1. Preparing for PARCC in the mathematics classroom Steve Hiner Lead 7-12 Mathematics Coordinator

2. 1. Make sense of problems and persevere in solving them What is the problem asking? What information is given? Do I have enough information? Is there information I do not need? Do I need a formula? Can I write my own equation? Mathematical Practices

3. 2. Reason abstractly and quantitatively Can a unit price be that high? Can the distance be a negative number? What do these numbers actually represent in this problem? Mathematical Practices

4. 3. Construct viable arguments and critique the reasoning of others I think this step is correct because... How can a negative number be correct here? Is that OK in this problem? I can defend my answer because... When you did this, how come... Mathematical Practices

5. 4. Model with mathematics Draw a diagram/picture of the problem. Use proper labels. Be mindful of information from the problem that is not needed to solve the problem. Mathematical Practices

6. 5. Use appropriate tools strategically Is a calculator needed for this problem? Be able to use a protractor, compass, ruler, etc. to solve a problem. Use graphing calculators and computer software in extension activities. Mathematical Practices

7. 6. Attend to precision Do I need to round in this problem? If so, to how many decimal places? Do I round at every step, or just the final answer? Is the answer in feet, inches, cubic miles... What units are necessary for this problem? Watch out for problems that have information given in one unit expecting an answer in another unit. Convert! Mathematical Practices

8. 7. Look for and make use of structure Can a problem be broken down into pieces? Be sure to follow the order of operations. Include your own ( ) where appropriate. Were all the steps followed in order? What do I need to do to find a sale price? Find the discount. Subtract it from the original price. Find tax. Add tax. Mathematical Practices

9. 8. Look for and express regularity in repeated reasoning Look for patterns. Are the numbers going up by 3s? Down by 4s? Is there addition or multiplication going on between numbers? In quadratics, when a is positive, the curve always opens upward. When negative, it opens downward. Can you come up with a formula? Mathematical Practices

10. PARCC Partnership for Assessment of Readiness for College and Careers. The PARCC member states share this fundamental goal: ensuring that every student graduates from high school prepared for success in college and the workplace.

11. PARCC Task prototypes were released in August 2012. Sample items were released beginning on August 15, 2013. All are available on their website at:http://www.parcconline.org/samples/ite m-task-prototypeshttp://www.parcconline.org/samples/ite m-task-prototypes

12. PARCC Practice tests are available. They can be completed online (similar to how students are expected to do the real assessments) so they can become familiar with the different innovative computer- based questions.

13. PARCC Teachers can click on a desired grade level and see the Type I, II and III tasks for each grade. Samples of each task follow the description of the task type.

14. Type I Tasks Tasks assessing concepts, skills, and procedures Type I tasks can be scored by machine. They will include innovative computer-based formats. (Example: sliders, radio buttons, dragging items on the screen, drop-down menus). These tasks will check for understanding of concepts. Students should be able to perform these tasks quickly and precisely.

15. Type I Tasks (continued) These tasks can contain any or all mathematic practice standards. Type I tasks will appear on End of Year (EOY) and Performance Based Assessment (PBA) components.

16. Type I Tasks - Example Here is an example of a Type I task question. The student should see that Part A is answered by adding 96+36 and obtaining 132 cubic meters. In Part B, the student must remember that the total volume was 132 cubic meters, then reason that he or she must subtract 18 from 132 to arrive at 114 cubic meters.

17. Type II Tasks Tasks assessing expressing mathematical reasoning These tasks ask for written arguments and justifications, a critique of reasoning, or precision (MP 3, 6). Type II tasks can include a combination of the machine-scored questions and hand- scored questions. Included on the PBA component.

18. Type II Tasks - Example The student computes the answer to Part A as 3. In Part B, the student has to find 80% of 210 which is 168. Then, the student must realize there is a 3:1 ratio here. Divide 168 by 4 to get 42. The small part (percussion) is 42. The large part (brass) is 42 x 3 = 126. This question is worth 4 points. Part A: one point: if correct (3) Part B: one point: shows/explains the 80% work Part B: one point: shows/explains 3:1 ratio Part B: one point: obtains the answer: 126

19. Type III Tasks Tasks assessing modeling / application Students model and apply real-world context and scenarios (MP 4). Combination of the machine-scored questions and hand-scored questions Included on the PBA component.

20. Type III Tasks - Example Notice that students have to click on “More tick marks” or “Fewer tick marks” to change the number line.

22. PARCC – Test Dates There will be a 20 day window for schools taking the computerized version of the tests. The test window for paper and pencil testing is reduced to 10 days.

23. PARCC – Approved Calculators Grades 3-5: No calculators are allowed, except for students with an approved calculator accommodation.

24. PARCC – Approved Calculators Grades 6-7: Four function calculators with square roots and percentage functions are permitted.

