Predestination stories (reading lessons)

who: J1 (guest appearances by J2 and J3)
when: early afternoon
where: in the dining room
what material did we use: pack of sight words, Usborne book of Fairy Tales, Jeffrey Archer collection of short stories.

---

We have started to be more consistent about the literacy activities we are doing with the kids.

Warm-ups

We have found very quick warm-up activities worked really well in the math classes we teach at school, so we thought we'd do the same for our literacy sessions. We are still in the process of collecting appropriately short and fun activities, but here is a short list of things we've done so far:

• Sight word sentences: using a pack of sight words, draw 2 and then form a sentence with them. The sillier, the better!
• Sight word story: take 6 or 8 sight words and form a short story with them. 
• Crazy Sentences: reading the strange sentences that come out of this program which was inspired by a game from Peggy Kaye (whose site looks like a good source for other qiuck games).
• Talk about a picture: this is a direct translation of one of our math warm-up activities

Intro to predestination (aka Sleeping Beauty)

For the main event, J1 read (or re-read) the first story in our fairy tale book. As he was reading, I wrote out a couple of questions for us to discuss:

1. What is the location of the story?
2. Who are the main characters (2-4)?
3. What is the conflict in the story?

Of course, these are generic questions we can discuss for almost every story he reads. There were several highlights in our discussion.

What happens with the mean fairy?
In our version, the mean fairy only shows up once, explicitly, in the story, to curse Rose. It is implied in the pictures, that she shows up later to introduce the fated spinning wheel. J1 was strongly drawn to this interpretation based on his own narrative sense of closure and connection. We were a little disappointed that she didn't figure in the ending sequence, but more on that later . . .

Why was Florien successful in rescuing Rose?
Prior to his attempt, several other chaps made an effort and were unsuccessful. J1 said that the reason he was successful seemed to have something to do with Rose drawing Florien's picture earlier in the story and Florien dreaming of Rose. Of course, we don't know how many pictures of princes Rose actually drew, how exact the likeness was to Florien, nor whether the unsuccessful princes had dreamed of Rose or not.

We talked about other stories and came up with these suggestions:

• Maybe Rose and Florien were partners in a prior life (an idea J1 got from the Thai Ramakien)
• Maybe Florien did something nice for the mean fairy and she granted him the ability to rescue Rose. J1's favorite version: The mean fairy turned into a squirrel to run through the forest. She accidentally got caught in a hunter's trap. Florein found her and bandaged her wounds.
• Maybe Florien defeated the mean fairy in battle and won the power to rescue Rose. This version was accompanied by some wild jumping around in a simulated sword (Florien) vs lighting blast (mean fairy) battle.

Predestination vs Free Will
I told J1 about two competing theories: predestination and free will and then we went back to the story to see whether/how each theory was represented. There was a very clear winner, with predestination getting all the points:

• Rose's story told in advance by the curse/blessings of the fairies.
• Rose predicts Florien saving her by her drawing
• Florien predicts saving Rose by his dream
• The other princes fail to save her "just because" (because they weren't fated to do so)
• The king acts to prevent the foretold curse by destroying spinning wheels in the land, but the fate is inescapable

The last point flagged up a classic element of predestination stories: even if the characters take action to change their fate, the results still end up the same. Often, the action taken to prevent the fate is somehow critical in causing it to happen.

Appointment with Death
By chance, I had just read this short story in a Jeffrey Archer anthology. I got it out and we read it together, then talked more about predestination vs free will.

Some other tidbits from the chat:
- who is Death? Why do people anthropomorphize death like this?
- why does the story seem to suddenly shift to first person, form Death's perspective? Is the story more or less clear written this way?

Daily Journal

J1 and J2 both have small notebooks for writing a daily journal. They usually write something about what happened that day, but are free to write whatever they want. Sometimes, it becomes a short story or even a never-ending story.
We talk about what they wrote and then make a vocabulary list related to their note. Usually, it is formed from words they mis-spelled, but the vocabulary words could be things they spelled correctly that highlight interesting patterns or a word they didn't use that is related to the topic.

What about the little one?

