Seventh Grade Math Grade Expectations

M7:1 Demonstrates conceptual understanding of rational numbers

with respect to percents as a means of comparing the same or

different parts of the whole when the wholes vary in magnitude (e.g.,

8 girls in a classroom of 16 students compared to 8 girls in a classroom of

20 students, or 20% of 400 compared to 50% of 100); and percents as a

way of expressing multiples of a number (e.g., 200% of 50) using

models, explanations, or other representations.*

M(N&O)–7–1

M7:2 Demonstrates understanding of the relative magnitude of

numbers by ordering, comparing, or identifying equivalent rational

numbers across number formats, numbers with whole-number

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

values, or numbers represented in scientific notation using number

lines or equality and inequality symbols.

M(N&O)–7–2

M7:3 Demonstrates conceptual understanding of operations with

integers, exponents, and square roots of perfect square numbers

and nonperfect square numbers using models, diagrams, or

explanations.

M7:4 Accurately solves problems involving proportional reasoning;

percents involving discounts, tax, or tips; and rates.

(IMPORTANT: Applies the conventions of order of operations

including parentheses, brackets, or exponents.)

M(N&O)–7–4

And accurately solves problems involving integers, raising numbers

to whole-number powers, and determining square roots of perfect

square numbers and nonperfect square numbers.

M7:5 No M7:5 at this grade level

M7:6 No M7:6 at this grade level

M7:7 Estimates and evaluates the reasonableness of solutions

appropriate to grade level.

M7:8 Applies properties of numbers (greatest common factor [GCF],

least common multiple [LCM], composition/decomposition,

divisibility, prime factorization, inverses, and identities), and

commutative, distributive, and associative properties of operations,

and exponents using powers of ten and scientific notation to solve

problems and to simplify computations.

M7:9 Uses properties of angle relationships resulting from two or

three intersecting lines (adjacent angles, vertical angles, straight

angles, or angle relationships formed by two nonparallel lines cut

by a transversal), or two parallel lines cut by a transversal to solve

problems. M(G&M)–7–1

M7:10 Applies theorems or relationships (triangle inequality or sum

of the measures of interior angles of regular polygons) to solve

problems. M(G&M)–7–2

M7:11 Applies the properties of number of vertices, number of edges,

faces, and types of angles, symmetry, to identify and distinguish

among three-dimensional shapes (rectangular prisms, triangular

prisms, pyramids, cubes) and uses properties to solve problems

involving three-dimensional shapes.

M7:12 Applies the concepts of congruency by solving problems on a

coordinate plane involving reflections, translations, or rotations.

M(G&M)–7–4

M7:13 Applies concepts of similarity by solving problems involving

scaling up or down and their impact on angle measures, linear

dimensions and areas of polygons, and circles when the linear

dimensions are multiplied by a constant factor. Describes effects

using models or explanations.

M(G&M)–7–5

M7:14 Demonstrates conceptual understanding of the area of circles

or the area or perimeter of composite figures (quadrilaterals,

triangles, or parts of circles), and the surface area of rectangular

prisms, or volume of rectangular prisms, triangular prisms, or

cylinders using models, formulas, or by solving related problems.

Expresses all measures using appropriate units.

M(G&M)–7–6

M7:15 Measures and uses units of measures appropriately and

consistently when solving problems across the content

strands. Makes conversions within systems. (See Appendix B

for benchmark units and equivalences for each grade.)

M7:16 No M7:16 at this grade level

M7:17 Sketches three-dimensional solids and the nets of prisms,

cylinders, and pyramids.

M7:18 No M7:18 at this grade level

(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 orsc _ symbols for finding specific cases of a nonlinear

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

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

twice the term number plus 1 orsc _ 2 n + 1).

M(F&A)–6–1

M7:19 Identifies and extends to specific cases a variety of patterns

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

graphs, or in problem situations; and generalizes a linear

relationship using words and symbols; generalizes a linear

relationship to find a specific case; or writes an expression or

equation using words or symbols to express the generalization of

a nonlinear relationship.

M(F&A)–7–1

M7:20 Demonstrates conceptual understanding of linear

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

by solving problems involving the relationship between slope and

rate of change, by describing the meaning of slope in concrete

situations, or informally determining the slope of a line from a table

or graph; and distinguishes between constant and varying rates

of change in concrete situations represented in tables or graphs; or

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)–7–2

M7:21 Demonstrates conceptual understanding of algebraic

expressions by using letters to represent unknown quantities to

write algebraic expressions (including those with whole-number

exponents or more than one variable); or by evaluating algebraic

expressions (including those with whole-number exponents or

more than one variable); or by evaluating an expression within an

equation (e.g., determine the value of y when x = 4 given y = 5 x3 – 2).

M(F&A)–7–3

M7:22 Demonstrates conceptual understanding of equality by

showing equivalence between two expressions (expressions

consistent with the parameters of the left- and right-hand sides

of the equations being solved at this grade level) using models or

different representations of the expressions, solving multistep linear

equations of the form ax ± b = c with a . 0, ax ± b = cx ± d with

a, c . 0, and ( x/ a) ± b = c with a . 0, where a, b, c and d are

whole numbers; or by translating a problem-solving situation into

an equation consistent with the parameters of the type of equations

being solved for this grade level.

M(F&A)–7–4

M7:23 Interprets a given representation (circle graphs, scatter plots that

represent discrete linear relationships, or histograms) 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

M7:24.) M(DSP)–7–1

And (Frequency charts, tables, bar graphs, pictographs, Venn

diagrams, line plots).

M7:24 Analyzes patterns, trends, or distributions in data in a variety

of contexts by solving problems using measures of central

tendency (mean, median, or mode), dispersion (range or variation),

or outliers to analyze situations to determine their effect on mean,

median, or mode; and evaluates the sample from which the

statistics were developed (bias). M(DSP)–7–2

M7:25 Identifies or describes representations or elements of

representations that best display a given set of data or

situation, consistent with the representations required in M7:23.

M(DSP)–7–3

Organizes and displays data using line graphs or histograms,

bar graphs, tables, frequency tables, line plots, 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

M7:24.)

M7:26 Uses counting techniques to solve problems in context involving

combinations using a variety of strategies (e.g., organized lists,

tables, tree diagrams, area models, Fundamental Counting

Principle, or others); or determines the possible outcomes for a

sample space that may or may not contain equally likely outcomes.

M7:27 For a probability event in which the sample space may or

may not contain equally likely outcomes, determines the

experimental or theoretical probability of a simple event or an event

in a problem-solving situation.

M(DSP)–7–5

M7:28 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

M7:24.)

M7:29 Compares and contrasts theoretical and experimental

probabilities of events; and uses theoretical or experimental

probabilities to determine the fairness of a game. Represents

probabilities using fractions, decimals, or percents.

M7:30 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.