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Alyssa Nugent, Part Part Whole Presentation

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- 1. Part-Part-Whole / Compare Addition Problem Situation Alyssa Nugent EDUC 517 Spring 2013
- 2. Part-Part-Whole O Two parts make up a whole! O It differs from other problem situations because there is no action (take away or add to). O There is a whole number and two numbers that are the parts of the whole number. One of the three is left off and must be determined.
- 3. Significance O When a student is able to understand part- part-whole situations they are able to begin to make a connection between a posed word problem and the number sentence that can be used to represent it. (Clements/Sarama, 69,78) O It supports students in being able to “count on” rather than counting all again. (Fosnot/Dolk, 36-37).
- 4. Trajectory O Before PPW: O Subitizing O Counting-all O Find result; find change O Join (result unknown) {4 apples, add 4 more} O After PPW: O Counting on O Counting-on-from-larger O Start Unknown {__+7=12} O Compare problems (more vs. less/fewer) O Numbers-in-numbers
- 5. Two Types O There are two types of part-part- whole/compare problems: OWhole Unknown OPart Unknown 5 3 Whole Unknown 8 5 Part Unknown
- 6. Whole-Unknown O This problem type is exactly what it sounds like: the students are given the two parts of a situation and must find the whole. O This is the simplest of the part-part-whole problems. O Example: There are four dogs and six cats on Mr. McAllister’s lawn. How many animals in all are on his lawn?
- 7. Whole Unknown The number sentence written by the student should read: (If thinking addition as in the example) 4+6=10 or 6+4=10 (If written to think subtraction) 10-4=6 or 10-6=4
- 8. Part-Unknown O Part-unknown problems give students one part and the whole and ask them to determine what the other part is.
- 9. Diagrams O Teachers will often use a diagram to help students with part-part-whole. The Clements text shows two variations: O Other examples could the one seen earlier in this presentation, found at: http://www.cbv.ns.ca/consultants/uploads/MathConsultant/Part-Part%20Whole.pdf
- 10. Teaching Methods O When teaching part-part-whole problems, students should be allowed to work with concrete manipulatives, and draw the manipulatives within the diagram given. O Later, teachers can add structures that help students connect part-part-whole to addition and subtraction problems, like these: http://www.cbv.ns.ca/consultants/uploads/MathConsultant/Part-Part%20Whole.pdf
- 11. Teaching Methods http://mathcoachscorner.blogspot.com/2012/01/composing-and- decomposing-numbers.html
- 12. Compare O Part-Part-Whole Comparison problems involve comparing how many more or fewer one part is from another. Compare problems can be difficult for students. O ‘How many more’ problems are easier for students than ‘how many fewer.’
- 13. Types of Compare Problems O There are three main types of compare problems: O Difference unknown O Larger unknown O Smaller unknown
- 14. Difference Unknown O This is the simplest form of a compare problem. O There are 4 buttons and 3 coins in Joe’s pocket. How many more buttons than coins are there? (How many more problem) O There are 6 bats and 4 bugs under the streetlight. How many fewer bugs than bats are there? (How many fewer problem)
- 15. Larger/Smaller Unknown O In the following slides, each example is based on the following premise: O 1 dish O 3 cookies O 5 chocolates O 8 pieces in total in the dish.
- 16. Larger Unknown O More than: There are 2 more chocolates than cookies in the dish. There are 3 cookies in the dish. How many chocolates are in the dish? O Fewer than: There are 2 fewer cookies than chocolates in the dish. There are 3 cookies in the dish. How many chocolates are in the dish?
- 17. Smaller Unknown O More than: There are 2 more chocolates than cookies in the dish. There are 5 chocolates in the dish. How many cookies are in the dish? O Fewer than: There are 2 fewer cookies than chocolates in the dish. There are 5 chocolates in the dish. How many cookies are in the dish?
- 18. Annotated Bibliography O Boucher, Donna. Blog entry: “Addition & Subtraction Structures, Part 2,” May 15, 2012. Accessed at http://mathcoachscorner.blogspot.com/2012/05/addition-subtraction-structures-part- 2.html 12 May 2013. O In depth discussion of part-part-whole teaching in a step by step manner from a 16-year classroom veteran and certified math coach. O Clements, Douglas H. and Sarama, Julie. Learning and Teaching Early Math: The Learning Trajectory Approach. Routledge, Taylor & Francis, NY, NY, 2009. ISBN: 978-0-415-99592-4. O Discusses the developmental learning trajectory surrounding part-part-whole education and some best practices and hands-on activities to aid teachers. O Fischer, Florence, E. “A Part-Part-Whole Curriculum for Teaching Number in the Kindergarten,” Journal for Research in Mathematics Education , Vol. 21, No. 3 (May, 1990), pp. 207-215. National Council of Teachers of Mathematics. Stable URL: http://www.jstor.org/stable/749374 O Developmentally situates part-part-whole in a curriculum, gives examples of best teaching practices for the concept O Fosnot, Catherine Twomey and Maarten Dolk. Young Mathematicians at Work: Constructing Number Sense, Addition and Subtraction. Heinemann, Portsmouth, NH, 2001. ISBN: 0-325-00353-X. O Talks about the reasoning behind part-part-whole knowledge and its importance . O Cape Breton-Victoria Local Schools, Nova Scotia. “Structures of Story Problems: Part-Part-Whole.” Accessed at: http://www.cbv.ns.ca/consultants/uploads/MathConsultant/Part-Part%20Whole.pdf on 12 May 2013. O Teacher PDF developed by district math consultants to give step-by-step information on teaching part-part-whole in primary grades.

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