LearnZillion
 forming arguments
 reading comprehension
 text analysis
 writing clearly
 equations
 fractions
 geometry
 measurement
 analyzing evidence
 making conclusions
 partwhole relationships
 thinking critically
Pros
It's super customizable, which means you can assign kids the lessons they need to work on most.Cons
Lacks an element of fun, which could make using the site feel like work for some kids.Bottom Line
An innovative way to enhance lessons and tailor learning for individual needs.Watch demonstration videos and get suggestions for effective use of the program. Once logged in, teachers can create classes, add students, assign lessons, and track progress. They can also download slides, listen to commentary for each lesson, and print handouts for parents.
It's easy to use, and visuals are appealing. While it may lack obvious hooks for engagement, kids should be drawn in by the desire to learn in a personalized way.
Developed by experienced teachers, the lessons are clear and concise. The practice exercises and prompts encourage kids to learn independently. With a teacher's help, personalized assignments can meet students right at their problem areas.
Many of the howto videos and lesson plans are helpful and demonstrate the site’s potential and utility in the classroom. Teachers can keep track of students’ progress as well.
Use LearnZillion to give your students an extra learning boost, to give them review on topics you've covered in class, or even to give them a springboard for new exploration. You can also find new lessons, give yourself inspiration, or learn how to explain a concept a different way. Full lesson plans, complete with teaching notes, necessary prerequisites, and more, provide a lot of the background work necessary for teaching a new concept.
You and your students can do these lessons as a whole class, or students can do them in small groups or on their own. For example, hold a “math lab” where kids work on slightly different sets of problems that are specifically tailored to their needs. Assign "just right" practice exercises to each student based on their level of understanding. As students work, move around the classroom to check in, guide, and assist where needed. Afterward, use the videos as a followup for homework or classwork. As needed, you can assign extra practice as an extension or for intervention.
Read more Read lessLearnZillion is an online database of short video lessons that address learning topics aligned to individual Common Core standards. The lessons cover a wide variety of math and English Language Arts topics for the whole K through 12 grade span. Experienced teachers create the 3 to 5minute videos and lessons, complete with leveled practice problems, anchor texts, and writing prompts. Whole lesson plans offer teacher hints, background information, and additional guidance in a readytopresent slidelike presentation that incorporates videos, visuals, and handson practice. Content is available on the web and on iOS and Android tablets.
For kids, the videos feature commentary, extra hints, tricks, and a “try it yourself” segment to help them practice on their own, using pencil and paper to follow the video’s guidance. Multiplechoice quizzes help assess students' learning. When both kids and teachers create accounts, teachers can assign lessons to individual students or to the whole class, see who's completed a lesson, and view students' scores.
Read more Read lessAt its best, the site acts as a mix of a teacher’s assistant and mentor. Not sure how to explain a new or difficult concept? You can get helpful guidance from another teacher who's found a successful method. Teachers who are spread thin, or those whose students may need extra help, can use LearnZillion to provide targeted attention to help students right where they need it most. For instance, before students try any particular math lesson, a series of links help teachers identify the necessary skills students will need to know. This is very useful in helping teachers identify any gaps in students' knowledge before they begin. Lessons also offer teachers a variety of extension and intervention ideas.
Teachers should know LearnZillion isn't a game; it's better as a teacher’s tool than as a superexciting activity for kids. However, what it may lack in fun factor, it makes up for in clear, instructive content. LearnZillion does so much of the background and presentation work for you, it may feel like a virtual teacher. But rather than thinking of it as a teacher substitute  there's no replacement for handson, facetoface interaction  think of it as a teacher enhancement. Live teachers are essential for choosing assignments wisely, tracking progress, and filling in the gaps when kids struggle. While the multiplechoice quizzes may not align perfectly with each lesson's content, they're serviceable. Teachers may still choose to do their own learning assessments offline. While the site provides answer keys, the inclusion of authentic student work samples and assessment criteria would offer a stronger picture of what quality work looks like.
