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Multiplication of two 2-digit numbers with Base Ten Blocks and other algorithms

 

Kids Show Their Thinking

 

Division with 2-Digit Divisor Using Base Ten Blocks

 

 

Race to 100 with BASE TEN BLOCKS

 

2014-2015 Tuesday Math Focus and Inquiry with Deb

Urchin Focus

Math Games and Puzzles

Focus with Deb

 

Final Day: January 6th


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

We had so much enthusiasm for extra math projects and investigations over the holiday that we declared everyone a LEVEL 5 CHAMPION and celebrated with our DONUTS and GAME day. Too much sugar was had by all!

We played Add it Up again, using the board to 24 with two 12-sided dice. We had lots of hard-core determination to keep the lower numbers freed up, until, running out of time, I declared the final round. The strategy changed completely as they subdivided the sums to use as many numbers as they possibly could.

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Screen Shot 2014-12-16 at 11.37.01 AM.png
Each player uses his or her own game board. At the start of play, players place one game piece in each square on the board, making sure the numbers on the board can still be seen. Roll the dice to decide who goes first.
 Players alternate turns rolling two dice, calculating the sum of the dice, and removing game pieces from the spaces on their own board. For example, say a player rolls the two dice and gets a sum of “7”. Then, he or she can choose to remove one combination of numbers that add up to that amount: 

  • Remove the piece from the 7 square
  • Remove the pieces from the 5 and 2 squares
  • Remove the pieces from the 4, 2, and 1 squares

A player should only remove one combination per roll of the dice. Depending on what pieces are available, a player may have a choice of several combinations. Only combinations that have all the needed pieces on the board can be used. In this example, 4 and 2 cannot be removed if 1 has already been taken off in a previous turn.
Educator tip: To remove the “1” from the board, it is easiest to remove it in a combination with other numbers. An example of a combination is “1 and 4.”
When there is no combination of open squares left on the player’s board adding up to the sum of the dice rolled, the game is over for that player. The other player can continue to roll and remove pieces until they also roll a combination that they cannot complete, or until they have no more pieces on the board. 
The object of the game is to remove as many game pieces as possible. The player with the fewest pieces on the board at the end of the game wins.

Focus with Deb

 

Weeks #10-11: Dec. 9 & 16, 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

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This week we played a game called How Close to 100? and had loads of fun. Our first round we only made it to 36 before we were stumped. The second game we made it to 94! I sent it home with them to play with you!

Here are the directions:

How Close to 100?
You need 
• two players
• two dice
• recording sheet (see next page)
This game is played in partners. Two children share a blank 100 grid. The first partner rolls two number dice. 
The numbers that come up are the numbers the child uses to make an array on the 100 grid. They can put the 
array anywhere on the grid, but the goal is to fill up the grid to get it as full as possible. After the player draws 
the array on the grid, she writes in the number sentence that describes the grid. The second player then rolls 
the dice, draws the number grid and records their number sentence. The game ends when both players have 
rolled the dice and cannot put any more arrays on the grid. How close to 100 can you get?
Variation
Each child can have their own number grid. Play moves forward to see who can get closest to 100. 

Last week we played Add it Up (which I also sent home with the kids so that they can play it with you!) and we investigated the second sock drawer puzzle, which was dissapointingly easy. 

Screen Shot 2014-12-16 at 11.34.00 AM.png

Screen Shot 2014-12-16 at 11.37.01 AM.png
Each player uses his or her own game board. At the start of play, players place one game piece in each square on the board, making sure the numbers on the board can still be seen. Roll the dice to decide who goes first.
 Players alternate turns rolling two dice, calculating the sum of the dice, and removing game pieces from the spaces on their own board. For example, say a player rolls the two dice and gets a sum of “7”. Then, he or she can choose to remove one combination of numbers that add up to that amount: 

  • Remove the piece from the 7 square
  • Remove the pieces from the 5 and 2 squares
  • Remove the pieces from the 4, 2, and 1 squares

