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Mathematics – Mastery Expectations Grade 6 |
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Note: * = No state testing |
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Number Sense & Operations |
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| 6N1 |
Demonstrate an understanding of
positive integer exponents, in particular, when used in powers of ten. |
| 6N2 |
Demonstrate an understanding of place
value to billions and thousandths. |
| 6N3 |
Represent and compare very large (billions) and
very small (thousandths) positive numbers in various forms such as
expanded notation without exponents. |
| 6N4 |
Demonstrate an understanding of fractions as a
ratio of whole numbers, as parts of unit wholes, as parts of a
collection, and as locations on the number line. |
| 6N5 |
Identify and determine common equivalent
fractions, mixed numbers, decimals, and percents. |
| 6N6 |
Find and position integers, fractions, mixed
numbers, and decimals (both positive and negative) on the number line. |
| 6N7 |
Compare and order integers (including negative
integers), and positive fractions, mixed numbers, decimals, and
percents. |
| 6N8 |
Apply number theory concepts-including prime and
composite numbers, prime factorization, greatest common factor, least
common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9 and 10 – to
the solution of problems. |
| 6N9 |
Select and use appropriate operations to solve
problems involving addition, subtraction, multiplication, division, and
positive integer exponents with whole numbers, and with positive
fractions, mixed numbers, decimals, and percents. |
| 6N10 |
Use the number line to model addition and
subtraction of integers, with the exception of subtracting negative
integers. |
| 6N11 |
Apply the Order of Operations for expressions
involving addition, subtraction, multiplication, and division with
grouping symbols (+, -, x, รท ) |
| 6N12 |
Demonstrate an understanding of the inverse
relationship of addition and subtraction, and use that understanding to
simplify computation and solve problems. |
| 6N13 |
Accurately and efficiently add, subtract,
multiply, and divide (with double-digit divisors) whole numbers and
positive decimals. |
| 6N14 |
Accurately and efficiently add, subtract,
multiply, and divide positive fractions and mixed numbers. Simplify
fractions. |
| 6N15 |
Add and subtract integers, with the exception of
subtracting negative integers. |
| 6N16 |
Estimate results of computations with whole
numbers, and with positive fractions, mixed numbers, decimals, and
percents. Describe reasonableness of estimates. |
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Patterns, Relations & Algebra |
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| 6P1 |
Analyze and determine the rules for extending
symbolic, arithmetic, and geometric patterns and progressions. |
| 6P2 |
Replace variables with given values and
evaluate/simplify. |
| 6P3 |
Use the properties of equality to solve problems,
e.g., if Δ + 7 = 13, then Δ = 13 – 7, therefore Δ = 6; if 3 x Δ = 15,
then 1/3 x 3 x Δ = 1/3 x 15, therefore Δ = 15. |
| 6P4 |
Represent real situations and mathematical
relationships with concrete models, tables, graphs, and rules in words
and with symbols, e.g., input – output tables. |
| 6P5 |
Solve linear equations using concrete models,
tables, graphs, and paper-pencil methods. |
| 6P6 |
Produce and interpret graphs that represent the
relationship between two variables in everyday situations. |
| 6P7 |
Identify relationships between 2 variables with a
constant rate of change. Contrast these with relationships where the
rate of change is not constant. |
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Geometry |
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| 6G1 |
Identify polygons based on their properties,
including types of interior angles, perpendicular or parallel sides, and
congruence of sides, e.g., squares, rectangles, rhombuses,
parallelograms, trapezoids, and isosceles, equilateral, and right
triangles. |
| 6G2 |
Identify three-dimensional shapes (e.g., cubes,
prisms, spheres, cones, and pyramids) based on their properties, such as
edges and faces. |
| 6G3 |
Identify relationships among points, lines, and
planes, e.g., intersecting, parallel, perpendicular. |
| 6G4 |
Graph points and identify coordinates of points
on the Cartesian coordinate plane (all four quadrants). |
| 6G5 |
Find the distance between two points on
horizontal or vertical number lines. |
| 6G6 |
Predict, describe, and perform transformations on
two-dimensional shapes, e.g., translations, rotations, and reflections. |
| 6G7 |
Identify types of symmetry, including line and
rotational. |
| 6G8 |
Determine if two shapes are congruent by
measuring sides or a combination of sides and angles, as necessary; or
by motions or series of motions. |
| 6G9 |
Match three-dimensional objects and their
two-dimensional representations, e.g., nets, projections, and
perspective drawings |
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Measurement |
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| 6M1 |
Apply the concepts of area and perimeter to the
solution of problems. Apply formulas where appropriate. |
| 6M2 |
Identify measure, describe, classify, and
construct various angles, triangles, and quadrilaterals. |
| 6M3 |
Solve problems involving proportional
relationships and units of measurement, e.g., same system unit
conversions, scale models, maps and speed. |
| 6M4 |
Find area of triangles and parallelograms.
Recognize that shapes with the same number of sides but different
appearances can have the same area; Develop strategies to find the area
of more complex shapes. |
| 6M5 |
Identify, measure, and describe circles and the
relationships of the radius, diameter, circumference, and area (e.g., d
= 2r, p = C/d), and use the concepts to solve problems. |
| 6M6 |
Find volumes and surface areas of rectangular
prisms. |
| 6M7 |
Find the sum of angles in simple polygons, up to
eight sides (with and w/o measuring the angles). |
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Data Analysis, Statistics and Probability |
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| 6D1 |
Describe and compare data sets using the concepts
of median, mean, mode, maximum and minimum, and range. |
| 6D2 |
Construct and interpret stem and leaf plots, line
plots, and circle graphs. |
| 6D3 |
Use tree diagrams and other models (e.g., lists
and tables) to represent possible or actual outcomes of trials. Analyze
the outcomes. |
| 6D4 |
Predict the probability of outcomes of simple
experiments (e.g., rolling a die) and test the predictions. Use
appropriate ratios between 0 and 1 to represent the probability of the
outcome and associate the probability with the likelihood of the event. |
