Merge Sorting Easter Eggs (Age 6 and 8)

The Activities

  1. Topic: Probability, Impossibility. Book: It’s Probably Penny by Leedy. Leedy is one of our favorite authors. The kids liked this book about what’s possible, probable, impossible and certain.
  2. Topic: Sorting. It’s Easter today, so I filled 102 Easter eggs with numbers ranging from 1 – 1011.  I hid all the eggs outside, and then kids did an egg hunt. Then each kid counted their eggs, then opened them and sorted the numbers inside.  Next I had each kid pick up their sorted numbers so the smallest one was on top. We then used merge sort to sort all the numbers together, on the sidewalk.

     

How did it go?

We had two younger kids this week, and 5 older kids, so decided to have a fun, combined circle and do an egg hunt since it is Easter today.

The kids loved the egg hunt, racing around at top speed. They especially liked trying to find the 3 golden eggs, which were so well-hidden they required clues. We gave the two younger kids a 30 second head start. In the end, the kids collected between 12 and 17 eggs. My daughter was proud to get the most (though she didn’t find any golden ones).

Next the kids opened the eggs and sorted their numbers. The big kids had no trouble at all. One of the younger kids needed some help recognizing numbers above 100. She seemed to know that 263 was bigger than 207, if I said it out loud, but I’m not totally sure.

Then I showed the kids how to carefully pick up their numbers so the biggest number was on the bottom of their pile and the smallest was on top. We then started sorting all the numbers together. We found 1, 2, 3, and 4 immediately (on top of various kids’ stacks). Then we tried to find 5…my son started sorting through his stack. I asked if it was possible that he 5 somewhere in his stack? He didn’t know, and wanted to look.  One of the bigger kids explained that it was not possible because his smallest number was already on top, and it was 12.

After this, the kids seemed to get the idea of the sort, although it took them awhile to figure out which number to put next, because the numbers were not consecutive. Also various kids dropped their whole stack of numbers several times, requiring re-sorting. Finally we go to the really big numbers (that had been inside the golden eggs), and added 1000, 1010, and 1011 to the end of our line.

I wanted to take a picture of the kids with our nicely sorted numbers, but my son scattered the numbers before I could gather everyone.

After circle today we had a picnic with the other families, which was really fun. At the picnic my daughter organized yet another egg hunt with eggs containing stickers and small treasures from her room.  All the kids played together really well.  At the end of the night the parents took turns playing tag with the kids.  There was sprinting, taunting, crashing and fun 🙂

Laziness is a Virtue (Age 8)

The Activities

  1. Topics: History of Math, Mathematicians: Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians (Volume One) by L. Reimer and W. Reimer, Chapter 5 (John Napier).
  2. Topics: Multiplication, History of Math:  I printed out one set of Napier’s Bones per kid.  I showed the kids how to use them to do multiplication of a large number by a single digit number.  A follow-up that we didn’t do this time is to use the bones for multiplying two large numbers.
  3. Topic: Sorting:  The kids attempted to sort cards with all numbers from 1 to 300.

How Did It Go?

We had four kids this week.

John Napier

The kids liked the (non-mathematical) stories about John Napier and the rooster and John Napier and the pigeons.  We’re now thankfully past the part of the book where the mathematicians all die at the end of the story.

Napier’s Bones

The kids understood how to use the bones fairly quickly.  One of the kids is very good at paper-and-pencil multiplication, so while I could slightly win on large number X single digit multiplication, the other kids couldn’t.  I showed them why it worked (see second picture above).  The place where the bones really shine is multiplying two large numbers, since you can use the same arrangement of the bones for each single digit multiplicand, so we should do that race at some point.