A player should only remove one combination per roll of the dice. Depending on what pieces are available, a player may have a choice of several combinations. Only combinations that have all the needed pieces on the board can be used. In this example, 4 and 2 cannot be removed if 1 has already been taken off in a previous turn.
Educator tip: To remove the “1” from the board, it is easiest to remove it in a combination with other numbers. An example of a combination is “1 and 4.”
When there is no combination of open squares left on the player’s board adding up to the sum of the dice rolled, the game is over for that player. The other player can continue to roll and remove pieces until they also roll a combination that they cannot complete, or until they have no more pieces on the board. 
 The object of the game is to remove as many game pieces as possible. The player with the fewest pieces on the board at the end of the game wins.

 

Focus with Deb

 

Week #9: Deb. 2, 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles


 

We continued our investigation of rectangular arrays. Last week, we defined a rectangle and agreed the mathematically, "All rectangles are not SQUARES, but all squares are RECTANGLES" even though that's not how we usually think about it. SO, given that squares are rectangles, we used tiles to find all the possible rectangles for a particular number (we did 1-12), the area of all the rectangles, the perimeter of the rectangles, the equations for the rectangles, and the factors of that number (or PRODUCT). It was a lot of ideas packed into a hands-on investigation.

MATH WORDS: Area, Perimeter, Product, Factor

Here's a snapshot of the rectangles for 12:

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Each rectangle has the same AREA. Each multiplication problem has the same PRODUCT. Each has the same number of TILES. 

Each rectangle has a different PERIMETER. Each multiplication problem has its own two FACTORS.

We eliminate the rectangles with the same FACTORS (for example, the 3x4 is the SAME as the 4x3, just flipped on its side). WE ONLY COUNT 3 Rectangles ~ 4x3, 2x6, and 1x12. Twelve tiles has three rectangles, and 12 has 6 factors, 1, 2, 3, 6, 12).

WHICH ONE HAS THE GREATEST PERIMETER? WHICH HAS THE SMALLEST PERIMETER?

See last week's post for the beginning of the chart we tested for:

Number of Tiles    Area    Perimeter(s)    # of Rectangles   Factors    # of Factors


Today, we continued our individual investigation of 16 tiles. Ask your kids about it!
 
Here are the questions that they worked on:

Figure out how many rectangles you can make with 16 tiles. Draw them here.

 

How many rectangles did you make?  ____________RECTANGLES.

Write an equation for each rectangle next to it.

 

Is 16 a square number? How do you know?

 

If these were pizzas, which one would have the most crust around the edges?

Show how you know:

What is the perimeter of the “most crust” rectangle? ___________TILES. Show how you know:

What is the area of this “most crust” rectangle? ___________TILES. Does it have more pizza (more tiles) than the other rectangles? Show how you know:

 

Week 8: November 25

We returned to our investigation of rectangular arrays. First, we defined a rectangle and agreed the mathematically, "All rectangles are not SQUARES, but all squares are RECTANGLES" even though that's not how we usually think about it. SO, given that squares are rectangles, we used tiles to find all the possible rectangles for a particular number (we did 1-12), the area of all the rectangles, the perimeter of the rectangles, the equations for the rectangles, and the factors of that number (or PRODUCT). 

It was a lot of ideas packed into an investigation. One of the groups discovered a perimeter error that I'd made, and then we started an individual investigation of 16 tiles. Ask your kids about it!

Here's the beginning of the chart we tested:

Number of Tiles    Area    Perimeter(s)    # of Rectangles   Factors    # of Factors

 

#

Area

Perimeter(s)

#Rectangles

Factors

# of Factors

1

1

4

1

 

1

1

2


 

2

6

1

 
 

1, 2

2

3


 

3

8

1

 
 
 

1, 3

2

4

4

8, 10

2

 
 
 
 
 
   
   

1, 2, 4

3

5

5

12

1

 
 
 
 
 

 

1, 5

2

6

 

6

10, 14

2

 
 
 
 
 
 

 

     
     

1, 2,

3, 6

4

 

Week #7: November 18

Focus with Deb

 

Week #7: Nov. 18, 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

 

Today we investigated some math games. We played "Area Antics"

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to compare area visually in a card game.

