Weekly Questions
Your weekly questions will be posted here as they are presented in
class.
August 31:
Explain
the connections among the cereal boxes, valentine exchanges, and
handshakes problems. Include explanations for the solutions
(both for 28 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 7:
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. You do not need to include all the
numbers along the way, it's ok to skip steps (like 1,2,3, … ,17,
18) but be sure to address the challenging issues.
September 14:
Explain
addition and subtraction. Include explanation and
justification for the properties of addition. 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. Include drawings of
models. Consider including Austrian subtraction.
September 21:
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 28: Explain three different interpretations of
division. Also explain different possible interpretations
of remainders.
October
5: Explain multidigit division. Include a
justification of both scaffolding and the standard long division
algorithm.
October 17:
Explain the
significance of prime numbers. Why is 1 not prime?
What does it mean that every natural number has unique prime
factorisation?
October 24:
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 26: Explain arithmetic (all four
operations) with integers. Include
models for all and include a justification for three
general sign rules for multiplying integers.
November 2:
Explain
the concept of a fraction. Refer to many different
models. Include both interpretations of fraction and an
explanation of equivalent fractions.
November 14: Explain arithmetic (all four operations) with
fractions. Include models.
November 21: Discuss how to model
decimals. Explain arithmetic (all four operations) with
decimals.
November 28: Discuss
the difference between rational and irrational numbers.
(Include justified information about fractions and decimals, as
well as examples.)