Mathematics Grade 7 Transition Alignment Guide (TAG) Tool

Transcription

1 Transition Alignment Guide (TAG) Tool As districts build their mathematics curriculum for , it is important to remember the implementation schedule for new mathematics TEKS. In 2012, the Teas State Board of Education (SBOE) adopted and approved new mathematics standards for Kindergarten through High School. Implementation dates for Kindergarten through Grade 8 will begin in , and implementation for High School will begin in Both implementation dates are contingent upon SBOE approval of instructional materials. For the purpose of this document, standards are referred to in the following manner: new standards = newly adopted 2012 mathematics standards that will be implemented in K 8 ( ) and high school ( ) current standards = mathematics standards that are currently required by law in the classroom With new mathematics standards on the horizon, teachers will begin to study the new standards and consider how the changes impact their current mathematics curriculum and instruction. To prepare for new standard implementation, CSCOPE suggests the following: Step 1: Teachers eamine the new standards in relation to the current standards. Contact your local Education Service Center for facilitating this Side-by-Side standard study. The state's Sideby-Side resource may be found at the following URL: 20side&sort_by=title&sort_order=DESC&items_per_pag e=50 Step 2: After teachers have studied the standards through the Side-by- Side, they determine if the changes between new standards and current standards produce potential gaps that affect current mathematics curriculum and instruction. Step 3: CSCOPE s newly developed Transition Alignment Guide (TAG) Tools will guide teachers through a process of determining the most significant potential curriculum gaps and how those gaps might be addressed in current CSCOPE curriculum documents. The CSCOPE TAG Tools are designed for K-12 and outline the following: 1.) the grade level and school year affected by the gap, 2.) the actual curricular gaps that eist between current and new standards, and 3.) the locations within the current CSCOPE Unit s where each potential gap could be addressed. The development of the CSCOPE TAG Tools focused on students moving from one grade level to the net during the transition years ( for K 8, and and for high school). The two gap considerations addressed in these tools include: 1.) gaps due to the new standard changes in the grade level they are entering and 2.) gaps due to new standards in which students did not receive instruction during the prior year. CSCOPE considered both of these possible situations by identifying new standards that reflect potential gaps in comparison to current standards and the current CSCOPE VAD specificity for all grade levels. 2013, TESCCC 06/01/13 page 1 of 40

2 Transition Alignment Guide (TAG) Tool The Transition Alignment Guide (TAG) Tools developed by CSCOPE have four components: #1 YAG Pacing Considerations: Reflects a summary of suggested ideas for re-calibrating the current YAG to reflect the suggested time considerations for infusing new standards into the current CSCOPE Unit s Provides guidance on how these new standards might be infused; however, the decision about pacing is left to teachers and local control on how best to compress or etend instruction based on student needs and the district s school calendar #2 Gap Identification Matri: #3 Gap Identification At-a-Glance: Identifies only the new standards that may create curriculum gaps in each grade level ( gap standards may come from multiple grade levels) Identifies specific content gaps created by these identified new standards Identifies the CSCOPE Unit (s) in the current CSCOPE mathematics curriculum where the identified gaps may be addressed Identifies only the TEKS number of each gap standard identified Identifies the CSCOPE Unit (s) in the current CSCOPE mathematics curriculum where the identified gaps may be addressed #4 Unit Consideration Tool: Suggests bundling identified gaps with TEKS from specific current CSCOPE Unit s ( gap standards may come from multiple grade levels) Suggests CSCOPE Unit curricular considerations for only the identified gaps, as appropriate Reflects suggested time considerations for infusing new standards Component #1: How do I read the YAG Pacing Considerations? Current CSCOPE Unit lists the CSCOPE Unit in which new mathematics standards may be infused Suggestions for Addressing and Additional Time identifies the new mathematics standards that may be infused in the CSCOPE Unit, along with the possible number of days that may be needed to address these new standards When considering adding new mathematics standards in the current curriculum, CSCOPE re-calibrated the current, published CSCOPE YAG to include the suggested additional time that may be needed. While we hope to provide guidance on how these new standards might be infused, the decision about pacing is left to teachers and local control on how best to compress or etend instruction based on student needs and the district s school calendar. 2013, TESCCC 06/01/13 page 2 of 40

