Alyssa Nugent, Part Part Whole Presentation

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.