Picking Pasta (Age 7)

The Activities

  1. Book: Alice in Pastaland: A Math Adventure by A. Wright.
  2. Topic: Combinations: Inspired by Alice in Pastaland, I asked the kids to figure out how many ways there are to choose two different kinds of pasta from ten different choices.IMG_1759
  3. Topics: Tangrams, Geometry: We did a number of tangrams from Tangrams: 330 Puzzles by R. Read.

How Did It Go?

We had four kids this week.

Alice in Pastaland

The kids were very excited to finish reading Alice in Pastaland.  It doesn’t have all that much math content, but it does mention numbers frequently.  It also inspired the next activity…

Choosing Pasta

We’ve investigated this problem before, but this time I wanted them to come up with the general formula.  When I gave them the problem, they had no idea how to proceed, and I’m sure they wouldn’t have gotten anywhere unless I got them started.  I said that a good problem solving strategy is to look at simpler versions of the same problem.

First, I asked how many ways if there were two kinds of pasta; they quickly got one as the answer.  Next I asked if there were three kinds.  They were able to demonstrate all three, using the picture of plates of pasta I drew (above).  Next I asked four kinds of pasta.  After some wronger guesses they settled on five, by finding five different answers.  I then wrote the table in the picture above: 4 columns of 3 rows each, AB/AC/AD, BA/BC/BD, CA/CB/CD, DA/DB/DC.  The highlight of circle was that they noticed the duplicate pairs themselves: AB vs BA.  They didn’t notice that every combination had one and only one match, but when I asked why there were the same number of originals as cross-outs, one of them realized they were in matched pairs.  For 4, they simply counted to 6.  Next we did 5, and one of the kids wrote out the entire table of 20 combinations (including duplicates), counted it, and divided by two.  I asked if there was a faster way to do this, and they saw they could use multiplication.  From here, with just a bit more help, one of the kids was able to answer the full problem.  Out of the four kids, two were pretty involved and (I think) understood the answer at the end, the others probably not.

For a reward, they all got a (very small) prize at the end of circle.

Tangrams

Unlike previous circles, we just did the puzzles straight out of the book.  This is quite a bit harder because they don’t have an outline to put their shapes in, and it’s quite a bit harder to understand the scale of the various parts.

The kids have varying abilities at Tangrams.  One interesting difference is that some of them still have trouble copying a completed Tangram.  They can get the shapes in the right general location but sometimes have problems with exactly orientation or positioning.

I started by giving each kid a different puzzle from the same page.  It turns out that none of them are ready yet to solve a puzzle without help.  So, I switched to having everyone work on the same puzzle.  The thing I tried to teach them is that they should first look for where the two big triangles are.  Some of the kids could solve some of the problems once they knew where the big triangles went.  Working as a group was a pretty good way to teach them strategies for solving tangrams, but the disadvantage is that it’s now a direct race to finish, so one of the kids got frustrated when they were slower than the others.  We ended up doing about six different puzzles as a group.

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Counting without Seeing (Age 5)

The Activities

  1. Topic: Zero, Multiplication, Addition. Book: A Place for Zero by Lopresti. This book covers the additive and multiplicative properties of zero in a very flavorful and engaging way.
  2. Topic: Counting. We used the Base 10 Blocks to count to 100 by 10s, and 1000 by 100s and 10s.IMG_20151129_175021
  3. Topic: Search, Pan Balances, Inference. I showed the kids a box that contained some number of plastic leaves.  I asked them to figure out how many leaves were in the box without opening the box.  I gave them a pan balance, and an identical, empty box.IMG_20151129_174846

 

How did it go?

There were only 3 kids at circle this week due to Thanksgiving travel.  It was a really good, focused circle.  All three kids paid attention and took turns very nicely.

A Place for Zero

The kids really enjoyed this book, about poor Zero who has no place in numberland. One kid predicted that Zero would be paired with a One to make 10 (which turned out to be true).

The book first shows how any number + Zero = the number.  Next Zero headed off to multiplication land to try to multiply himself.  At this point, I paused the book, and used Base 10 Blocks to teach the kids about multiplication.  Two of the kids had not done multiplication before, but I explained that 2 * 3 means you make 2 groups with 3 items in each group, and then count how much you have.

We did a couple small problems like that, and then I asked how much would 0 * 7 be? Two kids thought it should be 7.  My son said it would be 0.  I said, well, if we make Zero groups each with seven cubes, how may cubes do we have?  The kids agreed that would probably be zero, but were not super convinced.  I figured that 7 * 0 was probably easier to explain.