3 Transition Alignment Guide (TAG) Tool Component #2: How do I read the TAG Tool: Gap Identification Matri? TEKS (Adopted 2012) column identifies new standards that reflect potential gaps in comparison to current standards and the current CSCOPE VAD specificity. Districts are encouraged to eamine their implemented curriculum to identify additional gaps as appropriate. o The new standard s Knowledge and Skill Statement o The new standard s Student Epectation; underlined words reflect the content gaps from current standards to new standards Si Weeks columns reflect each grading period U01, U02, U03, etc. columns reflect each CSCOPE Unit within each grading period; X indicates the CSCOPE Unit in which the identified gaps may be addressed Component #3: How do I read the TAG Tool: Gap Identification At-a-Glance? TEKS (Adopted 2012) column identifies new standards that reflect potential gaps (Student Epectation number only) Si Weeks columns reflect each grading period U01, U02, U03, etc. columns reflect each CSCOPE Unit within each grading period; X indicates the CSCOPE Unit in which the identified gaps may be addressed 2013, TESCCC 06/01/13 page 3 of 40

4 Transition Alignment Guide (TAG) Tool Component #4: How do I read the TAG Tool: Unit Consideration Tool? Within each bundled CSCOPE Unit, you will find the following: The number of additional days that may be needed for each unit The new standard Knowledge and Skills statement(s) The new standard Student Epectation(s); underlined words reflect the content gaps from current standards to new standards Unit Considerations addressing the new standard gaps with the school years affected. The CSCOPE Unit considerations include: Suggested specific CSCOPE Unit s in which the identified gaps may be addressed or suggested teacher-created new unit (s) to address the identified content gaps Identified gaps for each standard in the CSCOPE Unit (from the TAG Tool: Gap Identification Matri) 2013, TESCCC 06/01/13 page 4 of 40

5 TAG Tool: YAG Pacing Considerations What are the implications regarding the current CSCOPE Year-at-a-Glance (YAG)? When considering adding new mathematics standards in the current curriculum, CSCOPE re-calibrated the current, published CSCOPE YAG to include the suggested additional time that may be needed. While we hope to provide guidance on how these new standards might be infused, the decision about pacing is left to teachers and local control on how best to compress or etend instruction based on student needs and the district s school calendar. The YAG Pacing Considerations below reflects a summary of the suggested time considerations for infusing new standards into current CSCOPE Unit s and should be used in conjunction with the current CSCOPE YAG: Current CSCOPE Unit Unit 01 Unit 02 Unit 03 Unit 04 Unit 05 Unit 06 Unit 07 Unit 08 Unit 09 Unit 10 Unit 11 Unit 12 Teacher-Created Unit A Teacher-Created Unit B Teacher-Created Unit C YAG Pacing Considerations Suggestions for Addressing and Additional Time 6.2B; 7.2 (no additional days may be needed); 6.2C, 6.2D (1 additional day may be needed) 7.3A, 7.3B (1 additional day may be needed) 6.4C, 6.4D, 6.4F; 7.5A (no additional days may be needed) 6.11 (no additional days may be needed) No suggested changes 6.4A; 6.6A, 6.6B; 7.4A; 7.7 (no additional days may be needed) 6.8A; 7.9C (no additional days may be needed); 7.11C (1 additional day may be needed) 7.8A, 7.8B; 7.9A (1 additional day may be needed) 6.12A, 6.12C, 6.12D; 6.13A, 6.13B; 7.12A (2 additional days may be needed); 7.6G (no additional days may be needed) No suggested changes No suggested changes Replace current unit with three new teacher-created units (See Unit A, Unit B, and Unit C.); current CSCOPE Unit 12 may be an optional outside project. Inequalities and Relationships: 7.10A, 7.10B, 7.10C; 7.11A, 7.11B (4 additional days may be needed) Etending Measurement: 7.4E; 7.9D (3 additional days may be needed) Etending Probability and Statistics: 7.6A, 7.6B, 7.6C, 7.6D, 7.6H, 7.6I; 7.12C (3 additional days may be needed) 2013, TESCCC 06/01/13 page 5 of 40