For J3, we have been working on phonics and letter recognition. Each evening, we have a focus letter or sound that we ask her to find as we read bedtime stories together. Also, we have been singing phonics songs, particularly ones from this collection: Jolly phonics

3 little number devils

Who: J1, J2, and J3, mostly engaged on separate activities (J0 and P supporting roles). Note: All activities were done together, so there is cross-talk and listening, even if I only talk about one major protagonist in each activity.
When: throughout the day (no school, so all are at home the whole day)
Where: mainly in our reception room

---

School is out and new year festivities are all around us. Lest you think we have been (mathematically) idle, here are some notes of how we've been keeping busy recently.

J3's 3rd counting challenge

We have a little duck sorting game, given to us years ago a by a cousin. Put the ducks on the blue escher-stream and then take turns trying to collect all of  your tribe with common belly markings.

How many ducks are there? How do you count them when they are "swimming" on their stream?

For J3, this is quite a challenge to count all the ducks when they are in motion. She is still at the stage of counting individual objects (in contrast to recognizing clusters) and then she isn't able to keep track of which have already been counted.

Since there are a nice number of ducks, we take turns grouping them in various different ways and talking about the shapes on their bellies.

Arranging and Folding

You may have noticed I created a new page of Upcoming Activities. This is where I keep notes for things I want to remember to do with the kids. True to the promise of that page, J2 and I looked at regular polyhedra and folding. These were inspired by these posts: 3d-2d and Nets&Decorations.

Tetrahedra
Starting simple is always good.  So what arrangements of 4 equilateral triangles are there? Which of these fold to a tetrahedron?

J2 found three ways to arrange 4 equilateral triangles into a contiguous polygon. Two, on the right, fold into tetrahedra while the one on the left doesn't (but is useful for making a square pyramid).

I asked him how we could tell that the three arrangements were really different. Of course, this is a strange question because we can clearly see that they aren't the same, but I persisted and asked how we can be sure that no rotation, translation, or flip will get them to be the same. We talked about this for a while and eventually came up with two ideas:

1. For each triangle in our arrangement, how many other triangles connect to it? For the triangle, we have 1-1-1-3 while the other two have 1-1-2-2. This let us distinguish the triangular arrangement, at least.
2. How many sides does our polygon have? The three arrangements have 3, 4, and 6 sides, respectively. This was strong enough to distinguish all of them.

In the course of discussing how many sides, someone said that one arrangement had 13 sides. I asked them to figure out why that couldn't possibly be correct (4 triangles have 12 sides when they are separate, putting them together can only reduce the number of sides).

Hexominoes/Cubes
Ok, done with tetrahedra, we moved on to cubes. What arrangements of 6 squares fold to a cube? Which don't?

We identified the longest line of squares in our arrangement as an interesting characteristic to classify and called it the "spine." We had 6-spines (just one), 5-spines, 4-spines, 3-spines, and 2-spines. For example, the picture below shows a 2-spine that does fold into a cube

It was fun seeing when J2 would realize that an arrangement did or didn't make a cube and hear his reaction. We talked a bit about how we would know whether we had tested all of the arrangements, but I won't claim we were comprehensive in this exploration. He did develop one hypothesis about 4-spines:

If both "tentacles" of a 4-spine are on opposite sides of the spine, it can fold into a cube. If they are on the same side, it cannot.

Pictures below are our cubable hexominoes and the ones that just don't work out:

At the end, I tried to rearrange things and start talking about pentominoes, but this exploration was already as long enough and he was ready to move on to something else.

How fast do Fibonacci numbers grow?

Both J1 and J2 have recently been introduced to Fibonacci numbers, powers of 2, squares, and cubes. Writing down the Fibonacci sequence, J1 said: "these are growing really fast!" I asked J1 and J2: "do they grow faster than squares?"

This led to a discussion about what my question meant. J2 pointed out that, at the beginning, the squares are growing faster. Very detail oriented he pointed to the first two Fibonacci terms (1, 1) and said "they aren't even growing at all." J1 pointed farther down the sequence and said it looked like they were much larger at some point.

Here, J2 went off to do something else while J1 and I continued talking about the sequences relative to each other. I built a simple spreadsheet and then asked what we should do to compare. Some discussion later, we decided to add the ratio of the sequences and the difference. Through both measures, we saw that, indeed, the Fibonacci sequence becomes much larger than the squares. One little observation he really liked was seeing that the twelfth Fibonacci number (144) is also the 12th square, so the sequences are equal at that point.

