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Curriculum and Instruction – Office of Mathematics 4th Quarter Algebra I Introduction In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025, 80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, College and Career Ready standardsaligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor. Focus • • • • The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For algebra 1, the major clusters, algebra and functions, account for 73% of time spent on instruction. Supporting Content - information that supports the understanding and implementation of the major work of the grade. Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency. Major Content Supporting Content Coherence Rigor Thinking across grades: • The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Conceptual understanding: • The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. • Procedural skill and fluency: • The Standards call for speed and accuracy in calculation. While the high school standards for math do not list high school fluencies, there are suggested fluency standards for algebra 1, geometry and algebra 2. Linking to major topics: • Instead of allowing additional or supporting topics to detract from course, these concepts serve the course focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems. Additional Content TN Algebra I Standards Application: • The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content. Shelby County Schools2015/2016 Revised 3/9/16 1 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter Algebra I While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards. These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II. Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections Problem Solving Connection Representation Major Content Supporting Content Additional Content TN Algebra I Standards Reasoning and Proof Communication Shelby County Schools2015/2016 Revised 3/9/16 2 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter Look for and express regularity in repeated reasoning Look for and make use of structure Make sense of problems and persevere in solving them Algebra I Reason abstractly and quatitatively Mathematical Practices Attend to precision Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice. How to Use the Mathematics Curriculum Maps This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that ultimately our students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics. Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the standards and teaching practices that teachers should consistently access: Major Content Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 3 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter Algebra I The TNCore Mathematics Standards The Tennessee Mathematics Standards: https://www.tn.gov/education/article/mathematicsstandards Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at each respective grade level. Mathematical Shifts Focus The standards are focused on fewer topics so students can http://achievethecore.org/shifts-mathematics learn more Coherence http://achievethecore.org/shifts-mathematics Topics within a grade are connected to support focus, and learning is built on understandings from previous grades Rigor http://achievethecore.org/shifts-mathematics The standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, and application and modeling Curriculum Maps: Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to an essential understanding in the second column. Consult your Pearson/Prentice Hall or Glencoe Algebra 1 Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction. Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that making objectives measureable increases student mastery. Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a particular standard or set of standards. The additional resources provided are supplementary and should be used as needed for content support and differentiation. Review the Literacy Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested literacy strategies, in your instruction. Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard. Using your Pearson/Prentice Hall or Glencoe TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to include differentiated activities for small-group instruction and math stations. Major Content Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 4 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings Content & Tasks Literacy Connections Descriptive Statistics ( Allow 3 weeks for instruction, review, and assessments) S-ID Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable. S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots) S-ID Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variables. S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. S-IDInterpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable. S-ID.2 Statisticians summarize, represent, and interpret categorical and quantitative data in multiple ways since one method can reveal or create a different impression than another. There are many ways to organize and visually display data. Sometimes it is helpful to organize numerical data into intervals. Students will: Make and interpret frequency tables and histograms. Essential Question How can I communicate the properties of a data set to illuminate its important features? You can use different measures to interpret and compare sets of data. Students will: Find the mean, median, mode, and range. Pearson 12-2: Frequency and Histograms Glencoe 0-3 Representing Data MICA Items: S-ID.1 Question # 66 ID # 43350 S-ID.1 Question #67 ID # 44274 S-ID.5 Question #69 ID# 37180 S-ID.5 Question #70 ID# 44088 Pearson 12-3: Measures of Central Tendency and Dispersion Pearson Videos Finding mean, median, and mode(s) Finding range and using it to compare the spread of two sets of data Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. 