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Gamification Bonus Point Form

If you want to submit bonus points, please fill out this form. Write a total of the bonus points you think you've earned, and in the box below, write what you did and how much it was worth. Thanks!

If you had a good WEBSITE reocmmendation, please write that in the BONUS POINT description box as well!

Gamification Levels:

Screen shot 2014-11-04 at 1.28.11 AM.png
 

Standings as of 12/3/14

Level 4 Champions

E.B.  70

Level 3 Champions

S.H. 65

G.P. 55

B.B.R. 53

A.E.  49

L.H.  47

J.P.  45

S.G.  44

A.D.  44

Level 2 Champions

J.R.  32

S.M. 32

M.C. 38

N.S. 31

L.L. 39

S.S. 27

Level 1 Champion

K.L. 18

BONUS POINT problem

This one is worth 3 points if you can explain it to me. You can use problem solving logic and/or algebra. I found it helped to use tangible items!

The first SOCK DRAWER CHALLENGE:

 

DRAWER 1: 

  • Three times as many blue socks as black
  • Two more blue socks than red
  • One fourth as many black socks as white
  • 20 socks in all

THE URCHINS FIGURED IT OUT WITH UNIFIX CUBES

BONUS POINT problem

LEVI's

FUNCTION MACHINE

CHALLENGE

 

IN          OUT

4             9

6            15

3             6

5            12

7            18     

WEBSITE 

suggestions from students:

BBR: Cool Math Games

40xESCAPE

Kahn Academy Puzzles 

ALIEN ABUDUCTION PROBLEM

Bonus Points:


Many of these are described somewhere on the website!

Parent's Choice

Sock Drawer Challenge

Kahn Academy Puzzle

Function Machines

Palindrome Problems

GRAPHING a FUNCTION we've done

Other PUZZLES

Things Hidden on other Pages!

Suggest something you've done IN WRITING (use the FORM)

REMEMBER: Bring in something substantial (written) toward a MATH NOVEL and earn 15 BONUS POINTS.

PAST INVESTIGATIONS:

We investigated NUMBER PALINDROMES. First we listed ALL the combinations of any TWO counting numbers (1, 2, 3, 4, 5, 6...) to make a sum of 12 (stopping when the numbers repeat, regardless of the order). We found that there are exactly six possibilities: 1 + 11 = 12, 2 + 10 = 12, 3 + 9 = 12, 4 + 8 =12, 5 + 7 = 12, 6 - 6 = 12.Then we investigated it with THREE counting numbers.   SEE THE URCHIN FOCUS GROUP to see the pattern written out for THREE counting numbers  

CONTINUE THE INVESTIGATION:  2-digit number where the digits are not equal. We'll order the digits from lowest to highest to create the smallest number, and from highest to lowest to make the largest number. We'll find the positive difference between the two numbers and repeat with more numbers, looking for patterns, making predictions.

Here's an example: 45.... Largest = 54, smallest = 45. What is 54 - 45? What about if you start with 73? What is 73 - 37? 

Anyone who races through these two investigations will try the same thing with any three digits (where not all three are the same).

159... 951 - 159 = 

662... 662 - 266 =

263... 632 - 236 = 

We'll continue with palindromes if anyone brings their investigation into class! COME PREPARED TO PROVE OR SHARE YOUR IDEAS AND WHAT YOU'VE DISCOVERED! BONUS POINTS!!! 

2014-2015 Wednesday Math Focus and Inquiry with Deb

Grouper Focus #1

Algebra Games and Puzzles

THIS FOCUS GROUP BEGINS AT 9:30 AND GOES UNTIL 10:30. PLEASE BE ON TIME!

We are looking at sustained problem solving, multiple strategies, and sharing our thinking as the primary goals of the group.

