dc cas anchor paper training mathematics (elementary)

DC CAS Anchor Paper TrainingMathematics (Elementary)

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:• 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.


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.


1 2 3 4 5 67


50 , 43, 36, 29, 22, 15, 8, 1

Grade 3 - #1818 Jenna has these math cards.

18-A Circle the card Jenna needs to finish her math test.

18-B What are two math facts Jenna can make with the numbers 3, 15, and 18?


Score Description

3 The response demonstrates a thorough understanding of operations and number facts. • Response is correct and complete.Part A

Part B (any two of the following)18 – 3 = 15 or 15 + 3 = 18 or 18 – 15 = 3• 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 operations and number facts.Part A – circles the correct symbol AND Part B – student gives only one correct math fact OR Part B student gives two correct math facts

1 The response demonstrates a minimal and/or limited understanding of operations and number facts.Part A – circles the correct symbolORPart B – student gives only one correct math fact

0 The response demonstrates no understanding of operations and number facts.


Grade 3-18/AB

Score:

Rationale: Part A is incorrectPart B is correct (two correct math facts)

2

Notice that two is underlined.

There are two lines to cue that there are two responses.


Grade 3-18/AC

Score:

Rationale: Part A is incorrectPart B is incorrect (response just copies prompt)

0


Grade 3-18/AD

Score:

Rationale: Part A is correct (correct card is circled)Part B is incorrect (response just copies prompt)

1

One point is earned because card is circled.


Grade 3-18/AF

Score:

Rationale: Part A is correct (correct card is circled)Part B is correct (two correct math facts)

3


Grade 3 - #59

59 The tally chart below shows the number of bananas some students ate last week.

Complete the bar graph below so that it shows the same information as the tally chart. Be sure to write the graph labels and a title. Do not shade in the bars.


Score Description

3 The 3 other bars (or straight lines) are completed correctly on the bar graph. A title and labels are both present and appropriate. (Labels and titles are also correct.)

2 Give two points for 3 correct graphing and 1 or 2 correct labels or title.Give two points for 2 correct graphing and 1 or 2 correct labels or title.Give two points for 1 correct graphing and 1 correct label AND title.Also allow points if students draw a straight line in place of a bar graph.

1 Give one point for 1 correct graphing or 1 correct label OR correct title.Lack of a relevant title will cost a point.Correct labels comprise another point. These include “Number of Bananas Eaten” (OR “Bananas Eaten”) and “Student”.

0 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.


Grade 3-59/BB

Score:

Rationale: Response is entirely correct

3


Grade 3-59/BC

Score:

Rationale: Response is entirely incorrect

0

Where could the student get one point?


Grade 3-59/BD

Score:

Rationale: Response receives a point for correct title

1

What is Tanner’s mistake?


Grade 3-59/BE

Score:

Rationale: Response is entirely correct except for the graphing of the number of bananas that Marge and Tanner ate.

2

Precision is the difference between a 2-

point and a 3-point response.


Capture Sheet - Reflection

• What have you learned from these anchor papers which addressed Number Sense and Operations 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?


DC CAS Anchor Paper TrainingMathematics (Grade 4)


Grade 4 - #9

9 Jeremiah made the Input-Output table below.

9-A On the line in the answer booklet, write the rule used in the Input-Output table to find the Output number.

9-B On the line in the answer booklet, write the Output number if the Input number is 12.

9-C Jeremiah makes a new Input-Output table. The rule to find the Output number in the new table is “Divide by 3.” On the line in the answer

booklet, write what the Output number would be in the new Input- Output table if the Input number was 12.


Score Description

3 Response is correct and complete.All three parts completely correct.Part A:Divide by 6Part B:2Part C:4

2 Give 2 points if two parts are completely correct.

1 Give 1 point if one Part is completely correct.

0 The response demonstrates no understanding of determining how change in one variable relates to a change in a second variable (e.g., input-output tables). Response is incorrect, incomplete, or missing.


Grade 4 – 9/CA

Score:


3


Grade 4 – 9/CB

Score:

Rationale: Student receives a point for Part C

1

Is one question easier than the other?


Grade 4 – 9/CC

Score:


0

What questions would you ask to scaffold the student to get the correct answer?


Grade 4 – 9/CD

Score:

Rationale: Student receives a point for Part A.Student receives a point for Part B.

2

Use of symbol to describe “divide” is

acceptable.


Grade 4 - #66

66 Emma has a marble collection.

66-A The drawing below shows Emma’s marble collection.

In the answer booklet, fill in the table to show what types of marbles Emma has, and how many marbles she has of each type.

66-B Kaye also has a marble collection. Kaye made the graph below to show the types of marbles in her marble collection.

In the box in the answer booklet, draw Kaye’s marble collection. Make sure to show the right number of each type of marble.


Score Description

3 Type of Marble – Number of MarblesPlain 5Dark 2Spotted 5Striped 4

Student may use different descriptions or drawings for marbles.2 Give 2 points if one part is completely correct AND one part is partially correct

(correct descriptions with one type of marble counted incorrectly; OR drawing has one error).

1 Give 1 point if one part is completely correct OR if BOTH parts are partially correct (correct descriptions with one type of marble counted incorrectly; drawing has one error)

0 The response demonstrates no understanding of collecting, organizing, and displaying data from observations and generating original data from bar graphs.


Grade 4-66/DA

Score:

Rationale: Part A is partially correct (dots should have five marks instead of four)Part B is partially correct (there is an extra striped marble)

1


Grade 4-66/DB

Score:

Rationale: Part A is incorrect Part B is incorrect

0

How “close” is

this response

?


