Cooperative Chess

It’s hard to play chess when you have a toddler who wants to get his hands on everything. Luke and Noah (our latest foster child) wanted to play together the other night. I managed to help them get the board set up but then I had to take Nathan into another room to keep him from grabbing all the pieces. In my absence, the game quickly devolved into cries of “You can’t move it like that; you’re wrong.” and “I just want to play the game and he’s not letting me!”

I realized that while Luke knows the rules of chess, he’s a little short on the diplomacy required to teach them. It doesn’t help that Noah gets very upset if he loses or is otherwise thwarted from his goals.

As I brushed my teeth the next morning, I pondered the problem and had an idea: what if I put the kids on the same team and had them play cooperative chess? Instead of pitting them against each other so that one of them is doomed to lose, I could be the opponent and give them enough of an advantage that they would be able to beat me reliably. The two of them would get the satisfaction of winning and I would get the satisfaction of a peaceful bedtime game.

I tried it out and it’s been working pretty well!

How to Play Cooperative Chess

Give each child a piece of the same color to control and take the opposing king for yourself. Rooks are good to start with. In later games they can graduate to two pieces, but keep it simple to start out.

Place each piece in its standard starting position. The kids take turns moving their pieces according to the regular rules of chess. Instead of taking turns in a circle (kid-kid-grownup), the grownup gets a move after each kid move (kid-grownup-kid-grownup). For the very simple game with just three pieces, the grownup wins by capturing one of the kid pieces and the kids win by capturing the grownup’s king.

(I think the concept of checkmate is a little abstract to start out with at this age. It’s hard to for them to pursue a goal if they can’t visualize it. Physically capturing the king is concrete and easy to understand.)

Our Initial Experiences

We played a couple of these basic rounds and it’s been great so far! I like how Noah gets to focus on learning one new piece at a time. It really cuts down on his frustration when he doesn’t have a constant sense of failure. He still makes the occasional illegal move but I can give him a gentle reminder and have him try again without too much drama. I also give him a warning if he moves a piece into danger so he can take a do-over if he wants to.

I think Nathan is old enough to learn basic board game etiquette (i.e. don’t knock down the chess pieces), but he can only learn to follow these rules if I give him the opportunity. Instead of limiting our games to times when he’s asleep, I’ve been letting him hang out at the table with us. There are plenty of extra pieces for him to play with and when he does take a swipe at the board, it’s easy to recover since we only have a handful of pieces in play.

Since then I’ve learned that it’s important not to let them talk me into adding too many pieces to the board and I shouldn’t let Noah join my team β€” at least not right before bedtime when he doesn’t have a chance to play again if he loses. The sweet spot for us right now is two pieces per kid plus a king for them to defend.

Though maybe next time I will see how it goes if they each get four pawns…

Exploding Dots Machine (Binary for Preschoolers)

I am a big fan of non-screen ways to teach computing concepts to little kids so I was excited to see this #tmwyk tweet from Peter Rowlett:

It seemed like the perfect introduction to binary for my four-year-old, especially as he’s been very interested in the concept of machines lately.

I googled Exploding Dots Machine and found the official website. Luke was still asleep so I watched the intro video by myself.

I tried out some of the interactive stations on the website and considered doing them with Luke but decided to stick with non-digital. I dug up a dry erase marker and surface to make it easier to erase.

Once Luke woke up, I drew the grid and explained that this is a 1←2 machine. If two dots are in the same box, they explode and a new dot appears in the box to the left.

He caught on to the exploding part right away. It took him a little while to figure out the code: how we write a 1 for a box with a dot and a zero for an empty box. But by the time we got up to 13 or 14 he was solid with working out the code so I persuaded him to take a turn with the marker. (He had taken over the eraser very early on.)

He did not want to skip any numbers so I haven’t shown him how to put multiple dots in the first box and resolve multiple explosions. We just kept adding one to the previous number. I’m thinking I’ll introduce adding multiple dots in a second session, later today or tomorrow.

After that we can look at addition and subtraction! I want to explore some more to see how far they take this.

This makes me wonder how we can put these binary codes to use. Maybe we could use different colored Duplos to encode a number. Oh yeah! We can play Guess my Secret Number with binary code patterns!

I bet he’s ready for other codes too, like A=1, B=2, etc. This’ll be fun. I’m very excited.

