Math Jeopardy

The Activities

1. Topic: Multiplication: Book: Mulitplying Menace: The Revenge of Rumplestiltskin by Calvert.

2. Topic: Many. Math Jeopardy.  Here are all the questions and pictures you need to play this.

We divided the kids into two teams and played a variation of Jeopardy. The categories were Multiplication, Estimation, Patterns, Tangrams, and Algebra.  The first team to write down their answer and raise their hand got to guess. If the first team was wrong the second team got 2.5 minutes to answer.  If they were wrong, then the first team got one last chance to guess. This way the teams are never just waiting for someone to answer.

My daughter working on a Tangram question.

My daughter working on a Tangram question.

The Jeopardy Board

The Jeopardy Board

How did it go?

We had 4 kids this week. The younger circle was cancelled because many of the kids were out of town, so my son was the score keeper for the big kids circle.

Rumplestiltskin

This book has a lot of story, and little bit of multiplication mixed in.  All the kids were really into it, and my daughter asked if she could have it in her room at bedtime.

Jeopardy

We divided the kids into two teams of two, and explained the rules.  I think none of the kids had ever played trivia games before, so they didn’t know some basic strategy: for example, if the first team guesses wrong, the second team should take plenty of time before answering, to be sure to get it right.

Team 1 started out by getting pretty far ahead. This is mainly because one kid was really fast on all the multiplication problems, answering all of them except the 500 point one. No one got that one…it was 101 * 37.  Team 1 tried to do it by writing down 101 thirty-seven times, but they ran out of time. Team 2 tried to do it using base 10 blocks, making 37 piles of 101 each.  I really thought Team 2 might realized that 37 one hundred squares makes 3700, but they didn’t.

Both teams did very well on Algebra, with several kids being very close when the right answer was given.  They didn’t get to the 500 question.

Estimating was hard for the kids. The teams solved the first two by counting each object.  From the 300 onward they tried to estimate, but were never close enough to score points.

The 100 Tangram was pretty hard because the kids assumed our Tangram pictures would be to-scale. We had to give a couple hints for that one.  The kids did much better on the 200, 300, and 400, but ultimately the one kid from Team 2 solved all the Tangrams.

Patterns was a very close category, with multiple kids figuring out what the pattern was, but Team 1 was faster at writing down the answer. We only did the 100, 200, and 300.  The 300 was the hardest: Nov, Oct, Sept, Aug.  Team 2 guessed that the next three would be Sept, Oct, Nov.  Team 1 realized that it should be the months backward, but ended up guessing July, April, March.

Ultimately Team 1 by a score of 1900 to 1600.  Everyone was a good sport, though my daughter had started to get upset when Team 1 was pretty far ahead at the start (because they did all the multiplication problems early).

Overall this was very fun and motivating for the kids, and we’ll have to do it again!

Five Horses and Four People

The Activities

  1. Topic: Numbers: Book: On Beyond A Million: An Amazing Math Journey by D. Schwartz.
  2. Topic: Programming: I made a simple program that took as input two numbers, added them together, and then printed them twice.  In the past, when I said “Pick a number”, I had them draw out of a bag; this time I had a section at the bottom saying “Input 1: 3, 5” and “Input 2: 8, 9”, and they needed to trace the program twice, once with each input.  Then, I asked them to write a program that multiplies the input by 3 and then prints it out.
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  3. Topic: Pigeonhole Principle: I gave them some simple Pigeonhole Principle problems such as “If there are 15 people in your class, prove that at least 2 have birthdays in the same month” or “How many people do you need to have before you know that two of them will have names that start with the same letter?”  Then, I asked them each to make up a new pigeonhole principle problem.
  4. Topics: Shapes, Geometry: I gave each kid a list of vegetables (and a few fruits), and they had to draw a garden where each vegetable was planted in a shape that started with the same first letter as that vegetable (each shape can only be used once).  This idea came from Math Fun with Tricky Lines and Shapes by R. Wyler and M. Elting.
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How Did It Go?

We had all five kids this week.

