Uno

Who: J1 eagerly, J2 reluctantly
When: before bedtime
What we used: Uno card deck
Where: bedroom floor

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The card game Uno has recently become popular at Baan Pathomtaam and J1 caught the bug. I picked up a pack last week and we've already played 20 (or 30, or 50?) times.  Apparently, there was even a solitaire game played at 5 am this morning.

I guess . . . that I don't really get the point of the game, so I'd welcome any comments pointing out interesting things that I'm missing.  Here's what I've considered so far:

• For very young children, this reinforces recognition of colors and numbers.
• Generating "uno" patterns: sequences of objects with two (or more attributes) where only one attribute changes for each step of the sequence.
• A bit of counting when you decide what color to call for a wild, executing a draw 2 or wild draw 4, and noticing that the other player has gotten to one card.
• Some strategic thinking to determine what cards to hold toward the end, or more advanced tactics if you can remember enough information to figure out what the other player is holding.
• You can modify the rules to introduce some arithmetic practice (some ideas are in the links below).

I've cheated a little.  Not at the game, but just in introducing a bit of extra math artificially.  When I deal out the starting 7 cards for each player, I put them in a grid so we get a quick reminder of one of our multiplication pictures:

Other ideas
That trusty friend, Google search, came up with some ideas for math games using Uno cards:

• place value war and 10s memory (both explained here: http://living.weelife.com/2012/08/two-uno-math-games.html) and 
• an uno progression (http://www.squidoo.com/how-to-teach-math-with-uno)
• a fun paper studying the structure of UNO by Erik and Martin Demaine et al: http://arxiv.org/pdf/1003.2851.pdf.

Baking math

Who: J3 (2 year old)
When: late morning, after J1 and J2 had gone to school
What did we use: water, yeast, flour, sugar, salt, oil, measuring cup, measuring spoon, scale, bread machine
Where: kitchen

See how little of the finished product was left before I remembered to take a picture:

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I'd posted before (here!) about some of the (mathematical) reasons to bake with kids.  Here is the math we did today while making bread:

1. counting
2. measuring volume and mass
3. estimating
4. next steps: ideas I forgot, but you can include them!

Counting
Maybe I go overboard, but my habit is to count everything around the smaller children.  Based on the recipe alone, there wasn't much scope for counting (2 eggs, 2 tsp salt, 2 tsp yeast) but we also counted the number of measuring spoons in our set and how many scoops of flour we needed to get our target mass. Along the way, we probably counted fingers and maybe even toes, too.

Measuring volume and mass
This is the obvious place to develop number sense while cooking.  We end up doing a lot of extra measuring during the process, playing with the different tools, and talking about comparisons between them.  For example, flour (21 ounces, about 600 grams) was the only thing we needed to weigh. What we actually weighed: flour for the bread, flour not used for the bread, the mixing bowl, the measuring cups (full and empty), a water bottle and box of crackers near us on the counter, the measuring spoons, and the sugar jar.
That allowed us to explore a range of weights from about 20 grams up to 1.5 kg.

We talked about metric and imperial units and looked at all the quantities in each. In particular, I use the imperial units as a good place to talk about fractions.  For today, I just read out the fractions close to what J3 measured, and included those in our chatter about comparisons.  My goal is to head off any (distant) future anxiety that comes from seeing fractions as a different "type" of number.

Estimating
I try to encourage them to estimate measures before they see the result.  This is easiest for mass, I just say "I think that will be 100 grams (or whatever I guess)" before they put the object on the scale. For the older kids, they will almost always respond "I think it will be less/more/[x grams]." J3 will usually just copy me, but she makes a delightful sound when we read the measurement together and comment on how close our estimate was.

Next steps
In truth, I didn't really go through every step with J3.  We measured the ingredients into a bread machine pan and then let the machine do the mixing and kneading.  Of course that saves a lot of time and effort, but we didn't see the exciting phase transitions where the dough goes from  separate liquid+dry flour to lumpy/sticky to smooth/elastic.  For older kids, it is interesting to ask them why they think the dough changes. Also, I did the shaping myself and that could be an opening to talk about braids/twists/knots.

As I wrote up these notes, however, I realized that I missed an opportunity with J3 to talk about temperature and time.  I think time was the big one: time for mixing/kneading the dough, time for a rise (actually there are 3 rises in this recipe) and time to bake.  With that in mind, I'll leave you with a picture of our kid-friendly timer:

patterns, estimation, communication (ideas for a grade 1 math course) (draft)

*UPDATE* this is not a class we are going to teach, but the ideas behind it and spirit inform the activities we do with the children.

Spirit of the class 1: "It is good to be confused."
Quote from Glenn Stevens (and Arnold Ross?) My initial thought on a Thai version is:

 ความสับสนเป็นสิ่งที่ดี

The goal is to operate within a realm of difficulty where the students are making some mistakes. From a music teacher, I got the heuristic that roughly 10-20% of the time is a reasonable target.

