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. McAllisters 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 Joes 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.