On Beyond A Million

We spent quite a bit of time on this book, the kids understood about number of zeroes being the difference between million, billion, etc., and maybe understood exponential notation.  They were quite into the really big numbers like decillion.  I read all the asides and number facts in the first half of the book, but had to start skipping them in order to leave time for the other activities.  We had the usual discussion about infinity, in particular whether it’s a number or not.  One kid asked whether a googol was bigger than a zillion.

Programming with Inputs

Tracing went reasonably well, a couple kids had some problems with the idea of input but were able to do the tracing after some explanation.  However, when I asked them to write the program that multiplied the input by 3 and printed it, it turned out that they didn’t really understand the idea of input.  There were various problems, such as thinking of the input as part of the program, not assigning “Pick a Number” to a box, and others.  I tried two things to help clarify: First, I simplified the problem so they just needed to print the input.  This helped for a couple kids but not the rest — only one kid successfully wrote this program, with a bit of help.  Second, I asked them what the first program “did”.  The answer was, “it prints 17 twice”.  I pointed out that with the first input it printed out 8 twice, but this didn’t help.  I asked them to explain in English what the program did, but this didn’t work, one said “Shiqi Shiqi” (“17 17” in Chinese).  I explained that it added the two input numbers and printed them twice, but I don’t think they understood.  In retrospect, I don’t think having “Input” at the bottom like that was a good idea, I think that we should stick to either “Ask A Friend” or “Pick From Bag”, because they make it clearer that the input is not part of the program.  And also, we should think about how to explore the difference between describing a program as a series of input/output pairs, vs. saying what the logical operation it’s doing is.  Several of the kids were off-task in this activity, which also made things harder.

One kid did fully understand the syntax and meaning of “Pick a number”, and wrote a program that took two numbers as input and printed the sum three times.  This is not that far from what I asked: I asked to print the number times three, which is very close to “Print the number three times”.

Pigeonhole Principle

We’ve done Pigeonhole Principle before, but I don’t know if we called it that; they didn’t recognize the name.  For the first problem, birthday months, it took them a while to get it.  Things went quicker after that.  Only 2 of the 5 kids knew how many months were in a year.  There was a lot of confusion about the “number” of a birthday (I asked “Prove that if there are 50 kids, then at least two have the same number in their birthday”), because they kept thinking about number of days in the year; so in the future I will probably drop this question.

They also were a bit slow to think of the their own problems, but we ended up with some good ones.  The first one was “If there are 5 horses and 4 people, then one person has 2 horses” and another kid pointed out they could have one leg on each horse.  Later someone suggested 8 horses and 5 people, with the much more reasonable answer that some of the people will have to share a horse (the phrasing “some will have to share” is very good and came from one of the kids).  We also got “7 lemonades and 5 people” and “6 cupcakes and 5 math circle friends”.  Less good was “100 people and 7 kernels of popcorn”.

After circle, my daughter said to my wife that if there were 15 people in a class, then at least 3 of them would have the same month.  Obviously this isn’t quite right, I think she’s thinking about the fact that either more than two have the same month, or else there are several pairs with the same month; but clearly there’s more to explore (e.g., how many different patterns of shared months are there?).

Shape Garden

The hardest shapes to come up with were “isosceles triangle”, “equilateral triangle”, and “ellipse”; one of them knew ellipse with hints, but I gave them the two types of triangles.  They thought of most of the others on their own, including “rhombus”, “cylinder”, and “nonagon”.  Drawing decagons and nonagons is hard, but when I said it didn’t have to be regular, it got a lot easier (if it doesn’t have to be convex it’s not hard at all).  The kids had a tendency to draw shapes that were too small to fit the vegetable names inside.

Monsters, Bears, and Division

The Activities

1. Topic: Prime Numbers. Book: You Can Count On Monsters by Schwartz. This is one of our family’s favorite books. Each page shows a number, starting with 1, and then if the number is prime, there is a picture of a new ‘monster’ representing that number. If the number is composite, the picture shows the factor monsters squished together.

A.  Read the first 15 or so pages of the book.  Count the dots, and look at the picture to see if the page is for a new prime monster, or which factor monsters are in the picture.

B. Give the kids print outs of the 1, 2, 3, 5, and 7 monsters. They can glue the numbers onto the paper to make their own composite number. When they are done, multiply all the factors together and tell the kid the number the made.

My son gluing monsters.

My son gluing monsters.