Students should be praised and encouraged when they say they don't understand something, when they ask questions.  Typical cues:
- show excitement (smile, eyes wider, raised voice pitch)
- emphasize this is where we get to learn
- ask them to explain how they are thinking, use words, symbols, numbers, draw a picture, etc
- ask other students for their thoughts
- ask everyone (including the original student) approaches for how they think we could figure out an answer

Spirit of the class 2: Always looking for patterns.

Communication
Throughout, emphasis is placed on having the students talk to each other about what they are finding, organize some of their thoughts, share with the class, write down what they think.  Written material will include:
- equations
- diagrams/pictures
- words (Thai and English)

Practice comparisons:
- X is similar to Y because A, B, C
- X is different from Y because A, B, C

Later, ask for things they know that are similar (and how those things might be different).  When appropriate ask for things that are close but different.

Patterns
Starting discussion:
- What is a pattern?
- What patterns do they know?
- What do they do with patterns?

using single trio blocks hidden in a paper/cardboard tube. For all, questions are

1. can they guess a pattern.  
2. how many patterns they can guess that fit the existing data. 
3. how much more data they need to see to test their hypothesis (confirm or reject).
4. For the pattern they guess, what color comes 30th in the sequence? What about 191st? or some other numbers that are moderately and then very large.

- repeated AAA etc pattern
- repeated ABAB pattern: what color is the 30th in the sequence?  What about the 191st?
- repeated (ABC)^n pattern: what color is the 30th in the sequence? What about the 191st?
-  prod_i=0...inf (A(B^i))
- prod_i=0...inf (A(B^(2i))
- random
- (AB)^8C: to show that there could be something else going on

Using a piano or violin, play patterns like:
- aural versions of the patterns above
- jumping up an octave
- CDCECFCGCACBCcCdCeCfCgCaCb
- CEDFEGFA etc
- CDEDEFEFGFGA etc
- forte, piano, forte, piano (single note or chord)
- different rhythms
- play a simple piece (e.g., twinkle) and stop before the last note.  Is there a pattern.  How do they know that the song doesn't feel finished?  This is just for discussion, no real expectation to have deep answers.

Movement patterns
- movement versions of some of the block patterns
- follow the leader patterns (everyone assigned to follow someone else, someone assigned to follow the teaacher, then teacher slowly walks a loop to allow the snake to form up)
- 2 separate snakes
- wall and monster: everyone assigned another person who is a monster (to them) and another person who is a wall (to them).  They try to walk so that their monster is on the other side of their wall.  Discussion: did it look like there was a pattern?  We had a rule about what was going on, but it was very complicated.  If another teacher came to watch, could they guess our rule?

Ending discussion:
- What other places can they find patterns?
- What are their favourite patterns?  What do they find appealing about those patterns?
- Are there any patterns they don't like?

Homework:

1. Find patterns in new places: movement, colors, shapes, in language
2. Find new patterns: for something they thought they already knew the pattern, can they find another rule that fits the data?  Maybe this one is too hard

Follow-up activity: 

Here are 4 things, find the one that doesn't belong.  

• Why doesn't it belong? What is the pattern or rule that the other three fit?
• Now, can you find another rule or pattern that kicks out a different object?
• For each of the four, can you find a rule that excludes it from the other three?

Estimation/Measuring
Note: other quantities to measure are listed here: http://3jlearneng.blogspot.com/2014/06/getting-started.html

How many are in my jar/box each day at the beginning of the day (can be something left out for the whole school to enter a figure.)

Temperature using the infrared thermometer gun
Distance using the tool

School run: give the students a gps to measure the following
- Time: how long does it take to get to school? Does it vary from day to day? How does it look over the course of a week?
- Distance: how far do they travel? Again, does it vary from day to day and how does it look over the course of a week?
- Speed: average and max speed as measured by the gps.  Which varies more over the course of a week?
Each day, ask for the data of the day and then ask for an estimate for the following day. Rotate through the students who has the GPS.

These will also be good for introducing graphs. I would just show the picture and explain what it meant, but not dwell on the graph.

Chains (part 2)

Who: J1

When: before bedtime

what: figuring out the rule for the 60-chain and finding other chains

why: because J1 wanted to discuss the chains exploration

J1 was getting more and more concerned as he looked for his homework folder and didn't find it.  Suddenly, his eyes lit up and he held up a crumpled piece of paper: "Daddy, look what I've got!"

It was our 60 chain from earlier in the week.

I suggested we try some other starting points: 0 2, which he then wrote down until we got back to 0 2.
Next, he asked what would happen if we started with 2 3.  I gave him time to think about it and then pointed to 2 3 in the 60-chain and asked what he thought that meant.

Next, I pointed out that our 0 2 chain had a 2 2, 4 4, 6 6, and 8 8. What about other doubles? He found the 60 chain had 1 1, 3 3, 7 7, and 9 9.  So, what was missing? Eventually, we got to this:

I left him with this challenge: there are two other chains, what are they?

