dc cas anchor paper training mathematics – secondary

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DC CAS Anchor Paper Training Mathematics – Secondary OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

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DC CAS Anchor Paper Training Mathematics – Secondary . OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436. Session Outcomes. By the end of the session participants will: - PowerPoint PPT Presentation

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Page 1: DC CAS Anchor Paper Training Mathematics – Secondary

DC CAS Anchor Paper TrainingMathematics – Secondary

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 2: DC CAS Anchor Paper Training Mathematics – Secondary

Session Outcomes

• By the end of the session participants will:• Examine various grade level anchor papers and

norm their scoring practices aligned to the rubric;• Discuss ways these anchor papers can be

effectively implemented into their instruction.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 3: DC CAS Anchor Paper Training Mathematics – Secondary

Protocol and Norms

• We will review a series of anchor papers from each grade level.

• We will review as a large-group, as well as independently and with elbow partners.

• This is a conversation. Please feel comfortable to ask questions and be respectful of each other in order to hear those questions being asked and comments made.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 4: DC CAS Anchor Paper Training Mathematics – Secondary

50

1 2 3 4 5 6Two players take turns adding the digits 1, 2, 3, 4, 5, and 6.

First person to get to 50 wins.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 5: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 7 - #6

6 John asked some of his friends how many first cousins they had. His results are shown below.

6-A What is the range of John’s data? In the box in the answer booklet, show your work and write your answer on the line.

6-B What is the mean of John’s data? In the box in the answer booklet, show your work and write your answer on the line.

6-C The mean and the range measure different things about a data set. Explain what the mean measures and how this is different from what the range measures. One the lines in the answer booklet, write your answer.

What MUST a student know about measures of central

tendency in order to successfully answer this

problem?

What does a student NOT have to know about measures of central tendency in order to

successfully answer this problem?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 6: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding to find, describe, and interpret appropriate measures of central tendency (mean, median and mode) and spread (range) that represent a set of data.• Response is completely correctA. 19 – 1 = 18B. 12 + 3 + 7 + 19 + 3 + 4 + 6 + 8 + 1 = 63 63 / 9 = 7C. Mean measures the middle, or average, of the data set. Range measures the spread of the data, or the difference between the maximum and minimum.• Response shows application of a reasonable and relevant strategy• Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed responses using words,

calculations and/or symbols as appropriate.

2 The response demonstrates a general and only a partial understanding to find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data.• Response is mostly correct, and may be only partially complete.A. 12 – 1 = 11B. 12 + 3 + 7 + 19 + 3 + 4 + 6 + 8 + 1 = 63 63 / 8 = 7.875C. Mean measures the middle of the data and range measures the ends.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as appropriate.

1 The response demonstrates a minimal and/or limited understanding to find, describe, and interpret appropriate measures of central tendency (mean, median and mode) and spread (range) that represent a set of data.• Response is only minimally correct and incomplete.A. 19B. Mean is 3 because there are 2 threes.C. The mean is different from range because mean is the one there is the most of and the range is the biggest number.• Application of a strategy is indicated or implied by the strategy may reflect a misunderstanding of the mathematical concepts

and/or procedures.• Mathematical ideas are expressed in a limited manner and are flawed. Words, calculations, and/or symbols are attempted to

be used as appropriate, but may be missing.

0 The response demonstrates no understanding to find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data.• No correct responses• Response is incorrect, incomplete, or missing• Response shows no application of a strategy or application

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 7: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Correct work and answerPart B: Correct work and answer - The work is OK, even though there should be parentheses around the sum to make it totally correct.Part C: The explanation is incorrect.

2

Grade 7 – 6/LA

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 8: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Correct work and answerPart B: The median is found in place of the mean. Part C: The explanations successfully describe how to find the range only.

1

Grade 7 – 6/LB

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 9: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Correct work and answerPart B: Correct work and answerPart C: The explanations describe how to find the range and the mean. This is one acceptable way of explaining the difference.