BOTH GROUPS: Watch this video FIRST

 

Week #9: Dec. 3

BONUS POINTS for THIS WEEK for BOTH MY GROUPS:

  • Bring in a description of good puzzle* that you worked on and what you did to try to solve it, get 5 points.
  • Work on a Kahn Academy brain teaser and take some notes, get 5 points.
  • And best of all, ask your parents what 10 point activity (anything they want you to work on or do with no complaints and a great attitude) and have them sign a note about it. You'll get 10 points!
  • The first SOCK DRAWER CHALLENGE (draw or write your solution):

    • Three times as many blue socks as black
    • Two more blue socks than red
    • One fougth as many black socks as white
    • 20 socks in all
    • THE URCHINS FIGURED IT OUT WITH UNIFIX CUBES

    • 5 points

  • MORE PALINDROME NUMBERS... (see my Urchin page Week #6, if you want to see the work we did for 12 and remind yourself how this works). Just like we did with 12:

    • TRY to SUM to 18 using two counting numbers = 5 points (SHOW ME YOUR WORK)
    • SUM to 18 using three counting numbers = 10 points (SHOW ME YOUR WORK)

CLASS WORK:

1. Watch three videos (snakes!)

2. Look at Urchin work with basic arrays

3. Complete task with Base Ten Blocks

4. Complete task with Algebra Tiles/FOIL box

 

*SOME Puzzles:

Magic Number Guess Your Color

What's a Fair Share

How Much Does It Cost?

How Much is Your Time Worth

Link to lots of puzzles just like these

Week #8: Nov. 19

Focus with Deb

Week #8: Nov. 19, 2014

Algebra Games and Puzzles

THIS FOCUS GROUP BEGINS AT 9:30 AND GOES UNTIL 10:30. PLEASE BE ON TIME! We are looking at sustained problem solving, multiple strategies, and sharing our thinking as the primary goals of the group.

2 points for sharing a Function Machine and recording it for the group!

I will then have several games for you to play including this one

Screen shot 2014-11-19 at 3.24.41 AM.png
 

and some work with ALGEBRA TILES.

2x - 2Screen shot 2014-11-09 at 8.36.28 PM.png

"I took the number and I added the number minus two."

x + (x - 2)Screen shot 2014-11-09 at 8.36.39 PM.png

I introduced ALGEBRA TILES and we SHOWED that these two expressions are the SAME. These represented the function machine we did in class when I introduced them.

.We may get as far as multiplying a binomial by a binomial and MAKING FOIL boxes. 


Function Machines from last week

BONUS POINTS: Five bonus points if you can solve and WRITE an ALGEBRAIC EXPRESSION for at least three of the function machines. Five bonus points if you graph the line of at least 3 of the function machines and find the slope of one of those lines.

      Molly

IN

OUT

1

14

2

30

0

2

3

46

4

62

5

78

 

 

 

 

 

 

Skye S.
IN OUT
2 1
3
0

-2

4  4
1
7
6 7
11 14½

Gloria

IN OUT
1 2
0  0
2 6
12 156
6 42
4 20
7 56
8 72
   
Netta
IN OUT
2 6
3 11
8 63
0 -4
12 65
5 12
1 1
7 13
14 66
Jonah
IN OUT
1 13.5
0 4.5
5 49.5
.66 10.44
2 22.5
10 94.5
3 31.5
9 85.5
11 103.5
Skye H.
IN OUT
0 18
24 51
1 27.5
2 29
5 33.5
3 30.5
3 30.5
7 25
 

 

Shelagh
IN OUT
1 1
2 6
3 11
0 -1
5 21
4 16
7 31
6 26
-1 -9

Screen shot 2014-11-04 at 1.28.11 AM.png

 

WEEK 7: Nov. 12

COME TO CLASS with a FUNCTION MACHINE to share...

ELANA will be in for me. You will share your FUNCTION MACHINES and each have about 3 minutes to take guesses. After that, please record your list and I'll put it on the website.

2 points for sharing a Function Machine during class and recording it for the group!

I will then have several games for you to play and some work with ALGEBRA TILES, or a chance to read any MATH NOVELS you've begun writing. CAN YOU COLLABORATE? 

