Task & Stdwork_trevor'scase
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Fractions, Decimals, & Percents Mr. Clark, a 7th grade teacher, is preparing to begin a new school year. He knows that fractions, decimals, and percents make up a large portion of the 4th - 6th grade curriculum, and wants to see how much his incoming 7th graders understand about ordering and comparing rational numbers. Therefore, he decides to give his students the following OGAP item because it doesn’t seem too intimidating for students at the beginning of the year and he hopes it will provide him with some useful baseline information.
P(M): 22 Trevor ordered the following numbers from smallest to largest. Is Trevor correct? Why or why not? Trevor’s Order .8 9% .55
1. Solve this problem in as many ways as you can, including ways in which you think Mr. Clark’s students might solve this problem.
2. What mathematics concepts might students need to understand to solve this problem?
3. Review Grade Expectation M_:2 from grade 3 to grade 8. At what grade are students expected to be able to solve this problem?
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
The following pieces of student work from Mr. Clark’s class were selected because they represent the range of responses seen in his classroom. Review each of the following pieces of student work. For each piece: • •
determine whether the student answered the question correctly or incorrectly analyze the strategy used
Student 1
Student 2
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 3
Student 4
Student 5
Student 6
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 7
Student 8
Student 9
Student 10
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 11
Student 12
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
After reviewing the student work respond to the following questions: What types of errors and/or misconceptions did you see in the collection of student work?
If you were Mr. Clark, how would this information impact your instructional plans for the beginning of the year?
In the next online session you will be asked to use this OGAP item with your students without any pre-teaching, to analyze the results, and then discuss the results on the discussion board.
Note: In a pilot of 267 6th-8th grade students, 81 solved this problem correctly while 186 solved it incorrectly.
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
P(M): 22 Trevor ordered the following numbers from smallest to largest. Is Trevor correct? Why or why not? Trevor’s Order .8 9% .55
1. Solve this problem in as many ways as you can, including ways in which you think Mr. Clark’s students might solve this problem.
2. What mathematics concepts might students need to understand to solve this problem?
3. Review Grade Expectation M_:2 from grade 3 to grade 8. At what grade are students expected to be able to solve this problem?
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
The following pieces of student work from Mr. Clark’s class were selected because they represent the range of responses seen in his classroom. Review each of the following pieces of student work. For each piece: • •
determine whether the student answered the question correctly or incorrectly analyze the strategy used
Student 1
Student 2
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 3
Student 4
Student 5
Student 6
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 7
Student 8
Student 9
Student 10
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
Student 11
Student 12
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
After reviewing the student work respond to the following questions: What types of errors and/or misconceptions did you see in the collection of student work?
If you were Mr. Clark, how would this information impact your instructional plans for the beginning of the year?
In the next online session you will be asked to use this OGAP item with your students without any pre-teaching, to analyze the results, and then discuss the results on the discussion board.
Note: In a pilot of 267 6th-8th grade students, 81 solved this problem correctly while 186 solved it incorrectly.
version 4 July 2006 The Vermont Mathematics Partnership is funded by a grant provided by the US Department of Education (Award Number S366A020002) and the National Science Foundation (Award Number EHR-0227057)
