Tapestry Public Charter School Do You Hear What I Hear? (Sample 8th Grade Unit on Sounds) Sample Tapestry Educational Module Through collaborative planning, teachers at Tapestry will develop interdisciplinary educational modules such as that outlined below, which are generated by student interest and aligned with the Common Core Georgia Performance Standards. Teachers will ensure access to the curriculum by differentiating content, process, and product (Universal Design for Learning) and through the use of technology (Discovery Education’s Techbooks and Streaming Plus). The length of a module will vary depending on the goals and objectives for that module, but an average unit could last several weeks or even months. The module outlined below serves as a sample of the way student interest could inform an interdisciplinary module that is integrated across content area at Tapestry. Co-teachers will choose how to conduct daily lessons within these parameters. Checkpoints: ● Is content aligned with the Common Core Georgia Performance Standards? ● Are information and content presented in different ways? ● Can students demonstrate what they know in different ways? ● Are students stimulated, interested, motivated, engaged? ● Is learning hands-on and collaborative? ● Are there multiple opportunities for movement and self-regulation? Advisory The theme of sound is introduced in the advisory period. It is well established that many individuals with autism spectrum disorders (ASD) have auditory sensitivities, so this topic should especially be of high interest to students with ASD. Moreover, a discussion of the various sounds that students find pleasant or annoying allows them to take steps toward self-advocacy and self-regulation. They learn to identify situations in which focused listening is difficult, for example, when loud music is playing in the background or a plane is flying overhead. With their advisory group, students develop strategies for coping with annoying or distracting sounds, such as avoidance, holding ears, or even wearing noisereducing earmuffs. What are the socially appropriate means of avoidance, or socially appropriate ways to express displeasure with a sound someone is generating? How do we use different aspects of sound to convey meaning? Students will examine and practice various prosodic features of speech, such as inflection, pausing, rate, and tone to convey emotions or emphasis. Students will learn to identify nasal, raspy, breath, shrill, or booming voices, naming any qualities that they find pleasant or unpleasant. (Teachers are assisted by speech-language pathologists and occupational therapists.) English Language Arts Materials/Protocol: Discovery Ed Asset (source material): ● Hands-On Lab: Stop That Noise! (activity): What is that annoying sound? Students investigate different ways to reduce vibration that is producing a racket. Warm Up: For schema building, students first discuss the sounds they hear on a regular basis, including those that they like and those that they don’t like. The teachers encourage students to write the sounds on the board using graphic organizers such as Venn Diagrams to determine common sounds that all students enjoy. Next, students touch, hold, examine, and discuss several different recording devices – tape recorders, including older devices and contemporary digital handheld recorders, and larger studio-type recorders. (Teachers may solicit the help of the Tapestry AV partner, Kevin Hollingsworth, for this lesson. Field trips may be planned to visit the recording studio of sound engineer Rob Del Bueno, another Tapestry supporter.) Group Practice: Through a classroom “expedition,” students explore sounds in the environment and keep notes in their field journals. Observations will be made in the classroom environment, school environment, outdoors environment (drawing a distinction between man-made sounds, such as cars, sirens, or air conditioning units, and nature sounds, i.e. birds, crickets, and the wind). On the expedition, students will volunteer for different roles and will be arranged in small groups. One student in the group will record sounds with audio equipment (using a handheld digital recording device); another will take notes of the sounds recorded; a third student, using a free app called Decibel 10th, will measure the sounds the group encounters. (A falling leaf might be 10 decibels, a jackhammer may be 100 decibels, and a low-flying airplane may be 150 decibels.) After returning to the classroom, there is a whole-class listing and discussion of the different sounds students have heard on their journey. Working in small groups, students will then classify their sounds into categories, such as location, the producers of the sounds, amplitude, or purpose. The groups use graphic organizers to show their categories on the board. This serves as a brainstorming activity for classification/categorization writing, but throughout the unit, students will develop writing skills in other genres, such as narrative, process, and compare/contrast. Independent Practice Students choose reading assignments on topics related to sound based on their reading levels and interests. A search by either standard or topic enables teachers and students to access a variety of lexiled reading passages from their Discovery