Sixth Grade Math Grade Expectations

M6:1 Demonstrates conceptual understanding of rational numbers

with respect to ratios (comparison of two whole numbers by

division a/ b, a : b, and a χ b , where b . 0); and rates (e.g., a out of

b, 25%) using models, explanations, or other representations.*

Demonstrates conceptual understanding of proportional

reasoning, and fluently moves between equivalent representations

of commonly used fractions and decimals.

M(N&O)–6–1

*Specifications for area, set, and linear models for grades 5–8: Fractions: The number of parts in the whole is equal to the denominator, a multiple of the denominator, or a factor of the denominator. Percents: The number of parts in the whole is equal to 100, a multiple of 100, or a factor of 100 (for grade 5); the number of parts in the whole is a multiple or a factor of the numeric value representing the whole (for grades 6–8). Decimals (including powers of ten): The number of parts in the whole is equal to the denominator of the fractional equivalent of the decimal, a multiple of the denominator of the fractional equivalent of the decimal, or a factor of the denominator of the fractional equivalent of the decimal.

M6:2 Demonstrates understanding of the relative magnitude of

numbers by ordering or comparing numbers with whole-number

bases and whole-number exponents (e.g., 33 , 43 ), integers, or

rational numbers within and across number formats (fractions,

decimals, or whole-number percents from 1 to 100) using number

lines or equality and inequality symbols.

M(N&O)–6–2

M6:3 Demonstrates understanding of mathematical operations by

describing or illustrating the meaning of a power by representing the

relationship between the base (whole number) and the exponent

(whole number) (e.g., 33 , 43 ); and the effect on the magnitude of a

whole number when multiplying or dividing it by a whole number,

decimal, or fraction.

M(N&O)–6–3

M6:4 Accurately solves problems involving single or multiple

operations on fractions (proper, improper, and mixed), or decimals;

and addition or subtraction of integers; percent of a whole; or

problems involving greatest common factor or least common

multiple.

(IMPORTANT: Applies the conventions of order of operations with

and without parentheses.)

M(N&O)–6–4

M6:5 No M6:5 at this grade level

M6:6 Mentally multiplies and divides whole numbers through twelve

with accuracy.

M6:7 Estimates and evaluates the reasonableness of solutions

appropriate to grade level.

M6:8 Applies properties of numbers (factor, multiple, prime,

composite, greatest common factor [GCF], least common multiple

[LCM], composition/decomposition), divisibility, remainders), and

commutative and associative properties of operations to solve

problems and to simplify computations.

M6:9 Uses properties or attributes of angles (right, acute, or

obtuse) or sides (number of congruent sides, parallelism, or

perpendicularity) to identify, describe, classify, or distinguish

among different types of triangles (right, acute, obtuse, equiangular,

scalene, isosceles, or equilateral) or quadrilaterals (rectangles,

squares, rhombi, trapezoids, or parallelograms).

M(G&M)–6–1

M6:10 No M6:10 at this grade level

M6:11 Uses properties or attributes (shape of bases, number of lateral

faces, number of bases, number of edges, or number of vertices)

to identify, compare, or describe three-dimensional shapes

(rectangular prisms, triangular prisms, cylinders, spheres, pyramids,

or cones). M(G&M)–6–3

M6:12 Demonstrates congruency using the results of combining

and subdividing shapes (e.g., rectangle into two triangles), by

using transformations (flips, slides, and turns), and by using the

properties of angles, and length of segments.

M6:13 Demonstrates conceptual understanding of similarity by

describing the proportional effect on the linear dimensions of

polygons or circles when scaling up or down while preserving

the angles of polygons, or by solving related problems (including

applying scales on maps). Describes effects using models or

explanations. M(G&M)–6–5

And applies concepts of similarity using constant of

proportionality/scale factor to make larger and smaller scale

drawings.

M6:14 Demonstrates conceptual understanding of perimeter

of polygons, the area of quadrilaterals or triangles, and the

volume of rectangular prisms by using models, formulas, or by

solving problems; and demonstrates understanding of the

relationships of circle measures (radius to diameter and diameter

to circumference) by solving related problems. Expresses all

measures using appropriate units.

