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Math 6th Grade Team Jump to… Scope and Sequence Map Mathematics: 2012-13 to 2017-18 Units of Study Hoover City Schools Correlation of Standards Special Notes Scope and Sequence Map Domains, Content Clusters, & Standard Numbers 1st nwks Units of Study 2nd nwks 3rd nwks 4th nwks Ratios and Proportional Relationships (RP) 5 Analyze proportional relationships and use them to solve real-world and mathematical problems: 1, 2, 3 The Number System (NS) Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers: 4, 5, 6 2 Expressions and Equations (EE) Use properties of operations to generate equivalent expressions: 7, 8 Solve real-life and mathematical problems using numerical and algebraic expressions and equations: 9, 10 2 4 Geometry (G) Draw, construct, and describe geometrical figures and describe the relationship between them: 11, 12, 13 Solve real-world and mathematical problems involving angle measure, area, surface area, and volume: 14, 15, 16 5 8, 9 Statistics and Probability (SP) Use random sampling to draw inferences about a population: 17, 18 Draw informal comparative inferences about two populations: 19, 20 Investigate chance processes and develop, use, and evaluate probability models: 21, 22, 23, 24 Back to top 7 10, 11 Units of Study Unit 1 – Introduction to Math Team Standards Understand what makes math team different from other classes: a. Student is more responsible for own learning b. Material comes at a fast pace COS # CCSS # Basic Local Page 1 of 14 Indicators of Proficiency Proficient Advanced Math 6th Grade Team Unit 1 – Introduction to Math Team Standards Mathematics: 2012-13 to 2017-18 COS # CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced c. Many topics are not part of the course of study d. There are in-class contests as well as the Saturday competitions e. A solid foundation of 6th grade material is required for success Instructional Recommendations / Resources: th Unit 1: The required summer work will cover some of the 6 grade objectives and some from Unit 2. Parents will be expected to help students with some of th the standards that are being skipped in the jump from 5 grade to math team. We will spend class time on the summer work and sample competition questions. Back to top Unit 2- Operations with Rational Numbers Standards Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers a) Describe situations in which opposite quantities combine to make 0. b) Understand p +q as the number located a distance |q | from p c) Understand subtraction of rational numbers as adding the additive inverse d) Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. e) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. f) Convert a rational number to a decimal; know that the decimal form of a rational number COS # 4 CCSS # 7-NS1 5 7-NS2 Basic Indicators of Proficiency Proficient Perform operations on positive and negative numbers. Apply to real world contexts. Explain and use absolute value in terms of distance Define and use the commutative, associative and distributive properties when performing operations. Page 2 of 14 Advanced Use multiple methods to explain operations on positive and negative numbers. Math 6th Grade Team Unit 2- Operations with Rational Numbers Standards terminates in 0s or eventually repeats. Apply properties of operations to operations on rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form. Apply properties of operations to calculate with numbers in any form and convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies. Instructional Recommendations / Resources: Mathematics: 2012-13 to 2017-18 COS # CCSS # 6 7-NS3 9 7-EE3 COS # CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced Solve problems with integers, decimals, and fractions using any operations Write an expression to represent a problem then simplify to an equivalent expression. Justify answer using estimation and mental computation Back to top Unit 3- Operations with Number Bases Standards Convert numbers between base 10 and other bases a. Showing an understanding of place value b. using shortcuts based on the relationships of the bases Perform addition, subtraction, multiplication and division on whole numbers in other bases Instructional Recommendations / Resources: Basic Indicators of Proficiency Proficient Convert numbers from base 10 to other number bases. Convert to base 10. Local Create addition and multiplication tables in other bases. Convert between bases 2, 4 and 8 and between bases 3 and 9. Solve computation problems in other bases. Local Back to top Page 3 of 14 Advanced Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Unit 4 – Variables, Expressions, and Equations Standards COS # Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 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. 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. a) Solve word problems leading to px + q = r and p(x + q) = r, px+q>r or px + q <r, where p, q, and r are specific rational numbers. b) Graph the solution set of the inequality and interpret it in the context of the problem. CCSS # 7 7-EE1 8 7-EE2 Basic Hoover City Schools Indicators of Proficiency Proficient Apply properties of operations (commutative, associative, distributive) to collect like terms and simplify variable expressions. Distribute a variable expression, with rational number coefficients, to each term in a variable expression. Advanced Construct examples of properties of operations, including distributive property. Solve equations and inequalities in one variable fluently. 