Weekly Questions
Your weekly questions will be posted here as they are presented in
class.
August
27: Explain
the connections among the cereal boxes, valentine exchanges, and
handshakes problems. Include explanations for the solutions
(both for 31 students and for p students) to each and why they are
related to each other. (including images
will almost always be helpful; make sure you have reasons not only
answers).
September 3: Use
pennies, nickels, and quarters to explain counting in base
five. (Please note: do not explain coins -
assume your audience knows how to use coins and use them to
explain counting in base five.) Count as high as you can
using these coins and explain what coin you would need next in
order to continue beyond that. You do not need to include
all the numbers along the way, it's ok to skip steps after 110 (like 1, 2, 3, …
, 17, 18) but be sure to address the challenging issues. Do not count in base ten,
only in base five. Include some visual representation in
terms of coins for each of the numbers that you count.
September
10: Explain
addition and subtraction. Include explanation and
justification for the properties of addition (identity,
commutative, associative). Include a
basic explanation of what addition and subtraction mean along with
explaining the meaning of a process for addition and subtraction
of multi-digit numbers in any base (for both addition and
subtraction make sure you have three regroupings in your
examples). Include drawings of models. Consider
including Austrian subtraction.
September 17: What does multiplication
mean? Include explanation and justification for the
properties (commutative, associative, distributive, identity, and
zero) of multiplication. Explain multi-digit multiplication
using both standard and lattice organisations including the area
model for justification. Refer to examples in other bases.
September
24: Explain
three different interpretations of division. Also explain
different possible interpretations of remainders.
October 1: Explain
multidigit division. Include a justification of both
scaffolding and the standard long division algorithm.