6 TEKS (Adopted 2012) 6.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 6.2B Identify a number, its opposite, and its absolute value. 6.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 6.2C Locate, compare, and order integers and rational numbers using a number line. 6.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 6.2D Order a set of rational numbers arising from mathematical and real-world contets. 6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4A Compare two rules verbally, numerically, graphically, and symbolically in the form of y = a or y = + a in order to differentiate between additive and multiplicative relationships. 6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4C Give eamples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4 Proportionality. The student applies mathematical process TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 6 of 40

7 TEKS (Adopted 2012) standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4D Give eamples of rates as the comparison by division of two quantities having different attributes, including rates as quotients. 6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4F Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers. 6.6 Epressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is epected to: 6.6A Identify independent and dependent quantities from tables and graphs. 6.6 Epressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is epected to: 6.6B Write an equation that represents the relationship between independent and dependent quantities from a table. 6.8 Epressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is epected to: 6.8A Etend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 7 of 40

8 TEKS (Adopted 2012) relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is epected to: 6.11 Graph points in all four quadrants using ordered pairs of rational numbers Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is epected to: 6.12A Represent numeric data graphically, including dot plots, stem-andleaf plots, histograms, and bo plots Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is epected to: 6.12C Summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is epected to: 6.12D Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 8 of 40

9 TEKS (Adopted 2012) 6.13 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is epected to: 6.13A Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and bo plots Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is epected to: 6.13B Distinguish between situations that yield data with and without variability. 7.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 7.2 Etend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. 7.3 Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is epected to: 7.3A Add, subtract, multiply, and divide rational numbers fluently. 7.3 Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is epected to: 7.3B Apply and etend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 9 of 40

10 TEKS (Adopted 2012) 7.4 Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is epected to: 7.4A Represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt. 7.4 Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is epected to: 7.4E Convert between measurement systems, including the use of proportions and the use of unit rates. 7.5 Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is epected to: 7.5A Generalize the critical attributes of similarity, including ratios within and between similar shapes. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6A Represent sample spaces for simple and compound events using lists and tree diagrams. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 10 of 40

11 TEKS (Adopted 2012) 7.6B Select and use different simulations to represent simple and compound events with and without technology. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6C Make predictions and determine solutions using eperimental data for simple and compound events. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6D Make predictions and determine solutions using theoretical probability for simple and compound events. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6G Solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents. 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6H Solve problems using qualitative and quantitative predictions and comparisons from simple eperiments. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 11 of 40

12 TEKS (Adopted 2012) 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6I Determine eperimental and theoretical probabilities related to simple and compound events using data and sample spaces. 7.7 Epressions, equations, and relationships. The student applies mathematical process standards to represent linear relationships using multiple representations. The student is epected to: 7.7 Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = m + b. 7.8 Epressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is epected to: 7.8A Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas. 7.8 Epressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is epected to: 7.8B Eplain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas. 7.9 Epressions, equations, and relationships. The student applies mathematical process standards to TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 12 of 40

13 TEKS (Adopted 2012) solve geometric problems. The student is epected to: 7.9A Solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. 7.9 Epressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is epected to: 7.9C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. 7.9 Epressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is epected to: 7.9D Solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net Epressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is epected to: 7.10A Write one-variable, two-step equations and inequalities to represent constraints or conditions within problems Epressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is epected to: 7.10B Represent solutions for onevariable, two-step equations and inequalities on number lines. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 13 of 40

14 TEKS (Adopted 2012) 7.10 Epressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is epected to: 7.10C Write a corresponding real-world problem given a one-variable, two-step equation or inequality Epressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is epected to: 7.11A Model and solve one-variable, twostep equations and inequalities Epressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is epected to: 7.11B Determine if the given value(s) make(s) one-variable, two-step equations and inequalities true Epressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is epected to: 7.11C Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is epected to: 7.12A Compare two groups of numeric data using comparative dot plots or bo plots by comparing their shapes, centers, and spreads. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C 2013, TESCCC 06/01/13 page 14 of 40

15 TEKS (Adopted 2012) 7.12 Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is epected to: 7.12C Compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations. TAG Tool: Gap Identification Matri 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B Unit C standards listed reflect potential gaps in comparison to current standards and the current CSCOPE VAD specificity. Districts are encouraged to eamine their implemented curriculum to identify additional gaps as appropriate. 2013, TESCCC 06/01/13 page 15 of 40

