Florida Standards Assessment Algebra 1 EOC and Geometry EOC update

Transcription

1 Florida Standards Assessment Algebra 1 EOC and Geometry EOC update Terri L. Sebring Test Development Center

2 House Bill (HB) 7069

3 HB 7069 HB 7069 was signed by Governor Scott on June 15, HB 7069 became effective July 1, Individual sections of the bill may contain different deadlines for implementation of specific requirements. The following slides provide brief summaries of the testing-specific provisions of the bill. Resource: Annual DAC meeting

4 HB 7069: Changes Algebra 2 Removes the provision for an Algebra 2 end-of-course (EOC) assessment Grade 3 ELA Removes the requirement that the Grade 3 English Language Arts (ELA) assessment be computer-based in Uniform Assessment Calendar Moves the Department s requirement to publish the uniform assessment calendars for the next two school years from August to January each year, beginning in January Resource: Annual DAC meeting

5 HB 7069: Changes Test Mode Requires that grades 3 6 ELA and Mathematics assessments be delivered only in a paper-based format no later than the school year. Score Release Requires that assessment results be made available no later than June 30, except for the results for Grade 3 ELA, which must be available by May 31. Resource: Annual DAC meeting

6 FSA Item Specifications update to reflect HB 7069 There will be an update to grades 3 6 Item Specifications to reflect the changes from HB 7069 after Spring 2018 testing.

7 HB 7069: Changes Testing Windows Specifies testing windows and administration timeframes for the statewide assessments (excluding retake assessments), beginning in the school year, as follows: Grade 3 ELA and grades 4 10 ELA Writing cannot start earlier than April 1, and their window cannot exceed 2 weeks. All other paper-based assessments cannot start earlier than May 1, and their window cannot exceed 2 weeks. All assessments not specified above (i.e., computer-based assessments) cannot start earlier than May 1 and must be administered within a 4-week testing window. Resource: Annual DAC meeting

8 HB 7069: Changes Testing Windows (cont.) Assessments other than grade 3 ELA and grades 4 10 ELA Writing can only be administered during the final four weeks of each district s calendar but must be administered in the statewide four-week window. The bill analysis provided by legislative staff offers the following guidance (p.39): [HB 7069] requires school districts to administer the assessments associated with a May 1 assessment window no earlier than 4 weeks before the last day of school for the district. In effect, this will require the last 4 weeks of a school district s school year to overlap with the May 1 assessment windows to the extent necessary for all assessments in the district to be administered. This does not require the last 4 weeks of the school year to start with the May 1 assessment window; rather, school districts will have the flexibility to adjust their last day of school to provide sufficient time, based upon the district s capacity and needs, to administer these assessments within their respective assessment windows. Resource: Annual DAC meeting

9 HB 7069: Changes Score Reports Districts must report district-required assessment results to teachers within 1 week and to the student s parents within 30 days. Requires more comprehensive student score reports for statewide assessments, which districts must provide to parents within 1 week of their receipt. Report must contain an explanation of the student results; information on student strengths and weaknesses; specific actions that can be taken and resources that can be used for improving areas of weaknesses; comparative data; and, if available, longitudinal and predictive data. Resource: Annual DAC meeting

10 HB 7069: Changes Test Release Beginning June 30, 2021, the Department must begin releasing statewide ELA, Mathematics, Science, and Social Studies assessments on a triennial basis on a schedule to be determined by the Commissioner. The first release must include, at minimum, grades 3 and 10 ELA, and Algebra 1 EOC assessments. Each published assessment must have been administered during the most recent school year and must be accompanied by interpretive information. Resource: Annual DAC meeting

11 HB 7069: Changes Independent Study Requires the Commissioner to contract for an independent study to determine whether the SAT and/or ACT may be administered in lieu of the Grade 10 ELA and Algebra 1 EOC assessments, consistent with ESSA provisions for locally-selected, nationally-recognized high school assessments. The findings of the study are due to the Governor, President of the Senate, Speaker of the House, and the State Board of Education by January 1, Resource: Annual DAC meeting