3

Grade 7 – 6/LC

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 10: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: IncorrectPart B: IncorrectPart C: Incorrect

0

Grade 7 – 6/LD

When there is a

work space, show your work.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 11: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 7 - #29

29 Harold works at a pizza parlor for an hourly wage. For 3.5 hours, Harold earns $21.21-A What is Harold’s hourly wage? Show your work in the box in the answer booklet and write your answer on the line.

21-B On the coordinate grid in the answer booklet, plot how much money Harold earns for 3.5 hours, 4 hours, and 9 hours.

With two questions, we

need to examine the

rubric to determine where the

points exist for each item.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 12: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of creating and interpreting graphical representations of data.• Response is completely correctPart A: ($)6AND21/3.5 = 6OROther correct computation

Part B:

Points DO NOT need to be connected to receive credit.• Response shows application of a reasonable and relevant strategy• Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed

responses using words, calculations and/or symbols as appropriate.2 The response demonstrates a general and only a partial understanding of creating and interpreting graphical

representations of data.• Response is mostly correct, and may be only partially complete.

Give 2 points if Part A is completely correct, and Part B is incorrect.ORPart A is partially correct with work shown, and Part B is correct.

• Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as

appropriate.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 13: DC CAS Anchor Paper Training Mathematics – Secondary

1 The response demonstrates a minimal and/or limited understanding of creating and interpreting graphical representations of data.• Response is only minimally correct and incomplete.

Give 1 point if Part A is correct with no work shown ORPart B is completely correct.

• Application of a strategy is indicated or implied by the strategy may reflect a misunderstanding of the mathematical concepts and/or procedures.

• Mathematical ideas are expressed in a limited manner and are flawed. Words, calculations, and/or symbols are attempted to be used as appropriate, but may be missing.

0 The response demonstrates no understanding of creating and interpreting graphical representations of data.

• Part A and B are entirely incorrect.• Response is incorrect, incomplete, or missing• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 14: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: IncorrectPart B: Incorrect

0

Grade 7 – 29/MA

Where is the student misunderstanding

in this answer?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 15: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A is complete and correct (2 points)Part B is incorrect (0 points)

2

Grade 7 – 29/MB

Correct algorithm?Correct procedure?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 16: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A is complete and correct (2 points)Part B is complete and correct (1 point)Note: Points DO NOT have to be connected to receive credit.

3

Grade 7 – 29/MC

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 17: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A is correct but no work is shown (1 points)Part B is incomplete, the point for 3.5 hours is missing (0 points)

1

Grade 7 – 29/MD

Precision of points graphed

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 18: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 7 - #59

59-A Derek plans to make 2 ½ loaves of nut bread. Each loaf uses 1 2/3 cups of flour. In total, how many cups of flour will Derek use? In the box in the answer booklet, show your work.

Then write your answer on the line below the box.

59-B Each loaf of nut bread uses ¾ cup of walnuts. Derek has a total of 6 ¼ cups of walnuts.

How many cups of walnuts will Derek have left after making 2 ½ loaves of nut bread? In the box in the answer booklet, show your work. Then write your answer on the line below the

box.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 19: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of computation with fractions in real-world contexts.• Response is completely correct

A.

B.

• Response shows application of a reasonable and relevant strategy• Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed

responses using words, calculations and/or symbols as appropriate.2 The response demonstrates a general and only a partial understanding of computations with fractions in real-

world contexts.• Response is mostly correct, and may be only partially complete.

• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as appropriate.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 20: DC CAS Anchor Paper Training Mathematics – Secondary

1 The response demonstrates a minimal and/or limited understanding of computation with fractions in real-world contexts.• Response is only minimally correct and incomplete.

• Application of a strategy is indicated or implied by the strategy may reflect a misunderstanding of the mathematical concepts and/or procedures.

• Mathematical ideas are expressed in a limited manner and are flawed. Words, calculations, and/or symbols are attempted to be used as appropriate, but may be missing.