12-3: Concept Byte – Standard Deviation Glencoe 12-2 Analyzing Survey Results Major Content Supporting Content Additional Content TN Algebra I Standards Writing in Math 1. Compare & Contrast – What is the difference between a symmetric histogram and a skewed histogram? 2. How can you use a frequency table of a data set to construct a cumulative frequency table? 3. Compare & Contrast – Describe the differences and similarities between joint, marginal, and conditional relative frequencies. Vocabulary Frequency, frequency table, histogram, cumulative frequency table Writing in Math 1. How do mean, median, and mode describe the central tendency of a data set? Why are three different measures needed? 2. How is the range of a data set affected by an outlier? 3. How does subtracting the same amount from each value in a data set affect the mean, median, mode, and range? Explain. 4. How does dividing each value in a data set by the same nonzero amount affect the mean, median, mode, and range? Explain. Shelby County Schools2015/2016 Revised 3/9/16 5 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings Content & Tasks Khan Academy Videos Descriptive Statistics S-IDInterpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable. S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots) calculation from a context. Separating data into subsets is a useful way to summarize and compare data sets. Students will: Make and interpret box-and-whisker plots; Find quartiles and percentiles. Pearson 12-4: Box-and-Whisker Plots Glencoe 0-13 Representing Data MICA Items: S-ID.1 Question # 66 ID # 43350 S-ID.1 Question #67 ID # 44274 Literacy Connections Vocabulary Measure of central tendency, outlier, mean, median, mode, measure of dispersion, range of a set of data Writing in Math 1. Describe two methods you can use to write an equation of a line given its graph. 2. Must the third quartile of a data set be less than the maximum value? Explain. 3. Can you find the mean, median, and mode of a data set by looking at a box-and-whisker plot? Explain. Vocabulary Quartile, interquartile range, interpret boxand-whisker plot, percentile, percentile rank Khan Academy Videos Descriptive Statistics S-IDInterpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variables. S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. S-ID.6a You can determine whether two sets of numerical data are related by graphing them as ordered pairs. If the two sets of data are related, you may be able to use a line to estimate or predict values. Students will: Write an equation of a trend line and of a line of best fit; Use a trend line and a line of best fit to make predictions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and Major Content Supporting Content 5-7: Scatter Plots and Trend Lines 5-7: Concept Byte – Collecting Linear Data 9-7: Linear, Quadratic, and Exponential Models MICA Items: S-ID.6 Question # 71 ID # 44081 Making a scatter plot Using scatter plots and trend lines to Additional Content TN Algebra I Standards Writing in Math 1. Compare & Contrast – How are a trend line and the line of best fit for a set of data pairs similar? How are they different? 2. Describe three real-world situations: one with a positive correlation, one with a negative correlation, and one with no correlation. 3. Give and describe two data sets that are correlated but do not have a causal relationship. Justify your reasoning. 4. Explain how to decide whether a linear, exponential, or quadratic function is the most Shelby County Schools2015/2016 Revised 3/9/16 6 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings exponential models. Content & Tasks make predictions Writing an equation for a trend line Writing an equation for a line of best fit S-ID.6b Informally assess the fit of a function by plotting and analyzing residuals. Scatterplots/Linear regression and Correlation S-ID.6c Fit a linear function for a scatterplot that suggests a linear association. Literacy Connections appropriate model for a set of data. Vocabulary Scatter plot, positive correlation, negative correlation, no correlation, trend line, interpolation, extrapolation, line of best fit, correlation coefficient, causation Modeling data using a linear, quadratic, or exponential model - Example 1 Modeling data using a linear, quadratic, or exponential model - Example 2 Khan Academy Videos Scatter plots ; Linear Regression & Correlation Data Analysis & Probability ( Allow 3 