# Math Standards for Grade 6-8

## Grade Seven

By the end of grade seven, students will understand and
use rational numbers, including

signed numbers ; solve linear equations in one variable; sketch and construct
plane

figures; demonstrate understanding of transformations; use and apply properties
of

similarity ; examine properties of geometric shapes in space; describe and sketch
solid

figures, including their cross-sections; represent and describe relationships
between

variables in tables, graphs, and formulas; analyze the characteristics of linear

relationships;

and represent and analyze data using graphical displays,
measures of central tendency,

and measures of variation.

Instruction and assessment should include the appropriate
use of manipulatives and

technology. Topics should be represented in multiple ways , such as
concrete/pictorial,

verbal/written, numeric /data-based, graphical, and symbolic. Concepts should be

introduced and used, where appropriate, in the context of realistic phenomena .

**C o n c e p t s / S k i l ls t o M a i n t a i n
**Operations with positive rational numbers, including mixed numbers

Line and rotational symmetry

Surface area and volume

Ratio as a representation of quantitative relationships

**Numbers and Operations
**Students will further develop their understanding of the concept of rational
numbers

and apply them to real world situations.

**M7N1 Students will understand the meaning of positive and negative rational**

numbers and use them in computation.

a. Find the absolute value of a number and understand it as the distance from

numbers and use them in computation.

zero on a number line.

b. Compare and order rational numbers, including repeating decimals .

c. Add, subtract, multiply, and divide positive and negative rational numbers.

d. Solve problems using rational numbers.

**Geometry**

Students will further develop and apply their understanding of plane and solid

geometric figures through the use of constructions and transformations. Students

will explore the properties of similarity and further develop their understanding of

3-dimensional figures.

**M7G1 Students will construct plane figures that meet given conditions.**

a. Perform basic constructions using both compass and straight edge, and appropriate

technology. Constructions should include copying a segment;

copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular

lines, including the perpendicular bisector of a line segment; and

constructing a line parallel to a given line through a point not on the line.

b. Recognize that many constructions are based on the creation of congruent

triangles.

**M7G2 Students will demonstrate understanding of transformations.**

a. Demonstrate understanding of translations, dilations, rotations, reflections,

and relate symmetry to appropriate transformations.

b. Given a figure in the coordinate plane , determine the coordinates resulting

from a translation, dilation, rotation, or reflection.

**M7G3 Students will use the properties of similarity and apply these concepts to**

geometric figures.

a. Understand the meaning of similarity, visually compare geometric figures for

geometric figures.

similarity, and describe similarities by listing corresponding parts.

b. Understand the relationships among scale factors , length ratios, and area ratios

between similar figures. Use scale factors, length ratios, and area ratios to

determine side lengths and areas of similar geometric figures.

c. Understand congruence of geometric figures as a special case of similarity: The

figures have the same size and shape.

**M7G4 Students will further develop their understanding of three-dimensional**

figures.

a. Describe three-dimensional figures formed by translations and rotations of

figures.

plane figures through space.

b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and

prisms.

Algebra

Students will demonstrate an understanding of linear relations and fundamental

algebraic concepts .

**M7A1 Students will represent and evaluate quantities using algebraic expressions .**

a. Translate verbal phrases to algebraic expressions.

b. Simplify and evaluate algebraic expressions, using commutative, associative,

and distributive properties as appropriate.

c. Add and subtract linear expressions.

**M7A2 Students will understand and apply linear equations in one variable.**

a. Given a problem, define a variable, write an equation, solve the equation, and

interpret the solution.

b. Use the addition and multiplication properties of equality to solve one- and

two-step linear equations.

**M7A3 Students will understand relationships between two variables.**

a. Plot points on a coordinate plane.

b. Represent, describe, and analyze relations from tables, graphs, and formulas.

c. Describe how change in one variable affects the other variable.

d. Describe patterns in the graphs of proportional relationships , both direct (y =

kx) and inverse (y = k/x).

**Data Analysis and Probability
**Students will demonstrate understanding of data analysis by posing
questions, collecting

data, analyzing the data using measures of central tendency and variation,

and using the data to answer the questions posed. Students will understand the

role of probability in sampling.

**M7D1 Students will pose questions, collect data, represent and analyze the data,**

and interpret results.

a. Formulate questions and collect data from a census of at least 30 objects and

and interpret results.

from samples of varying sizes.

b. Construct frequency distributions.

c. Analyze data using measures of central tendency (mean, median, and mode),

including recognition of outliers.

d. Analyze data with respect to measures of variation (range, quartiles, interquartile

range).

e. Compare measures of central tendency and variation from samples to those

from a census. Observe that sample statistics are more likely to approximate

the population parameters as sample size increases.

f. Analyze data using appropriate graphs, including pictographs, histograms, bar

graphs, line graphs, circle graphs , and line plots introduced earlier, and using

box-and-whisker plots and scatter plots.

g. Analyze and draw conclusions about data, including a description of the relationship

between two variables.