I said, “If I give you 7 bags which each have 0 pieces of candy in them, how much candy did you get?” All three kids immediately saw that they would have no candy.  After circle, I quizzed one girl, in front of her mother: “What’s 1,000,000 times 0?” and she instantly said “0”, and went on to explain that 1 million bags, each with no candy, makes 0 pieces of candy. 🙂

After we got a bit of intuition about multiplication, I finished the books, and the kids were all excited to see that 0 multiplied by any number made 0.  They also loved seeing 0 and 1 pair up to make 10 and lots of other big numbers.

Base 10 Blocks

After the book, I had the kids try out some big addition problems, like 22 + 33, using base 10 blocks.  First you make 22 by getting two 10-bars, and 2 unit cubes.  Then make 33, and combine the two piles and count the result.  All three kids were able to do this.

My son looooves addition and multiplication, so these problems were too easy for him, but he was thankfully very patient during this activity.  He begged the other kids to give him a hard problem, and the hardest one they thought of was 100 – 2.  My son said 98, and we all checked that he was right by counting 2 higher than 98.

Next we used 100 squares to count by 100 to 1000.  Then we used 10 bars to count by 10s to 1000. The kids each made 100 out of 10 bars, and I carefully added it to our stack, so in the end we had a block of 10 bars the same size and shape as the 1000 cube.

Counting Without Seeing

Next I showed the kids the pan balance, and said they should use it to figure out how many plastic leaves were in a treasure box (without opening it). If they could get it right, they would each earn a treasure.

They quickly got the idea of putting a handful of leaves in the empty box and weighing it vs the treasure box. They were very good at interpreting the result, knowing that if their box weighed more than the treasure box, then they should take out some leaves.  They even understood that they should only adjust it by a few leaves if the boxes were close in weight.

At one point, it looked like the boxes weighed the same, but the kids wanted to test to make sure, so they first added one leaf (too heavy), then took away two leaves (too light), then added back a leaf to get a match.

To find our answer, we opened up the kids’ box and made piles with 5 leaves in each. We had 41 leaves.  We then checked the treasure box, and found 41!! Everyone cheered!

Self-Portrait in Blocks (Age 7)

The Activities

  1. Topic: Arithmetic. Book: Alice in Pastaland, by Wright. This book is a re-telling of Alice in Wonderland with a light math theme. The kids loved the theme of the book, and were happy to work out the various math problems. It’s a longer book, so we only read the first half.
  2. Topic: Programming. We brought back our old pen-and-paper programming language.   Here are the programs.IMG_20151122_165849
  3. Topic: Geometry. We gave each kid a strip of paper with a word on it, like cat or crab or rainbow. The kid then tried to make that object using wooden pattern blocks. When done, the other kids tried to guess what it was.
    IMG_20151122_171430

 

How did it go?

We had 4 kids this week. It was a very focused and fun circle. Everyone stayed on task the whole time.

Programming

Three of the four kids immediately remembered how the language worked. They zoomed through the programs quickly, making progress on their own.  There were still a few mistakes, but very few.  The trickiest program we had today had nested loops:

Do 4 times {

Do 2 times {

Print “B”

}

}

One kid figured this out completely independently. Two others got it with help.

The fourth kid was less comfortable with programming. They understood assignment and printing, but still didn’t fully understand the concept of a loop.  For example, which lines should you repeat? What’s inside the loop and outside?  With some one-on-one help they completed five or six programs, but they still need more practice.

Pattern Block Pictures

Everyone loved this activity. The kids quickly made surprisingly good pictures of cats, crabs, tree, flower, star, airplane.  The hardest ones were: pizza, dragon, and car.

We had a few minutes left after we finished all the words I had prepared. Three kids decided to write their own cards for me and the other kid to make.  One of the cards I got said “Corey” (my name).  So I made a lovely self-portrait out of blocks:

IMG_20151122_173100

 

 

Flowers, Stars, and Crabs (Age 5)

The Activities

  1. Topic: Comparisons: Book: Anno’s Math Games II by M. Anno, Chapter 2.  This chapter has a number of side-by-side similar pictures, and you have to find the similarities and differences.
  2.  Topic: Logic: We did “Boole Says” again — I said something like “Stand up if you are a boy OR are wearing socks.”  This time, the kids each got to come up with a command, and we also did some commands using “not” (“stand up if you are NOT wearing socks”).
  3. Topics: Patterns, Geometry: We used pattern blocks to draw pictures.  I named 2 or 3 different kinds of shapes (e.g., triangles and squares), and then each kid made a picture using those shapes.  Each time, we each went around and said what we had made.  We did about 5 rounds total.
  4. Topics: Scale, Astronomy: We explored The Scale of the Universe 2 web app for a while.  This is a visualization of the universe from the smallest scales (Planck length) to the largest (size of the observable universe).  Starting at human scale, we scrolled both bigger and smaller and discussed what we saw.

How Did It Go?

This circle went really well, the kids were very interested in all the activities.

Anno’s Math Games II

We spent a while finding all the differences in the most complicated of the activities.