Some thoughts about the connection between BASE TEN BLOCKS and ALGEBRA TILES

 

Week #6: Nov. 5

 Focus with Deb

Week #6: Nov. 5, 2014

Algebra Games and Puzzles

THIS FOCUS GROUP BEGINS AT 9:30 AND GOES UNTIL 10:30. PLEASE BE ON TIME! We are looking at sustained problem solving, multiple strategies, and sharing our thinking as the primary goals of the group.


Screen shot 2014-11-04 at 1.28.11 AM.png

We looked at the function machine, trying to explain what different kids were doing to find the output number given a particular input number.

We came up with two different ways of SAYING what we did:

"I took the INPUT number and doubled it, then subtracted two."

We decided that, for this and similar wording (multiplied it by two, etc.) the expression would be

2x - 2

"I took the number and I added the number minus two."

x + (x - 2)

I introduced ALGEBRA TILES and we SHOWED that these two expressions are the SAME.

Screen shot 2014-11-09 at 8.36.28 PM.png
Screen shot 2014-11-09 at 8.36.39 PM.png

IN

OUT

1

0

4

6

8

14

0

¯2

7

12

9

16

15

28

6

10

14

26

 

We looked at the WEBSITE and discussed the GAMIFICATION that I'm trying out.
 

FOR MORE INFO AND ARCHIVED SUMMARIES GO TO GROUPERS WITH DEB

Week #5: October 29

Algebra Games and Puzzles

We started by reviewing the border problem and translating algebraic expressions into strategies to solve it. 

 If s = the side of the array, how many tiles will it take to make the border?

4s-4

s + s + (s-2) + (s - 2)

s + (s-1) + (s-2) + (s-3)

4(s-1)

s² - (s-2)²

Even though these were some of the equations offered by one of the many books investigating this problem, Shelagh discovered that one of them is incorrect so we replaced it with a correct version. Netta also discovered one more equation that worked for her strategy. 

We looked at a function machine, trying to guess what the output number would be for a given input number. Here's the list of in and out numbers that we came up with:

 

IN OUT
1 0
4 6
8 14
0 ¯2
7 12
9 16
15 28
6 10
14 26

After that we investigated NUMBER PALINDROMES. First we'll list ALL the combinations of any TWO counting numbers (1, 2, 3, 4, 5, 6...) to make a sum of 12 (stopping when the numbers repeat, regardless of the order). We found that there are exactly six possibilities: 1 + 11 = 12, 2 + 10 = 12, 3 + 9 = 12, 4 + 8 =12, 5 + 7 = 12, 6 - 6 = 12.

Then we investigate it with THREE counting numbers. Next, we'll pick any 2-digit number where the digits are not equal. We'll order the digits from lowest to highest to create the smallest number, and from highest to lowest to make the largest number. We'll find the positive difference between the two numbers and repeat with more numbers, looking for patterns, making predictions. Anyone who races through these two investigations will try the same thing with any three digits (where not all three are the same).

We'll continue with palindrome next week. COME PREPARED TO PROVE OR SHARE YOUR IDEAS AND WHAT YOU'VE DISCOVERED! Also next week I'll introduce algebra tiles, we'll start a math novel, and I'll introduce a point system for the rest of the semester. (See detials to the right).

Week #4:Oct. 22

Algerbra Games and Puzzles
 

We looked at a BORDER problem and a CONTAINER problem. We came up with algebraic solutions for the border problem that we will review next week, translating the different algebra solutions back into various strategies for thinking about the solution. If s = the side of the array, how many tiles will it take to make the border?

4s-4

s + s + (s-2) + (s - 2)

s + (s-1) + (s-2)+(s-3)

4(s-1)

s² - (s-2)²

 

We also played with a container problem: You have one 5 quart container and one 3 quart container. You have unlimited water. Put exactly 4 quarts of water into the 5 quart container. 

 

Math Games and Puzzles

We also played with the container problem: You have one 5 quart container and one 3 quart container. You have unlimited water. Put exactly 4 quarts of water into the 5 quart container. After that we all shared different logic problems and worked on them as a group.