Exploring Sets with Knobbed Cylinders

I had our little set of Knobbed Cylinders near my desk and it caught my eye when I was looking for something to give to Luke so he’d let me get some work done.

I don’t recommend buying the mini Montessori knock-off cylinders, by the way. We have not gotten much use out of them. I hear the full-size ones (with ten pieces per row instead of five) are better but they’re also so expensive that I’m not sure they’re worth it for home use.

Luke has long outgrown our mini cylinder set. Nathan’s starting to be a good age but I can’t let him play with it unsupervised because it is full of choking hazards. I had it stashed on my desk and when Luke was pestering me about something, I passed it to him to give him something to do.

Then I remembered the post about sets I had read the other day on the Fairy Math Mother. (Isn’t that a wonderful name for a blog?) Kelly writes about sorting objects into sets based on different attributes.

I’ve also been seeing “which one does not belong” prompts on Twitter. These are designed so that one can make an argument for each object being different from all the others, so the fun is seeing how different people think. Is it the top right because it has no peel or the bottom left because it’s only half of a Cutie? (And who cuts a Cutie anyway?)

So first with Luke, I made little sets of three cylinders and asked him what was the same and what was different about them. Some were all the same height but with different widths and some had the same width but different heights.

He was using “bigger, medium-er and littler” to describe both how tall and how wide. This was a good opportunity for me to introduce vocabulary like height and width.

Then I made a few sets where there was an odd one out and we talked about how that one was different and did not belong in the set.

At the end we sorted all the pieces into sets based on how tall they were. I pointed out one set that was different from all the others, because it had pieces that were the same height and width.

I asked Luke if he noticed any other sets that were different from all the others. He pointed out the set that had a lot of pieces in it. The set with eight tall pieces was different because all the other sets only had three pieces.

Pickle and the Boolean Logic Baby Gate

Pickle liked to play in the playroom. He liked to build with blocks and drive trains and make race cars out of Duplos.

Baby Pickle liked to play with blocks and trains and Duplos too, but Pickle did not like it when Baby Pickle would knock down his buildings and break apart his train tracks and put extra Duplos on his Duplo race car where they did not belong.

“I will get a gate,” said Pickle, “to keep Baby Pickle out when I want him to stay out and only let him come in when I want him to come in.

Pickle went to the hardware store and bought a gate with a custom filter function. He took it home and set it up in the door of the playroom. He put in a filter function that said, “If x equals Pickle then x can go through.”

When Pickle went up to the gate, the gate put Pickle into the function as x and thought, “If Pickle equals Pickle, then Pickle can go through. Pickle does equal Pickle so Pickle can go through.” So the gate let Pickle go into the playroom.

Pickle started to build a big castle out of blocks. Then Baby Pickle came over to the gate to see what Pickle was doing. The gate put Baby Pickle into the filter function as x and thought, “If Baby Pickle equals Pickle, then Baby Pickle can go through. But Baby Pickle is not equal to Pickle so Baby Pickle cannot go through.” The gate did not let Baby Pickle go into the playroom so Baby Pickle was sad. He wanted to play with Pickle but he just had to watch from the outside.

Then three bunnies came into Pickle’s house. “Ooh, bunnies!” Pickle thought. “I want to play with those bunnies so I will change the filter function to let them come through.” Pickle added a condition to the filter function so it said, “If x equals Pickle or x equals a bunny then x can go through.”

As soon as a bunny came over to the gate, the gate put the bunny in as x and thought, “If a bunny equals Pickle or a bunny equals a bunny, then the bunny can go through. A bunny does not equal Pickle but a bunny does equal a bunny, so the bunny can go through.”

The bunny hopped over to Pickle’s castle and went inside. The bunny was very careful not to knock over any of the blocks. Pickle was happy to see a bunny inside his castle. He started to build a wall around the castle. The bunny jumped over the wall and did not knock it down.

Then Pickle heard the doorbell ring. “Who’s there?” he asked.

“It’s Blaze,” said Blaze.

“Come in, Blaze,” said Pickle. “Come look at my castle.”

Blaze came over to the gate and the gate put him in as x in the filter function: “If Blaze equals Pickle or Blaze equals a bunny, then Blaze can come through.” Blaze did not equal Pickle and Blaze did not equal a bunny so the gate did not let him come through.

“I can’t get in,” said Blaze.