Before he would go to sleep, he wanted to discuss a little whether it was easier to find long chains or short ones.  Eventually, he came to the conclusion that long chains might seem more complicated, but they are easier to find. Can you see why he thought that?

Scaling (part 2)

Here is an example of an activity that didn't really work out.  I'm curious if you have ideas why and I'll explain my take on the situation.

Who: J1 and J2
When: mid-afternoon when I am working
Where: in my home office
What: drawing pictures in larger scale using a grid copying technique
Why: build intuition for scaling as multiplication and distract them while I was busy

Background
I wrote about one plan to have the J's play with scaling through a collection of grid drawings here:

http://3jlearneng.blogspot.com/2014/07/multiplication-scaling-and-groups.html

After getting that inspiration, I prepared several pages using pencilcode and some pre-grided pictures I found on the web.  Then, I even went a step further and got an Asterix action shot and made it into a grid drawing:

Here's my pencilcode directory.

How could the older J's not love it?

In play
 At first, both J1 and J2 seemed interested. They asked me to print particular pictures, compared how many gridlines each had (some are 4x4 and others 5x5) and then asked me if I could find other pictures (leading me to put together the Asterix one).

From there, J1 made an attempt on the butterfly pattern, but I don't think J2 even made any progress on his.

Post mortem
Here are my ideas for why they didn't get into the activity:
(1) it was too hard
(2) they were distracted by something else
(3) I wasn't doing it along with them.

Sometimes, it is frustrating to spend time planning and organizing an activity for it to fizzle out. When it happens, though, I think it is important not to keep pushing the activity.  Sometimes, it can be introduced again at a different time or place. Sometimes, in fact, they will ask about the activity on their own, helping to prove that often something goes in, even when they don't seem to be listening.

Pattern Blocks (mini follow-up)

Who: J1

When: 5 minutes in between other play

What: finding an area relationship and learning a surprising technique

How: I made a design and then we admired it together

A pretty little picture, no?

Last month (specifically, here: http://3jlearning.blogspot.com/2014/06/tease.html) I asked you to calculate the areas of the different pattern blocks. One of the trickier ones is the thin, tan parallelogram. This arrangement gives you one way to see a relationship that might be hard to spot.

I set out the blocks and arranged them as in the picture.  At some point in his play, J1 paused and started looking at the blocks.  I moved the top two (orange square and green triangle) away from the others and said "hmm." That was enough to launch us into a discussion of
(a) are the two clusters the same shape
(b) are they the same area
(c) are the green triangles the same
(d) can we draw any conclusions?
(e) if they are the same area, why can't we make a square from the two parallelograms?
(f) what equations can we write that describe our picture?

Do you know other examples that are like this (you add something to a problem/picture/system that suddenly makes it more clear rather than more complex)?

One example that recently came to my mind was completing the square for a quadratic equation. A more sophisticated example is moving from affine to projective space to look at curve intersections in algebraic geometry.

Number sense, calculating, and stuff

Apologies, this post is a bit of a grab-bag of different things we have been doing recently. They are a mix of activities across each of the age groups, done at different times of the day and different levels of engagement, though most of the one-on-one time with J1 comes just before bedtime.

Number Sense: J3
We have made a conscious effort to surround the children with numbers and are often looking for good ways to present concepts in a different format, especially one that has physical objects and some relationship to their body.  Meals are often rich with opportunity, especially if you don't mind a little bit of playing with the food.  Here, J3 has matched up 10 almonds with each of her fingers, counting as we made the layout , then counting again as the almonds got put in a little cup, then counting again as she ate them.

Similar ideas:

• counting stairs going up and down
• counting musical beats as you listen to a song
• weighing food, weighing each other
• estimations (amount, length, weight)

Snakes and Ladders, err, Dinosaurs and Dinosaurs
I've mentioned before and will repeat frequently that I enjoy playing games, but snakes-and-ladders format aren't really games since you can't actually do anything. For now, though, the kids like them and the provide an opportunity for two things: (1) asking interesting questions about structure and (2) introduction to probability.  Along the way, there is practice calculating, but this is just small addition problems and not especially rich.

Tonight, J1 and I played a dinosaur version, you go down if you land on a land-dinosaur head square and up if you land on a designated square associated with a flying reptile:

We made one big modification to the game: playing with two dice instead of one.

The main point of interest is hearing J1 calculate dice sums, which square he is jumping to, and analyzing the size of the boost (or drop) from hitting the bonus squares and the penalty squares. It fun to talk about the probabilities of hitting the bonus and penalty squares, particularly because he asked all the questions and did most of the talking.

Simple starter cues, if you want them:

• is it possible to get to x from where you are now?
• how many squares away are you from y?
• How many ways are there to roll a 5?

Toys

Really, all of this post is just leading up to praise for some toys the kids really like and that can soothe parental anxiety about "stimulating development."  Frankly, I don't really care, since I enjoy playing with these, too!

Rainbow Loom

Extremely popular in J1's school group and even J2 can weave a nice design on his own.

