Wednesday Groupers
Writing Groups, 2018
Plot, Character, & Scenes:
How to construct and deconstruct FICTION
We are looking at plot and how it operates across many stories, understanding that:
"Plot is a series of scenes that are deliberately arranged by cause and effect to create dramatic action filled with tension and conflict to further the character's emotional development."
—Martha Alderson, Blockbuster Plots Pure and Simple
We have looked at the three act structure and three important plot points: Inciting Incident, Crisis, and Climax. We will also be looking at the halfway point (point of no return), the dark night of the soul, and the resolution. I sent home a chapter called "The Universal Story." I highly recommend that the kids start looking at stories (books, movies) that they know well and try to identify where these plot points show up.
In class, we devised some characters from Magic cards, and we wrote (started) a scene where the character wants something, but things keep getting in the way. Next week we will write battle scenes. The following week, we'll all take a whack at revising a scene.
End of first semester
UMGOCK Math Group
Deb's Focus Group 9:3510:35
11/29: Satisfying Statements, Statement Snap, Summing Consecutive Numbers, Happy Numbers, Calendar Capers...
Summing Consecutive Numbers
Stage: 3
Watch the video to see how numbers can be expressed as sums of consecutive numbers.
Investigate the questions posed in the video and any other questions you come up with.
Can you draw any conclusions?
Can you support your conclusions with convincing arguments or proofs?
Happy Numbers
Stage: 3
Take any whole number between 1 and 999 inclusive and add the squares of the digits to get a new number. For example, starting from 138 we get 1+32+82=74.
We can repeat this process using the squares of 7 and 4 to get 65 and then continue the process indefinitely.
Start with 145 and see what happens.
Now we come to the most important step! Show that, whatever number we start with less than 1000, we always get another number which is less than 1000.
Choose some numbers less than 1000 and, each time, repeat the process until you notice a pattern.
Make some conjectures about what happens in general.
Satisfying Statements
Stage: 3
Alison, Becky, Sam and Matt are playing a game.
Each of them writes down a statement that describes a set of numbers.
Alison writes "Multiples of five".
Becky writes "Triangular numbers".
Sam writes "Even, but not multiples of four".
Matt writes "Multiples of three but not multiples of nine".
Can you find some twodigit numbers that belong in two of the sets?
Can you find some twodigit numbers that belong in three sets?
What is the smallest number that belongs in all four sets?
How could you describe the pattern of the numbers that satisfy both Alison's and Sam's statements?
How about the numbers that satisfy both Alison's and Matt's statements?
Can you describe patterns for other pairs of statements?
Statement Snap
Stage: 2 and 3
To play the game, you'll need to print and cut out this set of cards.
This game works well for 2 to 4 players.
How to play
Shuffle the cards, and place them face down on the table.
Turn over two cards so that all the players can see them.
The object of the game is to find a number that satisfies the statements on both cards.
For example, if the cards said "A multiple of 6" and "A factor of 90" you could pick the number 30.
After ten seconds, everyone declares a number that satisfies both cards, and then the next round
begins by turning over the next two cards.
Scoring
There are a few different scoring options for the game:

Score a point if you find a number that satisfies both cards

Score a point if you think of the highest number that satisfies both cards

List as many numbers as you can that satisfy both cards, and then score a point for each one.

List as many numbers as you can, and then score a point for each number on your list that doesn't appear on anybody else's list.
Let's make Function Machines:
11/15: We looked at the Fibonacci sequence (1,1,2,3,5,8,13,21,34,55...).
We worked on a Get It Together group pattern puzzle and a double Marcy Cook Tile pattern:
And we looked at a number sequence on a function table, trying to find the rule or equation:
1  7 
2  16 
3  25 
4  34 
500  ? 
11/8:
Number Talk: Mental Math Strategies (Relationships)
TRUE or FALSE? How do you know?
37 + 56 = 39 + 54
33 – 27 = 34 – 26
471 – 382 = 474 – 385
674 – 389 = 664 – 379
583 – 529 = 83 – 29
37 x 54 = 38 x 53
60 x 48 = 6 x 480
5 x 84 = 10 x 42
64 ÷ 14 = 32 ÷ 28
42 ÷ 16 = 84 ÷ 32
11/1:
Reviewed homework of the Rice on the Chessboard Problem
Today's Homework: Play with Charlie's Delightful Machine
10/25:
Today we played with the M&M problem in
We did more Marcy Cook tiles and looked at PencilCode.
Homework was the Rice on the Chessboard Problem
10/18:
Today we played with Stick Problem Three, and reviewed the powers of TWO.
After that we did some Marcy Cook Tiles, including this one (using a set of tiles from 09, fill in the blanks)
The kids really enjoyed these, and we'll do some more next week. I sent home the following problem:
The Square of My Age
When you add the square of Thomas's age to Lauren's age the total is 62. When you add the square of Lauren's age to Thomas's age the total is 176. How old are Thomas and Lauren?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
See all short problems arranged by curriculum topic in the short problems collection
This problem is taken from the UKMT Mathematical Challenges.
♦
10/11:
Today we did another quick team problem (Stick Problem 2) from the book Get It Together!
We did a cursory lesson on powers, starting with powers of 2:
2^{0} = One, multiplied times two (ZERO times) = 1
2^{1 }= One, multiplied times two (ONE time) = 1 x 2 = 2
2^{2 }= One, multiplied times two (TWO times) = 1 x 2 x 2 = 4 = TWO SQUARED (makes a square)
2^{3} = One, multiplied times two (THREE times) = 1 x 2 x 2 x 2 = 8 = TWO CUBED (makes a cube)
2^{4} = One, multiplied times two (FOUR times) = 1 x 2 x 2 x 2 x 2 = 16
2^{5} = One, multiplied times two (FIVE times) = 1 x 2 x 2 x 2 x 2 x 2 = 32
We then played with POWER MAD from NRICH.com
Power Mad!
Powers of numbers behave in surprising ways...
Take a look at the following and try to explain what's going on
For which values of n will 2^{n} be a multiple of 10?
For which values of n is 1^{n}+2^{n}+3^{n} even?
Work out 1^{n}+2^{n}+3^{n}+4^{n} for some different values of n.
What do you notice?
What about 1^{n}+2^{n}+3^{n}+4^{n}+5^{n}?
What other surprising results can you find?
Here are some suggestions to start you off:
4^{n}+5^{n}+6^{n}
2^{n}+3^{n} for odd values of n
3^{n}+8^{n}
2^{n}+4^{n}+6^{n}
3^{n}+5^{n}+7^{n}
3^{n} − 2^{n}
7^{n}+5^{n}−3^{n}
Can you justify your findings?
♦
10/4 Today we did a quick team problem from the book Get It Together! that helped us start a list of things we like and things we do NOT like during our math workshop. Here's the team problem, made with popsicle sticks:
We then began our investigation of the Four Fours problem, including square roots and factorials. Next week we will share some of our favorite solutions.