12 Concordant and Comparative Scores

13 Update: Rule 6A Concordant and Comparative Scores Existing concordant and comparative scores may be used until new scores are adopted by the State Board of Education. As such, the October 1, 2017, implementation date presented during the June 12, 2017, workshop is no longer in effect. FDOE continues to solicit and review feedback from stakeholders and continues to perform additional analyses using newly-available data. Resource: Annual DAC meeting

14 Update: Rule 6A Concordant and Comparative Scores There will be an additional public workshop prior to presenting the Commissioner s recommendations to the State Board of Education for its approval. The dates of the additional public workshop and State Board meeting are yet to be determined. Resource: Annual DAC meeting

15 Test Administration reminders

16 CBT Practice Tests CBT students are required to participate in a practice test session prior to testing. Students retaking an assessment who previously completed this requirement for the test they will take (EOC or Retake) are not required to participate in another practice test. Students with CBT accommodations must use the appropriate accommodated practice test. Ensure test administrators do not start an Operational Session for practice. Resource: Annual DAC meeting

17 PBT Practice Tests Students who will take an FSA ELA Reading or Mathematics paper-based test are required to participate in a PBT Test Item Practice Session to familiarize themselves with the various item types they may encounter on the assessments. Grade 3 FSA ELA Reading Grades 4 10 Reading PBT Accommodations Grades 3 8 Mathematics PBT Accommodations Students taking PBT ELA Writing are not required to take a practice test, but they are strongly encouraged to do so to become familiar with the amount of space they will have for their responses. Resource: Annual DAC meeting

18 FSA Algebra 1 Assessment Calendar First-Time Test Takers Fall EOC (9/18 10/6) Results will be delivered prior to Winter EOC Winter EOC (11/27 12/15) Spring Algebra 1 Retake* (3/19 4/6) Spring EOC (4/16 5/11) Summer EOC (7/9 20) X X X X Retakers X X X X *The department continues to evaluate the impact of hurricane season on affected school districts. In consideration of the potential for the development of additional storm systems this hurricane season, we expect to communicate information regarding any potential changes to spring 2018 assessment plans after the conclusion of hurricane season.

19 Equation Editor Keypad EOC The size of the keypad will adjust based on the width of the item.

20 Multi-interaction items

21 FSA Item Specifications and Practice tests Grades 7 and 8, Algebra 1, and Geometry will be adding another practice item. The item will be a multiinteraction item. These items have more than one part. Each part can be a different item type. To include the new item type and to remove any reference to Algebra 2, the item specifications will be updated. There may be other minor changes. All changes will be listed in Appendix B.

22 Algebra 1 Multi-interaction Practice item F-LE.1.1a

23 Geometry Multi-interaction Practice item G-CO.2.8

24 Geometry Multi-interaction Practice item

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26 Lessons Learned Anecdotal evidence gathered from educator committees and test construction activities

27 Algebra 1 EOC Students are doing well on understanding functions and evaluating functions. F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Prior Knowledge - MAFS.8.F.1.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

28 Algebra 1 EOC Students are doing well on linear functions. Students show an understanding of writing and solving linear equations. A-CED.1.1, A-CED.1.2, A-REI.1.1 and A- REI.2.3 Note: A-CED.1.1 and A-CED.1.2 can include function types other than linear. Students are struggling on the other function types. Students show an understanding of interpreting the slope and points of linear functions and the rate of an exponential function in simple exponential functions. A-SSE.1.1a, F-IF.2.4, S-ID.3.7, F-LE.2.5 Students show an understanding of rewriting a difference of two squares and expressions with common factors. A-SSE.1.2

29 MAFS.8.F.2.4 Keep in mind Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

30 Equivalent Forms for EQ item types If an item requires the student to write an equation, the student will not be restricted to give that equation in a certain form unless the standard requires a particular form. For example, if a student has to write an equation using a real-world context, all of these forms are accepted as correct. Please note that the options could be in different format if an item is a MC item. Educators review these and consider what form is appropriate for the real-world context. 10x 4y = 18 y = 2.5x 4.5 5x = 2y + 9 y + 7 = (5/2)(x + 10)