 

We also played Commutative Cookies

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to practice multiplication and to show that if you have 5 cookies with 3 chocolate chips each, you will need the SAME number of chocolate chips for 3 cookies with 5 chocolate chips each.

 

We had a great time and everyone stayed focused and engaged the whole time!

 

  BONUS POINTS for GROUPERS or URCHINS: MORE PALINDROME NUMBERS... 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)

Week 6: Nov. 4

Focus with Deb

 

Week #6: Nov. 4, 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles


We investigated and reviewed the NUMBER PALINDROMES. First we'll 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 agreed on the patterns. We did the combinations of three counting numbers and found that being organized helped us to see the patterns.

1 + 1 + 10 = 12

1 + 2 + 9 = !2

1 + 3 + 8 = 12

1 + 4 + 7 = 12

1 + 5 + 6 = 12

1 + 6 + 5 = 12 (THIS IS A REPEAT FROM JUST ABOVE)


2 + 1 + 9 = 12 (THIS IS A REPEAT FROM THE ONES)

2 + 2 + 8 = 12

2 + 3 + 7 = 12

2 + 4 + 6 =12

2 + 5 + 5 = 12

2 + 6 + 4 = 12 (THIS IS A REPEAT FROM THE TWOS)


3 + 1 + 8 = 12 (THIS IS A REPEAT from the ONES)

3 + 2 + 7 = 12 (THIS IS A REPEAT from the TWOS)

3 + 3 + 6 = 12

3 + 4 + 5 = 12

3 + 5 + 4 = 12 (THIS IS A REPEAT from the THREES)


4 + 1 + 7 = 12  (THIS IS A REPEAT FROM THE ONES)

4 + 2 + 6 = 12 (THIS IS A REPEAT FROM THE TWOS)

4 + 3 + 5 = 12 (THIS IS A REPEAT FROM THE THREES)

4 + 4 + 4 = 12

4 + 5 + 3 = 12 (THIS IS A REPEAT FROM THE THREES AND THE FOURS)


5 + 1 + 6 = 12  (THIS IS A REPEAT FROM THE ONES)

5 + 2 + 5 = 12 (THIS IS A REPEAT FROM THE TWOS)

5 + 3 + 4 = 12 (THIS IS A REPEAT FROM THE THREES)

5 + 4 + 3 = 12 (THIS IS A REPEAT FROM THE FOURS and FIVES)

5 + 5 + 2 = 12 (THIS IS A REPEAT FROM THE TWOS and FIVES)

5 + 6 + 1 = 12 (THIS IS A REPEAT FROM THE ONES)

5 + 7 + ? THIS ONE DOESN'T WORK


6 + 6 + ? THIS ONE DOESN"T WORK and all the rest would be repeats...

WE PROVED THAT there are 12 combinations of three counting numbers that sum to 12... twice as many as the 6 combinations of two counting numbers that sum to 12. Hmmm. We wonder if this pattern would show up for other sums.

 

Everyone was engaged in the process except for two kids... so I decided to offer my GAMIFICATION point system. The goal is to help the kids understand the INTANGIBLE things I'm hoping to foster (engagement, struggle, willingness to think, to explain thinking, to listen to others, to enter into investigations for sustained problem-solving). For most of the kids this seemed to add some fun and engagement. 

 

I will bring them small treats when they LEVEL UP. It will get harder to level up after each level, and hopefully they will never get to the top level, though if they do, I bake them a cake. Ack! When the whole group gets to level 5, I bring donuts and we have a game day. I'm hoping this remains fun and lighthearted and somewhat effective to help them have a TANGIBLE thing (points) to encourage INTANGIBLE behaviors. 

