FOCAL POINTS AND TEKS COMPARISON TABLE SET GRADES 6-8

Transcription

1 FOCAL POINTS AND TEKS COMPARISON TABLE SET GRADES 6-8

2 Texas Response to Curriculum Focal Points Highlights Grade 6 The curriculum focal point and its description are presented on the summary page for each grade level.... a curriculum focal point is not a single TEKS statement; a curriculum focal point is a mathematical idea or theme that is developed through appropriate arrangements of TEKS statements at that grade level that lead into a connected grouping of TEKS at the next grade level -TxRCFP (2010) pg. 5 The content standards are listed below each focal point, and the actual SE statements are on the focal point page. Student expectations from one or more strands may be listed. The mathematical process standards are listed below each focal point. The Financial Literacy student expectations are listed here, and the actual SE statements are at the end of each grade level. The College and Career Readiness Standards addressed in each grade level are listed on the introductory page. The CCRS can be found at Student expectations may appear in more than one focal point Grade Level Connections are listed here, and the actual SE statements are after the last focal point for each grade level. All TEKS that did not fit into one of the curriculum focal points in a grade level were skills that either introduced material that would become a focus in a later grade or continued or extended materials from a previous grade. MSTAR Math Academy 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS

3 Texas Response to Curriculum Focal Points Highlights Grade 6 The curriculum focal point and its description are presented at the top of each page. The mathematical process standards are grouped and listed for each focal point. The complete mathematical process standards can be found on page 8 of the document. The student expectations for the content standards are provided on the focal point page. Student expectations from one or more strands may be listed within one focal point. Student expectation 6(6)(A) is from the expressions, equations, and relationships strand, and 6(11) is from the measurement and data strand Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS

4 Mathematical Process Standards Cards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. One set per group, print on tan cardstock. (1)(A) (1)(E) The student is expected to apply mathematics to problems arising in everyday life, society, and the workplace. The student is expected to create and use representations to organize, record, and communicate mathematical ideas. (1)(B) (1)(F) The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. The student is expected to analyze mathematical relationships to connect and communicate mathematical ideas. (1)(C) (1)(G) The student is expected to select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. The student is expected to display, explain, and justify mathematical ideas and arguments using precise mathematical language in written and oral communication. (1)(D) The student is expected to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Intentionally left blank 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

5 Focal Point Cards Two sets of cards are provided. One set per group, print on blue cardstock. Grade 8 Focal Points Representing, applying, and analyzing proportional relationships Students extend their understanding of proportionality to include representations on a coordinate plane and applications, including slopes of lines. They contrast proportional relationships with relationships that are not proportional. 8(1)(A)-(G); 8(3)(A)-(C); 8(4)(A)-(C); 8(5)(A)-(I); 8(10)(D) Using expressions and equations to describe relationships, including the Pythagorean Theorem Students select and use expressions and equations to represent and solve problems involving rational numbers. Students use geometric properties, including the Pythagorean Theorem, to solve problems. 8(1)(A)-(G); 8(6)(A)-(C); 8(7)(A)-(D); 8(8)(A)-(D); 8(9) Grade 8 Focal Points Representing, applying, and analyzing proportional relationships Students extend their understanding of proportionality to include representations on a coordinate plane and applications, including slopes of lines. They contrast proportional relationships with relationships that are not proportional. 8(1)(A)-(G); 8(3)(A)-(C); 8(4)(A)-(C); 8(5)(A)-(I); 8(10)(D) Using expressions and equations to describe relationships, including the Pythagorean Theorem Students select and use expressions and equations to represent and solve problems involving rational numbers. Students use geometric properties, including the Pythagorean Theorem, to solve problems. 8(1)(A)-(G); 8(6)(A)-(C); 8(7)(A)-(D); 8(8)(A)-(D); 8(9) Making inferences from data Students use representations of association, center, and variation to make inferences from data. 8(1)(A)-(G); 8(11)(A)-(C) Making inferences from data Students use representations of association, center, and variation to make inferences from data. 8(1)(A)-(G); 8(11)(A)-(C) 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

6 Two sets of cards are provided. One set per group, print on green cardstock. Grade 7 Focal Points Grade 7 Focal Points Developing fluency with rational numbers and operations to solve problems in a variety of contexts Students understand how operations extend across different sets of numbers. Students develop fluency with addition, subtraction, multiplication, and division of rational numbers and use the operations to solve problems. 7(1)(A)-(G); 7(2); 7(3)(A)-(B) Developing fluency with rational numbers and operations to solve problems in a variety of contexts Students understand how operations extend across different sets of numbers. Students develop fluency with addition, subtraction, multiplication, and division of rational numbers and use the operations to solve problems. 7(1)(A)-(G); 7(2); 7(3)(A)-(B) Representing and applying proportional relationships Students use reasoning about ratios, rates, proportionality, and percent to solve problems. 7(1)(A)-(G); 7(4)(A)-(E); 7(5)(A)-(C); 7(6)(A)-(I) Representing and applying proportional relationships Students use reasoning about ratios, rates, proportionality, and percent to solve problems. 7(1)(A)-(G); 7(4)(A)-(E); 7(5)(A)-(C); 7(6)(A)-(I) Using expressions and equations to describe relationships in a variety of contexts, including geometric problems Students select, justify, and use appropriate symbolic representations to solve problems in varied contexts, including use of geometric formulas for pyramids and circles. 7(1)(A)-(G); 7(8)(A)-(C); 7(9)(A)-(D); 7(10)(A)-(C); 7(11)(A)-(C) Using expressions and equations to describe relationships in a variety of contexts, including geometric problems Students select, justify, and use appropriate symbolic representations to solve problems in varied contexts, including use of geometric formulas for pyramids and circles. 7(1)(A)-(G); 7(8)(A)-(C); 7(9)(A)-(D); 7(10)(A)-(C); 7(11)(A)-(C) Comparing sets of data Students use representations of center, spread and shape to compare and form inferences about sets of data. 7(1)(A)-(G); 7(12)(A)-(C) Comparing sets of data Students use representations of center, spread and shape to compare and form inferences about sets of data. 7(1)(A)-(G); 7(12)(A)-(C) 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

