Problem Solving Concepts in K-8 Mathematics
Tue. 5-8 PM
Room 311 PKH, UTA
For the course syllabus, click here.
For problems worked or assigned in class, click here.
For links to the supplemental readings, click here.
For my math ed web resources page, click here.
For student interviewing tips, click here.
For the sample interview write-up, click here.
For tips on writing papers on math problems,
Instructor: Dr. Christopher Kribs
Office: 483 Pickard Hall
Office Hours, Fall 2015: Tue. noon & 4 PM, after class & by appointment
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 problem-solving paper.
- Session 1: Poisons --- complete, justified solution for both
classic Poison (with any number of counters) and Super Poison (generalizing
the number of counters one may take at a time to 1,2,3; etc.).
- Session 2: Rhinos by Pairs --- with a careful explanation of the
definitions of the variables, and the consequent chain of reasoning necessary
to write equations.
- Session 3: Pentominoes --- with a focus on rigorous justification
of the completeness of the list; also include generalizations.
- Session 5: Pick's Formula --- with proof.
- Session 6: Squares Problem 3 (p. 7).
- Session 10: The Stamps Problem --- be careful to distinguish
clearly conjecture from proven conclusion in discussing Question 3.
- Session 11: Triangle centers --- be sure to include reasoning
for the answers to Questions 2 and 3.
- Session 12: Geoboard Eighths --- include a line-by-line analysis
of the reasoning in the given response (i.e., don't just say "this line is
true" (or false), say why), in answering the questions on p. 16.
- Session 13: Triangles Around Cones --- justify the equation relating
cone angle to the sum of the vertex angles.
- Session 14: The Shepherds Problem --- a coherent narrative
(not "1. [answer] 2. [answer] etc.") addressing the questions on p. 19.
- Session 15: Linear Modeling --- answer the last question, and
discuss the salient features of each problem as regards linear models.
Links for specific class meetings
- Session 1: slides used in class
- Session 3: Lesson anatomy chart
- Session 5: Proofs of Pick's Theorem (be sure to develop your own
argument if you write about this problem in your two-problem paper)
- Session 6: Squares problem 3 -- a combinatorial approach
- Session 7: Modified versions of the Peas and Bagels problems
- If Calvin ate 16 peas on Monday, and he ate twice as many peas on Tuesday,
how many more peas did Calvin eat on Tuesday than on Monday?
- Calvin ate 16 peas on Monday and 32 peas on Tuesday. If he continues this
pattern, how many peas will he eat on Wednesday? on Thursday?
- Calvin ate some peas on Monday and then twice as many peas on Tuesday.
He ate 135 peas in all. How many peas did Calvin eat on Monday?
The solution could be found in various ways such as working backward, using
algebra, drawing a picture and guess and check. It differs from the original
comparison problem by using division instead of subtraction. In the original
problem, students have two known quantities to compare, while in the modified
version, students are working from a known total to split proportionally for
each day’s feeding. The modified version would be appropriate for 4th-5th
- If 3 bagels are shared equally among 5 people, how many bagels will each one get?
- If 3 dozen bagels are shared equally among 5 people, how many bagels will
each one get?
- Group 1:
On Monday, the Blazers scored 8 points. On Tuesday, the Blazers scored 20
points. How many more points did the Blazers score on Tuesday than on
In January, my chicken laid 50 eggs. In February, she laid 2 dozen eggs. In
which month did she lay more eggs? How many more eggs did she lay in this
If 3 dozen bagels are shared equally among six people, how many bagels will
each person get?
I'm having a party with 11 guests and I want all of us to get 2 slices of
pizza. If a pizza is cut into 8 slices, how many pizzas will I need to
- Group 2:
Calvin ate 16 peas on Monday. On Tuesday he ate 32.
On which day did he eat more?
Calvin ate 16 peas on Monday. On Tuesday he ate 5 peas more than on Monday.
How many peas did he eat on Tuesday?
If 3 bagels are shared equally among 5 people, how many bagels will each one get?
Five people ate 3/5 dozen bagels each. How many dozen bagels did they start with?
- Group 3:
If Calvin ate 32 peas on Monday and on Tuesday he ate 16 fewer peas, how many
peas did he eat on Tuesday?
Each pea pod has 3 peas. On Monday Calvin ate 5 pea pods and on Tuesday he ate
7 pea pods. How many more peas did Calvin eat on Tuesday than on Monday?
If 36 bagels are shared equally among five people, how many bagels will each
If 3 dozen bagels are to be shared equally among 5 people but 18 of the bagels
are moldy, how many dozens of bagels will each person get? What fraction of
the whole is this?
- Group 4:
If Calvin ate 5 peas at lunch and 10 peas for dinner, how many more peas did he
eat at dinner?
If Calvin ate 1/2 cup of peas on Monday and 3/4 cup on Tuesday, how much more
did he eat on Tuesday than on Monday?
If there are 12 bagels and 4 friends shared them equally, how many bagels did
each friend have?
Two area tasks to compare
A summary handout
on cognitive demand
- Session 11:
- GeoGebra applet 1
- GeoGebra applet 2
- This page,
with an encyclopedia of over 3000 different centers of a triangle,
includes interactive applets where you can click and drag triangle vertices
to see the effects of changing triangles. The first four centers listed
are the four we investigated in class.
- On a different topic: Virtual diffy box generator
- Session 13: Here's my clumsy attempt at a
proof of the triangles on cones formula.
- Session 14: NetLogo Shepherds problem
(see the documentation, and then click on "Run Shepherds in your browser")
- Session 15: spreadsheet with data for the 3 linear modeling problems
This page last modified 08 November 2017.