They also discovered that youtube has useful how-to videos and they even worked together!

So, what are the (future) mathematical benefits:

- pattern building and recognition

- building a mental model of how the structure fits together

- understanding algorithms (especially with repeated loops)

Snap Circuits

A fantastic kit with electronic components that all snap into a grid-circuit board for easy assemble and disassembly.

 There is a book of projects which show circuit layouts and give some commentary about what you should be examining to understand the operation of the circuit.  Usually, they introduce each new component in a show piece of its own so the kids can build a sense of function.

I do have one complaint about the kits, though: a lot of the projects depend on using an integrated circuit.  These are black-boxes, so it misses a bit of the fun of building everything up from truly elementary components.  For now, that's certainly fine for our kids level of sophistication since it is fast to build a fully functional circuit. We do miss out on really understanding what is going on inside the box, though.

Trains

Really just an excuse to post a picture that reminds me how much fun J3 had playing with one of our toy train sets:

Post XXVII (Roman Numerals and ninja stars)

Who: J1 and P
When: after bath, before bedtime
Where: In J1 and J2's bedroom
What: doing roman numeral calculations on the mini-white board
Why: hmm? Some ideas below
How: facilitated by J0 folding ninja stars to appease the restless on-lookers

Roman Numerals
In our RightStart math book, we got to a series of activities relating to roman numerals.  Mainly this consisted of translating back and forth between arabic numerals and roman numerals, along with debating the actual rules for roman numerals.  I will have to get P to write about how she introduced the topic. When I joined the conversation, J1 was in the process of writing out the natural numbers up to 40 (XXXX or XL?) in roman numeral form. Later, he went up to L (50), but he already knew the symbols for 100 (C), 500 (D) and 1000 (M). Next activity was converting from roman numerals back to arabic (for example: 377 = CCCLXXVII) and then he did a round of conversion back.

All of that is pretty straightforward . . . and probably not very interesting. So far, what he's getting is some practice calculating simple addition in his head, added flexibility of thinking of numbers using different representative symbols, and a familiarity with a number representation system that is justifiably extinct.

However . . .

Anything can be interesting
Basically, what questions do you ask, what questions does the child ask, and what questions do you explore?

For example, Who used this numbering system? Who uses it now? What other systems were used around the same time? When and why did it get replaced? Are the rules clear, how can you cheat, how can  you make the number expression as efficient as possible (within the basic spirit)? How does it compare to the arabic numbering system?

All of these are fun topics for exploration.  Let me expand on two that we discussed.

Comparison
"How do roman numerals compare with Arabic ones (or the Thai system)?"
"What's the same?"
"What is missing in one that exists in the other?"
"What are the advantages/disadvantages of each?"
"When would you want to use this one? that one?"

All generic questions that can be asked, in some form, about anything new you experience/see/learn and making a comparison like this is probably the most important habit in truly understanding the new idea.

I'm sure you can come up with a lot of similarities and differences. In case you didn't get them, though, here are two cool features that the roman numeral system lacks:

• symbol for 0
• place value

Cheating (aka are the rules clear?)
More ingrained than comparison, our 7 year old J1 has the habit that when he hears a list of rules, he immediately starts thinking of how to break them, alternatives, or cases that haven't clearly been covered. This was how he made the numerals up to 50 more fun:

"Can I write 5 as VX?"
"How do you know that XI doesn't mean -9?"
"I'm going to write 39 as (XI)L"
"What about VLI for 46?"

Throwing stars
Of course younger siblings J2 and J3 were enthralled by this discussion.  The alternative activity tonight was folding stars. If you don't know how to fold a paper star, these two videos will get you going: Ninja Star and Puffy Pentagon Stars.

Cute little projects.  My recommendations for when you do these with very small children:
(1) have a bunch of extra material
(2) expect a lot of mistakes and destroyed products
(3) have everyone try to make something
(4) give them plenty of opportunity to examine what you've done
(5) ask questions, get them to talk about what they see and what they are doing. Use the comparison questions above!

Chains (part 1)

What: starting to investigate chains (description below)
Who: J1
When: mid-day, after breakfast
Where: on the floor in the middle of everyone
How: pencil and paper
Why: pattern seeking, exploration, thinking about extensions

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To give you an idea of the challenge I presented to J1 today, we sat down and I told him that I was going to write down a sequence of numbers following a rule.  To start, I needed him to give me two numbers. He gave me 9 and 8.  I started writing the following, periodically asking him if he thought he knew the next number:

9 8 7 5 2 7 9 6 5 1
6 7 3 0 3 3 6 9 5 4
9 3 2 5 7 2 9 1 0 1
1 2 3 5 8 3 1 4 5 9
4 3 7 0 7 7 4 1 5 6
1 7 8 5 3 8 1 9 0 9 9 8

By that point, he had made many guesses, but hadn't gotten the rule.  I said that the sequence would repeat now and we talked about that a bit.  Basically, said it made sense because we had started with 9 and 8, so if that came up again it should be like starting again.