** Terms /Symbols
**natural number

whole number

sign

integer

opposite

negative

positive

absolute value

term

variable

commutative property

associative property

distributive property

algebraic expression

linear equation

direct and indirect

proportions

constant of proportionality

(y = kx)

variation

polyhedron

translation

rotation

reflection

dilation

symmetry

bisector

parallel lines

perpendicular lines

cross-section

similar

congruent

point

line

plane

line segment

endpoints

intersection

ray

similarity

rate

scale

drawings

corresponding sides

corresponding angles

diagonal

direct variation

inverse variation

inversely proportional

mean

median

mode

range

quartile

interquartile range

outlier

histogram

scatter plot

line plot

plot

box-and-whisker plot

Ε, ~, Η, ||, ∞,

**Process Standards
**The following process standards are essential to mastering each of the
mathematics

content standards. They emphasize critical dimensions of the mathematical proficiency

that all students need.

**M7P1 Students will solve problems (using appropriate technology).**

a. Build new mathematical knowledge through problem solving.

b. Solve problems that arise in mathematics and in other contexts.

c. Apply and adapt a variety of appropriate strategies to solve problems.

d. Monitor and reflect on the process of mathematical problem solving.

**M7P2 Students will reason and evaluate mathematical arguments.**

a. Recognize reasoning and proof as fundamental aspects of mathematics.

b. Make and investigate mathematical conjectures.

c. Develop and evaluate mathematical arguments and proofs.

d. Select and use various types of reasoning and methods of proof.

**M7P3 Students will communicate mathematically.**

a. Organize and consolidate their mathematical thinking through communication.

b. Communicate their mathematical thinking coherently and clearly to peers,

teachers, and others.

c. Analyze and evaluate the mathematical thinking and strategies of others.

d. Use the language of mathematics to express mathematical ideas precisely.

**M7P4 Students will make connections among mathematical ideas and to other**

disciplines.

a. Recognize and use connections among mathematical ideas.

disciplines.

b. Understand how mathematical ideas interconnect and build on one another to

produce a coherent whole.

c. Recognize and apply mathematics in contexts outside of mathematics.

**M7P5 Students will represent mathematics in multiple ways.**

a. Create and use representations to organize, record, and communicate mathematical

ideas.

b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical

phenomena.

**Reading Across the Curriculum
**Reading Standard Comment

After the elementary years, students are seriously engaged in reading for learning.

This process sweeps across all disciplinary domains, extending even to the area of

personal learning. Students encounter a variety of informational as well as fictional

texts, and they experience text in all genres and modes of discourse. In the study

of various disciplines of learning (language arts, mathematics, science, social studies),

students must learn through reading the communities of discourse of each of those

disciplines. Each subject has its own specific vocabulary; and for students to excel

in all subjects, they must learn the specific vocabulary of those subject areas in context.

Beginning in the middle grades, students start to self-select reading materials

based on personal interests established through classroom learning. Students

become curious about science, mathematics, history, and literature as they form

contexts for those subjects related to their personal and classroom experiences. As

students explore academic areas through reading, they develop favorite subjects

and become confident in their verbal discourse about those subjects.

Reading across curriculum content develops both academic and personal interests

in students. As students read, they develop both content and contextual vocabulary.

They also build good habits for reading, researching, and learning. The Reading

Across the Curriculum standard focuses on the academic and personal skills students

acquire as they read in all areas of learning.

**M7RC1 Students will enhance reading in all curriculum areas by:**

a. Reading in All Curriculum Areas

• Read a minimum of 25 grade-level appropriate books per year from a variety

of subject disciplines and participate in discussions related to curricular

learning in all areas.

• Read both informational and fictional texts in a variety of genres and modes

of discourse.

• Read technical texts related to various subject areas.

b. Discussing books.

• Discuss messages and themes from books in all subject areas.

• Respond to a variety of texts in multiple modes of discourse.

• Relate messages and themes from one subject area to messages and themes in

another area.

• Evaluate the merit of texts in every subject discipline.

• Examine author’s purpose in writing.

• Recognize the features of disciplinary texts.

c. Building vocabulary knowledge

• Demonstrate an understanding of contextual vocabulary in various subjects.

• Use content vocabulary in writing and speaking.

• Explore understanding of new words found in subject area texts.

d. Establishing context

• Explore life experiences related to subject area content.

• Discuss in both writing and speaking how certain words are subject area related.

• Determine strategies for finding content and contextual meaning for

unknown words.

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