Boole Says

The kids enjoy anything involving standing up and sitting down over and over :).  They did a pretty good job following the commands, a few of the kids got confused by AND vs. OR sometimes, but the other kids helped them.  When the kids were giving their own commands, I think every single one of the commands included themselves; and several of them ONLY included themselves.  One of the commands was “Everyone wearing flowers stand up”, and one of the kids didn’t realize they had flowers on their tights until everyone else pointed it out.

Pattern Block Pictures

The kids enjoyed this activity a lot.  There were a lot of flowers.  One kid’s pictures were noticeably different from the others — for example, one picture was a pretty good crab.  There were a few pictures that the kid didn’t know what it was.

The Scale of the Universe

The kids voted to go bigger first.  One of the kids has done a lot of astronomy things in the past, and was able to identify a bunch of the objects, such as the Lunar Lander, Apollo rocket, etc.  Smaller turned out to be less interesting — pretty quickly all you’ve got is particles, which aren’t too exciting.  The kids’ favorite thing was scrolling through the whole thing really fast, which looks like going through a tunnel because the way there are smaller and smaller concentric circles.

 

Arranging Angles (Age 7)

The Activities

Corey was gone this week, so two parents graciously volunteered to lead circle this week.

  1. Topic: Money:  Sold!  A Math Adventure by N. Zimelman and B. Barnard.
  2. Topic: Geometry: This activity explored the fact that the sum of the angles of a triangle is 180 degrees, and a (convex) quadrilateral 360 degrees.  Starting with various triangles and quadrilaterals, the kids cut off the corners and then arranged them next to each other.  They also tried to measure the angles using a protractor.
  3. Topic: Building: Using our collection of Magformers, the kids tried to build as tall a tower as possible.

How Did It Go?

There were some challenges this circle.

Adding Angles

The goal was to get them to discover that the sum of the angles was 180 or 360 degrees.  Apparently, this didn’t work out too well, and the kids ended up spending a lot of time cutting without much discovery.  Afterwards, several of them said (repeatedly) that “they didn’t know what the point was.”  This is a very nice activity, so we’re going to try it again later; the parents who led it suggested that it might work better if the shapes were smaller so it took less time to cut them out.

Tower Building

The two parents had a contest with the kids to see who could build a taller tower.  Unfortunately, one of the kids knocked over the parents’ tower partway through.  Tower building with Magformers works pretty well, but at a certain point the towers tend to collapse in on themselves.

20 Statements (Age 5)

The Activities

Corey was gone this week, so one of the other parents stepped in and led circle.  These are their notes.

  1. Topic: Logic: Book: Anno’s Math Games II by M. Anno, first chapter, about a transformation machine (i.e., “function”).
  2. Topic: Logic: A kid would pick a card with an animal on it.  I made a series of statements, and they had to say true or false, until I was able to figure out what animal it was.
  3. Topic: Logic: To practice the use of AND and OR,  I made up a bunch of statements like “stand up if you’re five and have long hair”, “stand up if you are a boy and don’t have socks on”, etc.
  4. Topic: Logic: We did a logic puzzle, borrowed from Boole2School.
    On Halloween,  four strange characters visited your school:
    a witch, a goblin, a ghost and a black cat. Each of them went into exactly one of these rooms: classroom 2, classroom 3, classroom 4 and the staff room.
    The goblin stole a notebook.
    The cat painted her paws.
    The ghost hid in a desk. .
    The witch left a present.
    Clue 1: Nothing was stolen from classroom 4.
    Clue 2: The ghost hid either in classroom 2, or in the staff room.
    Clue 3: Classroom 2 was not visited by a goblin.
    Clue 4: No notebooks or paints are ever kept in the staff room.
    Clue 5: The black cat did not prowl through classroom 4.

    Where did each of them go?

    IMG_20151108_184225 IMG_20151108_184328

  5. Topics: Logic, Puzzles: Fox, goose, grain puzzle: a boat, only 2 things can be transported across the river at a time, if you leave the fox with the goose or the goose with the grain, the goose/grain will be eaten.

How Did It Go?

Anno’s Math Games

All kids really liked the magical machine.  They figured out the patterns fairly well, and liked the “reverse time machine”, i.e. if they went in it would make then babies.

20 Statements

The first round went well, everyone took turns and I was able to figure the animal out fairly quickly.  Second round became disorganized, two kids always tried to help by telling me the animal.

Boole Says

The kids enjoyed this.  Two of them always liked to stand up, but after a few statements they paid closer attention with more success.

Halloween Logic

This was a good puzzle. I had them write in the name of their school.  This got their attention, but one of them became concerned if this really happened in their school.  I read them the clues and filled out the first part of the table, after that we went around and everyone filled in part of the truth table.  At the end, they were quite surprised and curious when the table revealed who went to which classroom. One kid was very good at interpreting the clues for the truth table.