16 TEKS (Adopted 2012) 6.2B 6.2C 6.2D TAG Tool: GAP Identification At-a-Glance 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B 6.4A 6.4C 6.4D 6.4F 6.6A 6.6B 6.8A A 6.12C 6.12D 6.13A 6.13B A 7.3B 7.4A 7.4E 7.5A 7.6A 7.6B 7.6C 7.6D 7.6G 7.6H 7.6I 7.7 Unit C 2013, TESCCC 06/01/13 page 16 of 40

17 TEKS (Adopted 2012) TAG Tool: GAP Identification At-a-Glance 1 st Si Weeks 2 nd Si Weeks 3 rd Si Weeks 4 th Si Weeks 5 th Si Weeks 6 th Si Weeks U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 Unit A Unit B 7.8A 7.8B 7.9A 7.9C 7.9D 7.10A 7.10B 7.10C 7.11A 7.11B 7.11C 7.12A 7.12C standards listed reflect two gap considerations: 1.) gaps due to the new standard changes in the grade level they are entering and 2.) gaps due to new standards in which students did not receive instruction during the prior year. CSCOPE considered both of these situations by identifying new standards that reflect potential gaps in comparison to current standards and in comparison to current CSCOPE VAD specificity for all grade levels. Districts are encouraged to eamine their implemented curriculum and their prior implementation of all CSCOPE VAD specificity to determine additional potential gaps. Unit C 2013, TESCCC 06/01/13 page 17 of 40

18 TAG Tool: Unit Consideration Tool Unit 01 Numerical Understanding: Integers and Positive Rational Numbers (1 additional day may be needed) Grade Standard(s) 6.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 6.2B Identify a number, its opposite, and its absolute value. 6.2C Locate, compare, and order integers and rational numbers using a number line. 6.2D Order a set of rational numbers arising from mathematical and real-world contets. Teacher Identify a number and its absolute value. Distance is always a positive value or zero. Relationship between absolute value and distance E: Relate the absolute value of a number to distance using a number line and understand that the distance of a number from zero is the same as the distance of the opposite of the number from zero. -3 = = 3 Absolute value the distance of a value from zero Locate, compare, and order rational numbers using a number line. Rational numbers include negative fractions, decimals, and percents. Comparative language (symbols and words) Locate multiple forms of rational numbers including negative fractions, decimals, and percents on number lines (marked with proportional, pre-determined intervals), open number lines (no marked intervals), and partially complete number lines (with at least two pre-determined, labeled numbers). Number line 1 E: Locate, 2.8, 2 ascending order. 1 2, 75%, 0, 2 5 1, , and 0.5 on the number line. Use comparative symbols to list the numbers in

19 TAG Tool: Unit Consideration Tool 3 3 Open number line: E: Locate 15%, 3.4, descending order. 7, 4, 8 1 1, 20%, 4 11, and on the number line. Use comparative symbols to list the numbers in Partially complete number line: 9 E: Locate 0.45,, 10%, 1.8, , 10, and 0.5 on the number line. Use comparative symbols to order the numbers from 8 greatest to least. 2 1 Order a set of rational numbers arising from mathematical and real-world contets. Rational numbers include negative fractions, decimals, and percents. Problems arising in everyday life, society, and the workplace Suggest Grade 6 teachers infuse new standards 6.2B, 6.2C, and 6.2D into their current curriculum. (See Grade 6 TAG Tool.) Standard(s) 7.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is epected to: 7.2 Etend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. 2013, TESCCC 06/01/13 page 19 of 40

20 TAG Tool: Unit Consideration Tool Teacher Etend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers. Visual representations to represent sets and subsets of rational numbers E: Venn diagram, tree diagram, etc. Rational Numbers Rational Numbers Integers Whole Numbers Counting Numbers Integers Whole Numbers Counting Numbers 2013, TESCCC 06/01/13 page 20 of 40

21 TAG Tool: Unit Consideration Tool Unit 02 Numerical Operations: Integers and Positive Rational Numbers (1 additional day may be needed) Standard(s) 7.3 Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is epected to: 7.3A Add, subtract, multiply, and divide rational numbers fluently. 7.3B Apply and etend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. Teacher Add, subtract, multiply, and divide negative rational numbers fluently. Multiple forms of rational numbers within a single problem to include negative fractions, decimals, and percents Relate algorithms for integer operations to algorithms for rational number operations. Perform operations with rational numbers fluently, meaning efficient application of procedures with accuracy. Apply and etend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. Rational numbers include negative fractions, decimals, and percents. Problems arising in everyday life, society, and the workplace 2013, TESCCC 06/01/13 page 21 of 40