Week #3: Oct. 15

Screen shot 2014-10-09 at 11.21.16 PM.png

Screen shot 2014-10-09 at 11.22.17 PM.png

Screen shot 2014-10-09 at 11.23.15 PM.png

Week #2 October 8, 2014

Focus with Deb

Week #2: Oct. 8, 2014

Algebra Games and Puzzles

We revisited the problem solving card trick (logic puzzle) with possible variations. We investigated and began to chart consecutive number sums (in small groups or pairs) for 1-35. We looked for patterns. What about 9? Can you find more than one solution for 9?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10...

1 = 0 + 1

2 = ?

3 = 1 + 2

4 = ?

5 = 2 + 3

6 = 1 + 2 + 3

As an additional puzzler to work on this week, I posed the Problem of Fours: Using just the number 4 (as many as you need) with any math you can think of, create the numbers 1-20. We took a look at a FAULTY LOGIC PROBLEM to really see how ALGEBRA can help us think: A ball and a glove together cost $10. If the glove cost $9 more than the ball, what is the cost of the ball? Ask your kids if they can show how ALGEBRA makes this easy to understand... because the answer isn't the obvious one!

Next week they will work in groups of four to solve a TUG of WAR problem involving acrobats, grannies, and a dog. They will design posters to share, explain, and prove their thinking.

Week #1: Sept. 29 2014

Day 1: We will calculate the “value” (in dollars) of each student’s name based on an alphabet conversion (Family Math: “The Value of Words”).

 

Screen shot 2014-09-30 at 11.59.30 PM.png

Students will use the total value of their name to find a partner. Partnerships add up to $110, $120, $130, and $145. Each pair will then use math clues to find the other pair that they will work with to make a team based on math puzzles that will help us discover what we know about the language and logic of math.

 

FOR EXAMPLE: “⅔ of your team’s SUM plus ⅕ of your team’s SUM plus ⅕ of your team’s team’s SUM equals your team’s team’s SUM.” “Your team’s SUM plus your team’s team’s SUM makes a number. MULTIPLY the DIGITS of that number to get a product of 50.” “The SUMS of your team and your team’s team’s make a SUM five less than the SUM of the other two teams combined.” “Your team’s SUM plus half of your team’s SUM plus half of your team’s team’s SUM is five more than the SUM of your two teams.”

Once in our teams, if we have time we will investigate a problem solving card trick with possible variations.

In groups of two, try to make this work:

Cards # 1-10. Turn over top card, it is an ace (1). Move next card to bottom of the deck and flip the following card. It is a 2. Move next cart to bottom of the deck and flip the following card. It is a 3. Continue until you get, in order, to ten.

 

Possible variations:

  • Pass two cards to the bottom of the deck each time.

  • Use the word of the number to count how many cards to pass to bottom of the deck (O ~ pass, N ~ pass, E ~ pass, Flip 1; T ~ pass, W ~ pass, O ~ pass, Flip 2 and so on through the deck).

  • Use all the cards up to the kings.

Is there a pattern to setting up the cards?

 


 

Day 2: We will investigate and chart consecutive numbers sums (in small groups or pairs) for 1-35. We will look for patterns. Faulty Logic problems. (Ch. 12)

 


 

Day 3: Perimeter problems (frame or pools). Container problems (p, 112). Allowance problems (p. 156).

 


 

Day 4: Building growing problems (algebraic equations for geometric patterns)

 


 

Day 5: Algebra Tiles

 


 

Check the website for details. We may decide to have weekly work at home to finish or extend our investigations. I will have each week’s summary and any homework posted on the CLASS DAY (WEDNESDAY) page by Friday.

 

For archived lessons, please refer here. You can navigate to this page from my TEACHER page (DEB) and click on GROUPERS on the left-hand side.

 

Grouper Focus #2

Math Games and Puzzles

THIS FOCUS GROUP BEGINS AT 11:10 AND GOES UNTIL 12:10. PLEASE BE ON TIME!

 

We are looking at sustained problem solving,multiple strategies, and sharing our thinking as the primary goals of the group.

 

Then watch this one. (Group #2, these are the videos we watched in class)

 

After the other two videos, this one should make more sense... 

 

Week #9: Dec. 3

<—   Read what I wrote for my other Grouper Focus Group (to the left).