“Oh,” said Pickle, “I will have to update the function.” Pickle changed the function so it said, “If x equals Pickle or x equals a bunny or x equals another monster truck then x can come through.”

Now Blaze could come through the gate because he was a monster truck. He and Pickle started to build a train track. They put all the track pieces together into one long train track. When they were done, they built some Duplo race cars so they could have a race between the train and the race cars.

Baby Pickle watched them through the gate. He did not want to be outside by himself. He wanted to come in and play. Baby Pickle tried again to go through the gate and the gate put him into the filter function as x: “If Baby Pickle equals Pickle or Baby Pickle equals a bunny or Baby Pickle equals another monster truck, then Baby Pickle can come through.” Well Baby Pickle did not equal Pickle or a bunny but he did equal another monster truck. The gate let him come through into the playroom.

Baby Pickle saw a big red Duplo so he picked it up and tried to stick it on the back of Pickle’s race car.

“No, Baby Pickle!” cried Pickle. “That’s not where that piece belongs.”

Then Baby Pickle picked up one end of the long train track and shook it around. Pieces flew off the end and Baby Pickle laughed.

“No, no, no!” cried Blaze. “Don’t take apart our train track, Baby Pickle.”

Then Baby Pickle went over to the castle and tried to go inside but he was too big to fit in there. He knocked down the blocks that were holding up the roof and the whole castle fell down.

“No, no, no, Baby Pickle!” cried Pickle. “Don’t knock over my castle. Help me put it back together.”

Baby Pickle brought a block and gave it to Pickle and they put the castle back together.

And that’s the story of Pickle and the Boolean Logic Baby Gate.


Avoiding Deadlock with Creative Problem-Solving

Luke has been building some elaborate train layouts lately. Earlier today, I remarked that he and Nathan have been able to play with (or at least near) each other surprisingly well. It used to be that as soon as Luke put together a train track of any significant length, Nathan would come over and shake it all apart.

Now Nathan is old enough that he also likes to put train tracks together and push trains around. The only problem is that sometimes he plops himself down right in the middle of where Luke’s trying to build, and he brings his own ideas of where the tracks should go. Also, sometimes Nathan just wants to roll around on the floor where the tracks are, nuzzle his head under Luke’s arm while Luke is reaching for a piece, and generally make a nuisance of himself.

(I didn’t get a picture of Nathan with the trains tonight so here’s a picture of him helping himself to Luke’s stash of carefully-unwrapped Hershey’s kisses.)

Luke is understandably frustrated when Nathan interferes like this but his attempts to guard his train track tonight were going too far. Luke was pushing Nathan hard enough to topple him over backwards, in addition to yelling at him and sometimes kicking at his legs when they got in his way.

My first response was to tell Luke that it wasn’t working for him to play with train tracks right now and that he’d have to find something else to play with.

This did not go so well for me because Luke was very resistant to stopping with the trains. I could see that if I continued escalating, I’d have to spend the rest of the evening enforcing time-outs and I wouldn’t be able to get any work done.

I tried to think of a different approach and remembered the problem-solving steps from How to Talk so Kids Will Listen. I hadn’t used this technique in awhile but it seemed like a good fit for the situation. We all wanted Luke to be able to play with trains but we needed a peaceful solution to the problem of Nathan’s interference that would also allow me to get my work done.

I started by bringing Luke downstairs, out of sight of the train tracks. I locked the door behind us so he would realize it was futile to try to squirm away from me. He was not getting those trains back until I was ready! That helped him calm down and pay attention to what I was trying to tell him.

I told him that I understood that he had a problem with Nathan messing with his train tracks but that he was not being safe by pushing Nathan so roughly. I told him we were going to write down a big list of ideas for how to solve the problem and he came over to the table to watch me write. Nathan sat on my lap to help decorate the page.

I started by writing down the problem:
Nathan is Messing Up Luke’s Train Tracks

As the first idea I put the solution Luke had been using:
1. Luke is pushing, kicking and yelling no at Nathan.

Then I put down one of my own ideas:
2. Luke could build a train track in the boundary.

When Luke voiced objections I reminded him that first we were going to write down as many ideas as we could think of and then afterward we would talk about whether or not we liked them.

He didn’t want to contribute any ideas at first so I wrote a few more of my own:
3. Luke could build a train track in the playroom.
4. Luke could pause with the train track and un-pause when Nathan goes to bed.

Then Luke had an idea:
5. Luke could stop Nathan by telling Mommy to stop him.

