Middle School

Information Technology 6 Syllabus

Information Technology 7 Syllabus

Information Technology 8 Syllabus

**CHRISTIAN LIVING**

**Course Overview**

**Christian Living **

Students will have an overview of the Bible. Books in the Old Testament will be introduced in the context of its historical significance and theological connection with the New Testament. The Gospels are central resources to acquire basic knowledge of the person and teachings of Jesus Christ. This year’s studies put a greater emphasis on morality which is founded on the greatest commandments of Jesus Christ- Love of God and Love of neighbor. The Faith community, which is the Catholic Church, is introduced as a venue where growth in human values as well as theological virtues can be realized, challenging students to benefit from the sacraments and share in the mission of Evangelization. Grade 6 Christian Living aims to inspire students to cultivate friendship and commitment with the person of Jesus Christ and become a responsible member of both the society and the Christian community.

**Language Arts **

English instruction, in sixth grade, emphasizes the importance of communication through the written word, building vocabulary skills and increasing reading comprehension. Middle School students will be introduced to a broad range of literary genres in order to encourage enjoyment of reading and to develop skills in critical thinking. We will read and discuss classical literature, poetry, short stories, novels, plays, fiction, and nonfiction by authors from a variety of cultures. Frequent writing assignments are bolstered by ongoing concentration on grammar and vocabulary skills.

**Mathematics **

This course is designed to give all students a solid foundation for exploring and understanding algebra and geometry concepts. This helps students to reason and communicate with each other about skills and ideas in mathematics leading to conceptual and computational development. Major themes and concepts in this course include place- value systems, applications of decimals, percents, fractions, ratios and proportions, geometry, integers and the coordinate plane and equations and probability.

In the context of the themes developed, students accomplish projects that would bring out the application of the concepts and make valid and meaningful correlations to the classroom learning.

**Science **

This course covers a broad spectrum of science concepts. The first part of the year will focus on life science. Students will learn about the classification system that scientists use to study the diverse forms of life on Earth. Eubacteria, archaebacteria, plants, protists, and fungi are kingdoms studied in detail. A brief unit on the relationships and interactions between these diverse life forms & ecosystems is introduced later. Students will, then, learn about rocks and minerals, earthquakes, physical geography, as well as natural processes such as erosion and weathering. Students will also explore properties and changes of matter. The content all throughout provides basis for variety of projects and investigations.

**Social Studies **

This course covers the rise of civilizations to modern age. The rise of civilizations contains studies about the early human life, Mesopotamia, Egypt, India, China, ancient Americas, and Africa. Later, it focuses on the spread of civilization studying Greece, Rome, Byzantium, Islam, cultural change in Africa, and East Asia. Next, the studies cover the Medieval Europe, the Renaissance, cultural centers such the Ming Dynasty and the age of Revolutions. Finally, it touches on the modern era in Europe, Africa, Asia, Australia, Central and South America, North America, and the Caribbean. Activities in this course are built around movies, related stories and songs, research projects, and written reports.

**Reading: Literature – Middle School (6,7,8)**

**Key Ideas and Details**

- ELA-Literacy.RL.6.1Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
- ELA-Literacy.RL.6.2Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
- ELA-Literacy.RL.6.3Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.

**Craft and Structure**

- ELA-Literacy.RL.6.4Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of a specific word choice on meaning and tone
- ELA-Literacy.RL.6.5Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, or plot.
- ELA-Literacy.RL.6.6Explain how an author develops the point of view of the narrator or speaker in a text.

**Integration of Knowledge and Ideas**

- ELA-Literacy.RL.6.7Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they “see” and “hear” when reading the text to what they perceive when they listen or watch.
- (RL.6.8 not applicable to literature)
- ELA-Literacy.RL.6.9Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics.

**Range of Reading and Level of Text Complexity**

- ELA-Literacy.RL.6.10By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.

**Reading: Informational Text – Middle School (6,7,8)**

**Key Ideas and Details**

- ELA-Literacy.RI.6.1Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
- ELA-Literacy.RI.6.2Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments.
- ELA-Literacy.RI.6.3Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes).

