1. Unpacking the EOC 8 th Grade Released Items Eligible Texas Essential Knowledge and Skills Texas Education Agency Student Assessment Division Fall 2010

2. “Think Around” the question and capture all thoughts by jotting down what is being said. In order for a 8 th grade student to be able to master this question what does the student need to know?

3. 2011 8 th Grade STARR Mathematics Released Item~Question 12 :Readiness 8.11.A (7.10.B, 6.9.B) (11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: 8.11.A (A) find the probabilities of dependent and independent events; 7.10.A (10) Probability and statistics. The student recognizes that a physical or mathematical model (including geometric) can be used to describe the experimental and theoretical probability of real-life events. The student is expected to: (A) construct sample spaces for simple or composite experiments; 6.9.B (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 relationship between the two. In order for a 8 th grade student to be able to master this question what does the student need to know? Let’s look at Vertical Alignment

4. 8 th Grade CSOPE Performance Indicators7 th Grade CSOPE Performance Indicators Unit 8 third Nine Weeks Create a presentation (e.g., brochure, poster, etc.) with the experimental and theoretical probabilities of dependent and independent events within a given real-life situation (e.g., baseball, snakes, sandwiches, etc.). Make conjectures from the probabilities of the real- life situation, and validate conclusions using mathematical properties and relationships. Design and simulate an in-class experiment with math manipulatives to compare the theoretical and experimental probabilities of a dependent real-life situation. (8.2B; 8.11A, 8.11B, 8.11C; 8.14A, 8.14C, 8.14D; 8.15A; 8.16A, 8.16B) Sample Performance Indicator: There are over 3,000 species of snakes in the world, and only 15% are considered dangerous to humans. Texas has 15 of the 25 species of poisonous snakes identified in North America. With each bite, one-half are “dry”, which means that the snake does not inject venom into the victim. Create an informational brochure to inform tourists about the venomous snakes that inhabit Texas. Include the probability of not receiving a “dry” bite from each type and category of snake, and predict which habitat is most likely to yield the least and most snake bites. Validate the predictions with mathematical properties and relationships. The rattlesnake is one of the most notorious snakes in the Lone Star State; identify the probability of being bit by a snake in a wooded area and it being a rattlesnake. Design and simulate an in-class experiment with math manipulatives to determine the experimental probability of being bit by a venomous snake in a wooded area and it being a rattlesnake. In writing, compare the experimental and theoretical probabilities of being bitten by a snake in a wooded area and it being a rattlesnake. Unit 7 Third Nine Weeks Create a written description (e.g., letter, email, etc.) that describes all possible outcomes offered of a given real-life situation that involves simple or composite events. Find the probability, as a percent or decimal, of an independent event within the problem situation. Validate conjectures by constructing the sample space of the given real-life problem situation and identify the problem-solving strategy used. (7.1B; 7.10A, 7.10B; 7.13A, 7.13C, 7.13D; 7.14A; 7.15A, 7.15B) 5F, 5G Sample Performance Indicator: A local copy store offers several choices for customers to select from for their copy needs A supply order was delivered, however pink and blue cardstock were left off the shipment. Write an email to the supply company identifying the percent of the orders placed that could involve pink or blue cardstock, and how this error could affect the business of the copy store. Validate the solution by constructing the sample space of the choices offered by Aesop’s Copy Shop and identify the problem-solving strategy used. 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

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

6. Readiness 8.1. A (6.1A, 7.1A) (1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: (A) compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; Number of steps it takes to solve the problem. 2 to 4 steps What part of the SE is being tested? Comparing rational numbers in terms of fractions. What do the students need to know in order to answer the question correctly? Students need to convert the mixed number into an improper fraction, convert to a decimal and then compare the values to determine the order. DOK: Level (Evidence) Level 2 retrieve information from a figure and use it to solve a problem requiring multiple steps. Academic Vocabulary Write (S) it is stated and (I) if it is implied Positive rational numbers (i) Percent (s) Fraction (s) How is it being tested? Comparing mixed number percentages to determine greatest to least. Taught in CSCOPE 1 st nine weeks Unit 1

7. Readiness 8.2B (6.2B, 7.2B) (2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to: (B) use appropriate operations to solve problems involving rational numbers in problem situations; Processing 8.14.A (7.12.A, 6.11.A) (14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; 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, 2 nd, 3 rd and 4 th nine weeks Units 2, 3, 5, 6, 7, 8, 9, 10

8. Supporting 8.2BD(6.2C, 7.2D) (2) Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to: (D) use multiplication by a given constant factor (including unit rate) to represent and solve problems involving proportional relationships including conversions between measurement systems. Processing 8.15.A (7.14.A, 6.12.A) (15) Underlying processes and mathematical tools. The student communicates about Grade 8 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 1 st, 2 nd, 3 rd and 4 th nine weeks Units 3, 4, 7, 11

9. Supporting 8.3A (3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non- proportional linear relationships in problem situations and solves problems. The student is expected to: (A) compare and contrast proportional and non- proportional linear relationships; Processing 8.14A (7.13A, 6.11A) (14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; 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, 2 nd, and 4 th nine weeks Units 3, 5, 11

10. Readiness 8.3B (6.3C, 7.3B) (3) Patterns, relationships, and algebraic thinking. The student identifies proportional or non- proportional linear relationships in problem situations and solves problems. The student is expected to: (B) estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Processing 8.14A (7.13A, 6.11A) (14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; 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, 2 nd and 4 th nine weeks Units 3, 4, 10

11. Readiness 8.4A (7.4.B) (4) Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description). 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 5, 9, 10, 11

12. Readiness 8.6A (7.6D) (6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to: (A) generate similar figures using dilations including enlargements and reductions; Processing 8.14C (7.13C, 6.11C) (14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; 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 Unit 4, 10

13. Readiness 8.7B (7.8C) (7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: (B) use geometric concepts and properties to solve problems in fields such as art and architecture; Processing 8.14B (6.11B, 7.13B) (14) Underlying processes and mathematical tools. The student applies Grade 8 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, 2 nd and 3 rd nine weeks Units 3, 4, 6, 7

14. Readiness 8.8C (6.8B, 7.9C) (8) Measurement. The student uses procedures to determine measures of three- dimensional figures. The student is expected to: (C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Processing 8.14B (6.11B, 7.13B) (14) Underlying processes and mathematical tools. The student applies Grade 8 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 and 4 th nine weeks Units 7, 10

15. Readiness 8.9.A (9) Measurement. The student uses indirect measurement to solve problems. The student is expected to: (A) use the Pythagorean Theorem to solve real-life problems; Processing 8.14B (6.11B, 7.13B) (14) Underlying processes and mathematical tools. The student applies Grade 8 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 and 4 th nine weeks Units 6, 10

16. Supporting 8.10.A (10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to: (A) describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; Processing 8.15.A (6.12A, 7.14A) (15) Underlying processes and mathematical tools. The student communicates about Grade 8 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 Unit 7, 10

17. Readiness 8.11.A (7.10.B, 6.9.B) (11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: (A) find the probabilities of dependent and independent events; 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 8, 10

18. Supporting 8.12C (6.10A, 7.11A) (12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to: (C) select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology. Processing 8.15.A (6.12A, 7.14A) (15) Underlying processes and mathematical tools. The student communicates about Grade 8 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, 11

19. Readiness 8.13B (13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to: (B) recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. Processing 8.15.A (6.12A, 7.14A) (15) Underlying processes and mathematical tools. The student communicates about Grade 8 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 Unit 9, 10