22 TAG Tool: Unit Consideration Tool Unit 03 Proportionality: Similar Figures, Representations, and Applications (no additional days may be needed) Grade Standard(s) 6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4C Give eamples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4D Give eamples of rates as the comparison by division of two quantities having different attributes, including rates as quotients. 6.4F Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers. Teacher Give eamples of ratios as multiplicative comparisons of two quantities describing the same attribute. Multiplicative comparison of two quantities a proportional comparison in which one quantity can be described as a multiple of the other E: The length of worm A to worm B is 9 cm to 6 cm, so worm A is 1.5 times as long as worm B, and worm B is 2 as long as worm A. 3 Give eamples of rates as the comparison by division of two quantities having different attributes, including rates as quotients. Comparison by division of two quantities a proportional comparison in which one quantity can be described as a ratio of the other E: 2 inches per 3 seconds is equivalent to 2 3 inches per second, or 4 inches for every 6 seconds, or 1 inch for each 1.5 seconds, etc. Represent benchmark percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers. Benchmark percents and their multiples using various representations Suggest Grade 6 teachers infuse new standards 6.4C, 6.4D, and 6.4F into their current curriculum. (See Grade 6 TAG Tool.) Standard(s) 7.5 Proportionality. The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships. The student is epected to: 7.5A Generalize the critical attributes of similarity, including ratios within and between similar shapes. 2013, TESCCC 06/01/13 page 22 of 40

23 TAG Tool: Unit Consideration Tool Teacher Generalize the critical attributes of similarity, including ratios within similar shapes. Ratios within similar shapes versus ratios between similar shapes Q 7.5 R T S Z Y X W 3 ratios within similar shapes QR 7.5 = = 2 ST 3.75 WX 3 2 YZ = 1.5 = ratios between similar shapes WX XY YZ WZ = = = QR RS ST QT = = = , TESCCC 06/01/13 page 23 of 40

24 TAG Tool: Unit Consideration Tool Unit 04 Geometry: Coordinate Plane Graphing Transformations, and Perspectives (no additional days may be needed) 6.11 Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is epected to: 6.11 Graph points in all four quadrants using ordered pairs of rational numbers. Teacher Graph points in all four quadrants using ordered pairs of rational numbers. Ordered pairs of rational numbers include negative fractions and decimals. Suggest Grade 6 teachers infuse new standard 6.11 into their current curriculum. (See Grade 6 TAG Tool.) 2013, TESCCC 06/01/13 page 24 of 40

25 TAG Tool: Unit Consideration Tool Unit 06 Algebraic Representations and Applications (no additional days may be needed) Grade Standard(s) 6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is epected to: 6.4A Compare two rules verbally, numerically, graphically, and symbolically in the form of y = a or y = + a in order to differentiate between additive and multiplicative relationships. Teacher Compare two rules verbally, numerically, graphically, and symbolically in the form of y = a or y = + a in order to differentiate between additive and multiplicative relationships. Differentiate between multiple representations of additive and multiplicative relationships. Verbal Additive Relationship Algebraic Multiplicative Relationship Verbal Algebraic Joe is 7 years older than his sister Carol. y = + 7 Steven earns $11.50 each hour he works at the grocery store. y = Joe Graph Carol Numeric Carol Joe Amount (dollars) Graph Time (hours) Numeric Time Amount (hours) (dollars) Additive relationship when a constant value is added to an input value to determine the output value (y = + a) Multiplicative relationship when a constant value is multiplied to an input value to determine the output value (y = a) Suggest Grade 6 teachers infuse new standard 6.4A into their current curriculum. (See Grade 6 TAG Tool.) 2013, TESCCC 06/01/13 page 25 of 40

