- Your second assignment is returned.
- There's no rule like "it's always better to switch": I can always rework a problem so that it's better to stick. Don't worship false gods....
- If you want to convince me that you've found a prime
number, tell me that you've checked all the primes up to the
square root of the number. What's
Sarah?
- Write out the prime factorization in the end.
- Annie and Kyle S. -- I'm calling you up to play!
- You do have an assignment due today.
- Review:
- Tallies -- make a mark for each one, and then hand it over
- Cairns -- a type of tally, only using stones to represent each participant
- One-to-One correspondence, usually with body parts. So pointing at a full set of fingers would mean "10" (but some civilizations may have pointed at a left hip to mean 26!).
- Then there's this "Counting by partition":
- "Divide and conquer"
- Is this how folks learned to count big numbers:
Dividing sheep into two groups, keeping track of the remainder, and then reporting the result?
- Upshot: We can count with only two fingers! Or two pens, or two symbols at any rate....
- Let's remind ourselves of how we might use a tree to represent the
solution to
the problem of counting 22 things: in the linked example, we
would get 10110 by writing the remainders from
left-to-right starting from the bottom of the tree.
(The result should always start with a 1 if done
correctly, since we always end with one sheep!)
- But can you go backwards?
- How many sheep is meant by 1,1,0,1,1,0,0?
- How many sheep is meant by 1,0,0,1,0,1,1,0,1?
Try making a tree with these remainders.
- and now let's count some coins:
- We'll be counting pennies - in small groups.
- Divide your penny rolls up (no need to do it evenly!)
- Get your answer, then swap with another nearby group.
- Compare (and record) your answers
(source)
- How does the game work?
- Can you win at the game? You should be able to do it every time!
- Each of you will be part of a team of three, taking turns playing the roles of contestent, Fraudini, and someone to check the play.
- Here's the handout for the cards, if you want to print off another copy.
- It relies on the "binary doubling doodah": 1, 2, 4, 8, 16, 32, ....