7 Focal Point Cards Two sets of cards are provided. One set per group, print on orange cardstock. Grade 6 Focal Points Grade 6 Focal Points Using operations with integers and positive rational numbers to solve problems Students extend understanding of and develop procedures for addition, subtraction, multiplication, and division of integers and positive rational numbers. 6(1)(A)-(G); 6(2)(B)-(E); 6(3)(A)-(E) Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships Students use their knowledge of multiplication and division and fractions to develop understanding of and solve ratio and rate problems. Students extend their understanding of equivalent fractions to create equivalent ratios that describe situations that involve proportionality and use various representations (e.g. graphs, tables, equations) to solve problems involving proportional relationships. 6(1)(A)-(G); 6(4)(A)-(H); 6(5)(A)-(C) Using operations with integers and positive rational numbers to solve problems Students extend understanding of and develop procedures for addition, subtraction, multiplication, and division of integers and positive rational numbers. 6(1)(A)-(G); 6(2)(B)-(E); 6(3)(A)-(E) Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships Students use their knowledge of multiplication and division and fractions to develop understanding of and solve ratio and rate problems. Students extend their understanding of equivalent fractions to create equivalent ratios that describe situations that involve proportionality and use various representations (e.g. graphs, tables, equations) to solve problems involving proportional relationships. 6(1)(A)-(G); 6(4)(A)-(H); 6(5)(A)-(C) Using expressions and equations to represent relationships in a variety of contexts Students use expressions and equations to represent relationships in a variety of contexts. Students use mathematical symbols to represent linear relationships and formulas. 6(1)(A)-(G); 6(6)(A)-(C); 6(7)(A)-(D); 6(8)(B)-(D); 6(9)(A)-(C); 6(10)(A)-(B) Using expressions and equations to represent relationships in a variety of contexts Students use expressions and equations to represent relationships in a variety of contexts. Students use mathematical symbols to represent linear relationships and formulas. 6(1)(A)-(G); 6(6)(A)-(C); 6(7)(A)-(D); 6(8)(B)-(D); 6(9)(A)-(C); 6(10)(A)-(B) Understanding data representation Students understand and use descriptions of center, spread and shape to summarize and compare data sets. Students organize and display data to pose and solve problems. 6(1)(A)-(G); 6(6)(A); 6(11); 6(12)(A)-(D); 6(13)(A)-(B) Understanding data representation Students understand and use descriptions of center, spread and shape to summarize and compare data sets. Students organize and display data to pose and solve problems. 6(1)(A)-(G); 6(6)(A); 6(11); 6(12)(A)-(D); 6(13)(A)-(B) 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

8 Focal Point Cards Two sets of cards are provided. One set per group, print on pink cardstock. Grade 5 Focal Points Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations of fractions with like denominators. Students make reasonable estimates of fraction and decimal sums and differences and add and subtract fractions and add, subtract, multiply, and divide decimals to solve problems. Students apply their understanding of multiplication and division to build understanding of multiplication and division of fractions. 5(1)(A)-(G); 5(3)(A)-(L); 5(7) Grade 5 Focal Points Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations of fractions with like denominators. Students make reasonable estimates of fraction and decimal sums and differences and add and subtract fractions and add, subtract, multiply, and divide decimals to solve problems. Students apply their understanding of multiplication and division to build understanding of multiplication and division of fractions. 5(1)(A)-(G); 5(3)(A)-(L); 5(7) Understanding and generating expressions and equations to solve problems Students use or generate expressions and equations to solve problems involving the four operations. 5(1)(A)-(G); 5(4)(B)-(H); 5(7) Understanding and generating expressions and equations to solve problems Students use or generate expressions and equations to solve problems involving the four operations. 5(1)(A)-(G); 5(4)(B)-(H); 5(7) Representing and solving problems with perimeter, area, and volume Students apply their understanding of measurement to select appropriate units for measuring perimeter, area, and volume in specific problem contexts. Students use a variety of representations to build connections between direct measurement of perimeter, area, and volume to the use of related formulas. 5(1)(A)-(G); 5(4)(G)-(H); 5(6)(A)-(B); 5(7) Representing and solving problems with perimeter, area, and volume Students apply their understanding of measurement to select appropriate units for measuring perimeter, area, and volume in specific problem contexts. Students use a variety of representations to build connections between direct measurement of perimeter, area, and volume to the use of related formulas. 5(1)(A)-(G); 5(4)(G)-(H); 5(6)(A)-(B); 5(7) Organizing, representing, and interpreting sets of data Students use appropriate graphic displays (e.g., table, bar graph, coordinate plane) to describe data based on the attributes of a particular data set. 5(1)(A)-(G); 5(8)(A)-(C); 5(9)(A)-(C) Organizing, representing, and interpreting sets of data Students use appropriate graphic displays (e.g., table, bar graph, coordinate plane) to describe data based on the attributes of a particular data set. 5(1)(A)-(G); 5(8)(A)-(C); 5(9)(A)-(C) 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