Read more Read lessKey Standards Supported
Language  
L.8: Conventions of Standard English  
L.8.1c  Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. 
Vocabulary Acquisition and Use  
L.8.5  Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. 
Reading Informational  
RI.2: Craft and Structure  
RI.2.4  Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area. 
Key Ideas and Details  
RI.2.1  Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. 
RI.3: Craft and Structure  
RI.3.6  Distinguish their own point of view from that of the author of a text. 
Integration of Knowledge and Ideas  
RI.3.7  Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur). 
Key Ideas and Details  
RI.3.2  Determine the main idea of a text; recount the key details and explain how they support the main idea. 
RI.3.3  Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect. 
Range of Reading and Level of Text Complexity  
RI.3.10  By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently. 
RI.4: Craft and Structure  
RI.4.5  Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text. 
Integration of Knowledge and Ideas  
RI.4.7  Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. 
Key Ideas and Details  
RI.4.1  Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. 
RI.4.2  Determine the main idea of a text and explain how it is supported by key details; summarize the text. 
RI.4.3  Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text. 
RI.5: Craft and Structure  
RI.5.4  Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a grade 5 topic or subject area. 
Key Ideas and Details  
RI.5.1  Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. 
RI.5.2  Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text. 
RI.5.3  Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. 
Range of Reading and Level of Text Complexity  
RI.5.10  By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently. 
RI.6: Craft and Structure  
RI.6.4  Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. 
RI.6.5  Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas. 
Key Ideas and Details  
RI.6.1  Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.6.2  Determine 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. 
RI.6.3  Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes). 
RI.7: Craft and Structure  
RI.7.4  Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. 
RI.7.6  Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others. 
Key Ideas and Details  
RI.7.1  Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.7.2  Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text. 
RI.7.3  Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events). 
RI.8: Craft and Structure  
RI.8.4  Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. 
RI.8.6  Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. 
Integration of Knowledge and Ideas  
RI.8.8  Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced. 
Key Ideas and Details  
RI.8.2  Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text. 
RI.910: Craft and Structure  
RI.910.5  Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). 
RI.910.6  Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose. 
Key Ideas and Details  
RI.910.1  Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.910.2  Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. 
RI.1112: Craft and Structure  
RI.1112.4  Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10). 
RI.1112.6  Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness or beauty of the text. 
Key Ideas and Details  
RI.1112.1  Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. 
RI.1112.3  Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text. 
Reading Literature  
RL.2: Craft and Structure  
RL.2.5  Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action. 
RL.2.6  Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud. 
Key Ideas and Details  
RL.2.1  Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. 
RL.2.3  Describe how characters in a story respond to major events and challenges. 
RL.3: Craft and Structure  
RL.3.4  Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language. 
RL.3.5  Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections. 
Key Ideas and Details  
RL.3.1  Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. 
RL.3.2  Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text. 
RL.3.3  Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. 
RL.4: Craft and Structure  
RL.4.5  Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text. 
Key Ideas and Details  
RL.4.1  Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. 
RL.4.2  Determine a theme of a story, drama, or poem from details in the text; summarize the text. 
RL.4.3  Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions). 
RL.5: Craft and Structure  
RL.5.4  Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes. 
RL.5.5  Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem. 
Key Ideas and Details  
RL.5.2  Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text. 
RL.5.3  Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact). 
RL.6: Craft and Structure  
RL.6.5  Analyze 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. 
RL.6.6  Explain how an author develops the point of view of the narrator or speaker in a text. 
Key Ideas and Details  
RL.6.1  Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.6.2  Determine 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. 
RL.7: Craft and Structure  
RL.7.4  Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama. 
RL.7.6  Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. 
Key Ideas and Details  
RL.7.1  Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.7.2  Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text. 
RL.7.3  Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot). 
RL.8: Craft and Structure  
RL.8.4  Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. 