weeks for instruction, review, and assessments) S-IC Making Inferences and Justifying Conclusions Make inferences and justify conclusions from a sample. S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. When collecting data to solve a problem, you need to make sure that your methods are fair and that you accurately represent the results. In preparation for Algebra II please select the following lessons: Students will: Classify data and analyze samples and surveys Pearson Algebra I 12-5: Samples and Surveys Glencoe Algebra I 12-1 Designing a Survey Writing in Math Compare & Contrast – What is the difference between univariate data and bivariate data? Give an example of each type of data. Vocabulary Quantitative, qualitative, univariate, bivariate, population, sample, bias MICA Items: S-ID.3 Question # 68 ID # 43062 S-CP Conditional Probability and the Rules of Probability Understand and apply basic concepts of probability. Major Content You can use counting methods to find the number of possible ways to choose objects with and without regard to order. Supporting Content Pearson Algebra I 12-6: Permutations and Combinations Using the counting principle Additional Content TN Algebra I Standards Writing in Math 1. Compare & Contrast – How are permutations and combinations similar? How Shelby County Schools2015/2016 Revised 3/9/16 7 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings S-CP.2 Use permutations and combinations to compute probabilities of compound events and solve problems. Students will: Find permutations and combinations. Content & Tasks Counting using permutations Using permutation notation Using combination notation Using combinations in probability Glencoe Algebra I 12-4 Permutations and Combinations Literacy Connections are the different? 2. Explain why nCn is equal to 1. Vocabulary Multiplication Counting Principle, permutation, n factorial, combination Khan Academy Videos Permutations and Combinations EngageNY Precalculus and Advanced Topics Module 5, Topic A, Probability Lesson 1: The General Multiplication Rule Lesson 2: Counting Rules—The Fundamental Counting Principle and Permutations Lesson 3: Counting Rules—Combinations Lesson 4: Using Permutations and Combinations to Compute Probabilities S-CP Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data. S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”). Major Content Probability provides a process to determine the likelihood of events and determine whether the occurrence of one event makes some other result more or less likely. The probability of an event, or P (event), tells you how likely it is that the event will occur. You can find probabilities by reasoning mathematically or by using data collected from an experiment. Pearson 12-7: Theoretical and Experimental Probability Finding experimental probability Finding theoretical probability Glencoe 12-7 Probability Simulations Students will: Find theoretical and experimental probabilities. Supporting Content Additional Content TN Algebra I Standards See Engageny Lessons for Exit Tickets/Discussion Questions. Writing in Math Compare & Contrast – What is the difference between theoretical probability and experimental probability? Give an example of each type of data. Vocabulary Outcome, sample space, event, probability, theoretical probability, complement of an event, odds, experimental probability Shelby County Schools2015/2016 Revised 3/9/16 8 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings S-CP Conditional Probability and the Rules of Probability Use the rules of probability to compute probabilities of compound events in a uniform probability model. S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. You can write the probability of a compound event as an expression involving probabilities of simpler events. This may make the compound probability easier to find.. Students will: Find probabilities of mutually exclusive and overlapping events; Find probabilities of independent and dependent events. Content & Tasks Pearson 12-8: Probability of Compound Events Finding the probability of dependent events Finding the probability of independent events 12-8: Concept Byte- Conditional Probability Glencoe 12-5 Probability of Compound Events S-CP Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data. S-CP.2 Understand that two events A and B are Literacy Connections Writing in Math 1. Are an event and its complement mutually exclusive or overlapping? Use an example to explain. 2. Use your own words to explain the difference between independent and dependent events. Give an example of each. Vocabulary Compound event, mutually exclusive event, overlapping events, independent events, dependent events independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. Modeling with Equations and Functions (Allow 3 weeks including TNReady assessment, instruction after TNReady, review, and assessments) (TNReady Part II, April 25-May 6, 2016) N-Q Quantities In preparation for students’ next school year in mathematics please select from the following lessons to build and reinforce the Algebra I content. Reason quantitatively and use units to solve problems. N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.