Marysville Exempted Village School District
Essential Learning
FOR
GRADE
7
Marysville Exempted Village School District
1000 Edgewood Drive z Marysville, Ohio 43040 z 937-644-8105
Larry Zimmerman, Superintendent
WHAT YOUR CHILDREN WILL BE TAUGHT IN GRADE 7
This guide provides parents with a description of the concepts and skills students will be taught in Language
Arts, Mathematics, Science, and Social Studies during the school year. The program is supportive and nurturing and provides students with numerous opportunities to learn and grow. MEVSD teachers use instructional strategies to excite, motivate and challenge all students. Throughout school, students learn to identify
various sources of information and how to gather, record and organize it. They are introduced to and use
many forms of writing for various purposes and audiences. Each learner uses technology tools as he/she
engages in learning experiences across subject areas. A variety of assessment strategies are used to determine each student’s progress and instructional needs. Your student’s progress report will reflect his or her
learning of these concepts and skills.
ENGLISH LANGUAGE ARTS
•
Monitor own comprehension by adjusting speed to fit the
purpose, or by skimming, scanning, reading on, looking back,
note taking or summarizing what has been read so far in text.
•
Use criteria to choose independent reading materials (e.g.,
personal interest, knowledge of authors and genres or recommendations from others).
•
Independently read books for various purposes (e.g., for enjoyment, for literary experience, to gain information or to perform a task).
Acquisition of Vocabulary
Being able to recognize clues in reading, ask
questions, listen and converse with adults and
peers.
•
Define the meaning of unknown words
through context clues and the author’s use of comparison,
contrast, definition, restatement and example.
•
Apply knowledge of connotation and denotation to
mine the meaning of words.
•
Infer word meanings through the identification of analogies
and other word relationships, including synonyms and antonyms.
•
Interpret metaphors and similes to understand new uses of
words and phrases in text.
•
Recognize and use words from other languages that have
been adopted into the English language.
•
Use knowledge of Greek, Latin and Anglo-Saxon roots and
affixes to understand vocabulary.
•
Use knowledge of symbols and acronyms to identify whole
words.
•
Determine the meanings and pronunciations of unknown
words by using dictionaries, thesauruses, glossaries, technology and textual features, such as definitional footnotes or
sidebars.
deter-
Reading Process: Concepts of Print, Comprehension
Through
Strategies and Self-Monitoring Strategies
reading, students will understand the basic concepts and meanings of different types of print materials.
Reading Applications: Informational, Technical and
Reading,
Persuasive Text
understanding, explaining and critiquing different kinds of written
materials such as magazines, essays, maps and online sites.
•
Use text features, such as chapter titles, headings and subheadings; parts of books, including index, appendix, table of
contents and online tools (search engines) to locate information.
•
Analyze examples of cause and effect and fact and opinion.
•
Compare and contrast different sources of information, including books, magazines, newspapers and online resources, to
draw conclusions about a topic.
•
Compare original text to a summary to determine the extent
to which the summary adequately reflects the main ideas,
critical details and underlying meaning of the original text.
•
Analyze information found in maps, charts, tables, graphs,
diagrams, cutaways and overlays.
•
Assess the adequacy, accuracy and appropriateness of an
author's details, identifying persuasive techniques and examples of bias and stereotyping.
•
Identify an author's purpose for writing and explain an author's argument, perspective or viewpoint in text.
Compare the treatment, scope and organization of ideas from
different texts on the same topic.
•
Establish and adjust purposes for reading, including to find
out, to understand, to interpret, to enjoy and to solve problems.
•
Predict or hypothesize as appropriate from information in the
text, substantiating with specific references to textual examples that may be in widely separated sections of text.
•
•
Make critical comparisons across text, noting author’s style as
well as literal and implied content of text.
Reading Applications: Literary Text
•
Summarize the information in texts, using key ideas, supporting details and referencing gaps or
contradictions.
