Math Games Class 5

Who: Baan Pathomtham 1st and 2nd grade classes
Where: Bangkok, Thailand
When: after science and before lunch

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Special note for class parents:
Thanks to all the parents who have been playing the math games with the kids. They were really excited to talk about it and it shows how much they appreciated working on the challenge with you.

The homework this week is to investigate some patterns. We haven't found a great translation of this word into Thai as there seem to be different words for each of the slightly different meanings. As you help the kids with their work, you can encourage them with the following questions:

• What do we notice? 
• Why is this happening? 
• What do we think is happening next? 
• What can we do to test our prediction? 

It will be great if you can spend some time talking about these issues, even if you don't feel that they got to a particular "answer."

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Today, we had a slightly different lesson plan:

• Skip counting
• Talking about the snugglenumbers game from last time
• Exploring some patterns
• Playing indian addition poker

Skip counting

For each class, we gave them a number to skip count and P said an initial number.  For example, 

skip count by 2, starting with 0. We would go around the class at least twice. Today, we skip counted by 2, 3, 4, and 1/2.

This was intended as a fast warm-up, so we didn't choose anything that was particularly challenging. Even so, it proved to be good practice for nearly every student.  Also, there was a moment of deeper interest in the 1st grade class when we were skip counting by 4 starting with 1 and someone asked: "will we get exactly 100?"  That led to a good discussion of the pattern and then the class was really interested to keep going to see if they were correct.

Snugglenumbers game

The kids were all enthusiastic about this game which, frankly, has surprised us a bit since the game play is very limited.  They wanted to talk about whether they won or their parents.  For grade 2, we posed the following questions:

• Are there any numbers that are very helpful? if so, can you say which are the most helpful and why?
• What is the maximum possible score? Does it matter whether you are playing with one deck or two?

We didn't have an exhaustive discussion for either set of questions. For parents at home, I would encourage you to discuss these questions with your children.  Full disclosure: J1 and I had already discussed the question of the maximum possible score last night, so I had sworn him to secrecy for the class today.  As it turned out, we didn't really discuss this in grade 1.

Patterns

This activity was shown to us by David Ott, the K-12 math coordinator at ASL, one of whose recent exploits can be seen here: Family Math Night.

Set up: using construction blocks, I set up 5 patterns, the hide them in rolled-up paper, then hide those in a small bag.

The big reveal:

One pattern at a time, one cube at a time, I reveal the colors. At most steps, I will ask the kids for a show of hands to vote which color they think comes next.  Rotating around the room, we then ask for some explanation of the choice. I will usually also tease them a bit to encourage them to think more broadly. When they have all settled on a particular pattern and agree (which I don't force or encourage) then I whose the whole stick and ask them for a continuation, for example, what color is the 20th or 40th or 100th cube in the sequence.

The reaction

The kids absolutely loved this activity.  They were really excited to predict what would come next, eager to argue their view in the voting and then really emotional when the next cube came out and either matched their expectation or disproved their prediction.

Here were the patterns we used today:

Simple tools to cause mathematical delight

Your challenges:

What is the color of the next cube for the pattern on the far left?  If the glare makes it hard to see, it is pink-red-pink-pink-red showing. What is your reasoning?  How many other possibilities can you think of for that color and what is your justification?

If the pattern in the middle stick is repeated, what is the color of the 100th cube? What if I tell you that the pattern I want to extend is increasing whole number red series with a single green separating the runs of red?

Indian addition poker

P introduced this game two weeks ago and blogged about it here: http://3jlearneng.blogspot.com/2014/11/math-games-class-3.html. As she wrote at the time, this is a really good game.  We played two rounds at the end of each class and I was really struck by how much respect the kids showed to themselves and each other.  They took their time calculating, didn't get frustrated, and those who discovered their number faster were encouraging for the other students. To recap: everyone is dealt a card that they hold on their forehead and the teacher reveals the sum of all the cards.  Students then try to figure out which card they have.

In second grade, we played with a full deck, making J= 11, Q= 12 and K= 13 (A=1 in both classes). In first grade, we took out the face cards so we had A through 10.

One other modification is once there are 3 or fewer students left and they seem to be stuck, we tell them the sum of the cards from the remaining players.

I would encourage families with several kids to try this at home.  An alternative version is to have everyone take a hidden card, then reveal sums of 3 cards.  Feel free to experiment and see if you can find another version you enjoy.

Homework

We asked students to work on the two more complicated patterns, the increasing reds with green punctuation and the increasing pink and red stick.  The questions they were asked were:

1. What is the color of the 100th cube? How do they know?
2. If the red/green pattern has a red cube in the 100th place (a strong consensus among the classes) then what is the place of the closest green cube to 100?

Note: these questions can be answered by brute force, building the sequence or writing it down. What we would like to encourage is, of course, looking for patterns. For example, for the red-green pattern, do they notice anything about where the green blocks appear?  Can they make predictions about when another green will occur?  In the pink-red pattern, can they say when a block of reds has ended, do they notice anything about those places?