9 A Vertical Look Discussion Questions Cards A Vertical Look Discussion Questions A Vertical Look Discussion Questions Are there any focal point concepts that end within the grade band? What are the implications of those endings? Are there any focal point concepts that end within the grade band? What are the implications of those endings? How do the focal points communicate articulation of ideas and concepts across the grade levels? How do the focal points communicate articulation of ideas and concepts across the grade levels? How do the focal points support the notions of depth and complexity? How do the focal points support the notions of depth and complexity? How do the focal points support algebra readiness? How do the focal points support algebra readiness? Are all focal points equally important? Are all focal points equally important? A Vertical Look Discussion Questions A Vertical Look Discussion Questions Are there any focal point concepts that end within the grade band? What are the implications of those endings? Are there any focal point concepts that end within the grade band? What are the implications of those endings? How do the focal points communicate articulation of ideas and concepts across the grade levels? How do the focal points communicate articulation of ideas and concepts across the grade levels? How do the focal points support the notions of depth and complexity? How do the focal points support the notions of depth and complexity? How do the focal points support algebra readiness? How do the focal points support algebra readiness? Are all focal points equally important? Are all focal points equally important? 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

10 Example Task Pocket Cut along the dashed lines. Two pockets are provided Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS

11 A VERTICAL LOOK AT KEY CONCEPTS AND PROCEDURES GRADE 6

12 The materials are copyrighted (c) and trademarked (tm) as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions: Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts and schools educational use without obtaining permission from TEA. Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA. Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way. No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty. For information contact: Office of Copyrights, Trademarks, License Agreements, and Royalties, Texas Education Agency, 1701 N. Congress Ave., Austin, TX ; phone: or ; copyrights@tea.state.tx.us Texas Education Agency All Rights Reserved Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 2

13 Revised TEKS (2012): Building to Grade 6 Number and Operations A Vertical Look at Key Concepts and Procedures The strand from the Revised TEKS (2012) is Order a set of rational Compare and order Compare and order Compare and order Compare and order Represent the Compare sets of found at the top of each numbers. The Revised TEKS two decimals (2012) to are the whole numbers to whole numbers up to whole numbers up to comparisons of objects up to 20. thousandths. 1,000,000, ,000. 1,200. two numbers page to along with the 100. grade level. Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Note: Comparing and ordering may be integrated into instruction related to unit rates, problems involving proportional relationships, and the personal financial literacy standards. student expectations adopted in 2012 that are scheduled to be implemented in pending funding. Compare two fractions with different numerators and different denominators. Compare two fractions having the same numerator or denominator. Locate, compare, and order integers and rational numbers using a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Name a point on a number line to tenths or hundredths. Locate fractions between 0 and 1 with specified denominators on a number line. Locate the position of a given whole number on an open number line. Grade 7 Grade 6 Use a visual representation of sets and subsets within the set of rational numbers. Classify whole numbers, integers, and rational numbers. Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity. Add, subtract, multiply, and divide rational numbers fluently. Key concepts and procedures for the identified grade level are in the shaded column. Multiply and divide positive rational numbers fluently. Add, subtract, multiply, and divide integers fluently. Add and subtract positive rational numbers fluently. Multiply with fluency a 3-digit by a 2-digit number. Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor. Add and subtract whole numbers and decimals to hundredths. Solve with fluency problems with multiplication and division (4-digit by 1- digit and 2-digit by 2- digit) Solve with fluency problems with addition and subtraction within 1,000. Grade levels for the concepts and procedures are identified in column headings for each set of key concepts and procedures. Multiply a 2-digit by a 1-digit number. The statements are summaries of student expectations that build up to each key concept and procedures. Not all student expectations for all grade levels are represented Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 3

14 Revised TEKS (2012): Building to Grade 6 Number and Operations A Vertical Look at Key Concepts and Procedures Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Note: Comparing and ordering may be integrated into instruction related to unit rates, problems involving proportional relationships, and the personal financial literacy standards. Order a set of rational numbers. Compare and order two decimals to thousandths. Compare and order whole numbers to 1,000,000,000. Compare two fractions with different numerators and different denominators. Compare and order whole numbers up to 100,000. Compare two fractions having the same numerator or denominator. Compare and order whole numbers up to 1,200. Represent the comparisons of two numbers to 100. Compare sets of objects up to 20. Locate, compare, and order integers and rational numbers using a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Name a point on a number line to tenths or hundredths. Locate fractions between 0 and 1 with specified denominators on a number line. Locate the position of a given whole number on an open number line. Grade 7 Grade 6 Use a visual representation of sets and subsets within the set of rational numbers. Classify whole numbers, integers, and rational numbers. Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity. Add and subtract positive rational numbers fluently. Multiply with fluency a 3-digit by a 2-digit number. Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor. Add and subtract whole numbers and decimals to hundredths. Solve with fluency problems with multiplication and division (4-digit by 1-digit and 2-digit by 2-digit) Solve with fluency problems with addition and subtraction within 1,000. Multiply a 2-digit by a 1-digit number. Multiply and divide positive rational numbers fluently. Add, subtract, multiply, and divide rational numbers fluently. Add, subtract, multiply, and divide integers fluently Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 4