Sorting to 300

The kids decided to use labels, this time making sure to have labels bigger than 200.  It took them 10-15 minutes to make the labels, so next time I’m going to count this time as part of the overall time.  In particular, they didn’t think of simply using the cards that were multiples of 10 as “labels”.  They went with the same strategy of running back and forth even though I tried to get them to come up with something better; our daughter said that she WANTED to run back and forth so she could get some energy out.  I let them go for 17 minutes (which meant that circle went over by ten minutes), and then got 200 of the 300 cards sorted.  One of the kids was feeling tired and decided to first find all the numbers between 1-100 and do those first, since that required less running.  If only more of them were lazy…

Corey’s Pretend Party IV (Age 6)

The Activities

  1. Topic: Graphs. Book: The Great Graph Contest by Leedy. In this book, a frog and a salamander compete to see who makes the best graphs. They make Venn Diagrams, Bar Graphs, Pie Charts, and others, covering a variety of subjects. Leedy is a great author, and the kids always love her book. This is no exception.
  2. Topic: Voting. Each year around the time of my birthday, I have the kids plan my pretend birthday party. This is the fourth year in a row we have done this activity (twice with the older circle, twice with the younger). This time, I planned to have each kid own one question, and have them collect votes. Then I wanted to make a fancy graph out of each, similar to the graphs in the The Great Graph Contest.
  3. Topic: Adding and Subtracting, Word Problems. The kids used Base Ten Blocks to solve problems about my age (36).
    1. How old will I be in 36 more years?
    2. How many years older am I than you?
    3. How much is my age plus yours?
  4. Topic: Advanced Birthday Math. My son is extremely good at calculation, so I knew he would cause problems during birthday math. I gave him a much harder problem to work on separately: How old will I be in the year 3022?

How did it go?

We had four kids this week. The circle was a bit scattered, partly due to me being less organized and partly due to the advanced birthday math not working out.

Happy Birthday to Me!

The kids all enjoyed coming up the questions for my party. We came up with:

  1. Where should the party be? Pump It Up, Park, Restaurant, Arcade.
  2. What treat should we have? Crackers, Oreos, Cupcackes, Tacos.
  3. What should be in the gift bag? Bouncy ball, Legos, Light Saber, Balloon.
  4. What drink should I server? Water, Apple Juice, Pink Lemonade, Grape Juice

Each kid owned one sheet for voting. Everyone voted on each other’s sheets. The kids made tally marks to record the votes. Two kids remembered that you can cross the fifth tally mark. We had an interesting discussion about why you should cross the fifth one. Some kids said it was because they had seen parents do it that way. I made an example on paper of 15 tallymarks, vs 3 groups of 5 tallymarks. Then one girl said that crossing the fifth meant you could count by fives. We then tried counting the two rows of marks, and found that counting by 5s was much faster.

I had planned to have the kids make graphs out of the votes, but they were getting a bit distracted by the end, and I hadn’t planned it out that well, so I decided to move on to birthday math instead.

Birthday Math

First I gave my son his problem (How old will I be in the year 3022?), then started working with the other three. First I asked each kid to count out 36 Base Ten Blocks. All three of them decided to use 10 bars, so they picked out 3 10-bars and 6 units.

Next I asked how old I would be in 36 more years? The kids had lots of silly guesses, like 1000 years old, but finally one girl suggested we should start at 36 and count up 36 more. I suggested counting out 36 more Base Ten Blocks, and then counting them to see how many there were in total.  The three kids eventually did this, though there was some messing around, and also some mistakes in counting (I got answers of 71, 72, and 73).

Meanwhile, my son had decided the advanced problem was too hard. He was trying to subtract 3022 – 2016 in his head, and had come up with 1008, which I said was close but not correct. This frustrated him, so he crumpled up the paper and threw his pencil. He then rejoined us at the table for a bit until he got too wild and had to sit on the couch for the rest of circle.

Next we each collected 36 blocks again. I asked, how old was I when each of you was born? No one knew how to figure this out. Some people said my age was negative, some people said I was 1000.  I suggested we could go back in time by taking away one block at a time. They enjoyed watching me take one block away saying: Now you’re 4, now 3, now 2, now 1, now 0. Then we counted how many blocks were left and found I was 31 years old when this student was born.

My final question what is your age plus my age? By this time, the kids were quite restless, some were saying it was too boring. But we persevered and figured it out, and we even added all 4 of our ages together. Everyone thought it was funny to think about being 53 years old (the sum of our ages).