Week #8: Nov. 19

Math Games and Puzzles

Week #8, November 19

Focus with Deb

THIS FOCUS GROUP BEGINS AT 11:10 AND GOES UNTIL 12:10. PLEASE BE ON TIME! We are looking at sustained problem solving, multiple strategies, and sharing our thinking as the primary goals of the group.

I will have several games for you to play and we might do some work with ALGEBRA TILES.


We looked at function machines, trying to explain what different kids were doing to find the output number given a particular input number. Here're the function machines that you came up with:

    Jamie

IN

OUT

5

30

4

25

3

20

7

40

9

50

2

15

1

10

0

5

8

50

Alex E.
IN OUT
2 2
4 8
0 0
3 4.5
7 24.5
1 0.5
5 12.5
8 32
20 200
Brennan
IN OUT
2 6
12 12
0 5
10 10
22 16
5 7.5
1000 505
3 6.5
   
Levi
IN OUT
2 24
4 100
0 0
7 504
1 6
3 60
6 336
8 720
-1 0
 
Alex D.
IN OUT
3 24
10 80
1 8
7 56
4 32
   
   
   
   
Everet
IN OUT
0 -4
2 14
4 34
6 54
5 44
12 114
7 64
1 4
100 994
Jamie 2
IN OUT
2 24R6
4 14R6
5 !3R6
6 10R10
0 0
1 45
10 9R5
   
   

 

Week #7: November 12

COME TO CLASS with a FUNCTION MACHINE to share...

ELANA will be in for me. You will share your FUNCTION MACHINES and each have about 3 minutes to take guesses. After that, please record your list and I'll put it on the website.

2 points for sharing a Function Machine during class and recording it for the group!

I will then have several games for you to play.

Some thoughts about the connection between BASE TEN BLOCKS and ALGEBRA TILES

 

Week #6: Nov. 5

Math Games and Puzzles

Week #7, November 12

Focus with Deb

 


Screen shot 2014-11-04 at 1.28.11 AM.png
 

I reviewed the point system for this class, it's intention, and the website organization to support it. Be sure to look at the web page again, as I will post some BONUS POINTS HERE.

Everyone gets 5 exp points just for showing up on time with a good attitude and an inquiring mind. Anyone who comes up to the front to try to explain his or her thinking to the group when I ask for that will get 2 points. Persisting, not quitting, bringing in good puzzles, taking risks, making good mistakes, supporting classmates will be the kinds of things that will gain points. Falling out of chairs, giving away an answer or strategy when someone else is still thinking, quitting, interrupting and such will result in loosing points. Some will be guaranteed, many will be surprises. Surprises are GOOD, even if they are bad surprises. They'll keep you on your toes.

I will post a mystery BONUS to gain points, (or sometimes a way to lose extra points) at the beginning of the class each day, revealing it at the end of class. I will post BONUS investigations here on the web site. BONUS POINTS for THIS WEEK: Bring in a good puzzle that you worked on, get 5 points. Work on a Kahn Academy brain teaser and take some notes, get 5 points. And best of all, ask your parents what 10 point activity (anything they want you to work on or do with no complaints and a great attitude) and have them sign a note about it. You'll get 10 points!

When the whole group gets to Level 5 the whole group gets donuts and a game day. If anyone gets to the highest level by the end of the semester, I'll bake you a cake! I'm already getting worried!

Check back on the web page for more information. Many things will NOT be announced anywhere but here! HAH! Now you'll check the website! ;-) We looked at a function machine, trying to guess what the output number would be for a given input number.

Here's the list of in and out numbers that we came up with:

 

IN

OUT

5

8

3

4

10

18

0

¯2

6

10

2

2

4

6

7

12

12

22

We looked at the function machine, trying to explain what different kids were doing to find the output number given a particular input number.

We came up with two different ways of SAYING what we did:

"I took the INPUT number and doubled it, then subtracted two."

We decided that, for this and similar wording (multiplied it by two, etc.) the expression would be

2x - 2

"I took the number and I added the number minus two."

x + (x - 2)

I introduced ALGEBRA TILES and we SHOWED that these two expressions are the SAME.