**Craft and Structure**

- ELA-Literacy.RI.6.4Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
- ELA-Literacy.RI.6.5Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas.
- ELA-Literacy.RI.6.6Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text.

**Integration of Knowledge and Ideas**

- ELA-Literacy.RI.6.7Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.
- ELA-Literacy.RI.6.8Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not.
- ELA-Literacy.RI.6.9Compare and contrast one author’s presentation of events with that of another (e.g., a memoir written by and a biography on the same person).

**Range of Reading and Level of Text Complexity**

- ELA-Literacy.RI.6.10By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range.

**Writing – Middle School (6,7,8)**

**Text Types and Purposes**

- ELA-Literacy.W.6.1Write arguments to support claims with clear reasons and relevant evidence.
- ELA-Literacy.W.6.1aIntroduce claim(s) and organize the reasons and evidence clearly.
- ELA-Literacy.W.6.1bSupport claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text.
- ELA-Literacy.W.6.1cUse words, phrases, and clauses to clarify the relationships among claim(s) and reasons.
- ELA-Literacy.W.6.1dEstablish and maintain a formal style.
- ELA-Literacy.W.6.1eProvide a concluding statement or section that follows from the argument presented.

- ELA-Literacy.W.6.2Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.
- ELA-Literacy.W.6.2aIntroduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.
- ELA-Literacy.W.6.2bDevelop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.
- ELA-Literacy.W.6.2cUse appropriate transitions to clarify the relationships among ideas and concepts.
- ELA-Literacy.W.6.2dUse precise language and domain-specific vocabulary to inform about or explain the topic.
- ELA-Literacy.W.6.2eEstablish and maintain a formal style.
- ELA-Literacy.W.6.2fProvide a concluding statement or section that follows from the information or explanation presented.

- ELA-Literacy.W.6.3Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.
- ELA-Literacy.W.6.3aEngage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.
- ELA-Literacy.W.6.3bUse narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.
- ELA-Literacy.W.6.3cUse a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.
- ELA-Literacy.W.6.3dUse precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events.
- ELA-Literacy.W.6.3eProvide a conclusion that follows from the narrated experiences or events.

**Production and Distribution of Writing**

- ELA-Literacy.W.6.4Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.)
- ELA-Literacy.W.6.5With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grade 6here.)
- ELA-Literacy.W.6.6Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting.

**Research to Build and Present Knowledge**

- ELA-Literacy.W.6.7Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.
- ELA-Literacy.W.6.8Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources.
- ELA-Literacy.W.6.9Draw evidence from literary or informational texts to support analysis, reflection, and research.
- ELA-Literacy.W.6.9aApply
*grade 6 Reading standards*to literature (e.g., “Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories] in terms of their approaches to similar themes and topics”). - ELA-Literacy.W.6.9bApply
*grade 6 Reading standards*to literary nonfiction (e.g., “Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not”).

- ELA-Literacy.W.6.9aApply

**Range of Writing**

- ELA-Literacy.W.6.10Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

**Speaking and Listening – Middle School (6,7,8)**

**Comprehension and Collaboration**

- ELA-Literacy.SL.6.1Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly.
- ELA-Literacy.SL.6.1aCome to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.
- ELA-Literacy.SL.6.1bFollow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed.
- ELA-Literacy.SL.6.1cPose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.
- ELA-Literacy.SL.6.1dReview the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing.

- ELA-Literacy.SL.6.2Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study.
- ELA-Literacy.SL.6.3Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not.

**Presentation of Knowledge and Ideas**

- ELA-Literacy.SL.6.4Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.
- ELA-Literacy.SL.6.5Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information.
- ELA-Literacy.SL.6.6Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 6 Language standards 1 and 3 here for specific expectations.)

