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Unpacking the EOC 6 th Grade Released Items Eligible Texas Essential Knowledge and Skills Texas Education Agency Student Assessment Division Fall 2010

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“Think Around” the question and capture all thoughts by jotting down what is being said. In order for a 6 th grade student to be able to master this question what does the student need to know?

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2011 6 th Grade STARR Mathematics Released Item~Question 7 6.6. (7.6)Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: 6.6B identify relationships involving angles in triangles and quadrilaterals 7 (B) identify relationships involving angles in triangles and quadrilaterals; and In order for a 6 th grade student to be able to master this question what does the student need to know? Let’s look at Vertical Alignment

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6 th Grade CSOPE Performance Indicators7 th Grade CSOPE Performance Indicators Unit 6 Second Nine Weeks Use a drawing of a triangle or quadrilateral to find each angle measurement and classification. Generate a model (e.g., sketch, computer-generated, etc.) of the drawing, and label the angle measure using measurement notation and the classification (e.g., acute, obtuse, or right) for each angle. Validate each measure by explaining the angle relationships and problem-solving processes. (6.6A, 6.6B; 6.8C; 6.11B, 6.11C, 6.11D; 6.13B) Sample Performance Indicator: A government surveyor provided the following diagram of the new city park land. Sketch the diagram, and label the angle measure using measurement notation and the classification for each angle. Justify each measure by explaining the angle relationships and problem solving processes. Unit 7 Third Nine Weeks Generate a complete model (e.g., blueprint, design book, etc.) with labels of angle measures, dimensions, and a geometric classification of each figure in a given real-life problem situation which involves length and area. Use mathematical language to identify a pair of complementary and supplementary angles. Use the complete model to find a reasonable solution to the real-life problem situation. Validate all solutions with a calculator. Write a justification of the solution process describing the mathematical properties, relationships, and formulas used to determine the angles, dimensions, and geometric classifications of the figures in the problem. (7.2B, 7.2F, 7.2G; 7.3B; 7.4A; 7.6A, 7.6B; 7.8C; 7.9A; 7.13A, 7.13B, 7.13C, 7.13D; 7.14A; 7.15A, 7.15B) Sample Performance Indicator: Lisa has decided to replace the grass in her back yard and obtained a blueprint from her contractor. While inspecting the blueprint, she noticed that not all of the measurements were noted for her pond, wooden deck, and patio. She remembered that her yard is 14 yards long and 6 yards wide, the perimeter of the wooden deck is 28.75 ft, and the semi-circumference of the patio is 12.56 ft. Create a blueprint of Lisa’s backyard with labels of the angle measures and dimensions of the pond, wooden deck, and patio. Use mathematical language to identify a pair of complementary and supplementary angles and a classification of the geometric shape of the pond and wooden deck. Use the blueprint to determine the amount of grass in square feet Lisa should purchase and a reasonable estimate of the cost if she purchases a square foot of grass for $.75. Validate all solutions with a calculator. Write a justification of the solution process describing the mathematical properties, relationships, and formulas used to determine the area of the pond, wooden deck, and patio in order to find the amount and cost of grass needed for the backyard. CSCOPE Performance Indicators Please note that Fig. 19 D is assessed through performance indicators in every unit. Only a few were selected for this activity

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Examining STAAR 6 th GradeImplications for Teaching Number of Non-linguistic Representation Number of 7 th Grade Aligned SEs Number of 8 th Grade Aligned SEs

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Readiness 6.1.B (7.1.B, 8.1.B) (1) Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. The student is expected to: (B) generate equivalent forms of rational numbers including whole numbers, fractions, and decimals; Processing 6.11.B (7.13.B, 8.14.B) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Number of steps it takes to solve the problem. 3 to 4 steps What part of the SE is being tested? Generate equivalent rational number by converting a fraction to a decimal What do the students need to know in order to answer the question correctly? Students need to know how to pull the data from the table to determine the fraction as well as convert the fraction into a decimal. DOK: Level (Evidence) Level 2 Retrieve information from a table and use it to solve a multi-step problem Academic Vocabulary Write (S) it is stated and (I) if it is implied Equivalent forms of non-negative rational numbers (i) Decimal (s) Fraction (s) How is it being tested? It is asking students to find the fractions and convert to its decimal equivalent. Taught in CSCOPE 1 st and 4 th nine weeks Units 1, 10