10 7-EE4 COS # CCSS # Set up and solve an equation or inequality from a real world problem. Instructional Recommendations / Resources: Back to top Unit 5- Ratios & Proportional Relationships Standards Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Recognize and represent proportional relationships between quantities. a) Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a 1 Basic 7-RP1 Indicators of Proficiency Proficient Determine if a proportional relationship exists 2 7-RP2 Page 4 of 14 Advanced Compute unit rates ; compare to find the best buy Convert a recipe based on ratio of servings Explain why a relationship is or is not proportional Math 6th Grade Team Unit 5- Ratios & Proportional Relationships Standards coordinate plane and observing whether the graph is a straight line through the origin. b) Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c) Represent proportional relationships by equations. d) Explain what a point (x, y ) on the graph of a proportional relationships means in terms of the situation with special attention to the points (0, 0) and (1, r ) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Instructional Recommendations / Resources: Mathematics: 2012-13 to 2017-18 COS # CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced Use a scale factor or constant of proportionality to solve problems 3 7-RP3 11 7-G1 Solve proportional relationships, including percent problems, using both proportions and equations Create a scale drawing, given desired ratio of areas Determine when one method of solution is better than another Back to top Unit 6- Patterns in Numbers Standards COS # Recognize important groups of numbers and the patterns that exist within them. (Pascal’s Triangle, Fibonacci sequence, figurate numbers) Local Find the nth term rule, common differences, and sums of finite arithmetic sequences Find the nth term rule, common ratio, and sums of geometric sequences Create expressions to describe patterns found in real- Local CCSS # Basic Indicators of Proficiency Proficient Use the patterns to solve problems Know the sequences and reproduce parts of them to solve problems Solve competition problems involving these Local Solve competition problems involving these Local Use multiple representations of patterns Page 5 of 14 Advanced Math 6th Grade Team Unit 6- Patterns in Numbers Standards Mathematics: 2012-13 to 2017-18 COS # CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced to illustrate solutions found world problems. Show solutions to these problems as rules, tables, and graphs Instructional Recommendations / Resources: Back to top Unit 7- Taking a Chance Standards Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a) Understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b) Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. COS # CCSS # Basic Indicators of Proficiency Proficient Describe meanings of found probabilities as related to the problems that generated them 21 7-SP5 Compute compound probabilities using sample spaces and Fundamental Counting Principle 24 7-SP8 Instructional Recommendations / Resources: Back to top Page 6 of 14 Advanced Math 6th Grade Team Unit 8- Geometric Relationships Standards Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Instructional Recommendations / Resources: Mathematics: 2012-13 to 2017-18 COS # 12 13 15 CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced Sketch figures , draw accurate figures and use technology tools to create figures based on given conditions. 7-G2 Describe the plane figures that result from slicing three dimensional figures. 7-G3 Describe the changes in results based on the location and angle of the slice. Solve multistep problems for angle measures 7-G5 Back to top Unit 9- Circles and Polygons Standards Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Solve real-world and mathematical problems involving area, volume, and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prims. Learn some relationships that exist among lines in a circle and the arcs and angles that are formed. (inscribed angles, measures of arcs, inscribed COS # 14 CCSS # Basic 7-G4 Indicators of Proficiency Proficient Find area and circumference of a circle Define pi in terms of the circle and its parts Relate area and circumference of a circle Find surface area (total and lateral) and volume of three-dimensional figures 16 7-G6 Find area, surface area and volume of composed figures and those with holes Find measures of inscribed and central angles and their arcs Use proportions to find segment lengths of chords Local Page 7 of 14 Advanced Math 6th Grade Team Unit 9- Circles and Polygons Standards Mathematics: 2012-13 to 2017-18 COS # CCSS # Hoover City Schools Basic Indicators of Proficiency Proficient Advanced Basic Indicators of Proficiency Proficient Advanced polygons, segment lengths) Instructional Recommendations / Resources: Back to top Unit 10- Statistics Standards Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. COS # CCSS # Determine if a sample is representative of the population. 17 7-SP1 Discuss sampling methods and validity of results Describe a typical student based on random sampling of characteristics 18 19 20 7-SP2 7-SP3 Compare multiple sets of data by comparing measures of center and measures of spread. 7-SP4 Compare multiple sets of data by comparing measures of center and measures of spread. Instructional Recommendations / Resources: CMP Samples and Populations Back to top Page 8 of 14 Justify the validity of the results based on samples used Create data that would support the measures of center and spread that could represent the populations Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Unit 11- Probability Simulations Standards COS # Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a) Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. b) Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. c) Design and use a simulation to generate frequencies for compound events. Instructional Recommendations / Resources: CCSS # Basic Hoover City Schools Indicators of Proficiency Proficient Advanced Conduct trials using technology to collect data used for prediction 22 7-SP6 Create a simulation around elections where all candidates have an equal chance of winning; find out the winner 23 24 7-SP7 7-SP8 Create a simulation around elections with differing probabilities, based on money, name recognition and other categories; find the winner Create a simulation for compound events, including dependent and independent events Back to top Correlation of Standards Standards Key AL COS # CCSS # HCS Unit # 1 7-RP1 5 2 7-RP2 5 Ratios and Proportional Relationships Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Recognize and represent proportional relationships between quantities. a) Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the Page 9 of 14 Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Hoover City Schools Standards Key AL COS # CCSS # HCS Unit # origin. b) Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c) Represent proportional relationships by equations. d) Explain what a point (x, y ) on the graph of a proportional relationships means in terms of the situation with special attention to the points (0, 0) and (1, r ) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent problems 3 7-RP3 5 4 7-NS1 2 5 7-NS2 2 6 7-NS3 2 7 7-EE1 4 The Number System Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a) Describe situations in which opposite quantities combine to make 0. b) Understand p +q as the number located a distance |q | from p , in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c) Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q ). