# Performance Assessment Task Peanuts and Ducks Grade 2. Common Core State Standards Math - Content Standards

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4 Looking at Student Work Peanuts and Ducks Student A shows a clear picture to represent the situation. Student A uses a number sentence to find the total number of ducks, then uses words to complete the mathematical argument by saying that 12 is less than 15. Student A was also able to use a number sentence to explain how many peanuts were left. Student A Student B is able to abstract from the situation to use a mathematical model instead of drawing peanuts and ducks. The student also shows a clear understanding of number operation and can compute accurately. 4

5 Student B Student C demonstrates the ability to think abstractly and use mathematical symbols to make an accurate argument for having enough peanuts. 5

6 Student C Approximately 37% of the students were able to complete all the demands of Peanuts and Ducks. However many students had difficulty explaining their thinking or completing the logic required in part one. Student D does a nice job of seeing equal groups and using multiplication to find the total number of ducks. However the student does not show that 12 is less than 15. 6

7 Student D Student E is typical of many students. The drawing shows the number of ducks, but doesn t address the issue of peanuts. If you look at the bag of peanuts in Leonardo s hand, there are 4 nuts left instead of three. In part 2 of the task the student shows good number sentences, but the number sentences don t explain how he knows that there are 3 peanuts left. 7

8 Student E Student F is able to make sense of the situation by using concrete pictures. This allows the student to find the number of leftovers. Note that there is no use of abstraction or symbolic notation on the paper. 8

9 Student F Some students did not know how to choose the proper operation. They just put together several number problems to show they could do math, but the work does not relate to the meaning of the story. See the work of student G. 9

10 Student G Teacher Notes: 10

11 Frequency Distribution for each Task Peanuts and Ducks The maximum score for this task is 7 points. The cut score for a level 3 response is 4 points. Most students (about 90%) could make sense of the total number of ducks. Almost half the students (about 45%) could also justify that there were enough peanuts and find the number of leftovers. About 25% of the students could meet all the demands of the task including explaining how they found the leftovers. About 3% of the students scored no points on the task. 11

12 Peanuts and Ducks Points Understandings Misunderstandings 0 Almost all attempted the problem. The students were not able to make sense of how to use the numbers to solve the problem 1 Generally, these stude nts knew that there were enough peanuts to feed the ducks 2 Knew there were enough peanuts to feed the ducks. Usually represented the ducks but not the peanuts. 3/4 Could find the number of ducks and explain that they had enough peanuts. 5 Could tell how many were left over. Could justify that there were enough peanuts. 6 Knew that there would be peanuts left over. 7 Did extremely well on this problem. 37% of the students scored a 7. 88% of the students used modeling rather that drawing little peanuts and little ducks. Students used incorrect addition and subtraction. Other students gave addition and/or subtraction problems that were unrelated to the questions in this problem. Most students who scored a 2 got part one correct but didn t complete part two. Many of the students had incorrect drawings of the problem situation. These papers did not have explanations for part one or part 2. Either didn t give an explanation or the explanation didn t support problem question. The explanation did not include a written explanation nor a number sentence. Didn t explain their answer in number 1 completely. Either they left out reference to the ducks or to the peanuts. Based on teacher observation, this is what third grade students seemed to know and be able to do: Add the number of ducks (6+6 more) and subtract that from the number of peanuts Draw pictures to solve problems Areas of difficulty for second graders, these students struggled with: Completing the logic for having enough peanuts by stating that 15 is greater than 12 Showing how they knew that there were three peanuts left Knowing whether to add or subtract Organization of their process for solving 12

13 Questions for Reflection on Peanuts and Ducks How often do students in your classroom share their strategies? What types of questions do you ask them that help them make the transition from drawing everything to being able to do some kind of modeling? Why do you think modeling is important? What types of number sentences did your students make to find the number of ducks? Were any of them able to use multiplication to find the equal groups? How many of your students were able to write a number sentence for the subtraction in part 2? What opportunities have students had solving problems requiring more than one step? What are some good resources for these types of problems? Being able to make a comparison is a big issue across the collaborative. How many of your students could explain how they knew their would enough peanuts? Did they use: Matching/ using pictures or models Missing parts: 12+? = 15 Comparison Subtraction: =? Symbolic: 15 > 12 Didn t address this issue Teacher Notes: Instructional Implications: While many students were successful on this problem, teachers feel that students need more experiences that will move them from the concrete representation of the situation to the symbolic representation. The biggest problem area seems to be the ability to explain the answer in a logical and systematic manner. Students need more opportunity to work with multi-step problems and a variety of subtraction situations. Students also need to work with problems that require logical thinking and justification. Two good resources for these types of activities would be Cognitively Guided Instruction and Read It, Draw It, Solve It. The latter has a selection of many one step and multi-step problems while the former is a resource into the structure of problems and the thinking and justification for problems such as these. Teacher Notes: 13

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