J1 then suggested other sequences we could compare: multiples of 100, powers of 2, powers of 3, powers of 10. We did a little to play around with powers of bases between 1 and 2, but we didn't quite get to reveal the magic of the golden ratio.  At least not this time . . .

Number Devil

J1 and I, with occasional visits from J2, have been reading The Number Devil together just before he goes to sleep. Frankly, this was a book toward which I was only lukewarm. Mainly, I wasn't sure about how our kids would take the introduction about nightmares, the relationship between the number devil and Robert, and the negative comments about the math class and math teacher. As it turns out, all of these things are fine, either not taken too seriously or accepted as proof that Robert is a bona fide little boy.

On that last point, J1 was much more attuned to the fact that Robert is supposed to be 12 years old. When we got to a point in the story where the Number Devil asks Robert when he was born (answer: 1986), J1 immediately spotted something was wrong. He didn't know right away how old Robert was, but he had a sense, perhaps from knowing roughly when the 5th graders in his school were born? We spent a bit of time calculating how old Robert would really be in 2014 and then talked about what happened with his age in the story.

Otherwise, I'm finding that most of the math in the book is at just the right level. Mostly, we are reading about things that J1 and J2 have already encountered and they enjoy seeing a slightly different spin on these topics (including silly names for them). We do most of the calculations along with the characters and generally have a grand time.

Taking Mr. Men too seriously

Who: J2 and guest appearance from G1 (grandpa)
Where: in bed
When; at bedtime

---

There are a bunch of ways to take the Mr. Men too seriously, and I'm not even talking about this.

Reading out loud
We recently got the full set of Mr Men and Little Miss books.  J2 has especially enjoyed reading them and has his own routines for extracting the books that will be read each night, then collecting the books at the end and flipping the first book for the next night upside in the box.

He really seems to enjoy these books, whether we are reading to him, he is reading to us, or he is reading to his sister.

As he was reading to us tonight (Mr Impossible!) I was wondering about how to be a good listener when the Js are reading. A quick scan of literacy sites suggests that it is both easier to get this right and easier to mess it up than I had thought.

Mainly, I think you need to have the right attitude and, like so much of parenting, the answer here is to be playful and focus on enjoyment.  Choose books, talk about them, help with the reading, let the kids struggle, but all to a degree that it is fun for you and them.

More specifically, the 5 finger test: as the child is reading, have them hold up one finger whenever they encounter a word they don't know/can't read. If you have a full hand up, then the book is too hard for them.

Two nice references, I found are Trevor Cairney's Blog and a New South Wales schools brochure, if you want to pursue this further.

Estimation
When I started writing this post, it was only a reading note, but you know that I'm bound to see a math activity, exploration, or discussion in anything. There were a bunch of counting opportunities in Mr Strong, then we hit this picture:

So, what is the mass of the water in the barn carried by Mr Strong? We had to investigate.
To be honest, I was more interested than the little one who was absorbed in the story, so I'll leave you to come to your own conclusions about how much water there was.

Further exploration: how much pressure does Mr Strong exert on the ground when he walks?
Further further exploration: what happens to soil under that much pressure?

Attitudes

Ok, so further, further explorations about the Mr Men books:

- Is Mr Men vs Little Miss sexist?
- Does the whole series reinforce a fixed mindset?

Munchkin(s)

who: J1 (and occasionally J2)
when: many times this weekend, whenever we have some free time
where: wherever it is safe from J3's disruption
what: another game

---

Your friend is level six, armed with a grand collection of magic items (bonuses shown below) and has just started fighting the Stoned Golem. You could add a wandering Squidzilla to the battle and are trying to decide whether you need to add extra intelligence (+5 for the monsters' side).  Time to do some calculating . . .

We just started playing Munchkin together and J1 really loves it.  As you can see from the cards, it is a bit silly, fairly fast to play, and strategically simple. Also, unsurprisingly, the build-as-you-play characters really appeal to J1's 7 year old sense of gaming and achievement. I say "unsurprising" as this was part of the idea for the game, though in that context it was formulated as a parody take on the unsophisticated attitude of some players in role-playing games.

What do they learn?
First, many of the rules of the game are written on the cards themselves.  Look at the picture.  That wizard card is full of text explaining the strengths (most of them) and weaknesses (some of them) of being a wizard. J1 is at the level that he can read all the cards, but it takes some effort and is good practice for him.