My son's finished picture.

My son’s finished picture.

2. Topic: Numberline, Number Recognition.  Number guessing. The kids get seven guesses to get my number, which is between 1 and 40.  For example, they may guess 25, and I would say, “No, it’s lower than 25.”.   We had a number line on the table so the kids could cross off the numbers that are not possible.

The theme of this game was a bear who wants to steal our picnic food. If you don’t get the number in time, he steals one snack.

The bear is racing toward the snacks!

The bear is racing toward the snacks!

3. Topic: Symmetry, Division. Book: Rabbit and Hare Divide an Apple by Ziefert.  This is a funny book where two bunnies try to divide food evenly, while a ‘helpful’ raccoon eats it up.

4. Topic: Symmetry, Division. Divide a geometric shape into equal pieces. For example, divide a square in half, or in 4 pieces.

How did it go?

We had just 3 kids this week…Everyone behaved pretty well, though my son had to sit out briefly for telling another kid to ‘shut up’.

You Can Count on Monsters

The kids all enjoyed looking at the pictures and seeing which monsters were on each page.  They also liked counting the dots on the page to make sure it matched the number.  After about 15 pages, they started to get restless, so we skipped to the end of the book, since one kid wanted to know what the biggest number in the book was.

The kids also liked making the monster picture. Each kid had a different style. My son just glued every monster he could reach onto the page. Another kid glued on 12 three monsters, and the last one folded the paper carefully and glued on just 4 monsters.

As the kids finished, I used Google to multiply together all their factors. The numbers ranged from 175 to 1.1 billion.

Number Guessing to Save the Picnic

The kids like the excitement of the bear sneaking up to get the snacks.  This activity was really good number recognition and numberline practice for them. For example, if I say the number is higher than 15, then what numbers do you cross off the numberline?

The kids did not have any strategy for how to quickly find my number. The numbers ranged from 1 – 40.  One round started with one kid guessing 40, and the next kid guessing 1.  None of them noticed that those questions weren’t very helpful.  I did later point out when a guess allowed us to cross off lots of numbers. Eventually they’ll see strategy, but for now they’re just getting used to numbers.

Symmetry and Division

The kids enjoyed this activity, and did some interesting things like splitting a triangle non-symmetrically.

Mother’s Day Math

The Activities

1. Topic: Graphs: Book: The Great Graph Contest by Leedy. In this book, animals compete to make the coolest graphs. Everything by Leedy is awesome, including this book. The kids were very interested in the idea of a contest, and in the various graphs the animals made.

2. Topic: Origami: Each kid made a ‘Secret Heart Box’ origami model for their mother.

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3. Topic: Codes: Each kid wrote a short love letter to their mother, and then encoded it using a letter to number key I provided.  Then they folded up the notes and put them in the origami heart box.

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4. Topic: Graphs: The kids got a worksheet that list various points on the Cartesian Plane, e.g. (5, 3). When then plot the points, it draws a picture of a simple shape.

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How did it go?

I led the older kids circle this week. All five kids attended.

Origami

The kids all cheered when they heard we would do origami. My daughter complained because she did not want to give the heart box to me 😛

This model was a quite a bit harder than the ones the kids have done before, but they all did really well, staying patient and letting me help on the tricky steps. All 5 kids successfully completed the project.

Coded Letters

At first the kids were not sure what to write, but they soon each came up with their own mother’s day message. Some of the messages were quite a lot longer than others, so a couple kids had to finish their messages at the end of circle.  No one had any trouble translating their English message into coded numbers.

Coordinate Plane Graphing

None of the kids had graphed points before, but they very quickly caught on.  Some of the kids really zoomed through this.  They all enjoyed seeing what picture the coordinate drew.  The only question the kids had was whether they should start at 0 or start at the last point they had drawn.

