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.

November 21:  Discuss the difference between rational and irrational numbers.  (Include justified information about fractions and decimals, as well as examples.)