 

Mount Everest and Submarines (Age 6)

The Activities

  1. Topic: Addition: Book: Mission, Addition by L. Leedy.
  2. Topics: Tangrams, Geometry: We did six different easy tangram puzzles, download here.
    IMG_1837
  3. Topics: Numbers, Negative Numbers: I made a vertical number line from -10 to 10.  We played the number guessing game (higher/lower) with numbers in this range.  I had the secret number the first time, and then each kid took turns having a secret number.  Then I described several different places numbers are used — money, elevators, traveling on the Earth, and age.  For each one, I described what the positive numbers were, and then I asked what negative numbers would mean (for example, for money, it means you owe someone else money).
    IMG_1838

How Did It Go?

We had all five kids this week.

Mission, Addition

This book is slightly on the long side but we finished it.  The kids loved the last story, where the teacher gave them all bills for the food they ate but did the addition wrong (sometimes by a lot).

Tangrams

Everyone worked hard on the tangrams.  Some of them are pretty easy, and no one really had problems on them.  A few are harder, particularly the scarab beetle. Three of the kids finished all six pictures.  One of the kids (one of the two who didn’t finish all of them) liked to say how easy the problems were after they solved them but then asked for help more quickly than the other kids.

Negative Numbers

The guessing game went surprisingly well.  There were only a few times where someone went the wrong way for a negative number.  Having the vertical chart for them to look at helped a lot.

We had a pretty good discussion about the different scenarios.  We started with money, which they had discussed last week.  Of the things we discussed, I think they understood money the least well — except for our son, who has gone negative on his allowance before.  They figured out that elevators would go underground right away.  For traveling on the Earth, I described sea level and said how we were at about 50 feet above sea level and the nearby hills were a couple thousand feet above sea level.  One of the kids mentioned Mount Everest and I said it was 27K feet (I was wrong, it’s actually 29K).  Then I asked what negative was, and they said going underwater.  I asked how they would get there, they said submarine, and two of the kids had seen a movie about going deep underwater.   I asked how they would go negative where there wasn’t water, and they said dig.  For age, I asked them how old they were, and they said 5-6 years old.  Then I asked what -3 years old would mean.  Our son, who we’ve discussed this with, said you’d be an egg in your mommy.  I asked how old our son was when I was born, they enjoyed that.  I asked how old they were when the Universe was created.  A few kids got somewhat distracted by the end of the conversation, but overall they were very attentive and engaged.

Sorting Beyond 100 (Age 8)

The Activities

  1. Topic: Logic. Book: True Lies, by Shannon. We did chapters 6 – 9 this week. The stories were a bit uneven. For example one hinged on a pun of ‘poor scholar’ meaning both financially needy and ‘bad student’. We figure out several of the others though. All four kids came up with theories for at least one story.
  2. Topic: Sorting. My daughter saw the little circle sorting the numbers 1 – 100, and kept asking if her circle could do it again. Back in July, the older kids set a new record for sorting the cards 1 – 100 in only 5:40. This time I had cards from 1 – 200.

How did it go?

We had four kids this week. It was a fun, excited circle, though my daughter seemed over-tired. She had to be sent out a couple times because she was crying or being rude to other kids.

Big Sorting

I told the kids they got to sort 1 – 200 this week, but I wanted them to have a strategy first. One kid proposed breaking the cards into piles by decade: 0 – 10 in one pile, 10 – 20 in another, up to 190. She suggested using labels so we knew where to put each card.

After a bit of arguing the kids made labels for each set of 10 cards. One kid then laid the labels out close together, intending to put the cards in a stack under the label. Another kid suggested putting the cards downward from the label in sorted order. So you would put 53 under the ’50’ label, leaving space for 50, 51, 52.

A third kid felt very strongly that we should put the labels out on the floor as markers for where our row of cards should be. So we put 0 at one side of the room, and then ’10’ about 10 card-widths away. The kids laid out all the labels, which stretched across our bedroom, down the hall, into my son’s room.