0 The response demonstrates no understanding of computation with fractions in real-world contexts.

• No correct response• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy of application.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 21: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: Correct work and answerPart B: Correct work and answer

3

Grade 7 – 29/NA

What did the student do “right”?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 22: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: Correct setup with a wrong answerPart B: Incorrect work and incorrect answer

1

Grade 7 – 29/NB

How have you corrected this error with students?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 23: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: Correct work and answerPart B: Incorrect work and incorrect answer

2

Grade 7 – 29/NC

What strategies have you used to correct this

mistake?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 24: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: Incorrect work and incorrect answerPart B: Incorrect work and incorrect answer

0

Grade 7 – 29/ND

How would you use this anchor paper in your

classroom?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 25: DC CAS Anchor Paper Training Mathematics – Secondary

Capture Sheet – Reflection – Grade 7

• What have you learned from these anchor papers which addressed Data Analysis, Statistics, and Probability, Patterns, Relations, and Algebra, and Number Sense and Operations?

• What surprised you about the student responses?

• What key ideas will you implement when using these anchor papers in your classroom?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 26: DC CAS Anchor Paper Training Mathematics – Secondary

DC CAS Anchor Paper TrainingMathematics (Grade 8)

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 27: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 8 - #6

6-A Ms. Martinez runs a store. She pays $0.75 for a can of soup. She sells the soup for 80% more than she pays for it. What is the selling price of the soup? In the box in the answer

booklet, show your work and write your answer on the line.

6-B Ms. Martinez puts $2,400 in a savings account. She receives 4% interest on her money per year. How much money will

there be in the savings account after one year? In the box in the answer booklet, show your work and write your answer on the line.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 28: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of solving problems that involve markup, commissions, profits, and simple and compound interest.• Response is completely correctA. 0.75 X 1.8 = $1.35B. 2,400 X 1.04 = $2,496• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed responses using words,

calculations and/or symbols as appropriate.

2 The response demonstrates a general and only a partial understanding of solving problems that involve markups, commissions, profits, and simple and compound interest.• Response is mostly correct, and may be only partially complete.A. 0.75 X 1.8 = $1.35B. 2,400 X 1.4 = $3,360• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as appropriate.

1 The response demonstrates a minimal and/or limited understanding of a solving problems that involve markups, commissions, profits, and simple and compound interest.• Response is only minimally correct and incomplete.A. 0.75 + 0.80 = $1.55B. 2,400 X 0.04 = $96.00• Application of a strategy is indicated or implied by the strategy may reflect a misunderstanding of the mathematical concepts

and/or procedures.• Mathematical ideas are expressed in a limited manner and are flawed. Words, calculations, and/or symbols are attempted to be

used as appropriate, but may be missing.

0 The response demonstrates no understanding of solving problems that involve markups, commissions, profits, and simple and compound interest.• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 29: DC CAS Anchor Paper Training Mathematics – Secondary

Score:

Rationale: Part A: Correct $0.75 X 1.8 = $1.35Part B: Correct $2,400 X 1.04 = $2,496

3

Grade 8 – 6/PA

Work Space

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 30: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Partially Correct: An attempt at a correct process, attempted to find markup only and has a decimal error (didn’t convert the 80% to .80 but rather just 80)Part B: Partially Correct: Incomplete, found interest only

1

Grade 8 – 6/PE

What have you found effective to help students complete the process of finding markup?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 31: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: CorrectPart B: Partially Correct: An incorrect interest is determined by using 40% instead of 4%

2

Grade 8 – 6/PG

Is this “careless” or a “conceptual misunderstanding”?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 32: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: IncorrectPart B: Incorrect

0

Grade 8 – 6/PHIdentify the mistakes…

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 33: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 8 - #29

29 The table below shows the number of students attending State College over a 4-year period.

29-A If the school continues to grow at the same rate, how many students will be attending State College in year 7? In the box in the answer booklet, show your work and write your answer on the line.

29-B On the lines in the answer booklet, write an equation representing the data in the table and define the

variables you use in your equation.

What information would you want your students to

immediately recognize when examining a table of values?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 34: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of setting up and solving linear equations and inequalities with one or two variables using algebraic methods, models, and graphs.• Response is completely correct.

