# Expression and Equations

Math Monday: To complete an assessment using I-ready test 1 Tuesday: To understand the properties of integer exponents Wednesday: To understand the properties of integer exponents Thursday: To understand equations and graphing Reading Monday: To take an assessment on reading using an I-ready assessment Tuesday: To analyze the development of central ideas Wednesday: To summarize informational texts Thursday: To summarize informational texts WRITING

**1**8th grade lesson

#### 1 8th grade lesson

BACKGROUND: This lesson introduces integer exponents. It also addresses multiplying and dividing expressions with integer exponents and raising a power to a power. Students will learn the properties of exponents and use them to evaluate expressions with exponents, thereby generating equivalent expressions. Introduce: Explain integer exponent Vocabulary: square root, exponent, raising a power, integer Ask probing questions to model the teach strategy Close reading: and correctly, use problems from past assessments DURING INSTRUCTION: Teach Guided instruction (I do, we do, you do) 1. Multiplying powers with the same base MODEL- I DO, ADDITIONAL EXAMPLE: WE DO 2. Rule for dividing powers with the same base MODEL- I DO, ADDITIONAL EXAMPLE: WE DO POP: use models and visuals for stud ents who need it, use the video 3. Explain in your own words how to divide powers with the same base MODEL- I DO, ADDITIONAL EXAMPLE: WE DO 4. Quick check YOU DO 5. Quick write on summary: quick write: rate your learning and summarize the lesson, use three academic languages in your summary. YOU DO (FORMATIVE ASSESSMENT) Additional examples How does writing out the factors for each expression help you understand the rule for multiplying? Practice- Independent: Practice problems on the smart board Complete ten problems using same bases Further investigation How does writing out the factors for 35 x 43 show you that you cannot just add the exponents? Key Questions: How is (32 )4 different from (32) (34)? Discussion and Processing: Assess and re-teach Have students completed the practice problem, reteach those that responded incorrectly. Complete the work in small group AFTER INSTRUCTION Closure/ Ticket out the door Summary of the lesson’: and rate your skill Ticket out the door: Provide a problem where students model the integer exponent

Go to Iready log on and complete the assessment.

### Key Standards Supported

### Reading Literature

**RL.K.1**With prompting and support, ask and answer questions about key details in a text.

**RL.K.2**With prompting and support, retell familiar stories, including key details.

**RL.K.3**With prompting and support, identify characters, settings, and major events in a story.

**RL.K.4**Ask and answer questions about unknown words in a text.

**RL.K.5**Recognize common types of texts (e.g., storybooks, poems).

**RL.K.6**With prompting and support, name the author and illustrator of a story and define the role of each in telling the story.

**RL.K.7**With prompting and support, describe the relationship between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts).

**RL.K.8**(Not applicable to literature)

**RL.K.9**With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories.

**RL.K.10**Actively engage in group reading activities with purpose and understanding.

**RL.1.1**Ask and answer questions about key details in a text.

**RL.1.2**Retell stories, including key details, and demonstrate understanding of their central message or lesson.

**RL.1.3**Describe characters, settings, and major events in a story, using key details.

**RL.1.4**Identify words and phrases in stories or poems that suggest feelings or appeal to the senses.

**RL.1.5**Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types.

**RL.1.6**Identify who is telling the story at various points in a text.

**RL.1.7**Use illustrations and details in a story to describe its characters, setting, or events.

**RL.1.8**(Not applicable to literature)

**Rl.1.9**Compare and contrast the adventures and experiences of characters in stories.

**RL.1.10**With prompting and support, read prose and poetry of appropriate complexity for grade 1.

**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.2.2**Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.

**RL.2.3**Describe how characters in a story respond to major events and challenges.

**RL.2.4**Describe how words and phrases (e.g., regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song.

**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.

**RL.2.7**Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot.

**RL.2.8**(Not applicable to literature)

**RL.2.9**Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures.

**RL.2.10**By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range.

**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.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.

**RL.3.6**Distinguish their own point of view from that of the narrator or those of the characters.

**RL.3.7**Explain how specific aspects of a text’s illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting).

**RL.3.8**(Not applicable to literature)

**RL.3.9**Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series).

**RL.3.10**By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently.

**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.4.4**Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).

**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.

**RL.4.6**Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations.

**RL.4.7**Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text.

**RL.4.8**(Not applicable to literature)

**RL.4.9**Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.

**RL.4.10**By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range.

**RL.5.1**Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

**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.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.

**RL.5.6**Describe how a narrator’s or speaker’s point of view influences how events are described.

**RL.5.7**Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem).

**RL.5.8**(Not applicable to literature)

**RL.5.9**Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics.

**RL.5.10**By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently.

**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.6.3**Describe 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.

**RL.6.4**Determine 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.

**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.

**RL.6.7**Compare 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)

**RL.6.9**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.

**RL.6.10**By 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.

**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.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.7.5**Analyze how a drama’s or poem’s form or structure (e.g., soliloquy, sonnet) contributes to its meaning.

**RL.7.6**Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

**RL.7.7**Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film).

**RL.7.8**(Not applicable to literature)

**RL.7.9**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.

**RL.7.10**By 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.

**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.

**RL.8.3**Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.

**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.8.5**Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style.

**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.

**RL.8.7**Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors.

**RL.8.8**(Not applicable to literature)

**RL.8.9**Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new.

**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.9-10.1**Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

**RL.9-10.2**Determine a theme or central idea of a text and analyze in detail 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.

**RL.9-10.3**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.9-10.4**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.9-10.5**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.

**RL.9-10.6**Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature.

**RL.9-10.7**Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus).

**RL.9-10.8**(Not applicable to literature)

**RL.9-10.9**Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare).

**RL.9-10.10**By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range.

**RL.11-12.1**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.

**RL.11-12.2**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.11-12.3**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).

**RL.11-12.4**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.)

**RL.11-12.5**Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact.

**RL.11-12.6**Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).

**RL.11-12.7**Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)

**RL.11-12.8**(Not applicable to literature)

**RL.11-12.9**Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics.

**RL.11-12.10**By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.

### Expressions And Equations

**6.EE.1**Write and evaluate numerical expressions involving whole-number exponents.

**6.EE.2**Write, read, and evaluate expressions in which letters stand for numbers.

**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 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 = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

**6.EE.3**Apply the properties of operations to generate equivalent expressions.

**6.EE.4**Identify 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.

**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 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.

**6.EE.7**Solve 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.

**6.EE.8**Write 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.

**6.EE.9**Use 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.

**7.EE.1**Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

**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.”

**7.EE.3**Solve multi-step real-life 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**Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

**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.

**8.EE.1**Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

**8.EE.2**Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

**8.EE.3**Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

**8.EE.4**Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

**8.EE.5**Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

**8.EE.6**Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

**8.EE.7**Solve linear equations in one variable.

**8.EE.7.a**Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

**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.a**Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

**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.

**8.EE.8.c**Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.