So, what's my rule?

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*semi-spoiler alert*
Well, the point of this blog isn't particularly to set you math challenges (though I think this little exploration will still contain a lot of that). Here's what's going on and some of the things you can investigate.

A week ago, I saw a little warm-up exercise in RightStart Math called chains that caught my attention. They outline the following procedure:

1. pick one single digit numbers and write it down, for example 2.
2. pick another single digit number and write it down, for example 6.
3. Add them together and write down the ones-digit of the result.  Here, we would get 8.
4. Keep adding the last two numbers in your sequence and write down the ones digit of the result.
5. Continue until you repeat.

Staying with our example, our sequence would continue: 2 6 8 4 2 6.

You got the step 8+6 = 14, but only keep the 4, right? In case you think it this whole set-up was unfair to J1, just know that this type of modified addition was introduced at school, maybe even in kindergarten. 

If we reversed the starting order, the sequence changes: 6 2 8 0 8 8 6 4 0 4 4 8 2 0 2 2 4 6 0 6 6 2

I've highlighted the two digits where the sequence repeats, but I'd actually prefer to leave those out and think of it as a 4 step chain and a 20 step chain.  The one J1 seeded for us was a . . . 60 step chain (isn't it helpful how I arranged the numbers so nicely in a little array?)

Beyond the basic mystery of guessing the rule (which you could leave out), what's interesting here?  Some things to consider that will get you started:

• Does the order of your starting digits matter? (we've already seen above that it does)
• will every starting pair of numbers eventually repeat (form a chain)?
• Will you ever get a repeat somewhere in the middle of your sequence, so the sequence looks something like [x] [ y] [y][y].... where [x] is one sequence of digits and [y] is another?
• How many chains are there?
• What length are all the chains?
• Will every chain contain all the digits 0 to 9?

Some little hints:  at any step, how much information do you need to continue the sequence? Can you reverse the sequence?

Further exploration
Dropping the tens digit actually means we are working modulo 10.  It really just means we are treating 10 the same as 0, but that simple idea is very powerful. We could have chosen a different number than 10, say 13 or 140 or 5 or 2 (though 1 is a bit of a problem). So . . . how do our chains look when you play with those cases? At the very least, we would start by asking the same questions we had before:

• Will every starting pair of numbers eventually repeat (form a chain)?
• Will you ever get a repeat somewhere in the middle of your sequence, so the sequence looks something like [x] [ y] [y][y].... where [x] is one sequence of digits and [y] is another?
• How many chains are there?
• What length are all the chains?
• Will every chain contain all the numbers 0 to n-1 (where we are working modulo n)?

I don't know if I'll get to this level with J1 for a while, but it is something I get to play with myself when I'm waiting at their swimming lessons.

NIM

Who: J1 (7 years old) and daddy
When: just before bedtime, game lasted about 10 minutes
Where: on the floor
How: using pattern blocks (though any collection of small objects would have worked)

What: playing NIM (rules below), counting blocks, making array patterns with blocks

Why: finding some one-on-one time, adding another strategy game and building from this game we played before, reinforcing number sense.

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Following a good suggestion, I'm trying a new format with these notes.  Instead of just saying what we did, I'm going to try to give more of a recipe so that it will be easy (easier?) for all y'all to play along at home.  I'm giving the ages of the children involved as a rough guide to whether your kids might have a similar experience, but I hope you don't take that too seriously because:
- age is not a very good proxy for experience, sophistication, or interest
- most of the things we do are low threshold (almost anyone can get started) and high ceiling (almost anyone could find an interesting and challenging extension to the basic activity).

NIM rules:
split a bunch of little objects into several piles.  two players take turns removing as many objects as they want on their turn with two conditions: you can only take from one pile at a time and you have to take at least one object.

What we did
We played with the pattern blocks and didn't actually separate into piles. Instead, our rule was that you could only take one type of block at a time.

The first time, I poured out about 1/3 of the blocks and separated out the hexagons, trapezoids, and triangles.  We played one game that way, basically carelessly taking away various amounts for a while. I took away all the green triangles at one point to make the strategic positioning a little clearer.  When we got to a small number of blocks (about 5 -7 of each type), I started pausing before my moves which signaled J1 to start thinking ahead and considering strategy. We got to a configuration 1-4 on my move and his eyes narrowed when I reduced it to 1-1 as he saw that I was now in a winning position.

We played again with the other 3 types from the original pour.  Same general method of play, but J1 started thinking strategically a little earlier in the game.

Finally, we poured out the whole bucket and played with all 6 types.  Generally, same mode of play without extensive strategic analysis.

Secret Daddy addition (don't tell!)
whenever I took away blocks, I would arrange them in a grid of some form and state a multiplication equation associated with that array.  For examples:

• 12 green triangles: I arranged them into 4 x 3 and said "4 groups of 3 is 12"
• 5 yellow hexagons: I arranged them into a 1x5 line and said "1 group of 5 is 5"
• When J1 took away 9 orange squares, I asked if he could organize them and he made a 3x3 square.