Second, the basic game mechanic is really about repeated addition.  Every battle consists of simply comparing your combat strength to your opponents combat strength.  That means you start with a base level and add a collection of bonus or penalty modifiers.  As a result, most of the additions are +1, +2, +3, but powerful characters (like above) inspire a search for more efficient strategies than just adding every card individually.  That means grouping, skip counting, and multiplying.

In addition, there are opportunities to add wandering monsters to a battle and to double a monster, or fighting character. For a final extra set of calculations, the players can sell their treasure (value noted on the bottom of each card) for levels that determine the game winner.

On a more sophisticated level, they start to detect (more subtle) patterns.  For example, what are the weaknesses to playing as an elf?  They aren't listed on the elf cards, but you recognize them over time when you see that many of the monsters get an automatic bonus when they fight an elf.  Similarly, the listed benefits of playing as a dwarf seem minor, but then there are some powerful magical weapons and armour that are only available for dwarves.

Is it fun, as a game?
Yes, but . . .
One key element of the game is backstabbing your friends (the other players). Sometimes you help them, sometimes you harass them, sometimes you do both at the same time! However, like we experienced with Settlers of Catan, this type of game isn't for J2 (yet?) He was turned off the first time he thought he was going to defeat a monster and then J1 added an extra monster to the battle.

For more sophisticated players, there is probably a sweet spot for maximum enjoyment.  People who have some experience with D&D will enjoy the little puns and jokes more.  However, the game play is really simple, randomness is high and strategic choices are limited.

If you are in Bangkok, you are welcome to come play a round with us!

Currency conversion and 1001 nights

who: J1 (and a bit of J2)
where: bedroom
when: bedtime (particularly after lights out)
what materials: internet connection (not really necessary)

This is another Talking Math With Your Kids -style conversation.

• J1: Daddy, what's 100 pounds (British pounds) in Baht (Thai currency)?

some discussion about which way he wanted to convert as I hadn't really been listening

• D: Well, there are about 50 baht per pound.
• J1: So, I need 50 groups of .  . .can you use the computer to calculate it?
• D: Yes, I can, but we don't need to.  First, though, we need to figure out what calculation to do. You said you have 100 pounds and there are about 50 baht per pound

some mumbling, not really getting anywhere; I'm tempted to comment and guide, but hold back.

• J1: I have 100 groups of 50.  What's that?
• D: What about 10 pounds in baht?
• J1: (pause) that's 500
• D: how did you calculate that?

I was assuming some strategy for directly calculating 10 x 50, either just adding a zero or building from 10 x 5 (which he would calculate as 10-20-30-40-50), or 50-100-150-200-250-300-350-400-450-500.

• J1: well, I know 20 pounds is 1000 baht.  Then 10 is half of 20 and 500 is half of 1000.
• D: Interesting.  How many 20s are in 100?
• J1: (thinking) 5000 baht in 1000 pounds!

some conversation about what  you can buy with 5000 baht.

• D: what about 15,000 baht.  How many 5,000s are in 15,000?
• J1: 3, so 300 pounds.  Wow, that's a lot

Why did I find this so interesting?
First, I was really surprised by the strategy to calculate 10 x 50.  This reinforces the magical phrase "how did you think of that?" Sometimes my own preferred approach seems so obvious that I feel there won't be anything interesting gained by hearing the child's approach and, in this case, asking the question was just because I wanted to build a good habit.  I was so surprised by the answer that I forgot to tell him about an alternative strategy.

Second, there had been several other times earlier in the day when I tried to lead him into a mathematical conversation and he wasn't taking the bait. I guess I should relax and see where chances arise instead of controlling it.

Ok, but 1001 Arabian Nights?
We've started reading the Project Gutenberg version of 1001 nights. Nice mathematical title, no? Well, tonight we started The Story of the Husband and the Parrot. What you need to know is:

I am reading the story of Sheherezade to J1 and J2.  In this story . . .
. . . Sheherezade is telling King Shahriar The story of the Fisherman, in which . . .
. . .the fisherman is telling a genie The Story of the Greek King and the Physician Douban, in which . . .
. . .the King tells his Vizir about a story told by another vizir to King Sinbad, in which . . .
. . . we get The story of the Husband and the Parrot (which involves the Parrot telling the Husband a short story).

Counted generously, that's 6 stories-within-a-story.  And now I've told you, so that's 7 layers.