15 Revised TEKS (2012): Building to Grade 6 Proportionality A Vertical Look at Key Concepts and Procedures Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Determine the constant of proportionality in problem situations and represent k as a rate of change using multiple representations. Compare two rules using multiple representations to differentiate between y=ax (multiplicative relationships) and y=x+a (additive relationships). Grade 7 Grade 6 Calculate unit rates. Give examples of ratios and rates, including rates as quotients. Represent and solve problems involving ratios and rates. Generate a numerical sequence when given a rule in the form y=ax or y=x+a. Recognize the difference between additive and multiplicative numerical patterns. Use an input-output table to generate a pattern that follows a given rule. Represent real-world relationships using number pairs in a table and verbal descriptions. Grade 7 Grade 6 Grade 5 Grade 4 Solve problems involving ratios, rates, and percents. Represent and solve problems with percents. Convert between measurement systems, applying use of proportions and unit rates. Solve problems involving similarity. Convert within a measurement system, applying use of proportions and unit rates. Solve problems by calculating conversions within a measurement system. Convert within a measurement system, applying use of equivalent measures represented in a table Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 5

16 Revised TEKS (2012): Building to Grade 6 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Represent linear relationships that simplify to y=mx+b. Represent linear relationships in the form of y=kx or y=x+b using multiple representations. Write an equation that represents the relationship between independent and dependent quantities. Graph a relationship given in the form y=ax or y=x+a. Represent problems using an inputoutput table. Describe a multiplication expression as a comparison. Represent relationships with number pairs in a table. Grade 6 Grade 5 Generate equivalent expressions using order of operations and properties of operations. Generate equivalent expressions without exponents. Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Model, write, and solve one-variable, two-step equations and inequalities. Model, write, and solve one-variable, one-step equations and inequalities. Represent multi-step problems with letters standing for unknown quantities. Represent multi-step problems with letters standing for unknown quantities. Represent and solve one-and two-step problems with equations. Represent and solve addition and subtraction problems where unknowns may be any one of the terms in a problem. Determine the unknown whole number in and addition or subtraction equation when the unknown may be any one of the three or four terms in the equation. Grade 7 Grade 6 Grade 5 Grade 4 Represent solutions for one-variable, two-step equations and inequalities on a number line. Represent solutions for one-variable, one-step equations and inequalities on a number line. See the Number and Operations strand for connections to the number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). See the Number and Operations strand for connections to the number line Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 6

17 Revised TEKS (2012): Building to Grade 6 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 7 Grade 6 Grade 5 Model the relationship between attributes and formulas for volume of prisms and pyramids. Solve problems with volume of prisms and pyramids Solve problems with volume of rectangular prisms Determine the volume of a rectangular prism by connecting the number of layers to the number of unit cubes in the area of the base. Solve problems with volume (rectangular prism and cube), including the formula V = Bh Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Model the relationship between attributes and formulas of circles. Model the relationship between side lengths and the volume of a Model the relationship between side lengths and perimeter of rectangular prism. rectangles. Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes. Determine the area of a rectangle by connecting the number of rows to the number of unit squares in each row. Determine the area of circles and composite figures. Solve problems with area of rectangles, parallelograms, trapezoids, and triangles Solve problems related to perimeter and/or area Solve problems related to perimeter and area of rectangles Grade 7 Grade 6 Grade 5 Grade 4 Write and solve equations using geometry concepts, including the sum of angles in a triangle and angle relationships. Identify the sum of angles in a triangle, relationship between the lengths of sides and angle measures in a triangle, and whether or not a triangle is formed by three lengths See the Geometry and Measurement strand for connections to attributes and properties of 2-d figures. See the Geometry and Measurement strand for connections to angles and measuring angles Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 7

18 Revised TEKS (2012): Building to Grade 6 Measurement and Data A Vertical Look at Key Concepts and Procedures Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Represent and draw conclusions with: Comparative dot plots Comparative box plots Graphing on a coordinate plane is applied in the Expressions, Equations, and Relationships and Proportionality strands. Represent and draw conclusions with: Represent and solve problems with: Frequency Tables Bar graphs Represent and solve problems with: Frequency Tables Dot plots Dot plots Dot plots Dot plots Stem and Leaf Plots Stem and Leaf Plots Stem and Leaf Plots Histograms Box plots Graph ordered pairs of rational numbers in all four quadrants. Scatterplots Represent and solve problems with: Represent and solve problems with: Represent and draw conclusions with: Frequency Tables Bar graphs Bar graphs Bar graphs Grade 7 Grade 6 Compare two sets of data with shape, center, and spread Describe the center, spread, and shape of a set of data Determine mean, median, range, IQR, and mode Distinguish between situations that yield data with variability and without variability 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 6 8

19 A VERTICAL LOOK AT KEY CONCEPTS AND PROCEDURES GRADE 7

20 The materials are copyrighted (c) and trademarked (tm) as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions: Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts and schools educational use without obtaining permission from TEA. Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA. Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way. No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty. For information contact: Office of Copyrights, Trademarks, License Agreements, and Royalties, Texas Education Agency, 1701 N. Congress Ave., Austin, TX ; phone: or ; copyrights@tea.state.tx.us Texas Education Agency All Rights Reserved Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 2