Next stage/Extensions
Analyzing the strategy is an obvious next step. For us, I can build off J1's obvious calculations toward the end of the game in this way:
"Hey, when we got to 2 shapes, I noticed you thinking more carefully.  What were you analyzing?"
<discussion>
"What if we start with just 5 triangles, what would you do?" "9 triangles, 15 triangles, oh, its all kind of the same."
"what about 2 triangles and 1 square"
"can we make a list of when you know that you would win or when you know that I would win?"
"what patterns do you notice?"


There are a lot of possible variations and I think it is a great fun for the kids to think of alternatives and see which ones are interesting to play. Two alternatives that came up most readily when we played were misere (last player loses) and a points game where you get points for every block you pick up and the last player gets a bonus.

If you want to take it in a different direction, help them code a version of the game in your favorite programming language. Maybe pencilcode?

To involve other sense, play the game using small pieces of food that get eaten on each move. Or you can create a variation on your favorite musical instrument (say moving from left to right on a piano where every move has to be within an octave).

What do you learn?
Working back from the answer and building up from smaller examples are two generic strategies that you can practice in analyzing this game. This is also a place to introduce recursion or induction.

Programming Course Part 2

Follow-up to this post: http://3jlearneng.blogspot.com/2014/07/computer-programming-intro-5th-grade.html

Resources required
1. Computers that are connected to the internet
My initial preference is 1 computer for every two kids.
Students should have a computer with internet access at home in order to work on their homework. If someone doesn't have that, is there time available for them to work at the school?

2. Robot Turtles game *new idea*
In some lessons, we will use components from the game:
- command cards to command a human "turtle"
- how can you finish my program (intro activity). Teacher will set up a maze and some starting commands.  They need to select a further series of commands to get to the jewel.
- can you fix my program (intro activity). Teacher will set up a maze and a program that doesn't work.  They find the bug and how to correct it.

Anything else we should use?

First lesson
First half: Robot Turtle commands

1. We are going to make computers do what we want!
2. First, we are going to play a game.
3. <Give out sets of robot turtle motion cards>
4. What do you see? <discussion>
5. Let's do an example. You put down command cards that will make me move
6. <direct each student to choose 1 card to play at a time and rotate through the group 2x. teacher asks the students to show the card and say what the movement should be, then moves>
7. Okay, time for you to play
8. <break into pairs, one programmer, one turtle.  switch after 5 minutes>
9. <regroup and discuss>
10. On other days, we will play some more games with these robot turtles.

Second Half: pencilcode

1. We can do the same on a computer
2. <go to stations with a browser open to pencilcode.net>
3. I'm going to show you how to get started
4. <play around for a while, teacher will probably have to translate/explain some bits in Thai>
5. If you create something interesting, here's how you save it
6. <show>
7. There is a lot you can discover and explore.  You can look at what other people have created
8. <show pencilcode.net/edit>
9. And here is the code gym
10. <show gym.pencilcode.net>

Overall objectives:
By the end of the session, they understand
- Commands are the way they direct the computer
- a sequence of commands forms a basic program
- They know how to create an account, log-in, create a new program, run their program, explore other users' programs

Geometry play and misc activities

Our activities in the previous evening with J1:

- Skip counting by 6 using the 100 board and colored tiles

- arranging the fraction board pieces

- playing with the geometry pack (see below)

- talking about parallel and perpendicular lines

- talking about different triangle shapes

- talking about circles of different sizes

- playing the tidy-up game (take away 3) including a miscalculation by Daddy that allowed J1 to win!

Geometry Pack

The RightStart math pack came with a lot of fun toys.  One that we just opened was a little geometry kick.

It had a board and T-square:

And a safety compass (which I'd never seen before, but found pretty cool):

And two drafting triangles: 30-60-90 and 45-45-90 (which I didn't manage to photograph). You can also see in the previous pictures our fraction board with a one-unit length divided into 1, 2, 3, ..., 10 equal pieces.


The big focus, though, was just making an interesting picture (shown as work-in-progress):

Miscellaneous

When playing Robot Turtles the other day, we noticed a cardboard grid that held the playing pieces when the game was manufactured.  some brilliant mind (not mine!) had kept this instead of throwing it away. We will see what uses it finds, but have already come up with two: as a grid for the traffic lights game (see here http://3jlearneng.blogspot.com/2014/06/traffic-lights.html) and this nice pattern from J2

Games: Catan and Robot Turtles

As I noted in our kick-off post, I love games. There are educational benefits, but you will still get those if you are just playing for fun, so focus on the fun.  Even this can sometime be tricky with small children or kids at different developmental stages.  Below is a field report on a couple of games we played this weekend: Settlers of Catan and Robot Turtles.  If you don't know those games, skip below to the summary of the lessons we learned:

Settlers of Catan

If you don't know the rules, it is sufficient to know that this is a dice and board game where each player is trying to acquire territory and build.  Players don't (usually) attack each other directly, so it feels more like a race.  There are a lot of little pieces and cards and play can easily take an hour. Play with someone to learn the rules in detail; if you are in Bangkok, come play with us!