 

 

We investigated NUMBER PALINDROMES. First we listed ALL the combinations of any TWO counting numbers (1, 2, 3, 4, 5, 6...) to make a sum of 12 (stopping when the numbers repeat, regardless of the order). We found that there are exactly six possibilities: 1 + 11 = 12, 2 + 10 = 12, 3 + 9 = 12, 4 + 8 =12, 5 + 7 = 12, 6 - 6 = 12.Then we investigated it with THREE counting numbers.   SEE THE URCHIN FOCUS GROUP to see the pattern written out for THREE counting numbers  

Next, we'll pick any 2-digit number where the digits are not equal. We'll order the digits from lowest to highest to create the smallest number, and from highest to lowest to make the largest number. We'll find the positive difference between the two numbers and repeat with more numbers, looking for patterns, making predictions.

Anyone who races through these two investigations will try the same thing with any three digits (where not all three are the same). We'll continue with palindromes next week. COME PREPARED TO PROVE OR SHARE YOUR IDEAS AND WHAT YOU'VE DISCOVERED!

If we have time or interest we'll either look at the border problem (see Algebra group), the sock drawer problem, or we'll play a game (Set, Rumikub, or Sequence).

Week #5: October 29

Math Games and Puzzles

I introduced a point system for this class. I will work out the specific details over the weekend and post them here. Be sure to look at the web page again, as I will post some BONUS POINTS HERE.

Everyone gets 5 exp points just for showing up on time with a good attitude and an inquiring mind. Anyone who comes up to the front to try to explain his or her thinking to the group when I ask for that will get 2 points. Persisting, not quitting, bringing in good puzzles, taking risks, making good mistakes, supporting classmates will be the kinds of things that will gain points. Falling out of chairs, giving away an answer or strategy when someone else is still thinking, quitting, interrupting and such will result in loosing points. Some will be guaranteed, many will be surprises. Surprises are GOOD, even if they are bad surprises. They'll keep you on your toes.

I will post a mystery BONUS to gain points, (or sometimes a way to lose extra points) at the beginning of the class each day, revealing it at the end of class. I will post BONUS investigations here on the web site. BONUS POINTS for THIS WEEK: Bring in a good puzzle that you worked on, get 5 points. Work on a Kahn Academy brain teaser and take some notes, get 5 points. And best of all, ask your parents what 10 point activity (anything they want you to work on or do with no complaints and a great attitude) and have them sign a note about it. You'll get 10 points!

When the whole group gets to a certain level (I'll let you know what level by this weekend), the whole group gets donuts and a game day. If anyone gets to the highest level by the end of the semester, I'll bake you a cake!

Check back on the web page for more information. Many things will NOT be announced anywhere but here! HAH! Now you'll check the website! ;-) We looked at a function machine, trying to guess what the output number would be for a given input number. For Brennan and Everet, who didn't quite see the function during class, you can earn 5 BONUS points for solving the function!

Here's the list of in and out numbers that we came up with:

 

IN

OUT

5

8

3

4

10

18

0

¯2

6

10

2

2

4

6

7

12

12

22

We investigated NUMBER PALINDROMES. First we listed ALL the combinations of any TWO counting numbers (1, 2, 3, 4, 5, 6...) to make a sum of 12 (stopping when the numbers repeat, regardless of the order). We found that there are exactly six possibilities: 1 + 11 = 12, 2 + 10 = 12, 3 + 9 = 12, 4 + 8 =12, 5 + 7 = 12, 6 - 6 = 12.

Then we investigate it with THREE counting numbers.

Next, we'll pick any 2-digit number where the digits are not equal. We'll order the digits from lowest to highest to create the smallest number, and from highest to lowest to make the largest number. We'll find the positive difference between the two numbers and repeat with more numbers, looking for patterns, making predictions.

Anyone who races through these two investigations will try the same thing with any three digits (where not all three are the same).

We'll continue with palindrome next week. COME PREPARED TO PROVE OR SHARE YOUR IDEAS AND WHAT YOU'VE DISCOVERED!