Half-Hearts for Mother’s Day

The Activities

  1. Topic: Addition: Book: Monster Math Picnic by G. Maccarone.
  2. Topics: Numbers, Counting: I gave the kids a big pile of unit cubes from our Base Ten Blocks (about 125) and asked them to count the total.
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  3. Topic: Patterns: We made copies of Lessons 33 and 35 from Lollipop Logic, Book 2 which asked the kids to say what the next shape was in a simple repeating pattern.
  4. Topic: Graphs: We made printouts of a grid with letters on each row and numbers on each column.  Then, we have a series of coordinates (e.g., A9) along with what color to color that square.  When you’ve colored all the squares as indicated, you get a picture.  You can download this activity here.
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  5. Topics: Geometry, Symmetry: Book: Let’s Fly a Kite by S. Murphy.
  6. Topics: Geometry, Symmetry: I showed the kids how to make symmetric shapes by folding a piece of construction paper and then cutting out “half” the shape.  E.g., to make a kite you cut out a triangle along the fold line.  Then I gave them some challenges, such as “make a square”, and ended with “make a heart” for Mother’s Day.

How Did It Go?

We had 4 kids this week.

Monster Math Picnic

A simple book about different ways to divide 10 into two groups.

Counting Blue Blocks

They didn’t have any good ideas of how to start; a couple of the kids started trying to count one-by-one, but gave up around 30.  After a bit I suggested they should make piles of 10, which they all did.  After we had everything grouped into 10’s, they still didn’t quite know what to do, but once I started counting by 10’s, they caught on, and one of the kids added on the last 5 to get the right answer.

Lollipop Logic

This activity was pretty easy for all of them.  The main difficulty was concentrating on the activity instead of getting distracted.

Letter-Number Pictures

This one was a bit tricky, but all of them got the idea of finding the right square after a while.  They chose the right square a good fraction of the time.  Interestingly, the hardest thing seemed to be getting into the rhythm of finding the next coordinate pair, finding the square, coloring, finding the next, etc.  For many of the kids, when I helped them find the next coordinates, they could then color the square without help; but then they would just sit there and not move on to the next coordinates.  One of the kids was much more successful than the others and quickly finished the starting picture plus another 1.5 pictures; most of the kids only finished the starting picture plus half of another picture.  I think that the kids didn’t fully realize that they were going to get a picture once they were done, or else this just wasn’t that motivating to them for whatever reason.

Let’s Fly a Kite

This book had a bunch of nice examples of symmetry set inside a story about a babysitter and two arguing kids (who always wanted things to be fair).

Cutting Symmetric Shapes

The most interesting thing that happened in this activity was that when I asked the kids to make a square, they all ended up with a 2×1 rectangle, because they cut out a full square instead of a half square.  Making a heart was pretty tricky for them.  I let the kids have a while to cut whatever they wanted, so we got some interesting shapes.

A Ruler is 30 Centimeters Long

The Activities

  1. Topic: Dimensions: Book: A House For Birdie, by Murphy.
  2. Topic: Tesselations, Shapes: Free play with Pattern Blocks. After making some free-form shapes, I asked the kids to completely cover a half-sheet of construction paper, with no gaps.

    My son has covered the piece of paper entirely.

    My son has covered the piece of paper entirely.

  3. Topic: Measurement: Book: What is Big Compared To Me, by Harris.
  4. Topic: Measurement: I gave each kid a worksheet with various centimeter measurements on it: 1,2,4,7,9,11, etc. Then I dumped a big box of random toys out.  The kids used a ruler to find toys of each length, and then worked with a grown-up to write the toy name in the right place.
    A pile of toys!

    A pile of toys!

    One kid's chart.

    One kid’s chart.

How did it go?

I led the younger circle this week, and 4 kids attended.  It was a nice, calm circle today.  The kids were all engaged by the activities.

Tesselations

The kids all loved playing with the pattern blocks. Two of the kids used the blocks to draw objects like a car or a rocketship.  Another kid built a stack of hexagons out of the blocks. While they played, I started making a snowflake out of pattern blocks.  Immediately my son started copying my snowflake.  Another kid decided to help me instead of building her own shapes.

We played this way for 5 minutes or so, and then I convinced the kids to destroy their designs by first taking a picture of each of them with their creation.  My son took some serious convincing, especially since he was already frustrated because it was hard to copy my design.

Next I handed each kid a half-sheet of construction paper, and asked the kids to use the blocks to completely cover the paper.  Two of the kids started laying down random connected shapes. One kid started building a fancy star shape on her paper. The final kid used only squares to make a column covering the right and left side of his paper.