•
Select, create and use graphic organizers to interpret textual
information.
•
Answer literal, inferential, evaluative and synthesizing questions to demonstrate comprehension of grade-appropriate
print texts and electronic and visual media.
Organizing and interpreting results through collecting data to answer
questions and solve problems, show relationships and make predictions about different types of literature (e.g., fables, tales, short
stories).
MEVSD Essential Learning—Grade 7
•
Explain interactions and conflicts (e.g., character vs. self, nature
or society) between main and minor characters in literary text
and how the interactions affect the plot.
•
Write narratives that maintain a clear focus and point of view
and use sensory details and dialogue to develop plot, character
and a specific setting.
•
Analyze the features of the setting and their importance in a
text.
•
•
Identify the main and minor events of the plot, and
how each incident gives rise to the next.
Write responses to novels, stories, poems and plays that provide an interpretation, a critique or a reflection and support judgments with specific references to the text.
•
•
Identify and compare subjective and objective points of view and
how they affect the overall body of a work.
Write business letters that are formatted to convey ideas, state
problems, make requests or give compliments.
•
•
Identify recurring themes, patterns and symbols found in
ture from different eras and cultures.
•
Write informational essays or reports, including research, that
present a literal understanding of the topic, include specific
facts, details and examples from multiple sources, and create an
organizing structure appropriate to the purpose, audience and
context.
Explain the defining characteristics of literary forms and genres, including poetry, drama, myths, biographies,
autobiographies, science fiction, fiction and non-fiction.
•
Write persuasive essays that establish a clear position and include relevant information to support ideas.
•
Interpret how mood or meaning is conveyed through word
choice, figurative language and syntax.
•
Produce informal writings (e.g., journals, notes and poems) for
various purposes.
explain
litera-
Writing Processes
Writing Conventions
•
Generate writing ideas through discussions with others and from
printed material, and keep a list of writing ideas.
•
Spell high-frequency words correctly.
•
Conduct background reading, interviews or surveys when appropriate.
•
Use commas, end marks, apostrophes and quotation marks
correctly.
•
Establish a thesis statement for informational writing or a plan
for narrative writing.
•
Use semicolons, colons, hyphens, dashes and brackets
correctly.
•
Determine a purpose and audience.
•
Use correct capitalization.
•
Use organizational strategies (e.g., rough outlines,
diagrams, maps, webs and Venn diagrams) to plan writing.
•
Use all eight parts of speech (e.g., noun, pronoun, verb, adverb,
adjective, conjunction, preposition, interjection).
•
Organize writing with an effective and engaging
introduction, body and a conclusion that summarizes, extends or
elaborates on points or ideas in the writing.
•
Use dependent and independent clauses.
•
Use subject-verb agreement with collective nouns,
indefinite
pronouns, compound subjects and prepositional phrases.
•
Vary simple, compound and complex sentence structures.
•
Conjugate regular and irregular verbs in all tenses
•
Group related ideas into paragraphs, including topic sentences following paragraph form, and maintain a consistent
focus across paragraphs.
Research
•
Use precise language, action verbs, sensory details, colorful
modifiers and style as appropriate to audience and purpose.
•
•
Use available technology to compose text.
Generate a topic, assigned or personal interest, and openended questions for research and develop a plan for gathering
information.
•
Reread and analyze clarity of writing.
•
•
Add and delete information and details to better elaborate on a
stated central idea and to more effectively accomplish purpose.
Select an appropriate structure for organizing information in a
systematic way (e.g., notes, outlines, charts, tables and graphic
organizers).
•
•
Rearrange words, sentences and paragraphs, and add
transitional words and phrases to clarify meaning.
Analyze and organize important information, and select
appropriate sources to support central ideas, concepts and
themes.
•
Use resources and reference materials (e.g., dictionaries and
thesauruses) to select more effective vocabulary.