Blog tools

We've gotten feedback that it is hard to find particular content and navigate our blog. Today, I added two utilities that should help.

Search bar: pretty standard for all of us who use Google search everyday.  I haven't experimented much to see how the pages get ordered, so I'm interested to hear whether this is helpful.

Tag cloud: we try to tag all of our posts with key words.  These are shown with the most frequent tags at the top in a larger size, while the least used are small at the bottom. Clicking on a tag will take you to the collection of posts with that label. Make sure to check out some of the little-used tags as they are references to fun games or explorations.

What do you think? Is this enough structure to get you to the content you want to see?

Flowers, Squares, and Functions (programming class 11)

who: Baan Pathomtham Grade 5
when: Monday morning
where: at school

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Homework review
Forests/flower gardens (some of these were old?): 

Boongie made two versions: 

http://punwa.pencilcode.net/edit/flower and http://punwa.pencilcode.net/edit/flower2 

The first led very nicely into functions, the topic of the day as he had put the petal drawing into a function.  The second was a really nice cap to our discussions about for loops. In his original version, it drew one lime flower and three blue ones. Working together, the class modified the code so that all the flowers were a different color.

Win showed us his flower program, cryptically named untitled5: http://win.pencilcode.net/edit/untitled5

This is a good candidate for streamlining using a function.  Something for him to consider over the week.

To round out the discussion, I showed two related programs that I had found from other users and modified: http://jgplay.pencilcode.net/edit/otherPpl/flowerPattern

and http://jgplay.pencilcode.net/edit/otherPpl/forestRand


We didn't discuss this program as Titus thought it had gotten lost: http://titusorc.pencilcode.net/edit/flower/flowers

Focus for the day: Functions and vectors
Today, our plan was to build up a more complex function structure based around drawing some simple squares.

The first task was just to create a function that would draw a single red square. This code is an example.

Once completed, we added an input variable that would allow them to control the size of the square. Finally, we wanted them to make nested squares that would show why it is useful to capture a block of generic code in a function.  Here's our example.

At this point, Kan had two interesting ideas: First, he wanted to add the color as a parameter to the function.  That was pretty easy, but it was a nice way to see that functions can take numbers and words (in this case a color keyword) as arguments and that they can take multiple arguments.  His next idea was to include a variable that would tell the turtle to move after drawing the square. I've copied his code here 

http://jgplay.pencilcode.net/edit/class/kanBoxboxboxbox1234

He wasn't quite sure how to properly call the function.  Notice what he did: three arguments to the function, one of which is a vector!  Good stuff . . . and we will discuss this more next time.

We also talked about the idea of functions in mathematics and worked through three examples:

• f(x) = x+2
• goal(y) = 2y
• birthday(name) = {the day of that person's birthday}

Homework
The challenge this week is to write the birthday function that will work whenever a member of their immediate family is entered as the input variable.  This is not going to be easy, so we expect them to experiment, explore, and ask questions if they get stuck.

Some other interesting code
In preparation for the class today, I noticed Kan had created this program:
http://jgplay.pencilcode.net/edit/otherPpl/kanthapStinky

Both Win and Kan had these programs

• http://win.pencilcode.net/edit/dotcolor
• http://win.pencilcode.net/edit/songy123

At some point, we will return to these programs to talk about what they do and why.  I know the two were experimenting with them at the end of class and I'm eager to see what they can discover.

เกมคณิตศาสตร์ ป.1 - ป.2 (25/11/2014)

เกมใกล้เข้ามาอีกนิด

Source: Snugglenumber by Anna Weltman 
Link: http://recipesforpi.wordpress.com/2013/10/16/snugglenumber/

สิ่งที่ต้องเตรียม: ไพ่ 1 สำรับเอา 10, J, K ออก
วิธีเล่น:
     ๑. แจกไพ่คนละ ๑๑ ใบ
     ๒. ให้ A แทนเลข ๑ และ Q แทนเลข 0
     ๓. เด็กๆจะต้องนำไพ่ทั้ง ๑๑ ใบมาใช้ โดยที่ไพ่แต่ละใบใช้ได้ครั้งเดียว ให้เอาตัวเลขตามไพ่ที่ได้มา             ใส่ในช่องตามแผ่นเกมที่แจก (ดูตัวอย่างข้างล่าง)

              0     ____
              5     ____
             10    ____  ____
             25    ____  ____
             50    ____  ____
            100   ____  ____  ____
   
     โดยนับคะแนนดังนี้
            - ได้ ๓ คะแนนถ้าไพ่เท่ากับจำนวนพอดี
            - ได้ ๑ คะแนนถ้าค่าต่างไพ่กับจำนวนที่ต้องการไม่เกิน ๖
            - ไม่ได้คะแนนถ้าค่าต่างไพ่กับจำนวนที่ต้องการเกิน ๖
            