31 Algebra 1 EOC Students are struggling with writing quadratic equations and exponential equations. Writing quadratic equations or functions given a real-world context. A-CED.1.1 Writing exponential equations or functions given a real-world context. A-CED.1.1 and F-LE.1.2

32 A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). F-BF.1.1a Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. S-ID.2.6a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. Real-World Context Real-World Context Real-World Context Real-World Context Real-World Context

33 Equivalence In K-5, as students work with whole numbers, decimals, and fractions, they produce equivalent numeric expressions using properties of operations. Equivalence continues as students begin working with algebraic expressions in middle school. The standards in middle school also introduce the understanding of equivalence within a realworld context. Algebra 1 continues the theme of equivalence. For this reason, educators are encouraged to vary what is accepted as correct answers as well as how they present expressions, equations, and functions. It is also important to note that equivalence does not mean simplest form..

34 Algebra 1 EOC Students are struggling with equivalence. Writing equivalent expressions, equations or function. Completing the square - A-SSE.2.3b (expression), A-REI.2.4 (equation), and F-IF.3.8a (function). Distributing or factoring A-APR.1.1, A-SSE.1.1a, A-SSE.1.2, A-SSE.2.3b, and A-REI.2.4b Using properties of exponents A-SSE.2.3c, F- IF.3.8b, and N-RN.1.2

35 Algebra 1 EOC Students are showing some understanding of A-APR.1.1. Students are doing well with simple addition, subtraction, and multiplication of monomials, binomials, and trinomials. Students struggle when there is more than one operation.

36 A-SSE.2.3b Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Real-World Context A-REI.2.4a Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. Mathematical Context F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Real-World Context

37 Equivalent Forms If an item requires the student to write an equation, the student will not be restricted to give that equation in a certain form unless a form is required by the standard such as items that require the student to complete the square. For example, if the directive asked for the form y = a(x h) 2 + k y = 3 (x 2) 2-8 y = 3 (x + - 2) y = 3x 2-12x + 4

38 Algebra 1 EOC Students are struggling equivalent expresssions using properties of exponents. Rewriting monomials with fractional exponents in radical form and vice versa. N-RN.1.2 Rewriting expressions, equations, and functions with fractional exponents using properties of exponents. N-RN.1.2, A-SSE.2.3c, and F-IF.3.8b

39 N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Mathematical Context A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t (1.012) 12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Real-World Context

40 F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, and y = (1.2) t/10 and classify them as representing exponential growth or decay. Mathematical or Real-World Context

41 Equivalent Exponential Functions Example in A-SSE.2.3c The expressions from 1.15 t can be rewritten as (1.15 1/12 ) 12t (1.012) 12t N-RN.1.2 includes applying the properties of exponents for expressions that involve rational exponents. Understanding the properties and the equivalence of expressions can lay a foundation for A-SSE.2.3c as well as F-IF.3.8c. Both A-SSE.2.3c and F-IF.3.8c also require the student to explain properties of the expression/function. In the example, a student could be asked the growth rate for a month and the growth rate for a year. Suggested MFAS task:

42 Algebra 1 EOC Students are struggling with constraints and domain given a real-world context. Writing constraints for a function based on a real-world situation. A-CED.1.3 Interpreting domain for a real-world situation. F-IF.2.5

43 A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Real-World Context F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Real-World Context

44 #12 on the FSA Algebra 1 CBT practice test This item could also be used to ask students to interpret zeros and/or the maximum. Students could be asked to write C(x) in the form C(x) = (x h) 2 + k using the provided vertex. This could help the connection between the form and the graph. A student could also be asked to explain option B. Also discussing why a domain of all real numbers is not appropriate given the real-world context.