I put a few more of my own:
6. Luke could give Nathan a train piece and show him where to put it.
7. Luke could play with Legos in the boundary.

Finally Luke wanted to tell me another idea but he couldn’t think of anything. I reminded him of an idea he’d suggested earlier, when I was telling him he couldn’t play with trains anymore:
8. Luke could stop Nathan by putting the gate at the top of the stairs.

After we’d both run out of ideas, we switched to talking through the ideas we’d already written down to see if there were any that we both liked. I put smiley and frowny faces to record our feelings about each idea.

Luke shot down all of my ideas and I wrote down his concerns: the boundary is too small, the playroom has too many toys and even if I helped him clean them up, he wouldn’t remember how to rebuild his train track after moving it downstairs.

The only ideas Luke approved of were his own so we discussed my concerns: How would I get my work done if I had to stop Nathan every time he got in Luke’s way? Wouldn’t Nathan be sad if we put up a gate to stop him from coming upstairs where all the rest of us were? I told Luke that I was willing to give the gate idea a try but if Nathan cried, we’d have to pick something else from the list to do instead.

This gave Luke another idea: he could build Nathan a train track in the kitchen so he would not be sad about being stuck downstairs. Luke made a plan (“I’ll make a highway that goes up on one side and down on one side”) and then went off to collect the pieces he needed.

It was very sweet to see Luke building a train track for his little brother, but we never did get to test the gate idea. While Luke was still building his highway, Nathan got sleepy and I put him to bed.

(We’ll have to show this to Nathan tomorrow.)

With Nathan asleep, Luke had plenty of time to work on his own layout upstairs with no more little brother interruptions! I think the track he built might be bigger than anything he’s made before.

I was very happy with Luke’s willingness to work with me on a solution and I hope to do more collaborative problem-solving with him in the future!

Laundry Flowchart

  1. Is the dryer running?
    • Yes: Go to step 3
    • No: Is there damp laundry in the dryer?
      • Yes: Run it for another hour (or however much it needs) and go to step 3
      • No: Empty the dryer into a laundry basket and go to step 2
  2. Is there wet laundry in a laundry basket?
    • Yes: Is there a lot of wet laundry?
      • Yes: Run a dryer load prioritizing littles and go to step 3
      • No: Go to step 3
  3. Is the washer running?
    • Yes: Go to step 5
    • No: Is the water switched on?
      • Yes: Switch it off and run the washer on spin (09)
      • No: Is there laundry inside
        • Yes: Is the laundry inside still kind of wet?
          • Yes: Make sure the switch is all the way back and run the washer on spin (09)
          • No: Put the wet laundry in a laundry basket and go to step 4
        • No: Go to step 4
  4. Is there dirty laundry on the kitchen floor?
    • Yes: Is Claudiu running low on clean laundry?
      • Yes: Run a washer load prioritizing bigs and go to step 5
      • No: Are there lots and lots of littles?
        • Yes: Run a washer load prioritizing littles and go to step 5
        • No: Is the dryer running?Β 
          • Yes: Run a washer load prioritizing littles and go to step 5
          • No: Run a washer load prioritizing bigs and go to step 5
    • No: Is there dirty laundry in the bedroom?
      • Yes: Bring it to the kitchen and run a washer load and go to step 5
      • No: Is there dirty laundry anywhere in the house? (buddy clothing on the floor, wipes in the diaper pail, kitchen towel, bath mat, shower curtain)
        • Yes: Is there enough for a washer load?
          • Yes: Run a washer load and go to step 5
          • No: Go to step 5
        • No: Go to step 5
  5. Is there laundry on the porch?
    • Yes: Is it dry?
      • Yes: Take it down and go to step 6
      • No: Is it just a little bit damp?
        • Yes: Is there a laundry backlog?
          • Yes: Take down the damp laundry and put it in the kitchen to go through a short dryer cycle and go to step 6
          • No: Go to step 7
        • No: Go to step 7
      • No: Go to step 7
  6. Are there any laundry baskets with wet laundry?
    • Yes: Hang up laundry on the porch and go to step 7
    • No: Go to step 7
  7. Are there any laundry baskets with clean dry laundry?
    • Yes: Put it all away and go to step 1
    • No: Congratulations! You are caught up on laundry.

Musical Math: Baa Baa Black Sheep

I had a recent realization about Baa Baa Black Sheep: you can fill in any numbers you want!