I started the timer, and the kids all started running back and forth putting cards where they belonged. The kids seemed to enjoy it when they had a high number like 193, followed by a low one like 5 in their stack. They would run all the way to the opposite ends of the house to put down one card. No one sorted their stack before putting down the cards.

My daughter quickly got annoyed by the labels, and started to throw them away when she put down a card near a label. This worked out fine because the cards themselves acted as place markers by that point.

Everyone moved quickly, and the labels minimized the amount of time spent scooting cards down to make room for other cards. Overall it took 11:28 to sort all 200.

The kids were very energized by this, and really wanted to sort 300 cards now. I didn’t realize they meant they wanted to add 200 – 300 to the end of the already sorted cards, so my daughter got pretty upset when I picked up the cards 1 -200.

Eventually they decided they still wanted to sort all 300 cards. I said we had to talk strategy first. What went well during the last sort? A couple kids said everything went well.  What could have gone better? I thought they might mention that they had to run back and forth a lot. Instead, my daughter said that the labels were too confusing, and they should not use labels this time.  I was quite surprised. I asked, If we don’t have labels, how do I know where to put number 250? The kids said it’d be easy, and then each of them suggested totally different places to put it. One kid thought the line should curve out of my son’s room and go back down the hall. Another thought the middle of the line should go through the hall bathroom. It was clear no one knew where 250 went.

I asked if they were sure they didn’t need labels? They were all sure. I said ok, but I predict it will be very hard… I started the timer, and immediately confusion started. A bunch of kids gathered in my son’s room trying to decide what to do with the cards over 200. Eventually they gave up and sorted through their piles of cards, looking for cards less than 200. This was easier than it should have been because I didn’t shuffle very well. After finding a group of nearby cards, like a bunch of 50s, the kid would put them in place by roughly remembering where that decade had been during the last sort.

A couple kids said “This is hard…we should have had labels”. After 11:30, I stopped them because circle was over. They had sorted about 100 cards, and not a single card above 200 was sorted. This will be very interesting to follow up on in a future circle.

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My daughter starting the 1-200 sort, with the decade markers.

 

 

Pokemon on Parade (Age 8)

The Activities

  1. Topics: History of Math, Mathematicians:  Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians (Volume One) by L. Reimer and W. Reimer, Chapter 4 (Hypatia).  Note: I skipped the ending of this story, only briefly summarizing (see notes below).
  2. Topic: Decision Trees, Addition:  First I reviewed the Pokemon decision tree from last week (a couple kids weren’t there).  Next, each kid “drafted” a team of Pokemon cards.  I split the cards into 5 piles, gave one pile to each kid; they each picked one and passed the pile to the right, and we repeated until each kid had 5 Pokemon.  Then, I gave out prizes based on the attributes of the Pokemon; some were based on the single Pokemon (e.g., most HP), and others were based on the entire team (largest total weight).  You can download the prizes here (the Pikachus are to give out when there are ties).   After all the prizes were awarded, the kids worked together to built a decision tree which identified whose team each Pokemon was on (that is, the labels at the leaves were the kids’ names).  I did the initial few splits until I had 5 different leaves, numbered them 1-5, and then had each kid work on one of the pages.
    IMG_1832

How Did It Go?

We had all five kids this week.

Hypatia

I definitely wanted to read this one because it’s one of the few stories about a female mathematician.  Unfortunately, she was killed by a religious mob.  So I stopped about 2 pages from the end of the story and just summarized as “some people didn’t like that she asked questions about the things they believed in, and so they killed her”.  The kids really wanted to know how she died, but I said “No one knows for sure” (which is true, although it was almost certainly quite unpleasant).  Out of the four mathematician stories, three have ended with the murder of the mathematician — so if you decide to read this book to kids, be aware of that.  I checked out the Wikipedia page for Hypatia, and it’s consistent with the book, so they’re not making things worse than they actually were.

Pokemon Round-up

For the review, I had the kids who were there last week show the other 2 how to use the big decision tree from last week.  They had seen decision trees before, so they caught on very quickly.