•
Integrate quotations and citations into written text to maintain a
flow of ideas.
•
Proofread writing, edit to improve conventions (e.g., grammar,
spelling, punctuation and capitalization) and identify and correct
fragments and run-ons.
•
Use an appropriate form of documentation, with teacher assistance, to acknowledge sources (e.g., bibliography, works
cited).
•
Apply tools (e.g., rubric, checklist and feedback) to judge the
quality of writing.
•
Use a variety of communication techniques, including oral,
visual, written or multimedia reports, to present
information
that supports a clear position with organized and relevant evidence about the topic or research
question.
Using the steps of prewriting, drafting, revising and editing to publish different types of writing.
Writing Applications
Understanding and applying punctuation, grammar and spelling
rules.
correctly.
Knowing
how to gather information in all subjects using
different kinds of
tools (e.g., books, computers, magazines) and communicate what is
found.
Learning about, using and choosing appropriate words for different
kinds of writing, from letters to scientific reports, and for different
audiences.
MEVSD Essential Learning—Grade 7
•
•
Identify appropriate sources and gather relevant
information from multiple sources (e.g., school library catalogs, online
databases, electronic resources and Internetbased
resources).
Identify and explain the importance of validity in sources, including publication date,
coverage, language, points of view, and
describe primary and secondary sources.
Communication: Oral and Visual
Delivering presentations on different topics for different types of
audiences.
•
Demonstrate an understanding of place value using powers of 10
and write large numbers in scientific notation.
•
Explain the meaning of exponents that are negative or 0.
•
Describe differences between rational and irrational numbers;
e.g., use technology to show that some numbers (rational) can be
expressed as terminating or repeating decimals and others
(irrational) as non-terminating and non-repeating decimals.
•
Use order of operations and properties to simplify
numerical
expressions involving integers, fractions and decimals.
•
Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can
result in a lesser value.
•
Demonstrate active listening strategies (e.g., asking focused
questions, responding to cues, making visual contact).
•
Draw logical inferences from presentations and visual media.
•
•
Simplify numerical expressions involving integers and use integers to solve real-life problems.
Interpret the speaker’s purpose in presentations and visual
media (e.g., to inform, to entertain, to persuade).
•
•
Solve problems using the appropriate form of a rational number
(fraction, decimal or percent).
Identify and explain the persuasive techniques (e.g., bandwagon, testimonial, glittering generalities, emotional word repetition and bait and switch) used in presentations and media
messages.
•
Develop and analyze algorithms for computing with percents and
integers, and demonstrate fluency in their use.
•
Demonstrate an understanding of the rules of the English language and select language appropriate to purpose and audience.
•
Represent and solve problem situations that can be modeled
by and solved using concepts of absolute value, exponents and
square roots (for perfect squares).
•
Adjust volume, phrasing, enunciation, voice modulation and
inflection to stress important ideas and impact
audience
response.
•
Vary language choices as appropriate to the context of the
speech.
•
Deliver informational presentations (e.g., expository, research)
that: demonstrate an understanding of the topic and present
events or ideas in a logical sequence; support the controlling
idea or thesis with well-chosen and relevant facts, details,
examples, quotations,
statistics, stories and anecdotes;
include an effective introduction and conclusion and use a
consistent
organizational structure (e.g., cause-effect,
compare-contrast, problem-solution); use appropriate visual
materials (e.g., diagrams, charts, illustrations) and available
technology; and draw from multiple sources and identify
sources used.
•
Deliver formal and informal descriptive presentations that convey relevant information and descriptive details.
•
Deliver persuasive presentations that: establish a clear position; include relevant evidence to support a position and to
address counter-arguments; and consistently use common
organizational structures as appropriate (e.g., cause-effect,
compare-contrast).
MATHEMATICS
Measurement
Making accurate measurements using the appropriate tools, terms and
technology.
•
Select appropriate units for measuring derived
ments; e.g., miles per hour, revolutions per minute.
