# Trick or Treat Math (Age 6)

## The Activities

1. Topic: Counting. Book: How Many Donkeys? An Arabic Counting Tale, by MacDonald. In this simple book a man can’t figure out if he has 9 or 10 donkeys because he keeps forgetting to count the donkey he is riding. The kids caught on quickly and laughed whenever he got it wrong.
2. Topic: Maps, Spatial Reasoning, Logic: Fill in a map of a treat-or-treating neighborhood based on the following clues. Here is the clipart we used: halloweencharacters.
1. Directly to the West of your house is the Witch’s house.
2. The Zombie house is 2 houses West of the Witch’s house.
3. Olaf’s house is across the street from the Zombie’s house.
4. Elsa’s house is directly South of the Witch’s house.
5. The pumpkin house is directly East of your house.
6. The Spider house is on the very West end of the South side of the street.
7. The Butterfly is scared of the Spider. The Butterfly’s house is on the same side of the street as the Spider’s, but as far away as possible.
8. The Goblin is between the Zombie and the Witch.
9. The skeleton is directly across the street from the Spider.
10. Next to Elsa’s house is a Graveyard that takes up two houses.
11. The Ladybug’s house is right next to the Butterfly’s.
12. The Fairy can fly right across the street to the Ladybug’s house.
13. The Wizard’s house is East of the Fairy’s.
14. Anna’s house is next to Elsa’s house.

The completed puzzle

3. Topic: Estimation, Subtraction. Guess how much candy is in a container. Then put the same candy in a shallower container and guess again. Then count the candy and figure out whose guesses were the closest.

The Candy

4. Topic: Logic. Tape a Halloween character to each kid’s head. Then the kids ask each other yes/no questions to figure out who they are. The hardest part of the game is not telling your friends what is written on their heads.

## How did it go?

I wore my witch costume during circle, and I organized it so the kids would get to ‘trick or treat’ after completing each activity from my bucket of small prizes and candy.

#### Halloween Logic

Each clue was pretty easy for kids, especially after they understood what phrases like “directly West” means. The hardest clue was: “The Spider house is on the very West end of the South side of the street.” Two of the kids figured it out on their own. The other two needed some help from their friends to understand the “south side of the street”.

#### Candy Estimation

The kids were very excited to see so much candy, especially when I told them that the person who guesses closest would get to trick or treat twice after the activity. Interestingly, the guesses did not get closer after I spread out the candy. Most second guesses were at least as wrong as the first guess. I guessed after the candy was spread out (and I got within 2 of the correct number).

After everyone wrote down their guesses I asked the kids to count the candy. They immediately began discussing counting strategies. They eventually decided to sort the candy by type and then count each type. However, they soon realized that some types had too many pieces to be easily counted, and they didn’t know how to add the results anyway. So they switched to counting each piece of candy as it was thrown back into the tub. Two kids both wanted to throw in candy and everyone ended up missing a bunch of pieces when the two throwers could not coordinate. They came up with 67 pieces, but I counted it again and found 72 pieces.

#### Halloween Twenty Questions

The kids loved seeing costumes taped to their friends’ heads, especially when one boy got ‘Princess Leia’. I told them at the start that it is very important not to tell your friends what is written on their heads, and the kids did pretty well at this. However, some kids asked questions like “Am I a zombie?” because they saw “Zombie” on their friend’s head. The hardest to get turned out to be superman. The kid knew he was a strong hero who wears red and blue, and has an S, and has a cape, but couldn’t think of superman.  Everyone else figured theirs out eventually (with some hints from me about what questions to ask). Everyone really enjoyed this activity. At the end, we had five minutes left so one of the kids moms played and had to figure out she was a pumpkin. The kids loved hearing her questions and shouting out answers. “Can you eat me?” “Yes, but it’s yucky and too chewy!”

# Number Magic (Age 8)

## The Activities

This whole circle is built from activities described in the book Games for Math by Peggy Kaye.

1. Topic: Reducing Fractions.  Book: Fractions in Disguise by Einhorn. A millionaire collects fractions for fun, but then a villain steals a rare fraction and tries to disguise it. Only reducing the fractions to their true values can find the lost fraction.
2. Topic: Addition, Subtraction, Number Properties. I performed a math magic trick. Each kid picked a three digit number where no two digits could match, e.g. 581. Then I turned all their numbers into 1089 by:
1. Reverse the kid’s number.
2. Subtract the smaller number from the larger. (e.g. 581 – 185 = 396).
3. Reverse the result and add it to the result (e.g. 396 + 693 = 1089).
3. Topic: Logic, Strategy.  I taught the kids “Tapatan” a tic-tac-toe like game. Each person takes turns placing one of their three stones on the board. After all six stones are placed, you take turns sliding the pieces from point to point along the board lines. You cannot jump over another piece or land on top it. The first person to get their three stones in a line (vertical, horizontal, or diagonal) wins.
4. Topic: Logic, Addition. I gave the kids a series of ‘number bubble’ puzzles. Place the given digits in the bubbles to make each row add up to the required sum.

A solved puzzle, placing 1,2,3,4,5,6 so that each side adds to 12.

## How did it go?

There were only two kids this week, so it was a good, focused circle. My daughter had a few angry moments, but settled down after some warnings.

#### Fractions in Disguise

Both girls really enjoyed this book. The mystery of the stolen fraction was quite compelling, but they were each a bit reluctant to spend energy trying to reduce the fractions in the book.