The drafting went fine, although some kids were confused about the mechanics of the draft (only take 1 from each pile, don’t mix the ones you’ve already picked into the current pile, etc.)  Most kids picked carefully, but one picked randomly.  Overall, most of the kids were pretty excited by the theme.

The prize giving went well, everyone was motivated even when they had to do somewhat complicated sums.  The trickiest part was computing the total height, because it involved feet and inches.  Everyone got some prizes.  One of the kids really wanted to win the prize with the picture of Heracross (a bug with lots of attack).

I asked the kids whether they wanted to work alone or in pairs, 3 said pairs and 2 alone.  I worked with one of the 3.  They all had trouble getting started, but after some help they made pretty good progress on their own.  One kid noted that they could use a split to identify a single Pokemon that wouldn’t have worked earlier but because of an earlier split was now unique.  Some of the kids were drawing Pokemon by the end, but they did manage to finish the entire tree of 25 Pokemon.  They used a few interesting splits that were different from our big tree, including “Is bird?” and “Name starts with ‘s'”.

 

Saving My Allowance (Age 6)

The Activities

  1. Topic: Money, Negative Numbers: Less Than Zero by Murphy. In this book, Perry the Penguin wants to save 9 clams to buy a scooter, but ends up borrowing money from his friends and going negative. The kids really enjoyed this book, and eagerly followed along with the graphs in the book.
  2. Topic: Money. I ran a pretend store with items of different prices. The kids got $3 each as allowance, and could buy something or save their money. I kept track of each kid’s total on an allowance chart. The kids worked with me to add their new allowance and subtract the money they spent.
  3. Topic: Advanced Money. The adding and subtracting in the store activity were too easy for one kid, so I gave him a harder problem to work on. Otherwise he couldn’t stop himself from answering for everyone else.  His problem was: If you have $10, and each pack of cards costs $0.75, how many packs can you buy?IMG_20160306_174827Topic: Sorting. The kids worked together to sort the cards 1 – 100. They were trying to beat their previous record of 19 minutes.IMG_20160306_174806

How did it go?

We had all five kids this week. Everyone was very attentive, and enjoyed all the activities.

Shopping

I set out a ‘store’ with a bunch of small toys I found in my daughter’s room. I was very clear that the kids did not get to keep the toys they bought (my daughter would kill me!).

First I gave each kid $3 allowance, then asked if anyone wanted to buy anything? Three of the five kids bought something the first round. The other two kids saved their money.

No one tried to go negative, even though the book we had read was about a penguin spending more money than he had.

Next I put out some more toys in the store, and had the kids add their new allowance ($3) to the amount they currently had. Then we had a few more rounds of buying and getting allowance.

One kid decided to save all his money every time. He said there were so many things he wanted to buy, that he couldn’t pick any. He did enjoy having more money than anyone else.

The kids have gotten much better at adding since circle started last year. But several still needed help adding 3 to $15, for example. I showed them how to count up 3: 16, 17, 18.

Subtraction is much harder for everyone. Some kids could do problems like 5 – 3, but I helped other kids by showing it on my fingers.

Advanced Shopping

One kid had no problem adding and subtracting, but was having a problem with telling other people the answers before they had a chance.  I gave him a different problem, which he worked out on the floor. If you have $10, and each pack of cards costs $0.75, how many packs can you buy? He solved this by repeatedly subtracting 75 from 1000. At the end he counted up how many subtractions he had done, and found you could buy 13 packs, with 25 cents left over.

Sorting

Everyone was very excited to try sorting again. We discussed strategy beforehand, and said that it had worked better when all the cards were out on the floor. Then we started sorting, and only 2 of the 5 kids laid out their cards :-).  This time there were some new strategies: several kids started collecting all cards of one decade, for example, one girl had all the nineties. A boy had the seventies and the eighties.  The girl with the nineties actually sorted them in her hands, but they got mixed up again when she handed them off to the other kids.

Ultimately, the kids beat their old time by 4 minutes, and finished all 100 cards in just 15 minutes. If we follow up on the new bucket sorting strategy, we should be able to go faster.