•
Convert units of area and volume within the same
measurement system using proportional reasoning and a reference table
when appropriate; e.g., square feet to square yards, cubic meters
to cubic centimeters.
•
Estimate a measurement to a greater degree of precision than
the tool provides.
•
Solve problems involving proportional relationships and scale
factors; e.g., scale models that require unit
conversions
within the same measurement system.
•
Analyze problem situations involving measurement
concepts,
select appropriate strategies, and use an
organized approach to solve narrative and increasingly complex problems.
•
Use strategies to develop formulas for finding area of trapezoids
and volume of cylinders and prisms.
•
Develop strategies to find the area of composite shapes using the
areas of triangles, parallelograms, circles and sectors.
•
Understand the difference between surface area and volume and
demonstrate that two objects may have the same surface area,
but different volumes or may have the same volume, but different
surface areas.
•
Describe what happens to the surface area and volume of a
three-dimensional object when the measurements of the object
are changed; e.g., length of sides are doubled.
Number Sense and Operations
Using number sense and number skills, from basic counting to paper and pencil calculations, to age-appropriate use of
calculators and computers.
MEVSD Essential Learning—Grade 7
measure-
• Analyze linear and simple nonlinear relationships to explain how a
Geometry and Spatial Sense
Identifying, classifying and analyzing one-, two– and
three-dimensional objects,
understanding their
properties and using that knowledge to solve problems.
•
•
change in one variable results in the change of another.
• Use graphing calculators or computers to analyze change; e.g.,
distance-time relationships.
Use proportional reasoning to describe and
express relationships between parts and attributes of similar and congruent figures.
Data Analysis and Probability
Determine sufficient (not necessarily minimal)
properties that define a specific two-dimensional
figure or three-dimensional object. For example: Determine
when one set of figures is a subset of another; e.g., all squares
are rectangles. Develop a set of properties that eliminates all
but the desired figure; e.g., only squares are
quadrilaterals with all sides congruent and all angles congruent.
Organizing and interpreting results through data collection to
answer questions, solve problems, show relationships and make predictions.
•
Read, create and interpret box-and-whisker plots, stem-and-leaf
plots, and other types of graphs, when appropriate.
•
Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of
categories in a circle graph.
•
Use and demonstrate understanding of the properties of triangles. For example: Use Pythagorean Theorem to solve problems involving right triangles. Use triangle angle sum relationships to solve problems.
•
Analyze a set of data by using and comparing combinations of
measures of center (mean, mode, median) and measures of
spread (range, quartile, interquartile range), and describe how the
inclusion or exclusion of outliers affects those measures.
•
Determine necessary conditions for congruence of
•
•
Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures.
Construct opposing arguments based on analysis of the same
data, using different graphical representations.
•
•
Determine and use scale factors for similar figures to solve problems using proportional reasoning.
Compare data from two or more samples to determine how sample
selection can influence results.
•
•
Identify the line and rotation symmetries of two-dimensional
figures to solve problems.
Identify misuses of statistical data in articles, advertisements, and
other media.
•
•
Perform translations, reflections, rotations and dilations of twodimensional figures using a variety of methods (paper folding,
tracing, graph paper).
Compute probabilities of compound events; e.g., multiple coin
tosses or multiple rolls of number cubes, using such methods as
organized lists, tree diagrams and area models.
•
•
Draw representations of three-dimensional geometric objects
from different views.
Make predictions based on theoretical probabilities, design and
conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences.
triangles.
Patterns, Functions and Algebra
Representing patterns and relationships using tables, graph and symbols, and using them to solve problems.
• Represent and analyze patterns, rules and functions with words,
tables, graphs and simple variable expressions.
Mathematical Processes
Applying problem-solving and reasoning skills and communicating
mathematical ideas.
• Represent problem situations using a variety of formats and justify
the validity of the solution.
