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
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
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
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
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.
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.