Baa, baa, black sheep, have you any wool?
Yes sir, yes sir, ten bags full.
Two for the master, three for the dame,
And five for the little boy who lives down the lane,
Baa, baa, black sheep, have you any wool?
Yes sir, yes sir, ten bags full.

Sometimes I add three more to the total for each verse, to keep things evenly distributed. Twelve bags full means four for everybody! Sometimes we just go up by one bag at a time.

Sometimes I keep some left over and use the last line for the remainder. If I start with eight bags full and distribute six of them, the sheep ends up with two bags full.

Sometimes I give out none to the master and none the dame, so the little boy gets everything. Luke likes it when the little boy gets the most.

He’ll often supply me with a number for the next verse: “Now do one hundred!” Fortunately he hasn’t thought to request googolplex yet.

The driving force behind all this mathematical creativity is Nathan. As soon as I finish singing, he pipes up with “Mo’ Baa Baa Baa Agoo?” I think I’d fall asleep from the boredom if I had to sing it the same way every time!

Conversational Math: The Secret Number Game

I value any teaching techniques that require no preparation and that I can do while nursing the baby. Conversational math games fit the bill! I came across this game at Let’s Play Math the other day and Luke has been requesting it frequently ever since.

Me: I have a secret number. There was a cat who climbed up in a tree. The cat looked down and saw 3 white flowers and my secret number of pink flowers. The cat could see 17 flowers. Do you know my secret number?
Luke: How many pink flowers were there?
Me: That’s my secret number! I want you to figure it out. There were 17 flowers and 3 of them were white and the rest were pink.
Luke: How many pink flowers were there?
Me: That’s what you have to figure out! If you can’t do it just by thinking about it, maybe you can draw a picture to help you figure it out. There were 17 flowers, 3 of them were white and the rest were pink and that’s my secret number.
Luke: 17, 16, 15 β€” I think 15.
Me: Ok, so if you have 15 pink flowers and you add three white flowers, you get…
Luke: No, 16! I think it’s 16. Or 14. It’s 14.
Me: Ok, so if there are 14 pink flowers and you add 3 white flowers, you get… 15, 16, 17.
Luke: Your secret number is 14!
Me: You figured out my secret number! Agh, now I have to think of a new secret number. Hmph.


Celeste: Luke, I want you to learn to respect Isabel’s boundaries. A boundary is like a fence. Everybody has boundaries. I have boundaries, you have boundaries, Nathan has boundaries and Isabel has boundaries.
Luke: And Daddy. Except…. Jesus. Jesus doesn’t have boundaries.
Celeste: Jesus doesn’t have boundaries….
Luke: Jesus doesn’t have boundaries? Does Jesus have boundaries?
Celeste: I wonder. I wonder if Jesus has boundaries, and if they’re the same as our boundaries or if they’re different.

Math at Their Own Pace: Rainbow Numeral Tracing

Last week, Isabel’s kindergarten teacher gave her a list of hands-on activities, with the assignment to pick two per day. This was a fun change from the usual virtual kindergarten routine of video lessons and “draw a picture and write about it” assignments.

One of the choices was a number tracing activity that reminded me of Rainbow Numeral Tracing from Math at their Own Pace. Rather than having kids trace a dotted line, Greg Nelson recommends having them trace within the borders of large numeral outlines. This allows them to “focus upon the sweeping motion of their strokes rather than on moving from dot to dot.”

The book has templates in the back but when I tried to scan them with my copier, it was hard to keep the pages flat to get a good scan. I turned to the internet and found the perfect PDF to use instead. (Sometime I’ll have to explore the website it’s from, It looks like it has a lot of interesting resources!)

I figured Isabel and Luke would both benefit from some practice in drawing numerals so I printed them out and got down the special marker box. We each picked out a few favorite colors and went to work on a stack of numbers. After tracing each one, we’d pass it around the table for the next person to trace.

I like how they turned out! We were going to tape them up somewhere (“for Halloween” according to Isabel) but we never got around to it so they are still in a pile.

I should probably pull out the 8 for Isabel to practice with; she’s been spontaneously writing numbers lately and overall her formation is really good but I’ve noticed she writes her eights as a circle with an extra loop added onto the bottom afterward.

Looks like Luke’s got his 8’s down, but more often than not he writes his 7’s upside-down.