•
• Generalize patterns by describing in words how to find the next
term.
• Recognize and explain when numerical patterns are linear or
nonlinear progressions; e.g., 1,3,5,7... is linear and 1,3,4,8,16... is
nonlinear.
• Create visual representations of equation-solving processes that
model the use of inverse operations.
Communicate mathematical thinking using mathematical language
and symbols.
SCIENCE
Earth and Space
Understanding the interconnected cycles and systems of the universe,
solar system and Earth.
• Explain the biogeochemical cycles which move materials between
the lithosphere (land), hydrosphere (water) and atmosphere (air).
•
Explain that Earth's capacity to absorb and recycle
materials naturally (e.g., smoke, smog and
sewage) can change the environmental
quality depending on the length of time
involved (e.g. global warming).
• Justify that two forms of an algebraic expression are equivalent,
•
Describe the water cycle and explain the
transfer of energy between the atmosphere and
hydrosphere.
• Use formulas in problem-solving situations.
•
Analyze data on the availability of fresh water that is
essential
for life and for most industrial and agricultural processes. Describe
how rivers, lakes and groundwater can be depleted or polluted
becoming less hospitable to life and even becoming unavailable or
unsuitable for life.
•
Make simple weather predictions based on the changing cloud
types associated with frontal systems.
• Represent linear equations by plotting points in the
nate plane.
coordi-
• Represent inequalities on a number line or a coordinate plane.
and recognize when an expression is simplified; e.g., 4m = m + m
+ m + m or a · 5 + 4 = 5a + 4.
• Recognize a variety of uses for variables; e.g., placeholder
for an unknown quantity in an equation, generalization for a pattern, formula.
MEVSD Essential Learning—Grade 7
•
Determine how weather observations and measurements are
combined to produce weather maps and that data for a specific
location at one point in time can be displayed in a station
model.
•
Read a weather map to interpret local, regional and national
weather.
•
Describe how temperature and precipitation determine climatic
zones (biomes) (e.g., desert, grasslands, forests, tundra and
alpine).
•
Describe the connection between the water cycle and weatherrelated phenomenon (e.g., tornadoes, floods, droughts and
hurricanes).
Science and Technology
Understanding the relationship between science and technology to
design and construct devices to solve problems.
•
Explain how needs, attitudes and values influence the
of technological development in various cultures.
•
Describe how decisions to develop and use technologies often
put environmental and economic concerns in direct competition
with each other.
•
Recognize that science can only answer some questions and
technology can only solve some human problems.
•
Design and build a product or create a solution to a problem
given two constraints (e.g., limits of cost and time for design
and production or supply of materials and
environmental
effects).
Life Sciences
Understanding the structure and function of living systems and how
they interact with the environment.
Scientific Inquiry
direction
•
Investigate the great variety of body plans and internal structures found in multicellular organisms.
•
Investigate how organisms or populations may interact with
one another through symbiotic relationships and how some
species have become so adapted to each other that neither
could survive without the other (e.g., predator-prey, parasitism,
mutualism and commensalism).
•
Explain that variables and controls can affect the results of an
investigation and that ideally one variable should be tested at a
time; however it is not always possible to control all variables.
•
Identify simple independent and dependent variables.
•
Explain how the number of organisms an ecosystem can support depends on adequate biotic (living) resources (e.g., plants,
animals) and abiotic (non-living) resources (e.g., light, water
and soil).
•
Formulate and identify questions to guide scientific
investigations that connect to science concepts and can be answered
through scientific investigations.
•
Investigate how overpopulation impacts an ecosystem.
•
Choose the appropriate tools and instruments and use relevant
safety procedures to complete scientific
investigations.
•
Explain that some environmental changes occur slowly while
others occur rapidly (e.g., forest and pond
succession,
fires and decomposition).
•
Analyze alternative scientific explanations and predictions and
recognize that there may be more than one good way to interpret
a given set of data.