Ed Techbook (such as those below). Students journal, discuss, summarize, and extend their readings outside the classroom. They may demonstrate reading comprehension in a variety of ways. They play charades to review main ideas, they pantomime to dramatize major details, or they create ads or commercials to “advertise” the content and to review. Discovery Ed Assets: ● Sound Bites (reading passage): An understanding of how sound works is essential in everyday life. But how do we hear sounds? What is the speed of sound? What are the properties of sound? This passage answers many questions concerning sound. ● Getting to Know: Echolocation (reading passage): Learn the basics about Echolocation and uncover common misconceptions about the concept. Social Studies In the Social Studies class, students learn the historical context through which different cultures have used technological advances in sound, sound recording, and broadcasting to create music, the telephone, the radio, and film. The differences in sound and communication that vary cross-culturally may spark interest. Students who have a specific cultural identity assist with this extension. Others may research by interviewing people from different cultures living in the community. They learn that volume and tone can convey different meanings to different groups of people. They discover that variation in non-verbal communication, such as physical cues, personal space, wait time, and pauses can be seen when comparing cultures, ethnicities, people from different regions, and even families. Materials/Protocol: Discovery Ed Asset ● An Overview of the Music and Recording Industry (video segment): Today, when every life seems to have its own soundtrack, it’s hard to believe that we once could hear music only in live performances. “Technology and Society: When Machines Learned to Talk” introduces the remarkable inventors and innovations that brought a wealth of recorded entertainment and information to our everyday lives. After Edison proved that sound could be mechanically reproduced, an innovator, Eldridge R. Johnson, and his partner Emile Berliner developed a “talking machine” that paved the way for today’s recording industry. They also incorporated a groundbreaking marketing strategy; the image of the little dog, Nipper, listening to “his master’s voice” soon became one of the world's most recognizable logos. Talking machines introduced easily available entertainment and culture to America and the world – putting a skip in our step and a song in our hearts. This outstanding program traces the rise of this remarkable industry and clearly demonstrates the impact that technology’s advances can have on society. ● The History of Sound Recording (full video): Tracks the evolution of sound recording technology from the nineteenth century to the present. This program discusses the achievements of sound innovator Thomas Edison, the development of physical, mechanical, analog, and electric recording equipment, and groundbreaking audio devices like the music box, wire and tin foil recorders, the gramophone, phonograph, film, albums and LPs, CDs, and digital audio. Guided Practice: I. Students learn about the various goods and services produced in Georgia in different historical periods until present day. Students will explore Georgia music and film industries along with their related careers and their economic impact in Georgia using articles from the techbook and internet research as a class. II. Students will review notes and learn about the role of the legislative branch of government at the state level. Independent Practice: I. Data will be analyzed through class discussion and note-taking around these topics, tracing trends to influences such as demographics, policies, climate, and culture. Students will write to a prompt and/or make a presentation to share their findings. II. Students will analyze the role of the legislative branch and research various laws that relate to noise ordinances and noise pollution. A research project could involve comparing laws that exist in different areas of the state and identifying any gaps. What would it take to improve laws in the state? How does a bill become a law at the state level? Students design a plan to effect change. Science Materials/Protocol: Discovery Ed Asset ● Hands-On Activity: Investigating Sounds (activity): Students observe how sound travels through a solid, a liquid, and a gas. ● Dolphins and Echolocation: Feeding and Navigation (video segment): Leading cetacean conservationist Dr. Roger Payne guides an expedition to witness the intelligent hunting behavior of the killer whale and to learn how dolphins and other whales communicate with sound. Guided Practice I. Students learn that sound is a form of energy that travels as the result of vibration. Teachers use a toy slinky to demonstrate sound waves. Even when stretched, the coils of the slinky stay together the way sound waves do. A tuning fork is utilized to enable students to see and feel the vibration of sound. As a tuning fork vibrates, it causes the air molecules around it to move. The process results in the compressions and rarefactions that make up sound waves. Students learn that a sound wave is a compressional or longitudinal wave. II. Students also learn how we perceive sound through the auditory