**Language –Middle School (6,7,8)**

**Conventions of Standard English**

- ELA-Literacy.L.6.1Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
- ELA-Literacy.L.6.1aEnsure that pronouns are in the proper case (subjective, objective, possessive).
- ELA-Literacy.L.6.1bUse intensive pronouns (e.g.,
*myself, ourselves*). - ELA-Literacy.L.6.1cRecognize and correct inappropriate shifts in pronoun number and person.*
- ELA-Literacy.L.6.1dRecognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).*
- ELA-Literacy.L.6.1eRecognize variations from standard English in their own and others’ writing and speaking, and identify and use strategies to improve expression in conventional language.*

- ELA-Literacy.L.6.2Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
- ELA-Literacy.L.6.2aUse punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.*
- ELA-Literacy.L.6.2bSpell correctly.

**Knowledge of Language**

- ELA-Literacy.L.6.3Use knowledge of language and its conventions when writing, speaking, reading, or listening.
- ELA-Literacy.L.6.3aVary sentence patterns for meaning, reader/listener interest, and style.*
- ELA-Literacy.L.6.3bMaintain consistency in style and tone.*

**Vocabulary Acquisition and Use**

- ELA-Literacy.L.6.4Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.
- ELA-Literacy.L.6.4aUse context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase.
- ELA-Literacy.L.6.4bUse common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g.,
*audience, auditory, audible*). - ELA-Literacy.L.6.4cConsult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.
- ELA-Literacy.L.6.4dVerify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

- ELA-Literacy.L.6.5Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
- ELA-Literacy.L.6.5aInterpret figures of speech (e.g., personification) in context.
- ELA-Literacy.L.6.5bUse the relationship between particular words (e.g., cause/effect, part/whole, item/category) to better understand each of the words.
- ELA-Literacy.L.6.5cDistinguish among the connotations (associations) of words with similar denotations (definitions) (e.g.,
*stingy, scrimping, economical, unwasteful, thrifty*).

- ELA-Literacy.L.6.6Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

**Math: Ratios and Proportional Relationships – Middle School (6,7,8)**

**Understand ratio concepts and use ratio reasoning to solve problems.**

- Math.Content.6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
*For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”* - Math.Content.6.RP.A.2Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
*For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”*^{1} - Math.Content.6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- Math.Content.6.RP.A.3aMake tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
- Math.Content.6.RP.A.3bSolve unit rate problems including those involving unit pricing and constant speed.
*For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?* - Math.Content.6.RP.A.3cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
- Math.Content.6.RP.A.3dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

^{1} Expectations for unit rates in this grade are limited to non-complex fractions.

**Math: The Number System – Middle School (6,7,8)**

**Apply and extend previous understandings of multiplication and division to divide fractions by fractions.**

- Math.Content.6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
*For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?*.

**Compute fluently with multi-digit numbers and find common factors and multiples.**

- Math.Content.6.NS.B.2Fluently divide multi-digit numbers using the standard algorithm.
- Math.Content.6.NS.B.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- Math.Content.6.NS.B.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
*For example, express 36 + 8 as 4 (9 + 2).*.

**Apply and extend previous understandings of numbers to the system of rational numbers.**

- Math.Content.6.NS.C.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
- Math.Content.6.NS.C.6Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
- Math.Content.6.NS.C.6aRecognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
- Math.Content.6.NS.C.6bUnderstand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- Math.Content.6.NS.C.6cFind and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

- Math.Content.6.NS.C.7Understand ordering and absolute value of rational numbers.
- Math.Content.6.NS.C.7aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
*For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right*. - Math.Content.6.NS.C.7bWrite, interpret, and explain statements of order for rational numbers in real-world contexts.
*For example, write –3*.^{o}C > –7^{o}C to express the fact that –3^{o}C is warmer than –7^{o}C - Math.Content.6.NS.C.7cUnderstand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
*For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars*. - Math.Content.6.NS.C.7dDistinguish comparisons of absolute value from statements about order.
*For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars*.

