Weekly Questions
Your weekly questions will be posted here as they are presented in
class.
August
29: Explain
the connections among the cereal boxes, valentine exchanges, and
handshakes problems. Include explanations for the solutions
(both for 20 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 5: 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 12: 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 19: 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 26: Explain three different interpretations of
division. Also explain different possible interpretations of
remainders.
October 3: Explain multidigit division. Include a
justification of both scaffolding and the standard long division
algorithm.
October 10: Explain the significance of prime numbers.
Why is 1 not prime? What does it mean that every natural
number has unique prime
factorisation?
October 22: Explain
greatest common divisor and least common multiple. Include a
visual discussion of the meanings and models along with ways (both
by listing and by prime factors) to find them.
October 24: Explain arithmetic (all four operations) with
integers. Include models for all and include a
justification for three general sign rules for multiplying
integers. Be sure to include a justification for -1+1
= 0: this does not come from the manipulatives.
October 31: Explain the concept of a
fraction. Refer to many different models. Include both
interpretations of fraction and an explanation of equivalent
fractions.
November 12: Explain arithmetic (all four
operations) with fractions. Include models.
November 19: Discuss how to model decimals. Explain arithmetic (all four operations) with
decimals.