system. They learn that the scientific study of human sound perception is known as psychoacoustics. Through Discovery Ed images and streaming videos, students witness the process whereby sound vibrations hit the eardrum and a chain reaction occurs. III. Students will explore the wave nature of sound and electromagnetic radiation through research and project work driven by student interest. For example, the sounds of the ocean, noise pollution, and its effects on marine animals could be examined. Students learn through their Discovery Ed Techbook and Streaming Plus how marine animals communicate. They discover that water is a medium through which sound waves can travel and be heard for hundreds of miles by marine animals such as whales and dolphins, who have a complex system of communication and must be able to hear each other. A mother whale locates her calf by sending clicking sounds through the water. When the sound waves bump into her calf, they come back to the mother in an echo. Students watch videos and listen to various recordings of marine life and their songs. They read that whales must not only learn to communicate over loud environmental sounds such as waves and earthquakes, but man-made sounds are also creating a type of noise pollution that is harmful to marine life. Independent Practice: II. Students may draw diagrams, create 3D models, or even produce their own animated films that demonstrate the process of “hearing” and the function of the auditory system. III. Students read informational articles on noise pollution in the ocean to discover the causes and effects. A project might include the discovery of a solution for this serious issue. Other students may be particularly interested in sound recording, and could delve into a Digital Audio Recording and Editing Project. Music Materials/Protocol: Discovery Ed Asset ● Science of Sound (video segment): Kari Byron powers up a digital clock with a can of sauerkraut and explores the science of sound with rock group Metallica. Find out what chopped liver and hydrogen peroxide can do, and how rust can be good for you. Fellow MythBusters Adam and Jamie test the myth of Archimedes ancient death ray. Warm-Up: Students talk about their favorite music, songs, singers, and discuss their emotional response to music. They share their favorite music with each other, either through recordings or performances. Students develop both their musical skills and appreciation of music. What makes a good singer? How does one control pitch? Can one develop a range? What does it mean to project well when singing or talking? Guided Practice: Students learn the vocabulary of sound, including pitch (frequency - measured in Hertz) and volume (intensity or amplitude - measured in decibels). They also learn about different musical instruments in music class. They have previously learned about the history of musical instruments in social studies, but now they get hands-on experience with the instruments, discovering how they work and how to make music with them. Group/Independent Practice: Those students who can already play an instrument are encouraged to share their talents with the class. Guided by the music teacher, some students write or co-write their own music. They discuss mathematical-musical concepts such as rhythm, meter, and time signatures. Math Materials/Protocol: Discovery Ed Asset ● What Determines Sound Volume? (core interactive text): All sound waves carry energy, and the amount of energy determines the amplitude of the sound wave. On a diagram of a sound wave, the amplitude is indicated by the height of the wave. The greater the amplitude, the greater the volume of the sound and the louder it will be to the listener. Guided Practice: I. Students are exposed to musical notes and how their names can be viewed as variables for their frequency. Group/Independent Practice: In a two partner setting, one student operates a musical instrument; the other uses a downloaded tuner app on a tablet to detect the frequency of the generated notes. Students are then asked to prepare a chart where the names of one octave of musical notes fill the x-axis (C4, D4, E4, F4, G4, A4, B4), and their corresponding frequencies populate the y-axis (262, 294, 330, 349, 392, 440, 494). They then connect the values they plotted on the chart, and consequently discuss the resulting linear relationship between musical notes and their frequencies. According to the resulting line graph, students are asked to make predictions about additional octaves of notes and where their frequencies might fall when the line graph is extended. They can then test their assumptions by continuing to plot the added notes onto the chart. Additional math lessons can center on intervals and their ratios, probabilities in songwriting schemas or the mathematical similarities in the structure of Top 40 hits. Materials/Protocol: Discovery Ed Asset ● The Geometry of Groove: Triangles and Polygons (full video): Defines and classifies geometric triangles and polygons and their relationship to sound and vocal quality in music recording. This program discusses equilateral, isosceles, scalene, and right triangles, regular and irregular polygons, and concepts of apex, perpendicular, and sum to make sense of volume levels at shows and in the studio. The presentation also examines