- Math.Content.6.NS.C.7aInterpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
- Math.Content.6.NS.C.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

**Math: Expressions and Equations – Middle School (6,7,8)**

**Apply and extend previous understandings of arithmetic to algebraic expressions.**

- Math.Content.6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.
- Math.Content.6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.
- Math.Content.6.EE.A.2aWrite expressions that record operations with numbers and with letters standing for numbers.
*For example, express the calculation “Subtract y from 5” as 5 – y*. - Math.Content.6.EE.A.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
*For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms*. - Math.Content.6.EE.A.2cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
*For example, use the formulas V = s*.^{3}and A = 6 s^{2}to find the volume and surface area of a cube with sides of length s = 1/2

- Math.Content.6.EE.A.2aWrite expressions that record operations with numbers and with letters standing for numbers.
- Math.Content.6.EE.A.3Apply the properties of operations to generate equivalent expressions.
*For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y*. - Math.Content.6.EE.A.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
*For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*.

**Reason about and solve one-variable equations and inequalities.**

- Math.Content.6.EE.B.5Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
- Math.Content.6.EE.B.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
- Math.Content.6.EE.B.7Solve real-world and mathematical problems by writing and solving equations of the form
*x*+*p*=*q*and*px*=*q*for cases in which*p*,*q*and*x*are all nonnegative rational numbers. - Math.Content.6.EE.B.8Write an inequality of the form
*x*>*c*or*x*<*c*to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form*x*>*c*or*x*< c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

**Represent and analyze quantitative relationships between dependent and independent variables.**

- Math.Content.6.EE.C.9Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

**Apply and extend previous understandings of arithmetic to algebraic expressions.**

- Math.Content.6.EE.A.1Write and evaluate numerical expressions involving whole-number exponents.
- Math.Content.6.EE.A.2Write, read, and evaluate expressions in which letters stand for numbers.
- Math.Content.6.EE.A.2aWrite expressions that record operations with numbers and with letters standing for numbers.
*For example, express the calculation “Subtract y from 5” as 5 – y*. - Math.Content.6.EE.A.2bIdentify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
*For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms*. - Math.Content.6.EE.A.2cEvaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
*For example, use the formulas V = s*.^{3}and A = 6 s^{2}to find the volume and surface area of a cube with sides of length s = 1/2

- Math.Content.6.EE.A.2aWrite expressions that record operations with numbers and with letters standing for numbers.
- Math.Content.6.EE.A.3Apply the properties of operations to generate equivalent expressions.
*For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y*. - Math.Content.6.EE.A.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).
*For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*.

**Reason about and solve one-variable equations and inequalities.**

- Math.Content.6.EE.B.5Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
- Math.Content.6.EE.B.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
- Math.Content.6.EE.B.7Solve real-world and mathematical problems by writing and solving equations of the form
*x*+*p*=*q*and*px*=*q*for cases in which*p*,*q*and*x*are all nonnegative rational numbers. - Math.Content.6.EE.B.8Write an inequality of the form
*x*>*c*or*x*<*c*to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form*x*>*c*or*x*< c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

**Represent and analyze quantitative relationships between dependent and independent variables.**

- Math.Content.6.EE.C.9Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

**Math: Geometry – Middle School (6,7,8)**

**Solve real-world and mathematical problems involving area, surface area, and volume.**

- Math.Content.6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- Math.Content.6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas
*V = l w h*and*V = b h*to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. - Math.Content.6.G.A.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
- Math.Content.6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

**Math: Statistics and Probability – Middle School (6,7,8)**

**Develop understanding of statistical variability.**

- Math.Content.6.SP.A.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
*For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages*. - Math.Content.6.SP.A.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
- Math.Content.6.SP.A.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

**Summarize and describe distributions.**

- Math.Content.6.SP.B.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- Math.Content.6.SP.B.5Summarize numerical data sets in relation to their context, such as by:
- Math.Content.6.SP.B.5aReporting the number of observations.
- Math.Content.6.SP.B.5bDescribing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Math.Content.6.SP.B.5cGiving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- Math.Content.6.SP.B.5dRelating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.