•
Summarize the ways that natural occurrences and human
activity affect the transfer of energy in Earth's
ecosystems (e.g., fire, hurricanes, roads and oil spills).
•
Identify faulty reasoning and statements that go beyond the evidence or misinterpret the evidence.
•
Explain that photosynthetic cells convert solar energy into
chemical energy that is used to carry on life
functions or is
transferred to consumers and used to carry on their life functions.
Investigate the great diversity among organisms.
•
Use graphs, tables and charts to study physical phenomena and
infer mathematical relationships between variables (e.g., speed
and density).
•
Physical Sciences
Understanding physical systems, concepts and properties of matter,
energy, forces and motion.
•
Investigate how matter can change forms but the total amount
of matter remains constant.
•
Describe how an object can have potential energy due to its
position or chemical composition and can have kinetic energy
due to its motion.
•
Identify different forms of energy (e.g., electrical,
mechanical, chemical, thermal, nuclear, radiant and acoustic).
•
Explain how energy can change forms but the total amount of
energy remains constant.
•
Trace energy transformation in a simple closed system (e.g., a
flashlight).
Using scientific processes to ask questions, conduct
tions, gather, analyze and communicate information.
investiga-
Scientific Ways of Knowing
Understanding the relationship between science and technology to
design and construct devices to solve problems.
•
Show that the reproducibility of results is essential to
bias in scientific investigations.
•
Describe how repetition of an experiment may reduce bias.
•
Describe how the work of science requires a variety of human
abilities and qualities that are helpful in daily life (e.g., reasoning,
creativity, skepticism and openness).
MEVSD Essential Learning—Grade 7
reduce
SOCIAL STUDIES
History
Understanding the pattern of events that have happened in the past.
•
Group events by broadly defined historical eras and enter onto
multiple-tier time lines.
•
Describe the enduring impact of early civilizations in India,
China, Egypt, Greece and Rome after 1000 B.C. including: The
development of concepts of government and citizenship; Scientific and cultural advancements; The spread of
religions; Slavery and systems of labor.
•
Describe the conditions that gave rise to
feudalism, as well as political, economic and
social characteristics of
feudalism, in Asia
and Europe.
•
Explain the lasting effects of military conquests during the Middle
Ages including: Muslim conquests; The Crusades; The Mongol
invasions.
•
Describe the impact of new ideas and institutions on European
life including: The significance of printing with movable type;
Major achievements in art, architecture and literature during the
Renaissance; The Reformation.
•
Describe the importance of the West African empires of Ghana,
Mali and Songhay including: Trade routes; Products; The
spread of the Arabic language; The spread of Islam.
•
Describe the causes and effects of European exploration after
1400 including: Imperialism, colonialism and
mercantilism;
Impact on the peoples of sub-Saharan Africa, Asia and the
Americas.
People in Societies
Identifying both similarities and differences in the traditions of various
groups of people.
•
Use physical and historical maps to analyze the reasons that human features are located in particular places.
•
Describe the geographic factors and processes that
contribute to and impede the diffusion of people, products and ideas from
place to place including: Physical features; Culture; War; Trade;
Technological innovations.
Economics
Understanding how to make decisions in our economic system.
•
Compare the endowment of productive resources in world regions
and explain how this endowment contributed to specialization,
trade and interdependence in ancient times.
•
Describe the growth of cities and the establishment of trade routes
in Asia, Africa and Europe; the products and inventions that traveled along these routes (e.g., spices, textiles, paper, precious metals and new crops); and the role of merchants.
Government
Understanding why government is necessary and how it works.
•
Compare direct and representative democracy using
examples of ancient Athens, the Roman republic
and the United States today.
•
Describe the essential characteristics of the systems
of government found in city-states, kingdoms and
empires from ancient times through the Middle Ages.
Citizenship Rights & Responsibilities
Preparing to become active citizens.