25. PARCC – Approved Calculators Grade 8: Scientific calculators such as the red OGT style are permitted.

26. PARCC – Approved Calculators High School: Graphing calculators are allowed, such as the TI-84 and TI-nspire.

27. PARCC – Approved Calculators No calculators with Computer Algebra System (CAS) features are allowed. No tablet, laptop (or PDA), or phone-based calculators are allowed during PARCC assessments. Test administrators must confirm that memory on all calculators has been cleared before and after the testing sessions (or use press-to-test mode). Calculators with “QWERTY” keyboards are not permitted.

28. PARCC - Notes Students completing an online test can still use a hand-held calculator. Students taking an online test can use headphones to listen to the audio. Make sure students with IEPs have very detailed plans written.

29. PARCC - Notes Students enrolled in grade 7 and 8 math at the same time will only take the test for grade 8. Grade 8 students taking HS classes will take THOSE tests, not grade level tests. Students who have already taken Math I will automatically receive 3 points.

30. PARCC - Notes The EOY HS online practice tests are made for Algebra I and Geometry, not Math I and Math II. Refer to the online answer sheets to see which questions apply and which do not. Sample tests for PBAs are expected in January.

31. PARCC - Scoring Students will receive a cumulative score from 1 – 5 combining the PBA and EOY 1 – Limited 2 – Basic 3 – Proficient 4 – Accelerated 5 - Advanced Grad requirements: 18 points (tentative) English 9, 10 Integrated Math I, II Physical Science American History, American Government Students must earn at least 4 points from Math I and Math II. Students must earn at least 4 points from English 9 and English 10. Students must earn at least 6 points from Physical Science, American History, and American Government. Students cannot be retained for failing a PARCC exam They will still move on to the next math class. If a student is proficient but still does not have enough points to graduate, he or she can re-take an assessment with remediation.

32. Multiple-Choice Items: Multiple-Choice Items: PARCC Tutorial - Question types Represented by a circle. Allow just one response. Can be selected by clicking the text or circle to the left. http://parcc.pearson.com/tutorial/ Note: There are other tutorials available such as a paper/pencil tutorial, calculator info, and a guide on how to navigate through the online version

33. Multiple-Select Items: Multiple-Select Items: PARCC Tutorial - Question types Have at least five answer choices and no more than eight choices. The directions indicate multiple responses are required by the word all as in select all that apply. Represented by squares.

34. Drag-and-Drop Items: Drag-and-Drop Items: PARCC Tutorial - Question types May allow you to drag an answer choice into more than one drop area. Will only allow a choice to be dragged to one drop area at a time. May have drop areas which will limit the number of choices that can be dropped into the drop area.

35. Drag-and-Drop Items (cont.): Drag-and-Drop Items (cont.): PARCC Tutorial - Question types May need to have the choice dragged out of the drop area before you can put another one in. May require you to scroll down on the page to see all answer choices and drop areas.

36. Equation Editor Items: Equation Editor Items: PARCC Tutorial - Question types Basic: Allows for math only.

37. Equation Editor Items (cont.): Equation Editor Items (cont.): PARCC Tutorial - Question types Open-Response: Allows for math plus text. Has sub-menus of tools.

38. Fill-in-the-Blank Items: Fill-in-the-Blank Items: PARCC Tutorial - Question types Have a rectangular box to type in your response. Fractions cannot be entered! Use decimals! “Invalid input” if fraction bar is typed.

39. Hot-Spot Items: Hot-Spot Items: PARCC Tutorial - Question types May require selecting an image or a portion of the image. The parts of the image that can be selected will be light blue when not selected. When selected, they will turn dark blue.

40. Inline-Choice Items: Inline-Choice Items: PARCC Tutorial - Question types Require using one or more drop-down menus. Click on the arrow next to the drop- down box to display the menu. Make a selection by clicking directly on the choice shown in the menu.

41. Line Graph Items: Line Graph Items: PARCC Tutorial - Question types Require selecting two points on a graph to create a line. To plot a point on the graph, click a point. After selecting the second point, a line connecting the two points will be automatically drawn. To remove a point, click on the point again.

42. Bar-Graph/Histogram Items: Bar-Graph/Histogram Items: PARCC Tutorial - Question types Require extending the bar value to the correct place. To extend the bar, click and hold on the bar. While dragging to its desired length, a comment bar will indicate the bar’s name and length. Drag the bar to the height or length and release.

43. Function-Graph Items: Function-Graph Items: PARCC Tutorial - Question types Require choosing a function on the left hand side of the grid. Points will appear on the graph that you can manipulate. Adjust the graph by moving the points as needed. The vertex point will automatically appear at (0, 0). This can be moved. However, it will stay as the vertex in the equation.

44. Interactive Number Lines: Interactive Number Lines: PARCC Tutorial - Question types Require choosing rays or segments to plot on a number line. Solution set indicators will be available below the number line. Once the ray or segment is selected, it will appear on the number line. Move the end points to the correct spot.

45. Solution-Set-Graphing Items: Solution-Set-Graphing Items: PARCC Tutorial - Question types Require choosing dashed or solid line style and shading one or more areas created by the two lines in order to indicate a solution set for two inequalities. Select a line button. Plot two points. The line appears. Adjust as needed. Repeat for second line. Click the Solution Set button and click the region to shade.

