NUMBER AND OPERATIONS |
Multiply and divide fractions:
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N.MR.06.01 - Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = @, then 2/3 x @ = 4/5, so @ = 4/5 x 3/2 = 12/10.
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N.FL.06.02 - Given an applied situation involving dividing fractions, write a mathematical statement to represent the situation.
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N.MR.06.03 - Solve for the unknown in equations such as: ¼ ÷ @ = 1, ¾ ÷ = ¼ and ½ = 1 x @
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N.FL.06.04 - Multiply and divide any two fractions, including mixed numbers, fluently.
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Represent rational numbers as fractions, or decimals:
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N.ME.06.05 - Order rational numbers and place them on the number line.
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N.ME.06.06 - Represent rational numbers as fractions or terminating decimals when possible, and translate between these representations.
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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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Add and subtract integers and rational numbers:
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N.MR.06.08 - Understand integer subtraction as the inverse of integer addition; add and subtract integers, using integers from 10 to -10.
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N.FL.06.09 - Add, subtract, multiply, and divide integers between -10 and 10; use number line and strip models for addition and subtraction.
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N.FL.06.10 - Add, subtract, multiply and divide positive rational numbers fluently.
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Find equivalent ratios:
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N.ME.06.11 - Find equivalent ratios by scaling up or scaling down.
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Solve decimal, percentage and rational number problems:
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N.FL.06.12 - Calculate part of a number given the percentage and the number.
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N.FL.06.13 - Solve word problems involving percentages in such contexts as sales taxes and tips, and involving positive rational numbers.
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N.FL.06.14 - For applied situations, estimate the answers to calculations involving operations with rational numbers.
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N.FL.06.15 - Solve applied problems that use the four operations with appropriate decimal numbers.
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Use exponents:
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N.ME.06.16 - Understand and use integer exponents, excluding powers of negative numbers; express numbers in scientific notation.
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Understand rational numbers and their location on the number line:
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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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N.ME.06.18 - Understand that rational numbers are quotients of integers (nonzero denominators), e.g., a rational number is either a fraction or a negative fraction.
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N.ME.06.19 - Understand that 0 is an integer that is neither negative nor positive.
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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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ALGEBRA
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Calculate rates:
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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 3 ½ hours?
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Understand the coordinate plane:
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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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Use variables, write expressions and equations, and combine like terms:
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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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A.FO.06.04 - Distinguish between an algebraic expression and an equation.
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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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A.FO.06.06 - Represent information given in words using algebraic expressions and equations.
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A.FO.06.07 - Simplify expressions of the first degree by combining like terms, and evaluate using specific values.
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Represent linear functions using tables, equations, and graphs:
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A.RP.06.08 - Understand that graphs and tables can suggest relationships between quantities.
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A.PA.06.09 - Graph and write equations for linear functions of the form y = mx and solve related problems, e.g., given n chairs, the “leg function” is f (n) = 4n: if you have 5 chairs, how many legs? ; if you have 12 legs, how many chairs?
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A.RP.06.10 - Represent simple relationships between quantities, e.g., perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches; use verbal descriptions, formulas or equations, tables, and graphs.
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Solve equations:
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A.FO.06.11 - Relate simple linear equations with integer coefficients to particular contexts, e.g., 3x = 8 or x + 5 = 10, and solve.
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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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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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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, using calculators otherwise, and interpret the results.
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MEASUREMENT
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Convert within measurement systems:
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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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Find volume and surface area:
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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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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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GEOMETRY
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Understand and apply basic properties:
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G.GS.06.01 - Understand and apply basic properties of lines, angles, and triangles, including:
• triangle inequality
• relationships of vertical angles, complementary angles, supplementary angles.
• congruence of corresponding and alternate interior angles when parallel lines are cut by a transversal, and that such congruencies imply parallel lines.
• locate interior and exterior angles of any triangle and use the property that a exterior angle of a triangle is equal to the sum of the remote (opposite) interior angles
• know that the sum of the exterior angles of a convex polygon is 360°
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Understand the concept of congruence and basic transformations:
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G.GS.06.02 - Understand that for polygons, congruence means corresponding sides and angles have equal measures.
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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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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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Construct geometric shapes:
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G.SR.06.05 - Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line segments and angle bisectors, and justify informally.
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DATA AND PROBABILITY
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Understand the concept of probability and solve problems:
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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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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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