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d) Apply properties of operations as strategies to add and subtract rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b) Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then –( ) = = . Interpret quotients of rational numbers by describing real-world contexts. c) Apply properties of operations as strategies to multiply and divide rational numbers. d) Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Expressions and Equations Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Page 10 of 14 Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Standards Key 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. Solve multistep 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. 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. c) 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. d) 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. Hoover City Schools AL COS # CCSS # HCS Unit # 8 7-EE2 4 9 7-EE3 2 10 7-EE4 4 11 7-G1 5 12 7-G2 8 13 7-G3 8 14 7-G4 9 15 7-G5 8 16 7-G6 9 17 7-SP1 10 18 7-SP2 10 Geometry Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prims. Statistics and Probability Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. Page 11 of 14 Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Standards Key Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. c) Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. d) Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. d) Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. e) Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. f) Design and use a simulation to generate frequencies for compound events. Back to top Hoover City Schools AL COS # CCSS # HCS Unit # 19 7-SP3 10 20 7-SP4 10 21 7-SP5 7 22 7-SP6 11 23 7-SP7 11 24 7-SP8 7, 11 Special Notes This local curriculum document was developed from the 2010 Alabama Course of Study for Mathematics which was itself based on the newly adopted Common Core State Standards for Mathematics. State COS standards are keyed to CCSS (i.e. Common Core) standards using the lettering and number system employed by the CCSS so that instructional resources which are subsequently designed to support the CCSS can be easily matched back to lessons based on state and local requirements. The Standards for Mathematical Practice describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students. These standards were developed with input from the National Council of Teachers of Mathematics and the National Research Page 12 of 14 Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Hoover City Schools Council, and math teachers should reinforce these process skills when designing daily instructional lessons for students at all grade levels in the Hoover school system: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning According to the Alabama Quality Teaching Standards (AQTS), teachers of all grade levels and subjects are required to model and reinforce literacy skills for all students. The Alabama Course of Study for Mathematics defines specific college and career readiness “anchor standards” for grades 6-12 in the areas of reading and writing. Specific grade-appropriate criteria can be found in the state course of study document, but the general anchor standards are defined below: Reading Key Ideas and Details 1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text. 2. Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas. 3. Analyze how and why individuals, events, or ideas develop and interact over the course of a text. Craft and Structure 4. Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone. 5. Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g. a section, chapter, scene, or stanza) relate to each other and the whole. 6. Assess how point of view or purpose shapes the content and style of a text. Integration of Knowledge and Ideas 7. Integrate and evaluate content presented in diverse formats and media, including visually and quantitatively, as well as in words. 8. Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence. 9. Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the Page 13 of 14 Math 6th Grade Team Mathematics: 2012-13 to 2017-18 Hoover City Schools approaches the authors take. Range of Reading and Level of Text Complexity 10. Read and comprehend complex literary and informational texts independently and proficiently. Writing Text Types and Purposes 1. Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence. 2. Write informative / explanatory texts to examine and convey complex ideas and information clearly and accurate through the effective selection, organization, and analysis of content. 3. Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences. Production and Distribution of Writing 4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 5. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. 6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others. Research to Build and Present Knowledge 7. Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation. 8. Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism. 9. Draw evidence form literary or informational texts to support analysis, reflection, and research. Range of Writing 10. Write routinely over extended time frames (time for research, reflection, and revision) and short time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. Back to top Page 14 of 14