If we have time or interest we'll either look at the border problem (see Algebra group) or we'll play a game (Set, Rumikub, or Sequence).

Week #2 October 8, 2014

Focus with Deb

Week #2: Oct. 8, 2014

Math Games and Puzzles

We spent more time on the card problem. Several kids worked the whole time to solve it, or to investigate variations. Others played the 31 game.

 

The Thirty One Game: Played with four of each card ace through six. Lay them out face up, mixed. Decide who goes first. Turn one card face down, saying the number. Next player flips another card face down, saying the sum of the current total and the new card. Take turns until one player WINS by getting the sum of 31. Is there a pattern or strategy? Other sums?

 

I briefly introduced the game SET to those not absorbed in the card trick.

Screen shot 2014-10-09 at 9.01.59 PM.png

Coming up we will investigate consecutive number sums, 9-Lines Tic Tac Toe, Race to 1000, Bagels, and various logic puzzles. 

Week #1: Sept. 29 2014

Day 1: We will calculate the “value” (in dollars) of each student’s name based on an alphabet conversion (Family Math: “The Value of Words”).

Screen shot 2014-09-30 at 11.59.30 PM.png
 

Students will use the total value of their name to find a partner based on math puzzles that will help us discover what we know about the language and logic of math. FOR EXAMPLE:

 


 

“Your partner is odd.” “The digits of your sum ~ you and your partner ~ equal 5.” “If you add your digits with those of your partner together it equals 20.” “The difference between your sums is zero.” “Added together, you and your partner have the highest total value of any other team.” “The sum of your digits is ONE less than the sum of your partner’s digits.” “Your sums differ by 10.”

 


 

Each pair will then use math clues to find the pair that they will work with to make a team. These will be even more complex, FOR EXAMPLE:

“Add the digits of your team total and your team’s team’s total for a sum of 16.” “The team of your team and your team have a total sum of $222.” “The difference between the sum of your team and the sum of your team’s team is 50.” “Each person’s sum in your team and your team’s team share one identical digit.” “The difference of the sum of your team and the sum of your team’s team is 30.” “Your name makes a number when you add the digits of your sum. Do the same with your partner’s sum. These numbers are consecutive. Your team’s team can add the digit of either of their sums to make a sum consecutive to yours.”

 


 

Once in our teams, if we have time we will investigate a problem solving card trick (logic puzzle) with possible variations.

In groups of two, try to make this work:

Cards # 1-10. Turn over top card, it is an ace (1). Move next card to bottom of the deck and flip the following card. It is a 2. Move next cart to bottom of the deck and flip the following card. It is a 3. Continue until you get, in order, to ten. Possible variations:

  • Pass two cards to the bottom of the deck each time.

  • Use the word of the number to count how many cards to pass to bottom of the deck (O ~ pass, N ~ pass, E ~ pass, Flip 1; T ~ pass, W ~ pass, O ~ pass, Flip 2 and so on through the deck).

  • Use all the cards up to the kings.

Is there a pattern to setting up the cards?

 


 

Day 2: We will play several games and share strategies.

The Thirty One Game: Kids vs. Me (later to play in pairs) with four of each card ace through six. Lay them out face up, mixed. Decide who goes first. Turn one card face down, saying the number. Next player flips another card face down, saying the sum of the current total and the new card. Take turns until one player WINS by getting the sum of 31. Is there a pattern or strategy? Other sums?

We may also look at some 1-100 chart games or logic puzzles, or play Bagels (a logic game with digits to guess a number or a rule).

 


 

Day 3: We will investigate and chart consecutive numbers sums (in small groups or pairs) for 1-35. We will look for patterns.

 


 

Check the website for details. We may decide to have weekly work at home to finish or extend our investigations. I will have each week’s summary and any homework posted on the CLASS DAY (WEDNESDAY) page by Friday. For archived lessons, please refer here. You can navigate here from my TEACHER page (DEB) and click on GROUPERS on the left-hand side.

 

Week #9: Dec. 3

<—   Read what I wrote for my other Grouper Focus Group (to the left).