     ตัวอย่าง:
            มีไพ่ในมือดังต่อไปนี้  2, 2, 3, 5, 6, 6, 7, 8, 9, Q, Q  นำมาเรียง

              0     _Q__
              5     _6__
             10    _2__  _7__
             25    _2__  _8__
             50    _5__  _3__
            100   _Q__  _9__  _6__
  
         คะแนนที่ได้คือ 3, 1, 0, 1, 1, 1 รวมกันได้ 7
 
Update: some pictures of players in action

Nested Loops Review (Programming Class 10)

who: Baan Pathomtham Grade 5
when: Monday morning
where: at school

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Reviewing last week assignment

Last week, students were asked to draw this shape using double for loops if possible.  Only 1 in 4 students managed to use double for loops but none of them see this as drawing a triangle 3 times.

                                      

Nested for loops revisit

Using the homework as a starting point, I simplified the task by having them imagine the triangle to be just a line.  After they wrote the simplified program, I asked them to change the line into a triangle.  Eventually, we made our program to take any number of petals.

    num_petals = 3
    speed 10
    pen blueviolet
    for [1..num_petals]
      for [1..3]
        fd 50
        rt 120
      rt 360/num_petals

The next task is to get the students to understand how the use the counter in the for loops and the importance of placement of commands and indentation inside the for loops.  I actually had them do a simplified program before we get to the one below which creates 3 rows of colored dots (I first asked for one row of all the colored dots.)  Even these few lines of codes, it's still useful to breakdown the task into smaller, more simplified programs to learn the concepts.

    rt 90
    for x in [blue,green,pink]
      jump 25,-75
      for y in [yellow,orange,red]
        dot x, 21
        dot y, 7
        fd 25

Homework

Draw a flower garden using at least double loops.  I encouraged students to use triple loops or as many as they fancy.  I also mentioned that I didn't get to review functions but that could be handy for them to use for this homework.  Some of them seemed intrigued and I am hopeful that they will do their own review of functions to do this homework.

Fun with Polygons (Programming Class 9)

who: Baan Pathomtham Grade 5
when: Monday morning
where: at school

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Reviewing last week assignment

As usual, I started with homework review which is to draw a scary ghost with a bonus point if they can make their ghosts disappear and reappear.  Turned out to be a nice segue into my main agenda this week which is to review the for loop and a little bit of geometry.  I pointed out that their codes could be shorten by using for loops.

Fun with Polygons

Although my main goal for this session was to review for loops, I wanted to throw in a bit of geometry review (have been noticing that the kids were using too much trial and error strategy when they drew non-quadrilateral shapes).  The structure of this session was I asked them to draw various polygons using for loops: 
  - we started off with the basics: square and equilateral triangle   
  - Then I asked them to generalize their program to make any polygon.  This requires two things:
       1) Understand how to change the number of iterations in the for loops
       2) Recognize that the angle for the turtle to turn is 360/n where n is the sides of the polygon.  I showed them Josh's little program to illustrate this fact (http://jgplay.pencilcode.net/edit/explainer/extAngles)
  - Next I asked them to use for loops to draw a rectangle.  Here they have to recognize that the input into for loops can be other things than a sequence of natural numbers.

Things to Note (Debate?) for Future Lessons
 
Up til now, our main teaching approach has been to show them codes, run it to see what happens, and then ask the students to extend the codes.  While this show-don't-tell approach is great at stimulating their creativity and interest in class, my opinion is that our G5 students need a bit more explicit blackboard instructions to get a strong grasp of the concept.  Thus, I think we need a balance between learning by exploration vs. with explicit instructions.

Math Games (Class 3)

Who: Baan Pathomtham First and Second grade classes

Where: at school
When: mid-morning

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Here is the third installment of our math games series.  Despite shortage of staff (Josh is traveling), it's a successful session -- the kids loved it so much they begged for more after they finished their first round.

Indian Poker Addition Game
Source: www.mathsticks.com

This game is a twist to the indian poker.  Although it's more fun and challenging with more players, for younger kids, I find that 3-4 players work out best.

Equipment: A pack of cards with face cards (J,Q,K) removed.
Here's what we do:

- Deal one card face down to each player.  When given the signal, they hold the card outward on their forehead so they cannot see their own cards but only see their friends' cards.

- The card dealer announces the sum of all the cards. 

- Each player guess his or her number.

We have 7 children in each class so they have to add up 6 cards and then subtract from the announced sum.  For children who struggled, I gave additional hints -- I told them the sum of his or her card plus two other friends' cards so they only have to add up 2 cards.  

Close to 100

Equipment: A pack of cards with 10 and face cards (J,Q,K) removed.

Procedure: 

- Deal out 6 cards to each player

- Each player picks 4 cards from the 6 cards they were dealt to form a pair of 2-digit numbers.  The goal is to get the sum of the two numbers as close to 100 as possible but cannot exceed 100.