.G.7
Use measurements to examine the ratios between corresponding side lengths of scale models and similar figures.
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6.G.8
Select and use appropriate strategies, tools and units to estimate and solve measurement problems involving length, perimeter, area, volume, capacity, mass and weight.
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6.G.9
Use ratios to convert between customary units of length, mass, capacity and time.
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6.G.10
Use ratios and powers of 10 to convert between metric units.
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6.D
Working with Data: Probability and Statistics
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6.D.1
Compare sets of data between two populations, e.g., heights of two classes of students, or within a population, e.g., height vs. arm length of sixth-grade students, using a variety of graphical representations.
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6.D.2
Select, create and use appropriate graphical representations of data including, circle graphs, scatter plots, histograms, and stem and leaf plots.
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6.D.3
Describe the shape of numerical data sets using measures of spread (range) and central tendency (mean, median, mode) and outliers.
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6.D.4
Determine how the mean, median, mode and range change as a result of changes in the data set and describe in writing.
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6.D.5
Investigate and describe the relationship between the number of trials in an experiment and the predicted outcomes.
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6.D.6
Design and conduct probability experiments to test predictions about outcomes and fairness.
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6.D.7
Express probabilities as fractions, ratios, decimals and percentages.
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6.D.8
Find all possible outcomes by systematic listing and counting strategies to solve problems.
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