21 Revised TEKS (2012): Building to Grade 7 Number and Operations A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Order a set of real numbers. Note: Comparing and ordering may be integrated into instruction related to unit rates, problems involving proportional relationships, and the personal financial literacy standards. Order a set of rational numbers. Grade 8 Grade 7 Grade 6 Use a visual representation of sets and subsets: reals. The Revised TEKS (2012) are the student expectations adopted in 2012 that are scheduled to be implemented in pending funding. Use a visual representation of sets and subsets: rationals. Classify whole numbers, integers, and rational numbers. Compare and order two decimals to thousandths. Compare and order whole numbers to 1,000,000,000. Compare two fractions with different numerators and different denominators. Compare and order whole numbers up to 100,000. Compare two fractions having the same numerator or denominator. Compare and order whole numbers up to 1,200. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity Represent the comparisons of two numbers to 100. The strand from the Revised TEKS (2012) is found at the top of each page along with the grade level. Compare sets of objects up to 20. Key concepts and procedures for the identified grade level are in the shaded column. Multiply and divide positive rational numbers fluently. Multiply with fluency a 3-digit by a 2-digit number Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor Add and subtract positive rational numbers fluently. Add and subtract whole numbers and decimals to hundredths. Grade levels for the concepts and procedures are identified in column headings for each set of key concepts and procedures. Solve with fluency problems with multiplication and division (4-digit by 1-digit and 2-digit by 2-digit) Solve with fluency problems with addition and subtraction within 1,000. Multiply a 2-digit by a 1-digit number. The statements are summaries of student expectations that build up to each key concept and procedures. Not all student expectations for all grade levels are represented. Add, subtract, multiply, and divide rational numbers fluently. Add, subtract, multiply, and divide integers fluently Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 3

22 Revised TEKS (2012): Building to Grade 7 Number and Operations A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Order a set of real numbers. Note: Comparing and ordering may be integrated into instruction related to unit rates, problems involving proportional relationships, and the personal financial literacy standards. Order a set of rational numbers. Compare and order two decimals to thousandths. Compare and order whole numbers to 1,000,000,000. Compare two fractions with different numerators and different denominators. Compare and order whole numbers up to 100,000. Compare two fractions having the same numerator or denominator. Compare and order whole numbers up to 1,200. Represent the comparisons of two numbers to 100. Compare sets of objects up to 20. Grade 8 Grade 7 Grade 6 Use a visual representation of sets and subsets within the set of real numbers. Use a visual representation of sets and subsets within the set of rational numbers. Classify whole numbers, integers, and rational numbers. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity Multiply with fluency a 3-digit by a 2-digit number Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor Add and subtract whole numbers and decimals to hundredths. Solve with fluency problems with multiplication and division (4-digit by 1-digit and 2-digit by 2-digit) Solve with fluency problems with addition and subtraction within 1,000. Multiply a 2-digit by a 1-digit number. Multiply and divide positive rational numbers fluently. Add and subtract positive rational numbers fluently. Add, subtract, multiply, and divide rational numbers fluently. Add, subtract, multiply, and divide integers fluently Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 4

23 Revised TEKS (2012): Building to Grade 7 Proportionality A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Represent linear proportional situations with tables, graphs, and y=kx. Determine the constant of proportionality in problem situations and represent k as a rate of change using multiple representations. Compare two rules using multiple representations to differentiate between y=ax (multiplicative relationships) and y=x+a (additive relationships). Generate a numerical sequence when given a rule in the form y=ax or y=x+a. Recognize the difference between additive and multiplicative numerical patterns. Use an inputoutput table to generate a pattern that follows a given rule. Represent realworld relationships using number pairs in a table and verbal descriptions. Grade 8 Grade 7 Grade 6 Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship. Calculate unit rates. Give examples of rates, including rates as quotients. Divide positive rational numbers fluently. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Solve problems involving direct variation. Solve problems involving ratios, rates, and percents. Convert between measurement systems, applying use of proportions and unit rates. Solve problems with percents. Convert within a measurement system, applying use of proportions and unit rates. Solve problems by calculating conversions within a measurement system. Convert within a measurement system, applying use of equivalent measures represented in a table. Grade 8 Grade 7 Compare and contrast attributes of dilations on a coordinate plane. Generalize critical attributes of similarity. Use similar right triangles to develop an understanding of slope as a rate of change for any two points on the same line. Solve problems with similarity and scale drawings Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 5

24 Revised TEKS (2012): Building to Grade 7 Proportionality A Vertical Look at Key Concepts and Procedures Grade 7 Make predictions and determine solutions using experimental and theoretical probability for simple and compound events. Grade 7 Solve problems using data: Bar graphs Dot plots Circle graphs Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 See Measurement and Data strand for connections to data representations. See Data Analysis strand for connections to data representations. See Data Analysis strand for connections to data representations. See Data Analysis strand for connections to data representations. See Data Analysis strand for connections to data representations. See Data Analysis strand for connections to data representations Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 6

25 Revised TEKS (2012): Building to Grade 7 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 See Proportionality Strand for connections to representing proportional and nonproportional situations and identifying functions using multiple representations. Represent linear relationships that simplify to y=mx+b. Represent linear relationship in the form of y=kx or y=x+b. Write an equation that represents the relationship between independent and dependent quantities. Graph a relationship given in the form y=ax or y=x+a. Represent problems using an input-output table. Describe a multiplication expression as a comparison. Represent relationships with number pairs in a table. Grade 8 Grade 7 Grade 6 Grade 5 Model the relationship between attributes and formulas for volume of cylinders and cones. Model the relationship between attributes and formulas for volume of prisms and pyramids. Determine the volume of a rectangular prism by connecting the number of layers to the number of unit cubes in the area of the base. Solve problems with volume of cylinders, cone, and spheres. Solve problems with volume of prisms and pyramids. Solve problems with volume of rectangular prisms. Solve problems with volume (rectangular prism and cube), including the formula V=Bh. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Solve problems with lateral and total surface area of prisms, pyramids, and cylinders. See Two-Dimensional Shapes strand for connections to effects of dilations on linear and area measures. Model the relationship between attributes and formulas of circles. Determine the area of circles and composite figures. Solve problems involving lateral and total surface area of prisms and pyramids using the shape s net. Model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes. Solve problems with area of rectangles, parallelograms, trapezoids, and triangles. Model the relationship between side lengths and the volume of a rectangular prism. Solve problems related to perimeter and/or area. Model the relationship between side lengths and perimeter of rectangles. Solve problems related to perimeter and area of rectangles. Determine the area of a rectangle by connecting the number of rows to the number of unit squares in each row Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 7