A. 5,375 – 5,300 = 75 new students per year. (4 more years)(73 new students/year) = 300 new students 5,375 + 300 = 5,674 total students in year 7

B. S = 75y + 5,150 S = total number of students y = year

• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed

responses using words, calculations and/or symbols as appropriate.2 The response demonstrates a general and only a partial understanding of setting up and solving linear equations

and inequalities with one or two variables using algebraic methods, models, and graphs.• Response is mostly correct, and may be only partially complete.

A. 75 new students per year 5,375 + 75 = 5,450 students the next year

B. Y = 75x + 5,150 x = the number of students y = year • Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as

appropriate.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 35: DC CAS Anchor Paper Training Mathematics – Secondary

1 The response demonstrates a minimal and/or limited understanding of setting up and solving linear equations and inequalities with one or two variables using algebraic methods, models, and graphs.

• Response is only minimally correct and incomplete.

A. 75 new students per year 5,375 + 75 = 5,450 students the next year

B. y = 5,150x + 75

• Application of a strategy is indicated or implied by the strategy may reflect a misunderstanding of the mathematical concepts and/or procedures.

• Mathematical ideas are expressed in a limited manner and are flawed. Words, calculations, and/or symbols are attempted to be used as appropriate, but may be missing.

0 The response demonstrates no understanding of setting up and solving linear equations and inequalities with one or two variables using algebraic methods, models, and graphs.

• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 36: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: CorrectPart B: Correct

3

Grade 8 – 29/QA

Skip Counting is always a viable strategy.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 37: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Incorrect, but shows an attempt to add 75 to get the number of studentsPart B: Incorrect equation with variables defined; this simply shows understanding of adding 75 and would need an equation that more closely resembles S=75y+5, 150 to consider 2 points

1

Grade 8 – 29/QB

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 38: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: IncorrectPart B: Incorrect

0

Grade 8 – 29/QE

This is at least a good start to an explanation but lacks

specificity.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 39: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: CorrectPart B: Correct equation with variable definitions mixed up

2

Grade 8 – 29/QF

Defining variables is a difficult task. How can we do it better?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 40: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 8 - #59

59-A Look at the figure below.

In this figure, parallel lines cut by a transversal are shown. On the line in the answer booklet, list all of the angles that have the same measure as Angle A.

59-B Look at the figure below.

What is the measure of angle x? In the box in the answer booklet, show your work and write your answer on the line.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 41: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.• Response is correct and complete.A. D, E, and HB. 64˚ + x = 180˚; x = 180˚ - 64˚; x = 116˚• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed responses using

words, calculations and/or symbols as appropriate.

2 The response demonstrates a general and only a partial understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.• Response is mostly correct, and may be only partially complete.A. D, E, and HB. 64˚ + x = 180˚; x = 180˚ - 64˚; x = 126˚• Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as appropriate.

1 The response demonstrates a minimal and/or limited understanding of angles formed by intersecting lines, including parallel lines cut by a transversal.• Application of a strategy is indicated or implied but the strategy may reflect a misunderstanding of the mathematical

concepts and/or procedures.• Mathematical ideas are expressed in a limited manner and area flawed. Words, calculations, and/or symbols are

attempted to be used as appropriate, but may be missing.

0 The response demonstrates no understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 42: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: All 3 angles correctPart B: Correct

3

Grade 8 – 59/RA

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 43: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: 1 Correct Angle, 2 Incorrect AnglesPart B: Incorrect

1

Grade 8 – 59/RC

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 44: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: All angles listed; cannot distinguish between correct and incorrect anglesPart B: Incorrect

0

Grade 8 – 59/RD

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 45: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: 1 Correct AnglePart B: Correct

2

Grade 8 – 59/RI

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 46: DC CAS Anchor Paper Training Mathematics – Secondary

Capture Sheet – Reflection – Grade 8

• What have you learned from these anchor papers which addressed Number Sense and Operations, Patterns, Relations, and Algebra, and Geometry?