•
Explain how the participation of citizens differs under
direct democracy and representative democracy.
•
Describe the rights found in the Magna Carta and show
tions to rights Americans have today.
monarchy,
connec-
•
Analyze the relationships among cultural practices,
and perspectives of early civilizations.
•
Explain how the Silk Road trade and the Crusades affected the
cultures of the people involved.
Skills & Methods
•
Give examples of contacts among different cultures that led to
the changes in belief systems, art, science, technology, language or systems of government.
•
•
Describe historical events and issues from the perspectives of
people living at the time in order to avoid evaluating the past in
terms of today's norms and values.
Describe the cultural and scientific legacies of African, Greek,
Roman, Chinese, Arab and European civilizations.
•
Compare multiple viewpoints and frames of reference related to
important events in world history.
•
Establish guidelines, rules and time lines for group work.
•
Reflect on the performance of a classroom group in which one has
participated including the contribution of each member in reaching
group goals.
products
Geography
Identifying the location of places, understanding how places are connected and how human activity affects them.
•
For each of the societies studied, identify the location of significant physical and human characteristics on a map of the
relevant region.
•
On a map, identify places related to the historical
events being studied and explain their significance.
•
Describe changes in the physical and human characteristics of regions that occur over time and identify the
consequences of such changes.
Collecting information, organizing it and using it to make
decisions.
For More Information View
“A Standards Guide for Families”
At The
Ohio Department of Education
Website
www.OhioAcademicStandards.com
MEVSD Essential Learning—Grade 7
MATH VOCABULARY
Absolute Value the distance a number or variable is away from zero
Algebraic Expressions a combination of variables, numbers and at least one operation.
Algorithm a step by step problem solving procedure
Box and Whisker Plots a diagram that summarizes data using the median, upper and lower quartiles, and the
extreme values. A box is drawn around the quartile value and whiskers extend from each quartile to the extreme
data points.
Coefficient a number or quantity placed before multiplying another quantity. The number “a” in the expressions ax
is a coefficient.
Computations add, subtract, multiply, etc . . .
Congruent Figures figures that have the same size and shape.
Conjecture a statement proposing that some observed characteristic might be true in all cases. Further testing
and observation may validate or disprove the conjecture. (Also called supposition or hypothesis)
Continuous Data numbers between any two numbers that have meaning.
Convex Polygons a polygon that has a surface or boundary that curves or bulges outward, as the exterior of a
sphere.
Coordinate Plane a plane in which a horizontal number line (x-axis) intersects a vertical number line (y-axis).
Every point in the plane can be named by an (x , y) ordered pair.
Covariants varying in accordance with a fixed mathematical relationship
Dilation the process of reducing or enlarging an image in mathematics.
Dilations a proportional shrinking or enlargement of a figure.
Direct Variation a function that can be described by an equation y = kx where k is a nonzero constant.
Discrete Data some numbers between given numbers do not have meaning, defined only for an isolated set of
points.
Disjoint Sets two or more sets that have no common elements
Graphical Representation representing a set of data in the form of a graph.
Histogram a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.
Inequality a mathematical sentence that contains a less than, greater than, less than or equal to, greater than or
equal to, or not equal to symbol.
Integers All whole numbers and their opposites. …… -4,-3,-2,-1,0,1,2,3,4 ….
Interquartile Range the range of the middle half of a set of numbers.
Inverse Operation the operation that will undo another operation. Subtraction is the inverse operation of addition.
Multiplication is the inverse operation of division.
Inverse Variation two variables (x and y) vary inversely if y=k/x or xy = k, and k ≠ o. y is also said to be inversely
proportional to x. k is a constant. If one object increases at the same rate as another object decreases, the objects
are inversely proportional.
Irrational Numbers Is a nonrational number
Line of Symmetry a line that divides a figure into two halves that are reflections of each other.