external, internal, and right angles and degrees to reinforce the importance of geometry in everyday life. II. In another math class, students learn about the relationship between sound and area. They can record sounds in several rooms of different shapes and sizes, for example, a small closet, a classroom, and a gymnasium. They can record the same sound in each of the rooms, and measure the size of the rooms. Students will use these measurements to calculate the area of the rooms, and in hearing recordings of the sounds they can discuss the relationship between properties of sound (such as volume and sound quality) and room size. They can also create and complete their own word problems using sound as the subject. For example, the eighth grade classes may want to start a competition to see who can record the most sounds in a 20-day period. One class has two students record one sound each day. The other class decides to have three students record a sound every other day. Which class will have the most sounds recorded after 20 days? Cross-Curricular Assessment Formative assessment will be ongoing and could be either spontaneous or planned. In all cases, teachers will provide clear feedback. Examples of spontaneous formative assessment could include the following: ● Q & A during lessons ● Discussion ● Observing students during an activity ● Responding to students’ impromptu conversations Examples of planned formative assessment could include the following: ● Short tests, quizzes, and other activities (easily generated with Discovery Ed) ● Homework exercises (modified for each student) ● Graphic Organizers ● In-class assignments ● Simulation activities ● Peer and self-assessment ● Journaling Modules will culminate in either individual or group projects and may become end-of-year capstone presentations to be delivered at student-led conferences. For example, students could organize a symposium on how sound impacts the environment. One group of students may choose to write and develop a play or other dramatic performance to demonstrate knowledge acquired. Guided by teachers, the students would develop the presentations, advertising, and budget for the event. These creative projects and a writing component of each student’s choice will constitute the summative assessment for the module. In addition, required state-mandated tests will be used for summative assessment. Student Reflections In keeping an on-going record, both students and teachers should reflect on the following: ● What did we find compelling? ● How were our knowledge and skills challenged? ● What inquiries arose during the learning? ● What, if any, extension activities arose? ● How did we reflect—both on the unit and on our own learning? ● Which attributes of the learner profile were encouraged through this unit? ● What opportunities were there for student-initiated action? ● In what ways has the student become a more independent learner through this unit? Additionally, teachers should consider these questions: ● How successful was the collaboration with other teachers within my subject group and from other subject groups? ● What interdisciplinary understandings were or could be forged through collaboration with other subjects? English Language Arts Standards: CCSS.ELA-Literacy.SL.8.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others’ ideas and expressing their own clearly. CCSS.ELA-Literacy.SL.8.1a Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. CCSS.ELA-Literacy.SL.8.1b Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed. CCSS.ELA-Literacy.SL.8.1c Pose questions that connect the ideas of several speakers and respond to others’ questions and comments with relevant evidence, observations, and ideas. CCSS.ELA-Literacy.SL.8.1d Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented. CCSS.ELA-Literacy.SL.8.2 Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation. CCSS.ELA-Literacy.SL.8.3 Delineate a speaker’s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced. CCSS.ELA-Literacy.SL.8.4 Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation. CCSS.ELA-Literacy.SL.8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. CCSS.ELA-Literacy.SL.8.6 Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grade 8 Language standards 1 and 3 for specific expectations.) CCSS.ELA-Literacy.L.8.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. CCSS.ELA-Literacy.L.8.1a Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences. CCSS.ELA-Literacy.L.8.1b Form and use verbs in the active and passive voice. CCSS.ELA-Literacy.L.8.1c Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. CCSS.ELA-Literacy.L.8.1d Recognize and correct inappropriate shifts in verb voice and mood.* CCSS.ELA-Literacy.L.8.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. CCSS.ELA-Literacy.L.8.2a Use punctuation (comma, ellipsis, dash) to indicate a pause or break. CCSS.ELA-Literacy.L.8.2b Use an ellipsis to indicate an omission. CCSS.ELA-Literacy.L.8.2c Spell correctly. CCSS.ELA-Literacy.L.8.4 Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies. CCSS.ELA-Literacy.L.8.4a Use 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. CCSS.ELA-Literacy.L.8.4b Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede). CCSS.ELA-Literacy.L.8.4c Consult general and specialized 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. CCSS.ELA-Literacy.L.8.4d Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). CCSS.ELA-Literacy.