Grade 4-66/DD

Score:

Rationale: Part A is completely correct Part B is completely correct

3

What exemplary

behaviors did this student demonstrate to earn a “3”

on this prompt?


Grade 4-66/DE

Score:

Rationale: Part A is completely correct Part B is partially correct (one white marble is not illustrated)

2



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




Grade 5 - #19

19 Look at the grid shown below.

19-A What percent of this grid is shaded? Write your answer on the line in the answer booklet.

19-B What fraction of the grid is not shaded? Write your answer on the line in the answer booklet.

19-C Kim shades more small squares on the grid. After she has done this, 4/5 of the grid is shaded. How many more small squares did Kim shade? In the box in the answer booklet, show your work. Then write your answer on the line.

Three Questions = 3 points


Score Description

3 A. 35%B. 65/100 (Scoring Note: need not reduce)C. 4/5 = 0.8 = 80 of the small squares will be shaded

35 small squares already shaded80 – 35 = 4545 more small squares are shaded by Kim



0 The response demonstrates no understanding of interpreting percents as parts out of 100, using percent notation, and understanding simple equivalent fractions.


Grade 5 – 19/EA

Score: Rationale: Part A is correct for 1 pointPart B is correct for 1 pointPart C is correct for 1 point (work must be shown)

3

Work Space


Grade 5 – 19/EB

Score: Rationale: Part A is correct for 1 pointPart B is correct for 1 pointPart C is incorrect

2

This is a true statement. There are 20 squares shown.

However, the amount does not represent the amount needed to make the grid have 80% of

the boxes shaded.


Grade 5 – 19/EC

Score: Rationale: Part A is correct for 1 pointPart B is incorrect Part C is incorrect

1

What is a possible explanation for these incorrect student responses?

What are some possible ways to use this response as a teaching tool?


Grade 5 – 19/ED

Score: Rationale: Part A is incorrect Part B is incorrectPart C is incorrect

0


Grade 5 - #56

56 The graph below shows the distance traveled by a car over time.

56-A How far did the car travel in 3 seconds? Write your answer on the line in the answer booklet.

56-B What is the rate in meters per second, at which the car travels? Write your answer on the line in the answer booklet?

56-C Use the rate to determine the distance the car will travel in 10 seconds. Show your work in the box in the answer booklet and write your answer on the line.

Three Questions = 3 points


Score Description

3 Part A:45 metersPart B:15 meters per second or d = 15tPart C:d = 15 X 10 = 150 metersORExtends pattern of graph

2 Give 2 points if two Parts are completely correct OR work is shown for all three parts with error in calculation.

1 Give 1 point if one Part is completely correct OR work is shown for at least two parts with error in calculation.

0 The response demonstrates no understanding of interpreting graphs that represent the relationship between two variables in everyday situations.


Grade 5 – 56/FA

Score:

Rationale: Student receives a point for Part A and a point for Part B

2

Where is the error?

Skip Counting (Repeated Addition) is an acceptable strategy as long as

the computation is correct.


Grade 5 – 56/FB

Score:


3

Answer is circled.


Grade 5 – 56/FC

Score:


0


Grade 5 – 56/FD

Score:

Rationale: Student receives a point for Part A

1 What is correct about the student’s thinking in Part C?



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




Grade 6 - #11

11-A On the line in the answer booklet, list all the factors of 6. 11-B On the line in the answer booklet, list all the factors of 12. 11-C What is the greatest common factor of 6 and 12? Write your answer on the lines in the answer booklet and explain how you found your answer.


Score Description

3 Part A:Factors of 6 are 1, 2, 3, 6Part B:Factors of 12 are 1, 2, 3, 4, 6, 12Part C:6 is the greatest common factor. I found it by finding the largest factor that is common to both 6 and 12.



0 The response demonstrates no understanding of factors and finding the greatest common factor.


Grade 6 – 11/HA

Score: Rationale: Part A is incorrect, left out 1 (0 points)Part B is incorrect, left out 1 (0 points)Part C is correct (1 point)

1

List ALL


Grade 6 – 11/HB

Score: Rationale: Response is incorrect and incomplete (0 points)

0

Factors are Few.

Multiples are Many.


Grade 6 – 11/HC

Score: Rationale: Part A is correct (1 point)Part B is correct (1 point)Part C is incorrect (0 points)

2


Grade 6 – 11/HD

Score: Rationale: Part A is correct (1 point)Part B is correct (1 point)Part C is correct (1 point)

3


Grade 6 - #63

63 The price of each item on a clearance rack in a department store is shown in the stem-and-leaf plot below.

63-A What is the range in prices of these items? Write your answer on the line in the answer booklet.

63-B Two of the $15 items on the clearance rack are sold. What is the new mode? On the line in the answer booklet, write your answer.

2 Points for Part A

1 Point for Part B


Score Description

3 A. $36.00

B. $32.00

2 Give 2 points if Part A is completely correct

1 Give 1 points if Part B is completely correct

0 The response demonstrates no understanding of interpreting stem-and-leaf plots and describing and comparing data sets using the concepts of maximum and minimum, and range.


Grade 6– 63/KA

Score:

Rationale: Part A: 36 (2 points)Part B: NOT 32 (0 points)

2


Grade 6 – 63/KB

Score:

Rationale: Part A: NOT 36 (0 points)Part B: 32 (1 point)

1


Grade 6 – 63/KC

Score:

Rationale: Part A: 36 (2 points)Part B: 32 (1 point)

3


Grade 6 – 63/KD

Score:

Rationale: Part A: NOT 36 (0 points)Part B: NOT 32 (0 points)

0


Reflection

• What have you learned from this anchor paper about number sense and operations and data analysis, probability and statistics?




dc cas anchor paper training mathematics (elementary)

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