46. Pencil / Paper Based Testing PARCC Tutorial - Question types

47. Pencil / Paper Based Testing PARCC Tutorial - Question types

48. Pencil / Paper Based Testing PARCC Tutorial - Question types

49. Pencil / Paper Based Testing PARCC Tutorial - Question types

50. Pencil / Paper Based Testing PARCC Tutorial - Question types

51. Pencil / Paper Based Testing PARCC Tutorial - Question types

52. Pencil / Paper Based Testing PARCC Tutorial - Question types

53. Pencil / Paper Based Testing PARCC Tutorial - Question types

54. Pencil / Paper Based Testing PARCC Tutorial - Question types

55. Pencil / Paper Based Testing PARCC Tutorial - Question types

56. Pencil / Paper Based Testing PARCC Tutorial - Question types

57. Pencil / Paper Based Testing PARCC Tutorial - Question types

58. Important Vocabulary Words Grade 7: Constant speed, rate, order (as a verb), represents, proportional relationship, coordinates, relationship, proportional relationship, investment, quotient, withdraw/withdrew, increased, expression, perimeter, equivalent, factor, probability, scale (on a map), random, simulation, generates (a number), rate, combined area, random sample, more/less consistent, income tax, flat rate, taxable income, discounted (a percentage), sales tax, cube, right-square pyramid, two-dimensional-plane, horizontal slice (through a figure), cups, fluid ounces, quarts, estimate (a percentage), generalization, population, coordinate, region, right angle.

59. Important Vocabulary Words Grade 8: Right circular cone, vertex, circumference, base, diameter, equivalent, solution, coordinate place, intersect, system of linear equations, relationship, function, input, output, interval, increasing/decreasing over an interval, infinitely many solutions, parallelogram, image, rotation, transformation, equivalent, nonlinear, scatter plot, line of best fit, perpendicular, dimensions, perimeter, length, width, survey, slope, y-intercept, linear relationship, rate of change, context, linear function, proportional relationship, right- circular cylinder, right-circular cone, volume, ratio, solution (as in a mixture of items).

60. Important Vocabulary Words Math I: From Algebra I test: Function, solution set, linear inequality, coordinate plane, region, predicted, estimate, increase, base year, table of values, function (know that each x goes with only one y), random, proportion, participants (as in a study), capacity, represents, domain, whole number, non-negative, rational, irrational, integers, linear equation, ordered pairs, coordinate plane, solution set, x-y coordinate plane, intersect, point of intersection, grow exponentially, grow linearly, modeled (by the function), constants, system of equations, exponential function, predicted, linear function, nearest whole number, solution set, system of linear inequalities, region, given conditions. From Geometry test: Perpendicular, interior, trapezoid, legs, bisect, angle, plane, conclude, rotated clockwise, corresponding, reflected, rotated, diagonals, parallelogram, bisect, partial proof, quadrilateral, transversal, congruent, interior angle, complement, supplement, alternate interior, congruence, transformation, sequence of transformations, translation, prime notation (P’, etc.), respectively. From Algebra II test: Half-life, fractional exponent.

61. Important Vocabulary Words Math II: From Algebra I test: Zero(s), equivalent, rational, irrational, quadratic equation, integer coefficients, distinct zeroes, real, non-real, integer coordinates, portions (part of), function, solutions, expression, volume, radius, cone, expression, vertex form (of a quadratic), completing the square, minimum value, real, non-real, increase, fewer, revenue, maximize (revenue), summarized (in a table), histogram, slider (for testing), appropriate, median (time), interquartile range, generate (a graph), coordinate plane, area, x-y intercepts, lower bound, upper bound. From Geometry test: Vertices, right triangle, sin, cos, semicircles, tangent, image, respectively, dilation, scale factor, difference (pertaining to subtraction), angle of depression, cylinder, horizontal cross section (of a cylinder), altitude, linear range of view. From Algebra II test: Complex number, imaginary unit, product, real number, equivalent expression, respectively, point(s) of intersection (system of equations), two-way table, classification, gender, dominant hand, ambidextrous, events, independent, not independent. Graph types: Linear, absolute value, quadratic, exponential, logarithmic, sin/cos, tan/cotan.

62. Curriculum staff – here to help All math teachers of grades 7-12 can be enrolled in a Blackboard course for sharing lessons, worksheets, activities, and PARCC information. Activities will be designed to closely resemble actual PARCC test questions to aid in preparing teachers and students for the assessments.

63. Math Blackboard Course Shell Receive email updates regarding PARCC Share lessons with other teachers Find curriculum guides, new and old Eday lessons MS/HS leader meeting notes

64. Comments / Questions Please feel free to contact: Steve Hiner Lead 7-12 Mathematics Coordinator SHiner5842@columbus.k12.oh.us Office Location: South HS (614) 365-5541 ext. 301 (614) 440-8095 (cell)