45 Algebra 1 EOC Students are struggling with average rate of change. F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Students especially struggle when asked to determine the rate of change when the function is given symbolically. Please note that the assessment limits state that items for this standard should not be linear. This is because the standard states an average rate of change and because there are other standards that require interpretation of the rate of change of a linear function. Average rate of change is defined as the slope of the secant line.

46 #14 on the FSA Algebra 1 CBT practice test This item could also be used to ask students to find and interpret the average rate of change. The difference between rate of change and average rate of change can be approached without an understanding of calculus. Making the distinction conceptually while also connecting the slope formula f b f(a) b a misconceptions. may help students avoid

47 Algebra 1 EOC Students are struggling with A-REI.4.12.

48 Students struggle understanding just finding the solution set.

49 Algebra 1 EOC Students are struggling with F-BF.2.3. Identifying the effect of the transformation given a graph Graphing the transformed function Showing the transformation using a table of values This item could also be used to ask students to graph the function f(x) and its transformation. The transformation could be changed. Suggested activities:

50 Algebra 1 EOC Students are struggling with the Statistics standards. Students are struggling on all of the statistics standards except for S-ID.2.6a.

51 Geometry EOC Students are doing well on the following standards: G-CO.1.1 precise definitions of angle, circle, perpendicular line, parallel line, and line segment G-CO.2.6 rigid motions and definition of congruence G-CO.3.9 prove and use theorems about lines and angles G-CO.3.10 prove and use theorems about triangles G-GPE.2.4 using coordinates to prove simple geometric theorems algebraically.

52 Geometry EOC Students are struggling on G-C.1.2. G-C Identify and describe relationships among inscribed angles, radii, and chords. It is stated after the standard wording to include the relationship between central, inscribed, and circumscribed angles. Students struggle with all of these.

53 Geometry EOC Students are struggling on G-C.2.5. G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Students struggle with items that use radian measure. This includes items that ask students to find the area of a sector given the angle in radians.

54 Geometry EOC Students are struggling on G-GMD.1.3 and MG.1.3. G-GMD Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. G-MG Apply geometric methods to solve design problems. Prior Knowledge: MAFS.7.G.2.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. MAFS.8.G.3.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

55 Geometry EOC Students are struggling on G-GPE.1.1. G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Students learn to complete a square in Algebra 1 when rewriting quadratics. This process should not be new to students.

56 Geometry EOC Students are struggling on G-GPE.2.5. G-GPE Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MAFS.8.F.2.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

57 Equivalent Forms for EQ item types If an item requires the student to write an equation the student, will not be restricted to give that equation in a certain form unless the standard requires a particular form. For example, if a student has to write an equation using a real-world context, all of these forms are accepted as correct. Please note that the options could be in different formats if an item is a MC item. Educators review these and consider what form is appropriate for the real-world context. 10x 4y = 18 y = 2.5x 4.5 5x = 2y + 9 y + 7 = (5/2)(x + 10)

58 Geometry EOC Students are struggling on G-MG.1.2. G-MG.1.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Prior Knowledge: SC.8.P.8.3 Explore and describe the densities of various materials through measurement of their masses and volumes. Clarification: Students will describe density and/or calculate and compare the densities of various materials using the materials masses and volumes.

59 Geometry EOC Students are struggling on G-SRT.3.8. G-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. MAFS.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

60 New Online Calculator A new online calculator will be implemented in Spring The calculator is a modified Desmos calculator.

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64 Contact Information

65 Mathematics Contact Information Travis Barton, Mathematics Coordinator (850) Ext Trinidad Dixon, Content Specialist, Grades 3-5 (850) Ext Sarah Devereaux, Content Specialist, Grades 6-8 (850) Ext Terri Sebring, Content Specialist, Algebra 1 & Geometry terri.sebring@fldoe.org (850) Ext. 2226

66 Other TDC Contact Information Sally Rhodes, English Language Arts Coordinator (850) Ext Stacy Skinner, Social Studies Coordinator (850) Ext. 2238

67 Susan Taylor Executive Director Test Development Center (850) Ext. 2221

68 All TDC presentations from NCTM Orlando Regional 2017 can be found at this link.

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