The Bird and the Bikes (Age 9)

The Activities

  1. Topic: Money. Book: The Story of Money by Maestro.  We continued where we left off last time, and got as far as early money in the Americas.  My favorite part was the discussion of why paper money caught on better in China than in Europe (the government was more stable in China).
  2. Topics: Algebra, Arithmetic:  I wrote down the equation (5789 + 1286) x 549 = 3,884,175.  I used my phone to compute the right hand side.  Then I asked them a series of questions: What is the answer if you change 5789 to 5790 (the answer increases by 549)?  What if you change 549 to 550?  What if you change 549 to 1098?  Each time, using my phone, I checked that you got the same answer by evaluating directly vs. evaluating incrementally.IMG_2535
  3. Topic: Probability: I attempted to teach the kids how to flip a coin properly, and then each kid (and me) spent 5-10 minutes flipping coins and writing down the sequence.  Then, I asked several questions: “Do you expect more heads or tails?  Is heads more likely after you’ve just gotten three tails in a row?  Is heads-tails more likely than heads-heads?”  For each one, we counted in our sequences to see whether the results matched the kids’ intuitions.
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  4. Topic: Logic: I drew a picture of two bicycles riding toward each other at 5 mph, starting 10 miles apart, and asked them how long before the bicycles met.  Then, I added a bird flying at 20 mph back and forth between the bicycles, turning around and going back whenever is met a bicycle, and asked how far the bird flew before the bikes met.IMG_2533

How Did It Go?

We had four kids this week.  It was a pretty good circle, some distractions as always but a lot of good thinking as well.

The Story of Money

This book has been going well, our daughter was able to explain the China vs. Europe paper money difference later that day when we were talking about circle.

Incremental Algebra

The kids did quite well on this activity, many of them were comfortable with parentheses and they didn’t have much problem getting the right answers.  By the end they were getting confident enough they thought the checking was a waste of time.

Coin Flip Sequences

When I started asking questions, I got some answers like “more heads after 3 tails in a row” — but I was surprised that after hearing each others’ answers they quickly converged to 50/50 no matter what.  So they seem to have a decent grasp on the idea of independence of coin flips.  Flipping was kind of hard for them, they really wanted to move their whole hands instead of just their thumbs.  For this reason the results were slightly suspect.  And of course this is a probability exercise so the results never come out perfect.  But by the end I felt pretty confident that some of the kids understood the idea of evaluating probabilities by counting occurrences from a sequence of trials (i.e., statistics).  The trickiest part was that if you have a sequence of, say, 5 heads in a row, and you’re counting outcomes after 3 heads in a row, you use this sequence 3 times (first 3, second 3, and final 3).

The Bird and the Bikes

One of the kids got the clever answer to the full question almost immediately.  Partly this was because I made it easier by asking the bikes only question first.  But still, I was impressed.  We also started computing the “brute force” way where we figured out how far the bird flew before meeting the first bike (8 miles).  The kids did okay at this too even though it’s a bit tricky.

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Valentines Jeopardy! (Age 9)

The Activities

  1. Topic: Money. Book: The Story of Money by Maestro. This book traces the history of money from the earliest people to present day. We read until the Lydians invented the first coins. Both kids were really interested in this book, and didn’t want to stop reading. We had various interesting discussions, for example: what would happen if someone needed a blanket, but the blanket maker didn’t want any eggs.
  2. Topic: Story problems, coordinates, money, combinations. Valentines Jeopardy. We had 4 categories with 5 questions in each category. The questions were worth 100 – 500 points, with the higher point values being harder.  Our categories were “Broken Hearts”, “Time for Love”, “Map of My Heart”, and “Valentines Store”. Here are all the questions and answers.

Valentines Shop

Valentines Shop
Stickers…………12 for $2
Toys…………….5 for $3
Cards…………..25 for $4

Each Valentine is made of 1 card, 1 toy, and 1 sticker.

100: How much do 3 Valentines cost?
200: How much do 11 Valentines cost?
300: How much do 25 Valentines cost?
400: How much to 26 Valentines cost?
500: How much do 100 Valentines cost?

Time for Love

100: Katie sang a love song to Alex. She started singing at 5:22AM, and sang for 1 hour and 34 minutes. What time did she stop singing?
200: Fluffy bunny loved carrots so much she hopped around the garden with joy. Each hop was 2 feet long. She hopped 10 times per minute for 6 minutes. How far did she hop?
300: Luke has been waiting for Valentines day since December 8th. How many days did he have to wait?
400: Sam loves candy hearts. A pack contains 30 hearts, and it takes Sam 3 minutes to each one pack. How long does it take same to eat 5 hearts?
500: Corey loves numbers. She started at 5 and counted by fives for 30 minutes. She said one number every 2 seconds. What number did she end on?