Linear Functions on a rectangular graph, equations whose variables have no exponents other than one, and
where the variables are not multiplied or divided together. EX: y = x + 2, 2x – 3y = 5 or y = 5.
Mean the sum of the numbers in a set of data divided by the number of pieces of data.
Median the middle number in a set of data when the data are arranged in numerical order. If the data has an
even number, the median is the mean of the two middle numbers,
Mode the number or item that appears the most often in a set of data.
Monomials an expression that is the product of numerals and variables
Natural Numbers 1,2,3,4,5,6,7 ….
Nets a 2-dimensional shape that can be folded into a 3-dimensional figure is a net of that figure.
Nonlinear Functions these functions don’t have real numbers that exist for b and m such that every x in the domain of F, F(x) = mx + b
Numerical Expressions a mathematical expression that has a combination of numbers and at least one operation. 4 + 2 is a numerical expression.
Polynomials a monomial or a sum of monomials
Prisms a three-dimensional figure that has two parallel and congruent bases in the shape of polygons.
Probabilities the chance that some event will happen. It is the ratio of the number of ways a certain event can
occur to the number of possible outcomes.
Proportion, Proportional Reasoning (Relationships) an equation that shows two ratios (a comparison of 2 #’s)
are equivalent (equal)
Pyramids a solid figure that has a polygon for a base and triangles for sides.
Pythagorean Theorem describes the relationship between the legs and the hypotenuse of a right triangle. a2 + b2 = c2
Quadratic Equations an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers
and a = 0.
Quadrilateral a polygon that has four sides.
Quartile one of four equal parts of data from a large set of numbers.
Radicals square roots
Range the difference between the greatest number and the least number in a set of data.
Rational Numbers Any number that can be written as a ratio of two integers
Real Numbers the set of rational numbers together with the set of irrational numbers
Reflection A type of transformation where a figure is flipped over a line of symmetry.
Reflections the image created by flipping a point or set of points over a line to a new position on the opposite side of
the line, as if looking in a mirror. see also: transformation.
Regular Convex Polygons polygons with all sides equal and no interior angles greater then 180.
Rotation when a figure is turned around a central point.
Rotational Symmetry a figure has rotational symmetry if it can be turned less than 360 degrees and look exactly like
the original.
Scale Factors the ratio of a dilated image to the original image.
Scatterplots a graph consisting of points, one for each item being measured. The two coordinates of a point represent
the measures of two attributes of each item.
Scientific Notation a way of expressing numbers as the product of a number that is at least 1 but less than 10 and a
power of 10 to a power. In scientific, 5,500 is 5.5 X 10 to the third power.
Slope the rate at which a line rises or falls per horizontal unit. The slope of a non-vertical line is expressed in terms of
coordinates of any two points, (x , y ) and (x , y ): A number that tells how steeply a line slants: the ratio of rise to run.
Stem and Leaf Plots a system used to condense a set of data where the greatest place value of the data forms the
stem and the next greatest place value forms the leaves.
Systems of Linear Equations two or more equations that share a common solution.
Theoretical Probabilities the ratio of the number of ways an event can occur to the number of possible outcomes.
Translation one type of transformation where a figure is slid horizontally, vertically, or both.
Translations (of geometric figures: of vectors) in geometry this is a composite of two reflections over two parallel
lines, also called a slide. With vectors, this means each component of the vector has the same component added to it,
sliding the vector to a new position parallel to the original vector.
Transversal in a plane, a line that intersects two other lines in two different points.
Tree Diagrams a diagram used to show the total number of possible outcomes in a probability experiment.
Validate a Solution the process of checking the correctness, reasonableness, and appropriateness of answers to a
problem situation.
Vertex (plural vertices)the common endpoint of two rays in an angle, of two line segments in a polygon, or three or
more angles or edges in a space figure.
Whole Numbers 0,1,2,3,4,5,6 …..
Y-Intercept the y-coordinate of the point where a graph intersects the y-axis
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