Constructing Whole Number and Operation
Tuesdays 5-8 PM
Room 311 PKH, UTA campus
For the course syllabus, click here and here.
For problems worked or assigned in class, click here.
For a math ed web resources page, click here.
For links to the online readings, see below.
For student interviewing tips, click here.
For the sample interview write-up, click here.
For tips on writing papers on math problems,
For tips on writing the 2-Problem Paper in this course, click here.
Instructor: Dr. Christopher Kribs
Office: 434 Pickard Hall
Office Hours, Fall 2016: before and after class and by appt.
Instructor's web page for this course:
NOTE: Technical information such as prerequisites, text materials,
course format and assignments, and other details can be found in the syllabus,
a copy of which is provided in a link at the top of this page.
Problems appropriate for writing up in the two-problem paper.
Very strongly recommended to consult with the instructor prior to submission.
- Session 3: Models for multiplication -- use the summative question 5, supported by the other questions on these pages, to develop a cohesive, comparative explanation of the set and array models for multiplication and the relationship between them.
- Session 5: Numeration Systems -- use the summative question 7, supported by the other questions on these pages, to develop a cohesive, comparative explanation of the Roman and Babylonian systems in particular, and symbol value and place value systems in general.
- Session 5: Zeroes and Ones -- use the summative question 7, supported by the other questions on this page as well as the class discussion and responses, to explain options for designing numeration systems using only two meaningful characters (including true binary), and compare their properties.
- Session 6: Sticks and Stones, together with Mayan addition and subtraction from Session 8 -- use summative question at the end of the latter set, supported by the problems on both these pages, to develop a cohesive explanation of the Mayan system and how regrouping works in it, including a comparative analysis (relative to the Hindu-Arabic system).
- Session 7: Introduction to Bases -- use the summative questions at
the end of this activity to give clear sets of instructions for conversion to
base n using concrete [proportional] and symbolic representations, and
compare the two. Of course, you may use some of the problems in this activity
as examples, but be sure your instructions are stated in purely general
- Sessions 8-14: Mayan addition and subtraction, Driving in
Septobasiland, Regrouping in Other Bases, Mayan multiplication, Making Groups
in Other Bases, Money in Septobasiland, Mayan division, Division in Other
Bases, Arithmetic in Other Bases -- Use any one of these activities as a basis
for developing a general explanation of the traditional algorithm for
performing any one of the four arithmetic operations (choose one!) in terms of
a general base (i.e., not ten). Be careful to couch your general set of
instructions in terms of a general base, and not any specific one (although of
course all your examples or illustrations will use particular bases).
- Session 15: Russian Peasant algorithm -- Although the two-problem
paper is due before Session 15, some participants may be interested in
analyzing this intriguing alternative algorithm for multiplication. Work
through the questions in the handout, and write a paper which (a) briefly
explains the steps in the algorithm, (b) explains mathematically why the
algorithm is correct, (c) describes the mathematical skills needed and not
needed, and (d) uses these to speculate why a person might prefer this
algorithm over the traditional (partial products) multidigit multiplication
Links to related sites
Links for specific class meetings
- Session 1
- Session 2
- Session 4
- Session 5
- Session 6
of children using DigiBlocks (from learner.org)
- Case 13 from the old edition of BST
- Session 7
of a middle school classroom discussion of converting from base ten to base
five (from learner.org)
of the same middle school classroom discussing how to convert symbolically
from base five to base ten (from learner.org)
- Mini-cases (a) and (b)
- Mini-cases (c) and (d)
- Session 9
- Session 11
- Session 14
This page last modified 10 August 2016.