Broken Hearts

100: You have 2 colors. How many ways can you color in a heart split into two sections?
200: You have 4 colors. How many ways can you color in a heart split into two sections?
300: You have 4 colors, and each heart has to use two different colors. How many ways can you color a heart split into two sections?
400: You have 2 colors. How many ways can you color in a heart split into 5 sections?
500: You have 3 colors. Each heart much use each color. How many ways can you color a heart split into 3 sections?

Map of My Heart

What word do the letters at the given coordinates spell? Starting at 300, the words are scrambled.img_20170212_181129

100: (7, 17) (11, 19) (3, 12) (16, 10)
200: (20, 1) (16, 10) (8, 5) (18, 3) (2, 20)
300: (2, 2) (8, 5) (8, 2) (9, 11) (6, 21)
400:
(16, 10) (4, 6) (18, 7) (7, 17) (9, 11) (13, 1) (15, 5) (8, 5) (2, 20) (16, 10)
500: (19, 13) (5, 10) (2, 2) (18, 7) (6, 21)

How did it go?

We only had two kids in the circle, which was unlucky, since competitive activities like jeopardy usually go better if you have teams. Otherwise there can be too much pressure on individual kids. My daughter had an especially hard time with the competition aspect, especially after she fell behind early. She started ripping up all the materials and crying in between questions, but refused my attempts to turn the activity into group problem solving instead of a competition. Here’s the room after the activity was done. Notice all the ripped up paper bits strewn around.

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Ultimately my daughter came back from a 1400 to 100 deficit, to win 2000 to 1900. The other kid was a great sport throughout the activity. She answered 7 questions correctly, compared to 6 from my daughter, but the point value was a bit lower.

The questions were just about the right difficulty. They had to work hard for the 500s.

Time for Love: they missed the 300 and the 500. They were close on the 300, but pretty far away from being able to solve the 500.

Valentines Shop: My daughter solved the 100 – 400, but could not compute the 500 (how many 12s make 100?). The other girl was uncomfortable with this category, even though I worked through each problem right afterward to show how it goes. I think she felt overwhelmed by having to compute how many packs you need to buy for each of 3 objects.

Map of my Heart: The other girl solved 100 – 400 very quickly. She was able to guess the Valentines words from just a couple coordinates. For the 100, she guessed the answer was “LOVE” after seeing the L and that the word was four letters long. The 300 was scrambled (CANDY), and it took both girls a while to figure it out. The 400 went quickly, guessed before all letters were searched.  My daughter got the 500 (CUPID), which was the trickiest word to unscramble.

Broken Hearts: I thought this wouldn’t be that hard, but neither girl knew how to compute color combinations through multiplication. They wanted to enumerate the colors. They only answered the 300 correctly. This was because I had enumerated the 16 options for the 200, and my daughter realized she just needed to remove the double color choices to get the 300. (12).

At the end of circle all the kids got a chocolate covered strawberry that me and my daughter made this afternoon.

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Happy girl, before tragical jeopardy.

A Bag Full of Dice (Age 9)

The Activities

  1. Topics: Geometry, Three Dimensional Shapes: Book:  Sir Cumference and the Sword in the Cone by C. Neuschwander.
  2. Topics: Geometry, Three Dimensional Shapes:  A while ago we bought 5 full sets of “D&D dice” (4, 6, 8, 10, 12, and 20 sided).  We counted the edges, faces, and vertices for each of these and made a chart like in Sir Cumference, showing that “Faces + Vertices – Edges = 2”.  I also pointed out the dual relationship between 6 & 8 and 12 & 20 sided polyhedra (i.e., 6-sided has 6 faces, 8 vertices, and 12 edges; 8-sided has 8 faces, 6 vertices, and 12 edges; you can switch between the two by putting a vertex in the middle of each face and connecting adjacent vertices).img_2431
  3. Topic: Numbers: We did What’s the Secret Code? from youcubed.org.  There are some clues about what the secret number is like “The digit in the hundreds place is ¾ the digit in the thousands place.”  There is more than one answer which is cool.
  4. Topics: Origami, Geometry: We did Paper Folding from youcubed.org.  There are a number of folding challenges like “Construct a square with exactly ¼ the area of the original square. Convince yourself that it is a square and has ¼ of the area.”img_2432

How Did It Go?

We had four kids this week.  As usual some kids followed along better than others, but most people were engaged for both the dice activity and the paper folding.

Sir Cumference and the Sword in the Cone

The kids liked the book, they laughed at quite a few of the math puns.

Euler’s Polyhedron Formula

The kids definitely enjoyed making the chart.  They did a pretty good job staying on task (it was easy to get distracted and start rolling the dice).  Counting the edges on some of the dice was fairly tricky but was much easier with good grouping strategies.

What’s the Secret Code?

The kids did well on this except that they had trouble with the decimals.  They did find one of the decimal answers, because they knew that .5 = 1/2, but I believe there were other possible decimal answers as well.

Paper Folding

The kids solved all the tasks except the last one, which was making a non-diagonal 1/2 area square.  I figured out a pretty complicated way to do it (by transferring the side length of the diagonal answer onto a horizontal edge), they copied what I did but it was pretty tricky (see picture above).