★ Engageny Algebra I Module 5, Topic A Modeling with Equations and Functions Lesson 1: Analyzing a Graph Lesson 2: Analyzing a Data Set Lesson 3: Analyzing a Verbal Description A-CED Create equations Create equations that describe numbers or relationships A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MICA Items: A-CED.2 Question # 21 ID # 43726 F-IF Interpreting Functions Major Content Supporting Content See Engageny Lessons for Exit Tickets/Discussion Questions. Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 9 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings Interpret functions that arise in applications in terms of the context Content & Tasks Literacy Connections A-CED.2 Question # 23 ID # 44106 A-CED.2 Question # 24 ID # 44062 F-IF.4 Question #44 ID# 44115 F-IF.4 Question #45 ID# 42961 F-BF.1a Question # 51 ID # 44103 F-LE.1b Question #60 ID # 44331 F-LE.1c Question #61 ID# 44332 F-LE.2 Question #62 ID# 44091 F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ F-IF.5 . Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★ F-BF Building Functions Build a function that models a relationship between two quantities. F-BF.1 Write a function that describes a relationship between two quantities. ★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F-LE Linear, Quadratic, and Exponential Models ★ Construct and compare linear, quadratic, and exponential models and solve problems F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval Major Content Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 10 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards Algebra I Essential Understandings Content & Tasks Literacy Connections relative to another. F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). See Engageny Lessons for Exit Tickets/Discussion Questions. -------------------------------------------------------------------------N-Q.2 (see above) A-CED.2 (see above) F-IF.4 (see above) F-IF.5 (see above) F-BF.1 (see above) N-Q Quantities Reason quantitatively and use units to solve problems. N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.★ -----------------------------------------------------------MICA Item(s): N-Q.3 Question #7 ID# 43698 A-CED.1 Question # 15 ID # 37228 A-CED.1 Question # 17 ID # 42809 F-IF.6 Question #46 ID # 42962 A-CED Create equations Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.★ Engageny Algebra I Module 5, Topic B Completing the Modeling Cycle Lesson 4: Modeling a Contect from a Graph Lesson 5: Modeling from a Sequence Lesson 6: Modeling a Context from Data Lesson 7: Modeling a Context from Data Lesson 8:Modeling a Context from a Verbal F-IF Interpreting Functions Interpret functions that arise in applications in terms of the context. F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of Major Content Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 11 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter TN State Standards change from a graph. Algebra I Essential Understandings Major Content Content & Tasks Literacy Connections Description Lesson 9:Modeling a Context from a Verbal Description ★ Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 12 of 13 Curriculum and Instruction – Office of Mathematics 4th Quarter Algebra I RESOURCE TOOLBOX Textbook Resources Standards Pearson Videos Khan Academy Teacher Tube Math TV The Futures Channel CCSS www.phschool.com/math http://www.pearsonsuccessnet.com http://tncore.org/ http://www.ccsstoolbox.org/ http://parcconline.org/ http://www.poweralgebra.com Common Core Flip Book Achieve Glencoe ConnectED Site - Textbook and Resources TN Algebra I Standards TN Department of Education Math Standards Calculator http://education.ti.com/educationportal/activityexchange/activity http://www.atomiclearning.com/ti_84 TICommonCore.com Literacy Literacy Skills and Strategies for Content Area Teachers (Math, p. 22) Formative Assessment Using the UPS Strategy Glencoe Reading & Writing in the Mathematics Classroom Illuminations (NCTM) Discovery Education Get The Math Interactive Manipulatives Additional Sites http://www.shodor.org/interactivate/activities/ http://www.kutasoftware.com/free.html Illuminations_Resources for Teaching Math http://www.stemresources.com/ http://www.ilovemath.org/index.php?option=com_docman http://www.mathbits.com/ http://www.ixl.com/math/algebra-1 http://www.illustrativemathematics.org/ http://learnzillion.com/ http://teachers.henrico.k12.va.us/math/hcpsalgebra1/m odule1-1.html TeacherPayTeachers http://www.regentsprep.org/Regents/math/ALGEBR A/AV1/indexAV1.htm http://www.casioeducation.com/educators The Teaching Channel Tasks Mathematics Assessment Project (MARS Tasks) Dan Meyer's Three-Act Math Tasks Illustrative Math Tasks UT Dana Center Inside Math Tasks SCS Math Tasks (Algebra 1) Graphic Organizers (9-12) NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/Appli cationHelp.htm#UsingTestResults/MAPReportsFinder.htm Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum) https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores. Mica Items Major Content Supporting Content Additional Content TN Algebra I Standards Shelby County Schools2015/2016 Revised 3/9/16 13 of 13