Because of the time, patience required, and small board pieces, we usually play this when younger siblings aren't around. J1 and I took an opportunity when J2 and J3 were away to get out the board. I made two modifications when we played:

1. No trading resources between us: this wasn't a restriction I imposed, I just didn't offer it as a possibility.
2. J1 started with an advantage: I gave him 2 settlements, 2 road segments and all the associated resource cards to start, while I started with 1 settlement, a road segment, and the thee associated resource cards

This set up was fun for both of us, though the game was slow to get going as we had such limited resources and his advantage was a bit too big.

For our next attempt, J2 joined the game. I thought the previous game had worked well and started them with the following advantages: J0 gets 1 settlement+road+3 resources, J1 gets 2 settlements+2roads+6 resource, J2 got one city+one settlement+2 roads + associated resources (which turned out to be 8 instead of 9 b/c he put one his settlement on a coastal vertex).

This game ended badly as J2 got "robbed" twice in a row (and I wasn't even applying the rule about taxing half the resources which would have made it worse).  Though he still had a huge advantage over each of us, the feeling of getting picked on was too much to bear and he had a meltdown.

SoC lessons for next time:
- Playing with particularly young children: take the robber out of the game. This removes the only opportunity for direct "attacking" play.
- Playing with young children: add extra settlements at the start of play, particularly to level out play between people with different amounts of experience and sophistication. By adding extra settlements, you cut down the early game phase where people are really just waiting to accumulate resources so they can finally build (or trade).
- Domestic Trading: for my J's, I will continue to play without trading among players.  If someone thinks of it spontaneously, I won't prohibit it, but I won't suggest it.
-  International trading: I'll consider allowing better trading ratios.  That will mean a player who misjudges and is completely locked out of one resource type won't be excessively disadvantaged.

Robot Turtles: http://www.robotturtles.com/
This is a board game that introduces programming concepts.  In retrospect, perhaps playing thsi a couple of times set up the boys for pencilcoding. Both have Logo as their original inspiration.

This time, J1 and I were playing ("turtle masters"), while J2 was the ("turtle mover.") This was okay for our first game, but there was a constant tension about who was actually moving J1's turtle.  That tension erupted in the second game when J1 moved my turtle (which was a clear violation of J2's responsibility).

As we were playing, I finally read the little instruction book associated with the game.  They have some useful suggestions about progressions to increase the difficulty as kids get the ideas of constructing programs. Also, they have some guidelines about how multiple players of varying sophistication can play together. Most importantly, though, they provide these guidelines about the role of turtle mover:

Can the Turtle Masters move their own turtles?  

No. There are many reasons, but the best one is this: it changes the game from “kids bossing grownup around” to “grownup correcting kids’ mistakes.” That is guaranteed to kill the fun for everyone. Plus, once you let the kids touch the board, they’ll never want to go back to letting you do it. 

Ok, so that's my lesson learned for robot turtles.

Overall Lessons:
These are all ideas I have on things to consider when I'm playing games with the kids in the future.  No absolute rules, of course:
- Consider whether the children are ready for games in which they are directly "attacked." While they may love stealing your resource cards or capturing your pieces, it often doesn't seem any fun when they are on the other side of the exchange.
- Make modifications to speed up the active phase of the game.
- Stop if someone isn't having fun
- Only introduce one or two items of strategy each game.  Let them learn how to play by playing
- When it is possible, give them a starting advantage so you can play your best and they will still have a slight chance of winning. In our house, this makes it the most fun for everyone and a great source of pride when they say: let's play with an equal start, Dad.

Multiplication: scaling and groups

For unclear reasons, I have built up a mental picture that the introduction of multiplication is a major milestone, so I feel a bit of relief and surprise now that the moment has passed. Both emotions come from realizing that we already have been using multiplication (and division) concepts for some time!

Scaling
Scaling is one of the basic functions in pencilecode:

scale 2

Illustrated here: http://jgplay.pencilcode.net/home/scale2

to make the turtle and its movements twice as large. From the first day we starting playing with the system, using this to blow up the turtle has been a favorite part of nearly every session. I think there is a lot of promising scope to operate turtles at different scales, compare their movement and compare the figures that they draw. I've written a simple program that I will show them tomorrow: 

http://jgplay.pencilcode.net/home/scaleCompTurtles

For today, I was thinking about scaling drawings as a way to make this concept more physical.  I found a simple rabbit line drawing on the web and (using pencilcode again) made a little template for scaling up the picture: http://jgplay.pencilcode.net/home/gridDrawings. Jate mostly got the point, but I am planning to reinforce with several more simple figures:

Repeated Addition

I have started going through the Mathematics Mastery module introducing multiplication.  The initial idea is to put together equal groups and practice telling number stories about them of the form: "3 blocks +3 blocks is equal to 6 blocks" and "2 groups of three blocks is 6 blocks" and "2 threes is 6."