M(G&M)–6–6

M6:15 Measures and uses units of measures appropriately and

consistently, and makes conversions within systems when

solving problems across the content strands. (Benchmarks in

Appendix B.)

M(G&M)–6–7

M6:16 No M6:16 at this grade level

M6:17 No M6:17 at this grade level

M6:18 Solves problems using the Cartesian coordinate system (all

quadrants) to locate coordinates and to represent data from tables.

M6:19 Identifies and extends to specific cases a variety of patterns

(linear and nonlinear) represented in models, tables, sequences,

graphs, or in problem situations; or writes a rule in words or

symbols for finding specific cases of a linear relationship; or writes

a rule in words or symbols for finding specific cases of a nonlinear

relationship; and writes an expression or equation using words or _

symbols to express the generalization of a linear relationship (e.g.,

twice the term number plus 1 or 2 n + 1).

M(F&A)–6–1

M6:20 Demonstrates conceptual understanding of linear

relationships ( y = kx; y = mx + b) as a constant rate of change

by constructing or interpreting graphs of real occurrences and

describing the slope of linear relationships (faster, slower, greater,

or smaller) in a variety of problem situations; and describes how

change in the value of one variable relates to change in the

value of a second variable in problem situations with constant

rates of change.

M(F&A)–6–2

M6:21 Demonstrates conceptual understanding of algebraic

expressions by using letters to represent unknown quantities to

write linear algebraic expressions involving two or more of the four

operations and consistent with order of operations expected at this

grade level; or by evaluating linear algebraic expressions (including

those with more than one variable); or by evaluating an expression

within an equation (e.g., determine the value of y when x = 4 given

y = 3 x – 2).

M(F&A)–6–3

M6:22 Demonstrates conceptual understanding of equality by showing

equivalence between two expressions using models or different

representations of the expressions (expressions consistent with the

parameters of M(F&A)–6–3), solving multistep linear equations of

the form ax ± b = c, where a, b, and c are whole numbers with a . 0.

M(F&A)–6–4

M6:23 Interprets a given representation (circle graphs, line graphs,

or stem-and-leaf plots) to answer questions related to the data,

to analyze the data to formulate or justify conclusions, to make

predictions, or to solve problems.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M6:24.)

M(DSP)–6–1

And (frequency charts, line graphs, Venn diagrams, pictographs,

line plots, histograms).

M6:24 Analyzes patterns, trends or distributions in data in a variety

of contexts by determining or using measures of central

tendency (mean, median, or mode) or dispersion (range) to analyze

situations, or to solve problems.

M(DSP)–6–2

M6:25 Organizes and displays data using bar graphs, tables, frequency

tables, line plots, circle graphs, and stem-and-leaf plots to answer

question related to the data, to analyze the data to formulate or

justify conclusions, or to make predictions.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M6:24.)

M6:26 Uses counting techniques to solve problems in context involving

combinations or simple permutations using a variety of strategies

(e.g., organized lists, tables, tree diagrams, models, Fundamental

Counting Principle, or others).

M(DSP)–6–4

M6:27 For a probability event in which the sample space may or

may not contain equally likely outcomes, determines the

experimental or theoretical probability of an event in a problem-solving

situation.

M(DSP)–6–5

M6:28 In response to a teacher- or student-generated question,

makes a hypothesis, collects appropriate data, organizes the data,

appropriately displays/represents numerical and/or categorical

data, analyzes the data to draw conclusions about the questions or

hypothesis being tested, and when appropriate makes predictions,

asks new questions, or makes connection to real-world situations.

(IMPORTANT: Analyzes data consistent with concepts and skills in

M6:24.)

M6:29 Uses experimental probability to make and test conjectures or

design fair games. Represent probabilities using fractions, decimals,

or percents.

M6:30 Demonstrate understanding of mathematical problem solving2

and communication through:3

• Approach & Reasoning—The reasoning, strategies, and skills

used to solve the problem;

• Connections—Demonstration of observations, applications,

extensions, and generalizations;

• Solution—All of the work that was done to solve the problem,

including the answer;

• Mathematical Language—The use of mathematical language

in communicating the solution;

• Mathematical Representation—The use of mathematical

representation to communicate the solution; and

• Documentation—Presentation of the solution.