26 Revised TEKS (2012): Building to Grade 7 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Solve one-variable equations with variables on both sides of the equal sign using rational number coefficients and constants. Verify the values of x and y that simultaneously satisfy two linear equations in the form y=mx+b from a graph. Solve one-variable, two-step equations and inequalities. Solve one-variable, one-step equations and inequalities. Represent multi-step problems with letters standing for unknown quantities. Represent multi-step problems with letters standing for unknown quantities. Represent and solve one-and two-step problems with equations. Represent and solve addition and subtraction problems where unknowns may be any one of the terms in a problem. Determine the unknown whole number in and addition or subtraction equation when the unknown may be any one of the three or four terms in the equation. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 See Number and Operations Strand for connections to the number line. Represent solutions for one-variable, twostep equations and inequalities on a number line. See Number and Operations Strand for connections to the number line. Represent solutions for one-variable, one-step equations and inequalities on a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). See Number and Operations Strand for connections to the number line. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Use informal arguments to explain specific angle relationships with triangles and those created by transversals and parallel lines. Write and solve equations using geometry concepts, including the sum of angles in a triangle and angle relationships. Identify the sum of angles in a triangle, relationship between the lengths of sides and angle measures in a triangle, and whether or not a triangle is formed by three lengths. See the Geometry and Measurement strand for connections to attributes and properties of 2-d figures. See the Geometry and Measurement strand for connections to angles and measuring angles Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 8

27 Revised TEKS (2012): Building to Grade 7 Measurement and Data A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Represent and draw conclusions with: Represent and draw conclusions with: Represent and draw conclusions with: Represent and solve problems with: Represent and solve problems with: Represent and solve problems with: Comparative dot plots Dot plots Dot plots Dot plots Dot plots Scatterplots Scatterplots Graphing on a coordinate plane is applied in the Expressions, Equations, and Relationships and Proportionality strands. Comparative box plots Graphing on a coordinate plane is applied in the Expressions, Equations, and Relationships and Proportionality strands. Box plots Graph ordered pairs of rational numbers in all four quadrants. Grade 8 Grade 7 Grade 6 Determine mean absolute deviation. Compare two sets of data with shape, center, and spread. Describe the center, spread, and shape of a set of data. Determine mean, median, range, IQR, and mode. Distinguish between situations that yield data with variability and without variability. Grade 8 Grade 7 Simulate generating random samples to develop the notion of a random sample being representative of the population. Draw inferences about a population and compare two populations based on random sampling Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 7 9

28 A VERTICAL LOOK AT KEY CONCEPTS AND PROCEDURES GRADE 8

29 The materials are copyrighted (c) and trademarked (tm) as the property of the Texas Education Agency (TEA) and may not be reproduced without the express written permission of TEA, except under the following conditions: Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts and schools educational use without obtaining permission from TEA. Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of TEA. Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way. No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts, Texas Education Service Centers, or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from TEA and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty. For information contact: Office of Copyrights, Trademarks, License Agreements, and Royalties, Texas Education Agency, 1701 N. Congress Ave., Austin, TX ; phone: or ; copyrights@tea.state.tx.us Texas Education Agency All Rights Reserved Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 2

30 Revised TEKS (2012): Building to Grade 8 Number and Operations A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Order a set of real Order a set of Compare and order Compare and order Compare and order Compare and order Represent the Compare sets of TEKS (2012) is found at the numbers. rational numbers. two decimals to whole numbers to whole numbers up whole numbers up comparisons of objects up to 20. thousandths. 1,000,000,000. to 100,000. to 1,200. two numbers top of each to page along with The Revised TEKS (2012) are the 100. Compare two Compare two the grade level. student expectations adopted in 2012 that fractions with fractions having different the same are scheduled to be implemented in numerators and numerator or different denominator pending funding. denominators. Grade 8 Grade 7 Grade 6 Use a visual representation of sets and subsets within the set of real numbers. Use a visual representation of sets and subsets within the set of rational numbers. Classify whole numbers, integers, and rational numbers. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Locate rational number approximations of irrational numbers on a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Locate, compare, and order integers and rational numbers using a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Name a point on a number line to tenths or hundredths. Locate fractions between 0 and 1 with specified denominators on a number line. Locate the position of a given whole number on an open number line. Order whole numbers up to 120 using open number lines. Convert between standard decimal notation and scientific notation. Use expanded notation for decimals through the thousandths. Use expanded notation for whole numbers through 1,000,000,000 and decimals to the hundredths. Use expanded notation as appropriate for numbers up to 100,000. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity Key concepts and procedures for the identified grade level are in the shaded column. Add, subtract, multiply, and divide rational numbers fluently. Multiply and divide positive rational numbers fluently. Add, subtract, multiply, and divide integers fluently. Grade levels for the concepts and procedures are identified in column headings for each set of key concepts and procedures. Multiply with fluency a 3-digit by a 2-digit number Solve with proficiency for quotients of up to a four-digit dividend by a twodigit divisor Add and subtract positive rational numbers fluently. Add and subtract whole numbers and decimals to hundredths. Solve with fluency problems with multiplication and division (4-digit by 1-digit and 2-digit by 2-digit) Solve with fluency problems with addition and subtraction within 1,000. Multiply a 2-digit by a 1-digit number. The strand from the Revised The statements are summaries of student expectations that build up to each key concept and procedures. Not all student expectations for all grade levels are represented Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 3