26 TAG Tool: Unit Consideration Tool Grade Standard(s) 6.6 Epressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to describe algebraic relationships. The student is epected to: 6.6A Identify independent and dependent quantities from tables and graphs. 6.6B Write an equation that represents the relationship between independent and dependent quantities from a table. Teacher Identify independent and dependent quantities from tables and graphs. Independent quantities are represented by the coordinates or the input. Dependent quantities are represented by the y coordinates or the output. Write an equation that represents the relationship between independent and dependent values from a table. In a table of related data pairs, the y value (output) is dependent upon the value (input). Suggest Grade 6 teachers infuse new standards 6.6A and 6.6B into their current curriculum. (See Grade 6 TAG Tool.) Standard(s) 7.4 Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is epected to: 7.4A Represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt. Teacher Represent constant rates of change in mathematical and real-world problems, including d = rt. In d = rt, the d represents distance, the r represents rate, and the t represents time. Relate the constant rate of change r, in d = rt, to the constant of proportionality k, in y = k Standard(s) 7.7 Epressions, equations, and relationships. The student applies mathematical process standards to represent linear relationships using multiple representations. The student is epected to: 7.7 Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = m + b. 2013, TESCCC 06/01/13 page 26 of 40

27 Teacher Represent linear relationships using the form y = m + b. Equations with rational number coefficients and constants Rational numbers include negative fractions and decimals. TAG Tool: Unit Consideration Tool 2013, TESCCC 06/01/13 page 27 of 40

28 TAG Tool: Unit Consideration Tool Unit 07 Geometry and Measurement: Two-Dimensional (1 additional day may be needed) Grade Standard(s) 6.8 Epressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is epected to: 6.8A Etend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle. Teacher Etend previous knowledge of triangles and their properties to include determining when three lengths form a triangle. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Suggest Grade 6 teachers infuse new standard 6.8A into their current curriculum. (See Grade 6 TAG Tool.) Standard(s) 7.9 Epressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is epected to: 7.9C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. Teacher Determine the area of composite figures containing semicircles and quarter circles. Composite figures include combinations of polygons and circles Epressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is epected to: 7.11C Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. 2013, TESCCC 06/01/13 page 28 of 40

29 TAG Tool: Unit Consideration Tool Teacher Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. One-variable, two step equations using geometry concepts Equations, when given angle measures as numeric and/or algebraic epressions E: Sum of angles in a triangle Equation for sum of angles: 180 = (8 + 6) + (6 3) + ( ) = 8 (8 + 6) = 70º (6 3) = 45º ( ) = 65º 4 E: Other angle relationships Equation for determining missing measures: 90 = ( ) + ( ) = 1.7 ( ) = 28º ( ) = 62º 2013, TESCCC 06/01/13 page 29 of 40

30 TAG Tool: Unit Consideration Tool Unit 08 Measurement: Three-Dimensional (1 additional day may be needed) Standard(s) 7.8 Epressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is epected to: 7.8A Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas. 7.8B Eplain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas. Teacher Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas. Model the relationship between the volume of a rectangular prism and the volume of a rectangular pyramid to develop the formula for a rectangular pyramid (V = 1 3 Bh). Eplain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas. Eplain the relationship between the volume of a triangular prism and the volume of a triangular pyramid to develop the formula for a triangular pyramid (V = 1 3 Bh). Emphasize relationships of congruent bases and heights of prisms and pyramids with eamples and non-eamples Standard(s) 7.9 Epressions, equations, and relationships. The student applies mathematical process standards to solve geometric problems. The student is epected to: 7.9A Solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. Teacher Solve problems involving the volume of rectangular pyramids and triangular pyramids. 2013, TESCCC 06/01/13 page 30 of 40

31 TAG Tool: Unit Consideration Tool Unit 09 Statistical Representations and Analysis (2 additional days may be needed) Grade Standard(s) 6.12 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to analyze problems. The student is epected to: 6.12A Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and bo plots. 6.12C Summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution. 6.12D Summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution. Teacher Represent numeric data graphically, including histograms and bo plots. Histogram a graphical representation of adjacent bars with different heights or lengths to represent the frequency of data in certain ranges of continuous and equal intervals Compare the similarities and differences between a histogram and bar graph The bars of a histogram are adjacent because the intervals of the numeric data are continuous. The bars of a bar graph are independent because the categories are not dependent of each other. Bo plots (bo and whisker plots) Five number summary minimum quartile 1 (Q1 median of lower 50% of data) median quartile 2 (Q3 median of upper 50% of data) maimum interquartile range (IQR) Q1 minimum median Q3 maimum 50% of data 50% of data 2013, TESCCC 06/01/13 page 31 of 40