My intentions are not mired in extrinsic reward over intrinsic, but rather are aimed at finding the intrinsic rewards of persistence and hard thinking by actually... doing that. It brought nearly the whole group all in for the next challege ~ the first SOCK DRAWER CHALLENGE:

 

DRAWER 1: 

  • 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

WE FIGURED IT OUT WITH UNIFIX CUBES and mostly everyone was really willing to stick with it past the first moments of CONFUSION.

 

 

Next we might 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).

FOR MORE INFO AND ARCHIVED SUMMARIES GO TO URCHINS WITH DEB

Week #5: Oct. 28

Focus with Deb

 

Week #5: Oct. 28 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles


We will investigate 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). Then we'll do 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).

Week #4: Oct. 21

Focus with Deb

 

Week #4: Oct. 21 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

Screenshot 2014-10-14 at 4.14.52 PM.png
We investigated rectangles with tiles to compare area (in the example above, 12) with perimeter (in the example above, 14, 16, and 26). We discovered something about the perimeter of squares. We created a large multiplication problem (12 x 17) making a rectangle with Base Ten Blocks. We also began a game of Race to 100 and messed around with making towers and other structures with the BaseTen Blocks.

Week #3 October 14, 2014

Focus with Deb

 

Week #3: Oct. 14 2014


 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

Screenshot 2014-10-14 at 4.14.52 PM.png
We investigated rectangles with tiles. We started with 12 and made all of the rectangles we could find using 12 square tiles. Then we did the same for 16... we found a SQUARE. I challenged the groups to make a numberline up to 18 and start finding the possible rectangles for each number. Do all numbers have THREE rectangles? What other numbers make SQUARES? Next week, one group (who investigated the rectangles for 48!) wants to keep working on theirs. Will we find patterns? We'll investigate these on the 100's chart, and we'll try rectangles for two 2-digit numbers.... Factors, Multiples, Division, Multiplication investigations.

Week #2 October 7, 2014

 

Focus with Deb

 

Week #2: Oct. 7 2014


 

 

THIS FOCUS GROUP BEGINS at 9:40 and GOES UNTIL 10:40. PLEASE BE ON TIME!

 

Urchin Math Games & Puzzles

We revisited the 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?

 

We investigated and began to chart consecutive numbers sums (in small groups or pairs) for 1-35. We will look for patterns.

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

 

What about 9? Can you find more than one solution?

 

 

COMING UP:

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 play Bagels again (a logic game with digits to guess a number or a rule).

We will investigate multiplication arrays and logic puzzles to create patterns on 0-99 charts and 1-100 charts.

 
 
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.
 
FOR MORE INFO AND ARCHIVED SUMMARIES GO TO URCHINS WITH DEB

Day One

We had a successful romp through a hard problem as the kids tried to figure out the order of the cards to make the trick work. We also played Bagels. The rest we'll save for another time!

Week #1: Sept. 29 2014

 

THIS FOCUS GROUP BEGINS AT 9:40 AND GOES UNTIL 10:40. PLEASE BE ON TIME!

Urchin Math Games & Puzzles

 

This is the “plan” so far. It will change and grow or shrink to fit the group. We are looking at sustained problem solving, multiple strategies, and sharing our thinking as the primary goals of the group.

 

Day 1: 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?

 

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 play Bagels (a logic game with digits to guess a number or a rule).

 

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

 

Day 3: We will investigate multiplication arrays and logic puzzles to create patterns on 0-99 charts and 1-100 charts.

 

Urchin Inquiry

Tech and Lego 

with Deb and Justin

We have a large group wanting to do tech, including a group creating a movie with dolls and puppets.

12/16/14

LEVEL FIVE CHAMPIONS (110 points):

IF you ALL get to this level before our final class on Jan. 6 (you can email me about bonus points you earn) then we get a DONUT and GAME day! You are the closest group so far!!!!

 

LEVEL FOUR CHAMPIONS (70 points):

CP 85

RP 82

JC 81

TS 80

EC 75

LEVEL THREE CHAMPION (40 points):

ML 61

Gamification Point System

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