31 Revised TEKS (2012): Building to Grade 8 Number and Operations A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Kindergarten Order a set of real numbers. Grade 8 Grade 7 Grade 6 Use a visual representation of sets and subsets within the set of real numbers. Use a visual representation of sets and subsets within the set of rational numbers. Order a set of rational numbers. Classify whole numbers, integers, and rational numbers. Compare and order two decimals to thousandths. Compare and order whole numbers to 1,000,000,000. Compare two fractions with different numerators and different denominators. Compare and order whole numbers up to 100,000. Compare two fractions having the same numerator or denominator. Compare and order whole numbers up to 1,200. Represent the comparisons of two numbers to 100. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Locate rational number approximations of irrational numbers on a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Locate, compare, and order integers and rational numbers using a number line. Note: number lines may be integrated into instruction through (1)(D), (1)(E), and (1)(G). Name a point on a number line to tenths or hundredths. Locate fractions between 0 and 1 with specified denominators on a number line. Locate the position of a given whole number on an open number line. Order whole numbers up to 120 using open number lines. Compare sets of objects up to 20. Convert between standard decimal notation and scientific notation. Use expanded notation for decimals through the thousandths. Use expanded notation for whole numbers through 1,000,000,000 and decimals to the hundredths. Use expanded notation as appropriate for numbers up to 100,000. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Recall facts to multiply up to 10 by 10 with automaticity. Recall basic facts to add and subtract within 20 with automaticity Multiply with fluency a 3-digit by a 2-digit number Solve with proficiency for quotients of up to a four-digit dividend by a twodigit divisor Add and subtract whole numbers and decimals to hundredths. Solve with fluency problems with multiplication and division (4-digit by 1-digit and 2-digit by 2-digit) Solve with fluency problems with addition and subtraction within 1,000. Multiply a 2-digit by a 1-digit number. Multiply and divide positive rational numbers fluently. Add and subtract positive rational numbers fluently. Add, subtract, multiply, and divide rational numbers fluently. Add, subtract, multiply, and divide integers fluently Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 4

32 Revised TEKS (2012): Building to Grade 8 Proportionality A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Compare and contrast attributes of dilations on a coordinate plane. Generalize critical attributes of similarity. Grade 8 Grade 7 Graph proportional Calculate unit rates. relationships, interpreting the unit rate as the slope of the line that models the relationship. Grade 8 Grade 7 Grade 6 Grade 5 Solve problems involving direct variation. Solve problems involving ratios, rates, and percents. Solve problems with similarity. Solve problems with percents. Solve prediction and comparison problems, including contexts with probability and statistics. Solve problems by calculating conversions within a measurement system. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Represent proportional and non-proportional situations. Identify functions using multiple representations. See Expressions, Equations, and Relationships strand for connections to representing linear relationships that simplify to y=mx+b. See Expressions, Equations, and Relationships strand for connections to representing linear relationship in the form of y=kx or y=x+b and writing an equation that represents the relationship between independent and dependent quantities. See Expressions, Equations, and Relationships strand for connections to graphing a relationship given in the form y=ax or y=x+a. See Expressions, Equations, and Relationships strand for connections to representing problems using an inputoutput table. See Expressions, Equations, and Relationships strand for connections to describing a multiplication expression as a comparison and representing relationships with number pairs in a table Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 5

33 Revised TEKS (2012): Building to Grade 8 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Model the relationship between attributes and formulas for volume of cylinders and cones. Determine volume of a rectangular prism with layering of unit cubes. Solve problems with volume of cylinders, cone, and spheres. Solve problems with volume of prisms and pyramids. Solve problems with volume of rectangular prisms. Solve problems with volume (rectangular prism and cube), including the formula V=Bh. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Determine the area of circles and composite figures. Solve problems with area of rectangles, parallelograms, trapezoids, and triangles. Solve problems related to perimeter and/or area. Solve problems related to perimeter and area of rectangles. Solve problems with lateral and total surface area of prisms, pyramids, and cylinders. Solve problems involving lateral and total surface area of prisms and pyramids using the shape s net. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Explain the Pythagorean Theorem with models and diagrams. Identify acute, right, and obtuse triangles. Use the Pythagorean theorem and its converse to solve problems. Determine the distance between two points on a coordinate plane using the Pythagorean Theorem Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 6

34 Revised TEKS (2012): Building to Grade 8 Expressions, Equations, and Relationships A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Solve one-variable equations with variables on both sides of the equal sign using rational number coefficients and constants. Verify the values of x and y that simultaneously satisfy two linear equations in the form y=mx+b from a graph. Solve one-variable, two-step equations and inequalities. Represent solutions for one-variable, two-step equations and inequalities on a number line. Solve one-variable, one-step equations and inequalities. Represent solutions for one-variable, one-step equations and inequalities on a number line. Represent multi-step problems with letters standing for unknown quantities. Represent multi-step problems with letters standing for unknown quantities. Represent and solve one-and two-step problems with equations. Represent and solve addition and subtraction problems where unknowns may be any one of the terms in a problem. Determine the unknown whole number in and addition or subtraction equation when the unknown may be any one of the three or four terms in the equation. Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Use informal arguments to explain specific angle relationships with triangles and those created by transversals and parallel lines. Write and solve equations using geometry concepts, including the sum of angles in a triangle and angle relationships. Identify the sum of angles in a triangle, relationship between the lengths of sides and angle measures in a triangle, and whether or not a triangle is formed by three lengths. See the Geometry and Measurement strand for connections to attributes and properties of 2-d figures. See the Geometry and Measurement strand for connections to angles and measuring angles Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 7