• What surprised you about the student responses?

• What key ideas will you implement when using these anchor papers in your classroom?

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 47: DC CAS Anchor Paper Training Mathematics – Secondary

DC CAS Anchor Paper TrainingMathematics (Grade 10)

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 48: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 10 - #66 Use the graph and formulas below to answer the following questions.

6-A What is the midpoint of ST? Show your work in the box in the answer booklet and write your answer on the line.

6-B What is the distance between points S and T? Round your answer to the nearest tenth. Show your work in the box in the answer booklet and write your answer on the line.

6-C What is the slope of ST? Show your work in the box in the answer booklet and write your answer on the line.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 49: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of how to calculate the midpoints and slopes of segments, and distances between two points.• Response is correct and complete.A. (1, -2.5)B. 6.7C. 1/2• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed

responses using words, calculations and/or symbols as appropriate.2 The response demonstrates a general and only a partial understanding of how to calculate the midpoints and

slopes of segments, and distances between two points.• Response is mostly correct, and may be only partially complete.• Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as

appropriate.

1 The response demonstrates a minimal and/or limited understanding of how to calculate the midpoints and slopes of segments, and distances between two points.• Application of a strategy is indicated or implied but the strategy may reflect a misunderstanding of the

mathematical concepts and/or procedures.• Mathematical ideas are expressed in a limited manner and are flawed. An attempt is made to use words,

calculations, and/or symbols as appropriate, but may be missing.

0 The response demonstrates no understanding of how to calculate the midpoints and slopes of segments, and distances between two points.• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited

understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 50: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: CorrectPart B: CorrectPart C: Correct

3

Grade 10 – 6/SA

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 51: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Sign Error; student simply left off minus sign from -5/2 to 2.5Part B: Minor Error; did not square rootPart C: Correct, with limited work

2

Grade 10 – 6/SE

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Page 52: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Student used incorrect points and has an additional error in Part BPart A: OK, based on points usedPart B: Additional error; student took the square root of 64-9 instead of 64+9Part C: OK, based on points used

1

Grade 10 – 6/SI

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Page 53: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Incorrect and incompletePart B: Incorrect; student’s process is unclearPart C: Incorrect; student does not attempt to use the slope formula

0

Grade 10 – 6/SJ

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Page 54: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 10 - #29

29 Stacey asked 10 girls from her 10th grade English class which type of TV show is their favorite. The results of her survey are shown in the table

below.

After studying the data in the table, Stacey concluded that the favorite type of TV show for most of the students in her high school is comedy. On the lines in the answer booklet, give three reasons why Stacey’s conclusion is invalid.

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Page 55: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of describing and explaining how the relative sizes of a sample and the population affect the validity of predictions from a set of data.• Response is correct and complete.Reason 1 Gender bias (Only girls asked)Reason 2 Grade bias (Only 10th graders asked)Reason 3 Small sample (Only 10 people asked) OR Only one class asked (Asked only students in English class).• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed responses using

words, calculations and/or symbols as appropriate.

2 The response demonstrates a general and only a partial understanding of describing and explaining how the relative sizes of a sample and the population affect the validity of predictions from a set of data.• Response is mostly correct, and may be only partially complete.Give 2 points for two correct reasons listed.• Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as

appropriate.

1 The response demonstrates a minimal and/or limited understanding of describing and explaining how the relative sizes of a sample and the population affect the validity of predictions from a set of data.Give 1 point for one correct reason listed.• Application of a strategy is indicated or implied but the strategy may reflect a misunderstanding of the mathematical

concepts and/or procedures.• Mathematical ideas are expressed in a limited manner and are flawed. An attempt is made to use words,

calculations, and/or symbols as appropriate, but may be missing.

0 The response demonstrates no understanding of describing and explaining how the relative sizes of a sample and the population affect the validity of predictions from a set of data.• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited understanding.