RL.8.6  nalyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. 
Key Ideas and Details  
RL.8.1  Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.8.2  Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. 
Range of Reading and Level of Text Complexity  
RL.8.10  By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently. 
RL.910: Craft and Structure  
RL.910.4  Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone). 
RL.910.5  Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. 
Key Ideas and Details  
RL.910.3  Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme. 
RL.1112: Craft and Structure  
RL.1112.4  Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.) 
Key Ideas and Details  
RL.1112.2  Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text. 
RL.1112.3  Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). 
Writing  
W.2: Text Types and Purposes  
W.2.2  Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section. 
W.3: Production and Distribution of Writing  
W.3.5  With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. 
Text Types and Purposes  
W.3.1  Write opinion pieces on topics or texts, supporting a point of view with reasons. 
W.3.1a  Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons. 
W.3.1b  Provide reasons that support the opinion. 
W.3.1c  Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons. 
W.3.1d  Provide a concluding statement or section. 
W.3.2a  Introduce a topic and group related information together; include illustrations when useful to aiding comprehension. 
W.3.2b  Develop the topic with facts, definitions, and details. 
W.3.3a  Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally. 
W.3.3b  Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations. 
W.3.3c  Use temporal words and phrases to signal event order. 
W.4: Text Types and Purposes  
W.4.1  Write opinion pieces on topics or texts, supporting a point of view with reasons and information. 
W.4.1a  Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. 
W.4.1b  Provide reasons that are supported by facts and details. 
W.4.1c  Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition). 
W.4.1d  Provide a concluding statement or section related to the opinion presented. 
W.4.2  Write informative/explanatory texts to examine a topic and convey ideas and information clearly. 
W.4.2b  Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. 
W.4.2d  d.Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.4.2e  Provide a concluding statement or section related to the information or explanation presented. 
W.4.3  Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. 
W.4.3a  Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. 
W.4.3b  Use dialogue and description to develop experiences and events or show the responses of characters to situations. 
W.5: Production and Distribution of Writing  
W.5.5  With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. 
Text Types and Purposes  
W.5.1  Write opinion pieces on topics or texts, supporting a point of view with reasons and information. 
W.5.1a  Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose. 
W.5.1b  Provide logically ordered reasons that are supported by facts and details. 
W.5.1c  Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically). 
W.5.1d  Provide a concluding statement or section related to the opinion presented. 
W.5.2  Write informative/explanatory texts to examine a topic and convey ideas and information clearly. 
W.5.2c  Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). 
W.6: Research to Build and Present Knowledge  
W.6.8  Gather 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. 
W.6.9  Draw evidence from literary or informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
W.6.1  Write arguments to support claims with clear reasons and relevant evidence. 
W.6.1a  Introduce claim(s) and organize the reasons and evidence clearly. 
W.6.1b  Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text. 
W.6.1c  Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons. 
W.6.1e  Provide a concluding statement or section that follows from the argument presented. 
W.6.2a  Introduce 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. 
W.6.2f  Provide a concluding statement or section that follows from the information or explanation presented. 
W.6.3a  Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. 
W.6.3c  Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. 
W.6.3d  Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events. 
W.7: Production and Distribution of Writing  
W.7.5  With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. 
Research to Build and Present Knowledge  
W.7.9a  Apply grade 7 Reading standards to literature (e.g., “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”). 
Text Types and Purposes  
W.7.1a  Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically. 
W.7.1b  Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. 
W.7.1c  Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence. 
W.7.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.7.2  Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. 
W.7.2b  Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. 
W.8: Research to Build and Present Knowledge  
W.8.8  Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. 
Text Types and Purposes  
W.8.1a  Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. 
W.8.1b  Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. 
W.8.1c  Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. 
W.8.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.8.3a  Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. 
W.8.3b  Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. 
W.8.3c  Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. 
W.8.3d  Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. 
W.8.3e  Provide a conclusion that follows from and reflects on the narrated experiences or events. 