We often do this type of thing with blocks, toy cars, grapes, pretzels, balls, tiles, little books, or anything else we have on hand.  Tonight, we started rather late, so I just drew a couple of pictures for us to discuss.  The page got thrown away before I could preserve it, but this was the sequence I followed:

(a) draw 2 sets of 3 circles each and verbally discussed 2 groups of 3 is 6 and 3 plus 3 is 6.  Then, Jin wrote the equation 2 x 3 = 6 and I wrote down "3+3 ="  He drew an arrow to show that all three expressions are equal.

(b) draw 2 sets of 5 triangles, with each set inside a large circle and then an empty circle.  Ask Jin if he could complete the drawing of 3 sets of 5 triangles, which he did, then discuss how that could be represented in an equation.

(c) I drew 4 daisies, each with 5 petals and two leaves on the stems. I asked what number stories could be told about this picture, to which he wrote down 1x 4 = 4 and I filled in to complete "1 group of 4 flowers is equal to 4 flowers."  Then I asked how many petals were on each flower, Jate said 5 and then Jin wrote down 4 x 5 = 20.

(d) Naga picture.  I happened to have this picture on my phone from a recent visit to Chula University:

Though I showed it to the boys for non-mathematical reasons, of course one of the first observations was about how many heads the snake has.  Fitting in with the mathematical theme of the evening, I was pleased to show them this one next:

So we all got to enjoy "2 groups of seven heads is 14 heads."

Unfortunately, I left the table at that point and a fight broke out over who had possession of our multiplication tables place mat:

School theme ideas

What are some things that would be good themes for an elementary school semester?
Here are some ideas with brief explanations of related activities and sub-themes.

1. Myths/folklore
Study a collection of mythical stories from around the world. Related activities could involve:

• learning about the place where (geography) and time when (history) each story originated.
• For many, they will be attempted explanations for natural phenomena so we can compare against the modern understanding.
• writing our own mythical stories in parallel with modern scientific explanations for the phenomenon they attempt to explain
• Crafts illustrating the stories or location from which they originated
• Perform some of the myths
• Underlying this would be a lot of language activities around reading, performing, discussing, and comparing the stories.

Possible subthemes: stories from a particular place (especially Thailand), ancient stories

2. World religions
Introduction to the major global faiths

• learning about the place where (geography) and time when (history) originated.
• What are their major stories?
• What are their major messages with respect to morality?
• How are they similar? How are they different
• how have the interacted with each other: conflict/exchanges of ideas/absorbption
• do they change over time and how?

3. Brain and learning
4. Linguistics
5. Investments: overall project to build an investment portfolio and see how it performs
6. The financial system
7. Making instruments (scientific or musical)

Falkirk

Bedtime Math tonight introduced us to the Falkirk Wheel:

In retrospect, what I should have done was to find this video, play it for the kids and see what questions they asked (similar to this site: http://www.101qs.com/) Fortunately, I've made that error, so you don't have to!

If you want to hear a number of statistics about the wheel and add ambiance with a touch of the local accent, watch this:

Computer programming intro (5th grade)

This is an outline of a once-a-week introduction to computer programming for Jin's school.

Goal of the course:

1. Encourage the kids interest and curiosity about programming
2. Learn the basic concepts of programming using Pencilcode (see below)
3. Play with the fundamentals of coordinate geometry
4. Practice using precise language, working in pairs
5. Have fun!

Basic concepts of pencilcode

• Background manipulations: create, test, launch, share a program
• Turtle movement commands (fd, bk, lt, rt)
• Drawing commands (pen, dot)
• Loops and iteration (for)
• Input and output
• Functions and recursion
• Debugging

Structure of typical session

1. Students get started with a "Fix this program" challenge or sharing code they found from other pencilcode users (5 -10 minutes) 
2. Gather in a group, Teacher introduces an example program (usually short, sometimes very short)
3. Split into pairs and examine the example (5-10 minutes, depending on complexity of the example)
4. Regroup and discuss: what did we see? what was old that we already know, what was new? what questions do we have? what could we do with the new tool/technique? (10 minutes)
5. Split again and work on challenge task using the new concept (10-30 minutes)
6. Regroup, show and share: what have we done, how many different ways were there to meet the challenge, what else could we have done? (10 minutes)
7. Open experimentation/investigation/exploration (teacher will have some go-to activities)

Homework/Course Project

Ideally, it would be great if each student could write a substantial program of their own.  To use this as homework would require customizing for each student based on what they are trying to develop, but there are some modules that will probably be standard:

1. Select topic and write a description of what you want it to do
2. Design and draw the figures/pieces in the program
3. Define their movement
4. Define their interaction
5. Animate
6. Debug

For the first week, at least, the homework will also include looking for interesting examples from other pencilcode users and bringing those to share with the other students.

Course outline

My intention is to follow the examples in this pencilcode introduction book. I don't know the right pace for the kids, so we can customize as we go along.