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. CCSS.ELA-Literacy.RST.6-8.9 Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic. CCSS.ELA-Literacy.RH.6-8.3 Identify key steps in a text’s description of a process related to history/social studies (e.g., how a bill becomes law, how interest rates are raised or lowered). CCSS.ELA-Literacy.RH.6-8.4 Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies. CCSS.ELA-Literacy.RH.6-8.5 Describe how a text presents information (e.g., sequentially, comparatively, causally). CCSS.ELA-Literacy.RH.6-8.6 Identify aspects of a text that reveal an author’s point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts). CCSS.ELA-Literacy.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. CCSS.ELA-Literacy.RH.6-8.8 Distinguish among fact, opinion, and reasoned judgment in a text. CCSS.ELA-Literacy.RH.6-8.9 Analyze the relationship between a primary and secondary source on the same topic. CCSS.ELA-Literacy.RI.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. CCSS.ELA-Literacy.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. CCSS.ELA-Literacy.RI.8.3 Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). CCSS.ELA-Literacy.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. CCSS.ELA-Literacy.RI.8.5 Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept. CCSS.ELA-Literacy.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. CCSS.ELA-Literacy.RI.8.7 Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. CCSS.ELA-Literacy.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. CCSS.ELA-Literacy.WHST.6-8.1a Introduce claim(s) about a topic or issue, acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. CCSS.ELA-Literacy.WHST.6-8.1b Support claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources. CCSS.ELA-Literacy.WHST.6-8.1c Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. CCSS.ELA-Literacy.WHST.6-8.1d Establish and maintain a formal style. CCSS.ELA-Literacy.WHST.6-8.1e Provide a concluding statement or section that follows from and supports the argument presented. CCSS.ELA-Literacy.WHST.6-8.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. CCSS.ELA-Literacy.WHST.6-8.2a Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. CCSS.ELA-Literacy.WHST.6-8.2b Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples. CCSS.ELA-Literacy.WHST.6-8.2c Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts. CCSS.ELA-Literacy.WHST.6-8.2d Use precise language and domain-specific vocabulary to inform about or explain the topic. CCSS.ELA-Literacy.WHST.6-8.2e Establish and maintain a formal style and objective tone. CCSS.ELA-Literacy.WHST.6-8.2f Provide a concluding statement or section that follows from and supports the information or explanation presented. L6-8RH7: Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts L6-8WHST.7: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration CCSS.ELA-Literacy.WHST.6-8.8 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. CCSS.ELA-Literacy.WHST.6-8.9 Draw evidence from informational texts to support analysis reflection, and research. CCSS.ELA-Literacy.WHST.6-8.10 Write routinely over extended time frames (time for 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. Social Studies Standards: SS8CG2: The student will analyze the role of the legislative branch in Georgia state government. SS8CG3: The student will analyze the role of the executive branch in Georgia state government. SS8CG4: The student will analyze the role of the judicial branch in Georgia state government. SS8E4: The student will identify revenue sources and services provided by state and local governments. SS8E1 The student will give examples of the kinds of goods and services produced in Georgia in different historical periods. SS8E2 The student will explain the benefits of free trade. SS8E3 The student will evaluate the influence of Georgia’s economic growth and development. Science Standards: S8P4. Students will explore the wave nature of sound and electromagnetic radiation. a. Identify the characteristics of electromagnetic and mechanical waves. b. Describe how the behavior of light waves is manipulated causing reflection, refraction diffraction, and absorption. c. Explain how the human eye sees objects and colors in terms of wavelengths. d. Describe how the behavior of waves is affected by medium (such as air, water, solids). e. Relate the properties of sound to everyday experiences. f. Diagram the parts of the wave and explain how the parts are affected by changes in amplitude and pitch. Math Standards: MCC8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. MCC8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. MCC8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-‐way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? MCC8.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. MCC8.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. MCC8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. MCC8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. MCC8.EE.8c 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. Sources: discoveryeducation.com gadoe.org georgiastandards.org corestandards.org
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