32 TAG Tool: Unit Consideration Tool Summarize numeric data with numerical summaries including interquartile range (IQR) and use these summaries to describe the shape of the data distribution. Interquartile range calculated by IQR = Q3 Q1 Outliers calculated by (1.5 IQR) Shape of data (e.g., skewed left, symmetric, skewed right, etc.) Summarize categorical data with the percent bar graph. Percent bar graph a type of bar graph with independent bars that are layered (or stacked) that compares the related part(s) to the whole representing the total percent for each category Favorite Sport Grade 6 Grade 8 Soccer Football Basketball Other % 80% 60% 40% 20% Soccer Football Basketball Other Grade 6 Grade 8 Suggest Grade 6 teachers infuse new standards 6.12A, 6.12C, and 6.12D into their current curriculum. (See Grade 6 TAG Tool.) Grade Standard(s) 6.13 Measurement and data. The student applies mathematical process standards to use numerical or graphical representations to solve problems. The student is epected to: 6.13A Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and bo plots. 6.13B Distinguish between situations that yield data with and without variability. Teacher Interpret numerical data summarized in histograms and bo plots. Given a histogram or bo plot, determine and describe measures of center, shape, and spread of the data distribution. Distinguish between situations that yield data with and without variability. Data with variability can be summarized with a range. 2013, TESCCC 06/01/13 page 32 of 40

33 E: What are the ages of the children at the football game? Data without variability can be summarized with a single value. E: What is the age of the youngest child at the football game? TAG Tool: Unit Consideration Tool Suggest Grade 6 teachers infuse new standards 6.13A and 6.13B into their current curriculum. (See Grade 6 TAG Tool.) Standard(s) 7.6 Proportionality. The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships. The student is epected to: 7.6G Solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents. Teacher Solve problems using data represented in circle graphs, including part-to-whole and part-to-part comparisons and equivalents. Describe the proportional relationships of part-to-whole and part-to-part comparison in circle graphs. E: Given a circle graph representing a monthly budget with categories including rent, groceries, entertainment, and transportation, compare the amount spent on groceries to the entire budget (part-to-whole comparison) and compare the amount spent on groceries to the amount spent on transportation (part-to-part comparison) Standard(s) 7.12 Measurement and data. The student applies mathematical process standards to use statistical representations to analyze data. The student is epected to: 7.12A Compare two groups of numeric data using comparative dot plots or bo plots by comparing their shapes, centers, and spreads. Teacher Compare two groups of numeric data using comparative bo plots by comparing their shapes, centers, and spreads. E: Use bo plots to compare and contrast distributions of two groups of numeric data. Student Population Class A Class B , TESCCC 06/01/13 page 33 of 40

34 TAG Tool: Unit Consideration Tool Student Population ( ) Class A Class B Number of Students 2013, TESCCC 06/01/13 page 34 of 40

35 TAG Tool: Unit Consideration Tool Teacher-Created Unit A Inequalities and Relationships (4 additional days may be needed) Standard(s) 7.10 Epressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is epected to: 7.10A Write one-variable, two-step equations and inequalities to represent constraints or conditions within problems. 7.10B Represent solutions for one-variable, two-step equations and inequalities on number lines. 7.10C Write a corresponding real-world problem given a one-variable, two-step equation or inequality. Teacher Write one-variable, two-step inequalities to represent constraints or conditions within problems. E: Macy s cell phone bill costs $24 each month plus $0.15 per minute. Macy cannot spend more than $120 per month for her cell phone bill. Write an inequality to represent the relationship between the number of minutes Macy can use each month and her total cell phone bill. ( ). Represent solutions for one-variable, two-step inequalities on number lines. E: The solutions to the inequality < 29 can be represented using a number line Standard(s) 7.11 Epressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is epected to: 7.11A Model and solve one-variable, two-step equations and inequalities. 7.11B Determine if the given value(s) make(s) one-variable, two-step equations and inequalities true. Teacher Model and solve one-variable, two-step inequalities. Solution models (e.g., concrete, pictorial, algebraic, etc.) 2013, TESCCC 06/01/13 page 35 of 40