The kids continued to work on their tesselations for about 10 minutes. At that point my son had finished covering his paper.  All the kids admired his work, which was nice 🙂  The other kids had more work to do, so I let them have a couple more minutes before taking a photo of their work, and cleaning up.

Measurement

Two dads joined me to help with this activity. The kids are pretty willing to sound out words on their own, but I thought having a couple more parent to help with the writing would help.

The kids were very interested in the pile of toys, but they also did a pretty good job focusing on measuring the toys instead of playing. In fact, all 4 kids completely finished their chart!

The kids started to get a sense for the size of a centimeter.  They learned that a 1 centimeter toy is very small compared to a 24 centimeter toy.  The biggest length on the chart is 30 centimeters.  Three of the kids found a Barbie doll that was 30 centimeters long.  The fourth kid decided to measure a ruler, which is 30 centimeters!

A Goodbye Circle

The Activities

  1. Topic: Probability: Book: A Very Improbable Story by E. Einhorn.
  2. Topics: Probability, Pigeonhole Principle: First I asked some problems similar to those in “A Very Improbable Story”, such as “What’s the chance that two random socks picked out of a drawer will match match, if the drawer has 40 socks, 10 each in 4 different colors?” Next I asked some simple pigeonhole principle question about the same drawer, such as “If you wanted to get a matching set of horseshoes (socks) for a pony, how many horseshoes would you need to be sure you got one?”  The final hardest question was “If you have a drawer with 400 horseshoes, 100 each in 4 different colors, and you had 4 ponies, how many would you need to draw to guarantee a complete set for each pony (not necessarily of different colors)?”
  3. Topic: Codes: I made a letter substitution code (go here to make your own) with a going-away letter to one of our kids who is moving to India, pictured below.  The kids had to solve it without a key.  Note that the full letter started with “Dear XXXX”, which is important because their first foothold into the code was guessing that it would mention XXXX.
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  4. Topics: Sudoku, Logic: We did a Unifix Soduku puzzle as a group.

How Did It Go?

All six kids attended.  This week was the going-away party for one of our math circle kids, who is moving to India.  She made us this card:

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A Very Improbable Story

This was a pretty entertaining book and had several interesting probability computations.

Sock Drawer

There were a lot of wrong guesses for all the questions.  They needed step-by-step guidance in order to answer the probability questions, but once I led them through it, they were able to answer (although still not right away): “After the first sock, how many matching socks are in the drawer?”  “How many socks are in the drawer?”  They did understand that this meant that the probability was “X out of Y”, perhaps definitionally (this is a pretty decent of probability though, so that’s fine).

Similarly, they didn’t get the pigeonhole principle questions right away, although we’ve done similar in the past.  With some help they solved all the simple ones.  The final question was quite a bit harder, but they did get the right idea in the end and answered the question (with me doing the “bookkeeping” on a piece of paper).  The colors of the horseshoes were gold, silver, black, and clear.  For solving the hard question, the kids all got a small prize at the end of circle.

Letter Cipher

It took them quite a while to get started.  They noticed apostrophes in various places, and even guessed “don’t” for one of the words, but didn’t actually try out whether it looked promising.  Eventually one of the kids suggested it might be about kid XXXX, but even then it took them a while to decide to try finding a word of the right length.  Once they had written in XXXX, I encouraged them to put all the matching letters in other places to see if it worked.  Only some of the kids were engaged, and there were a number of times when someone wrote in a random guess, which I discouraged (except in the rare case where they guessed correctly, just to keep it moving along).  It was also quite loud during this activity.  The kids aren’t that great at the “algorithm” of letter ciphers, which is, determine some word you know, find all the instances of the numbers in that word, and then look for another word you know.  They were scattershot about which letters they filled in.  In the end, they did solve the whole puzzle, which mysteriously mentioned logic puzzles; I then gave kid XXXX a present of Mindware Math Perplexors: Basic Level (a book of logic puzzles).

Unifix Sudoku

The kids were definitely able to answer questions like “In this region, where does the red square have to be?”  So with me picking the questions, we solved it pretty quickly.  Of course, to solve a Sudoku, you also need to have a good search strategy to ask the right questions, which is the next step.  Amazingly, we made it through the whole puzzle without anyone destroying board.