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Readiness 6.2.B (7.2.B, 8.2.B) (2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (B) use addition and subtraction to solve problems involving fractions and decimals; Processing 6.11.B ( 7.13.B, 8.14.B) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 1 st, 3 rd and 4 th nine weeks Units 3, 7, 11, 12

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Readiness 6.2.C (7.2.D, 8.2.D) (2) Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. The student is expected to: (C) use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates; Processing 6.11.B ( 7.13.B, 8.14.B) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Number of steps it takes to solve the problem.What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd, 3 rd and 4 th nine weeks Units 4, 7, 10, 11, 12

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Readiness 6.3.C (7.3.B, 8.3.B) (3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to: (C) use ratios to make predictions in proportional situations. Processing 6.11.B (7.13.B, 8.14.B) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd, 3 rd and 4 th nine weeks Units 4, 8, 11, 12

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Readiness 6.4.A (7.4.C, 8.5.C) (4) Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: (A) use tables and symbols to represent and describe proportional and other relationships such as those involving conversions, arithmetic sequences (with a constant rate of change), perimeter and area; Processing 6.12.A (7.14.A, 8.15.A) (12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd and 4 th nine weeks Units 4, 5, 11, 12

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Readiness 6.5.A (7.5.B, 8.5.A) (5) Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation. The student is expected to formulate equations from problem situations described by linear relationships. Processing 6.12.A (7.14.A, 8.15.A) (12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd and 4 th nine weeks Units 5, 11

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Supporting 6.6.B (7.6.B) (6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: (B) identify relationships involving angles in triangles and quadrilaterals; and Processing 6.13.A (7.15.A, 8.16.A) (13) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd nine weeks Unit 6

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Readiness 6.6.C (6) Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: (C) describe the relationship between radius, diameter, and circumference of a circle. Processing 6.12.A (7.14.A, 8.15.A) (12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 3 rd nine weeks Unit 7

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Supporting 6.7.A (7.7.A, 8.7.D) (7) Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. The student is expected to locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. Processing 6.11.D (7.13.D, 8.14.D) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 2 nd nine weeks Unit 5, 9

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Readiness 6.8.B (7.9.C, 8.8.C) (8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), area, time, temperature, volume, and weight; Processing 6.11.D (7.13.D, 8.14.D) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 3 rd and 4 th nine weeks Units7, 8, 11

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Supporting 6.8.D (8) Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: (D) convert measures within the same measurement system (customary and metric) based on relationships between units. Processing 6.11.B (7.13.B, 8.14.B) (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 3 rd nine weeks Unit 8

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Supporting 6.9.B (7.10.B, 8.11.A) (9) Probability and statistics. The student uses experimental and theoretical probability to make predictions. The student is expected to: (B) find the probabilities of a simple event and its complement and describe the relations Number of steps it takes to solve the problem. What part of the SE is being tested?What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 4 th nine weeks Unit 10

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Readiness 6.10.D (10) Probability and statistics. The student uses statistical representations to analyze data. The student is expected to: (D) solve problems by collecting, organizing, displaying, and interpreting data. Processing 6.12.A (7.14.A, 8.15.A) (12) Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models; Number of steps it takes to solve the problem. What part of the SE is being tested? What do the students need to know in order to answer the question correctly? DOK: Level (Evidence) Academic Vocabulary Write (S) it is stated and (I) if it is implied How is it being tested? Taught in CSCOPE 3 rd and 4 th nine weeks Units 9, 10

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