W.910: Production and Distribution of Writing  
W.910.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.910.5  Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. 
Research to Build and Present Knowledge  
W.910.9  Draw evidence from literary or informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
W.910.1a  Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence. 
W.910.1b  Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns. 
W.910.1c  Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. 
W.1112: Production and Distribution of Writing  
W.1112.5  Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. 
Research to Build and Present Knowledge  
W.1112.9  Draw evidence from literary or informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
W.1112.1a  Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence. 
W.1112.1b  Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases. 
W.1112.1c  Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. 
W.1112.1d  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
W.1112.2a  Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. 
W.1112.2b  Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. 
W.1112.2c  Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. 
Expressions And Equations  
6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.  
6.EE.2.a  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. 
6.EE.2.b  Identify 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. 
6.EE.2.c  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld 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 = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. 
Reason About And Solve OneVariable Equations And Inequalities.  
6.EE.5  Understand 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. 
6.EE.6  Use variables to represent numbers and write expressions when solving a realworld 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. 
6.EE.7  Solve realworld 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. 
7.EE: Solve RealLife And Mathematical Problems Using Numerical And Algebraic Expressions And Equations.  
7.EE.3  Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 
7.EE.4.a  Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 
7.EE.4.b  Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. 
Use Properties Of Operations To Generate Equivalent Expressions.  
7.EE.2  Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” 
8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations.  
8.EE.7.b  Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 
8.EE.8  Analyze and solve pairs of simultaneous linear equations. 
8.EE.8.b  Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 
Geometry  
8.G: Solve RealWorld And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres.  
8.G.9  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 
Understand Congruence And Similarity Using Physical Models, Trans Parencies, Or Geometry Software.  
8.G.3  Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 
8.G.5  Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 
Number And Operations In Base Ten  
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4  
3.NBT.1  Use place value understanding to round whole numbers to the nearest 10 or 100. 
3.NBT.2  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 
3.NBT.3  Multiply onedigit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 
5.NBT: Understand The Place Value System.  
5.NBT.1  Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 
5.NBT.2  Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. 
4.NBT: Generalize Place Value Understanding For MultiDigit Whole Numbers.  
4.NBT.1  Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 
4.NBT.2  Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 
4.NBT.3  Use place value understanding to round multidigit whole numbers to any place. 
Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.  
4.NBT.4  Fluently add and subtract multidigit whole numbers using the standard algorithm. 
4.NBT.5  Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 
4.NBT.6  Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 
Number And Operations—Fractions  
5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions.  
5.NF.3  Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 
5.NF.6  Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 
5.NF.7  Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 
5.NF.7.b  Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. 
Use Equivalent Fractions As A Strategy To Add And Subtract Fractions.  
5.NF.1  Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 
4.NF: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers.  
4.NF.3.a  Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 
4.NF.3.d  Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 
4.NF.4.a  Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). 
4.NF.4.b  Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) 
4.NF.4.c  Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 
Extend Understanding Of Fraction Equivalence And Ordering.  
4.NF.2  Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 
3.NF: Develop Understanding Of Fractions As Numbers.  
3.NF.1  Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 
3.NF.2.a  Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 
3.NF.2.b  Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 
3.NF.3.b  Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. 
3.NF.3.c  Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. 
3.NF.3.d  Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 
Ratios And Proportional Relationships  
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.  
6.RP.1  Understand 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.” 
6.RP.2  Understand 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 
6.RP.3.a  Make 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. 
6.RP.3.c  Find 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. 
7.RP: Analyze Proportional Relationships And Use Them To Solve RealWorld And Mathematical Problems.  
7.RP.1  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 
7.RP.2.a  Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 
7.RP.3  Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 
The Number System  
7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.  
7.NS.1  Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 
7.NS.3  Solve realworld and mathematical problems involving the four operations with rational numbers. 
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Students Learn to Advocate with Reasoned ArgumentEnglish Language ArtsGrade 55 steps
February 2, 2016