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Page 56: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Not a valid reason (0 points)Small sample (1 point)No reason listed (0 points)

1

Grade 10 – 29/TA

Never leave an answer blank

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 57: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Grade bias (1 point)Only one class asked (1 point)Gender bias (1 point)

3

Grade 10 – 29/TB

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Page 58: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Not a valid reason (0 points)Not a valid reason (0 points)Not a valid reason (0 points)

0

Grade 10 – 29/TC

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 59: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Small sample (1 points)Gender bias (0 points)Not a grade bias (0 points)

2

Grade 10 – 29/TD

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Page 60: DC CAS Anchor Paper Training Mathematics – Secondary

Grade 10 - #59

59-A Look at the equation below.

y = 3x – 2

On the coordinate grid in the answer booklet, graph this equation.

59-B What are the x- and y-intercepts of this line? Write your answer on the lines in the answer booklet.

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Page 61: DC CAS Anchor Paper Training Mathematics – Secondary

Score Description

3 The response demonstrates a thorough understanding of the relationship between a linear equation and the graph of a line and finding the equation of a line from its intercepts.• Response is correct and complete.

A.

B. x-intercept is (2/3, 0); y-intercept is (0, -2)• Response shows application of a reasonable and relevant strategy. • Mathematical ideas are expressed coherently through clear, complete, logical, and fully developed responses using

words, calculations and/or symbols as appropriate.

2 The response demonstrates a general and only a partial understanding of the relationship between a linear equation and the graph of a line and finding the equation of a line from its intercepts.• Response is mostly correct, and may be only partially complete.

A.

B. x-intercept is (6,0); y-intercept is (0, -2)• Response shows application of a reasonable and relevant strategy, though may be only partially applied.• Mathematical ideas are expressed generally or only partially using words, calculations, and/or symbols as

appropriate.

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Page 62: DC CAS Anchor Paper Training Mathematics – Secondary

1 The response demonstrates a minimal and/or limited understanding of the relationship between a linear equation and the graph of a line and finding the equation of a line from its intercepts.• Response is only minimally correct and incomplete.

A.

B. x-intercept is (0, -2); y-intercept is (6,0)

• Application of a strategy is indicated or implied but the strategy may reflect a misunderstanding of the mathematical concepts and/or procedures.

• Mathematical ideas are expressed in a limited manner and are flawed. An attempt is made to use words, calculations, and/or symbols as appropriate, but may be missing.

0 The response demonstrates no understanding of the relationship between a linear equation and the graph of a line and finding the equation of a line from its intercepts.• Response is incorrect, incomplete, or missing.• Response shows no application of a strategy or application of an irrelevant strategy.• Mathematical ideas cannot be interpreted or lack sufficient evidence to support even a limited

understanding.

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 63: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Incorrectly graphed line, but consistent with the intercepts (1,0) and (0, -2)Part B: Incorrect x-intercept; partially correct y-intercept (coordinates are reversed)

1

Grade 10 – 59/WA

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Page 64: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Correctly graphed linePart B: Incorrect x-intercept; but close approximation according to graph; correct y-intercept

2

Grade 10 – 59/WB

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 65: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Correctly graphed linePart B: Correct x-intercept; correct y-intercept (parentheses are not necessary)

3

Grade 10 – 59/WF

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436

Page 66: DC CAS Anchor Paper Training Mathematics – Secondary

Score: Rationale: Part A: Incorrect graphPart B: No correct intercepts

0

Grade 10 – 59/WH

2/3-2

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Page 67: DC CAS Anchor Paper Training Mathematics – Secondary

Capture Sheet – Reflection – Grade 10

• What have you learned from these anchor papers which addressed Patterns, Relations, and Algebra and Data Analysis, Statistics, and Probability?

• What surprised you about the student responses?

• What key ideas will you implement when using these anchor papers in your classroom?

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Page 68: DC CAS Anchor Paper Training Mathematics – Secondary

Closure

• Thoughts and Comments• Feedback / Evaluation• Next Steps• PD Certificates

OSSE | Office of Assessment & Accountability | 810 First Street NE | Washington, D.C. 20002-4227 | 202-727-6436