35 Revised TEKS (2012): Building to Grade 8 Two-Dimensional Shapes A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Represent translations, reflections, rotations, and dilations on a coordinate plane algebraically. Generalize properties of orientation and congruence for translations, reflections, rotations, and dilations. Model effect of dilations on linear and area measures. Determine the area of circles and composite figures, including nets. Solve problems with area of rectangles, parallelograms, trapezoids, and triangles. Solve problems related to perimeter and/or area. Solve problems related to perimeter and area of rectangles Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 8

36 Revised TEKS (2012): Building to Grade 8 Measurement and Data A Vertical Look at Key Concepts and Procedures Grade 8 Grade 7 Grade 6 Grade 5 Represent and draw conclusions related to association between bivariate data with: Represent and draw conclusions with: Represent and draw conclusions with: Represent and solve problems with: Scatterplots Note: The use of scatterplots is implied through the graphing of data on the coordinate plane. Note: The use of scatterplots is implied through the graphing of data on the coordinate plane. Scatterplots Grade 8 Grade 7 Grade 6 Determine mean absolute deviation. Compare two sets of data with shape, center, and spread. Describe the center, spread, and shape of a set of data. Determine mean, median, range, IQR, and mode. Distinguish between situations that yield data with variability and without variability. Grade 8 Grade 7 Simulate generating random samples to develop the notion of a random sample being representative of the population. Draw inferences about a population and compare two populations based on random sampling Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: A Vertical Look at Key Concepts and Procedures: Grade 8 9

37 Amplifying Instructional Task Grade 7 Example Original Task Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b. 7(7)(A) Mr. Mott recorded the number of plants in each row of the Children s Park garden as shown below. Garden Row Number of Plants r p Write an equation that could be used to determine p, the number of plants in the rth row of this garden Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

38 Amplifying Instructional Task Grade 7 Example Amplified Task Materials to make available: Circular dot paper Garden Store Sales Ad Word bank Set of 3 circles 2, 3, 4 radius (1 of each made of card stock/cardboard) Standard measurement tools Chart paper Image Search: Key words - images of circular gardens Video: Start Organic-How to Build a Circular, Raised Bed Garden Network San Jose, Ca. Task A (Amplified Task): You are to construct a circular garden for the Children s Park. The center of the garden will feature a water fountain that has a diameter of 2 feet. The first row of plants will form a circle 6 inches from the base of the water fountain. Each row of plants must be 6 inches apart. The first four rows of the garden are illustrated below. Water Fountain Represents 1 Potted Plant: The installation of the water fountain will cost $ Each plant is $13.69, and each bag of stones costs $35. These prices include labor and tax. What is the cost to create a garden that has 5 rows? What algebraic generalization can be made to determine the cost of the plants needed for the nth row of this garden? You will need to cover the area between each row of the garden with colored stones. If one bag of colored stones will cover an area of 16 square feet, about how many bags of colored stone will be needed for a garden that has 5 rows? Write a letter to the board of the Children s Park explaining the design of the garden and cost Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

39 Amplifying Instructional Task Grade 7 Example Task B (Scaffolded Task): You are to construct a circular garden for the Children s Park. The center of the garden will feature a water fountain. Water Fountain Represents 1 Potted Plant: How many plants will be needed for the 10 th row? What algebraic generalization can be made to determine the number of plants in the nth row of this garden? Row Number Number of Plants Write a letter to the grounds keeper of the Children s Park explaining how he could determine the number of plants needed for any row of the garden Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

40 Amplifying Instructional Task Grade 7 Example Task C (Scaffolded Task): You are to construct a circular garden for the Children s Park. The center of the garden will feature a water fountain. Water Fountain Represents 1 Potted Plant: How many plants will be needed for the 10 th row? What algebraic generalization can be made to determine the number of plants in the nth row of this garden? Write a letter to the grounds keeper of the Children s Park explaining how he could determine the number of plants needed for any row of the garden. Children s Park Grounds Keeper 1026 Avenue E Houston, Texas Dear Mr. Johnson, To find the number of plants in any row of the circular garden, you would Sincerely, 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

41 Amplifying Instructional Task Grade 7 Example Task D (Enriched Task): Mr. Mott created the following circular garden. Water Fountain Represents 1 Potted Plant: Determine the relationship between the row number and the number of potted plants in Mr. Mott s garden. Create a garden using a different geometric design. The relationship between the rows and the number of potted plants should be linear when graphed. Use a garden center sales ad to determine a detailed estimate of the cost to create 5 rows of your design Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison

42 Side-by-Side TEKS Comparison Highlights Grade 8 The 2012 TEKS are the student expectations adopted in 2012 and are scheduled to be implemented in pending funding. Supporting Information includes: Student expectations that are new to the grade level are in blue and are indicated by a + in the first column. Student expectations that are leaving the grade level are in pink and are indicated by a in the first column. Clarification on mathematics vocabulary Clarification on added specificity Clarification on current TEKS that have been joined, separated, or subsumed within the 2012 TEKS Clarification on the intent of the TEKS Information about movement to another grade level Information about connections with the process standards A legend for the colors and symbols is found on the bottom of each page. The symbols aid in reading the document should it be printed in black and white. Student expectations that remain in the grade level are in green and are indicated by a circle in the first column. Content that stays in the grade level is indicated by the symbol. Content that remains with an addition is indicated by the symbol +. Content that remains with a deletion is indicated by the symbol Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Focal Points and TEKS Comparison