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6.N
Number and Operations
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6
Multiply and divide fractions
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6.N.MR.06.01
Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = __, then 2/3 * __ = 4/5, so __ = 4/5 * 3/2 = 12/10.
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6.N.FL.06.02
Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation.
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6.N.MR.06.03
Solve for the unknown in equations such as ¼ ÷ __ = 1, ¾ ÷ __ = ¼, and ½ = 1 * __.
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6.N.FL.06.04
Multiply and divide any two fractions, including mixed numbers, fluently.
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6
Represent rational numbers as fractions or decimals
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6.N.ME.06.05
Order rational numbers and place them on the number line.
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6.N.ME.06.06
Represent rational numbers as fractions or terminating decimals when possible, and translate between these representations.
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6.N.ME.06.07
Understand that a fraction or a negative fraction is a quotient of two integers, e.g., -8/3 is -8 divided by 3.
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6
Add and subtract integers and rational numbers
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6.N.MR.06.08
Understand integer subtraction as the inverse of integer addition. Understand integer division as the inverse of integer multiplication.
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6.N.FL.06.09
Add and multiply integers between -10 and 10; subtract and divide integers using the related facts. Use the number line and chip models for addition and subtraction.
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6.N.FL.06.10
Add, subtract, multiply and divide positive rational numbers fluently.
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6
Find equivalent ratios
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6.N.ME.06.11
Find equivalent ratios by scaling up or scaling down.
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6
Solve decimal, percentage and rational number problems
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6.N.FL.06.12
Calculate part of a number given the percentage and the number.
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6.N.MR.06.13
Solve contextual problems involving percentages such as sales taxes and tips.
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6.N.FL.06.14
For applied situations, estimate the answers to calculations involving operations with rational numbers.
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6.N.FL.06.15
Solve applied problems that use the four operations with appropriate decimal numbers.
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6
Use exponents
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6.N.ME.06.16
Understand and use integer exponents, excluding powers of negative bases; express numbers in scientific notation.
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6
Understand rational numbers and their location on the number line
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6.N.ME.06.17
Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0, and are on opposite sides and at equal distance from 0 on a number line.
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6.N.ME.06.18
Understand that rational numbers are quotients of integers (non zero denominators), e.g., a rational number is either a fraction or a negative fraction.
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6.N.ME.06.19
Understand that 0 is an integer that is neither negative nor positive.
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6.N.ME.06.20
Know that the absolute value of a number is the value of the number ignoring the sign; or is the distance of the number from 0.
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6.A
Algebra
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6
Calculate rates
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6.A.PA.06.01
Solve applied problems involving rates, including speed, e.g., if a car is going 50 mph, how far will it go in 3½ hours?
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6
Understand the coordinate plane
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6.A.RP.06.02
Plot ordered pairs of integers and use ordered pairs of integers to identify points in all four quadrants of the coordinate plane.
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6
Use variables, write expressions and equations, and combine like terms
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6.A.FO.06.03
Use letters, with units, to represent quantities in a variety of contexts, e.g., y lbs., k minutes, x cookies.
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6.A.FO.06.04
Distinguish between an algebraic expression and an equation.
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6.A.FO.06.05
Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means "two times x, plus 1" and 2(x + 1) means "two times the quantity (x + 1)."
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6.A.FO.06.06
Represent information given in words using algebraic expressions and equations.
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6.A.FO.06.07
Simplify expressions of the first degree by combining like terms, and evaluate using specific values.
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6
Represent linear functions using tables, equations, and graphs
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6.A.RP.06.08
Understand that relationships between quantities can be suggested by graphs and tables.
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6.A.PA.06.09
Solve problems involving linear functions whose input values are integers; write the equation; graph the resulting ordered pairs of integers, e.g., given c chairs, the "leg function" is 4c; if you have 5 chairs, how many legs?; if you have 12 legs, how many chairs?
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6.A.RP.06.10
Represent simple relationships between quantities using verbal descriptions, formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches.
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6
Solve equations
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6.A.FO.06.11
Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular contexts and solve.
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6.A.FO.06.12
Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution.
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6.A.FO.06.13
Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solutions.
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6.A.FO.06.14
Solve equations of the form ax + b = c, e.g., 3x + 8 = 15 by hand for positive integer coefficients less than 20, use calculators otherwise, and interpret the results.
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6.M
Measurement
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6
Convert within measurement systems
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6.M.UN.06.01
Convert between basic units of measurement within a single measurement system, e.g., square inches to square feet.
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6
Find volume and surface area
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6.M.PS.06.02
Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets).
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6.M.TE.06.03
Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides, using formulas.
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6.G
Geometry
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6
Understand and apply basic properties
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6.G.GS.06.01
Understand and apply basic properties of lines, angles, and triangles, including:
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6.G.GS.06.01.1
triangle inequality
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6.G.GS.06.01.2
relationships of vertical angles, complementary angles, supplementary angles
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6.G.GS.06.01.3
congruence of corresponding and alternate interior angles when parallel lines are cut by a transversal, and that such congruencies imply parallel lines
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6.G.GS.06.01.4
locate interior and exterior angles of any triangle, and use the property that an exterior angle of a triangle is equal to the sum of the remote (opposite) interior angles
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6.G.GS.06.01.5
know that the sum of the exterior angles of a convex polygon is 360º.
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6
Understand the concept of congruence and basic transformations
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6.G.GS.06.02
Understand that for polygons, congruence means corresponding sides and angles have equal measures.
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6.G.TR.06.03
Understand the basic rigid motions in the plane (reflections, rotations, translations), relate these to congruence, and apply them to solve problems.
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6.G.TR.06.04
Understand and use simple compositions of basic rigid transformations, e.g., a translation followed by a reflection.
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6
Construct geometric shapes
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6.G.SR.06.05
Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors; justify informally.
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6.D
Data and Probability
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6
Understand the concept of probability and solve problems
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6.D.PR.06.01
Express probabilities as fractions, decimals, or percentages between 0 and 1; know that 0 probability means an event will not occur and that probability 1 means an event will occur.
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6.D.PR.06.02
Compute probabilities of events from simple experiments with equally likely outcomes, e.g., tossing dice, flipping coins, spinning spinners, by listing all possibilities and finding the fraction that meets given conditions.
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