#### Number Magic

The kids were quite impressed by this trick. Right away they started trying to figure out how it worked. One girl noticed that the middle digit is always 9 after the initial subtraction. Both kids wanted to try again several times.

I told them there is one class of numbers that the trick does not work for. Eventually, my daughter stumbled upon it. If the first and last digits are consecutive, then the final answer will be 198 instead of 1089. For example: 231 – 132 = 99, 99 + 99 = 198. We noticed how the subtraction always results in 99 in this case.

#### Tapatan

This game proved to be pretty fun. The girls quickly started thinking a move or two ahead to make sure they didn’t let their opponent win. My daughter was quite a poor sport whenever she lost, crumpling up the board, or throwing the pieces. The other girl was very calm during these tantrums. There is a lot more to this game than to tic tac toe. We added one extra rule: you cannot undo a move on your next turn, i.e. you can’t move a stone back to the same place it had been the previous turn. This helps prevent stalemates.

#### Bubble Logic

Both girls quickly got the idea of these problems, and had some good insights. On the first class of problems, with the 4 bubbles in a cross shape, my daughter quickly noticed that you should always put the middle two numbers together, and the largest and smallest together.

Later, when we switched from the L-shaped 5-bubble puzzle to the cross-shaped 5-bubble puzzle, both girls independently realized that they could reuse their answer from the L-shape. This was a great insight.

We stayed late at circle a few minutes, because both girls wanted to finish all the bubble puzzles.

# 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).

# 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?Topic: Sorting. The kids worked together to sort the cards 1 – 100. They were trying to beat their previous record of 19 minutes.

## 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.

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.

# How Much For The Whaleshark? (Age 6)

## The Activities

1. Topic: Money: Book: Follow the Money! by L. Leedy.
2. Topics: Money, Addition, Subtraction: I ran a “store” where the kids could (pretend) buy various small toys.  Each round, I gave each kid 4 or 5 “dollars” (play money), and then they chose something to buy and payed me for it.  Some things cost more than \$5, so if they wanted to buy them they had to buy something cheap so they’d have enough next round.  We did three rounds, then reset.  The second run through, I paid them using \$5 bills so they had to make change.  The third run through, I had them keep track on a “ledger” in addition to paying me with physical play money.
3. Topics: Counting, Sorting: We repeated the activity where the kids sorted dominoes according to the sum of the spots.  I gave them 6 dominoes to start, and gave them 3 more at a time when they finished.  I went up to dominoes with 9 spots on each side.  One of the kids has learned his times tables, so he sorted by product instead.  After we used up all the dominoes, I had the kids sort the entire set (by sum).

## How Did It Go?

We had all five kids this week.

This book didn’t have a ton of math, but it did show making change a number of times.  It also introduced the various dominations and was a nice introduction to the next activity.

#### Play Store

The kids got the hang of buying things quickly.  However, they weren’t very good at making change — I think several of the kids didn’t ever quite understand what it meant.  Also, some of them can’t do subtraction, so they also couldn’t do it directly.  That is, if you have a 5 dollar bill and need to pay \$3, either you can make change into ones and pay 3 of them, or you can subtract 3 and get back 2.  Some of the kids didn’t understand either; some understood the change method, and some understood both.  The ledger was also a challenge for many of them, both because they didn’t know subtraction and they didn’t understand how it related to paying for things.  A few got it, but at best the others understood the mechanics but not the meaning.  So we can definitely explore more both the ideas of making change and keeping track of quantities using a running tally.

After we finished the money activity, I had each kid make up a story about a simple math problem.  For example, I would write “3 + 2” and they would say “There were 3 birds sitting on a branch, and then 2 more came, so there were 5 birds”.  Some of the kids closely followed earlier stories, but we got several different types of stories by the end.

#### Sorting Dominoes

The kids were pretty good at this.  All of them were able to finish on their own, with only a few mistakes here and there.  They even handled the 9 spot dominoes pretty well.  For the group sorting, it took them a while to get organized, but once they had at least one domino in each position they made faster progress.  Not everyone participated the whole time but they all contributed.

# Double U, not W (Age 5)

## The Activities

1. Topic: Subtraction: Book: Taking Away with Tigers by T. Steffora.
2. Topics: Geometry, Spatial Reasoning:  I went to a different part of the kitchen where the kids couldn’t see what I was doing, and using pattern blocks I made a shape.  Then, I described the shape to the kids and they had to make it just from my description.
3. Topics: Games, Addition: We again played the game where we rolled two dice with varying numbers of sides and then either jumped or clapped a number of times equal to the sum of the numbers on the dice.
4. Topic: Reflections: I gave them a picture I drew with reflected versions of every letter hidden inside, and they had to find all the reflected letters.
5. Topic: Graphs: The kids were given a grid with letters on the rows and numbers on the columns, and a set of coordinates grouped into one or more colors.  They had to find those cells and color them the right color (similar to counted cross-stitch).  You can download the materials here.

## How Did It Go?

We had all five kids this week.

#### Taking Away with Tigers

A very simple introduction to subtraction; very easy for some kids but about right for others.  The most interesting part was probably the tiger facts at the end.  One kid’s review was “I didn’t care about that book.”

#### Describing Patterns

The kids were much better at this than I expected.  They got almost every shape that I described, including “3D” shapes with some pieces standing on edge.  One thing that helped was they all could look at what each other was doing; because I was away from the table, I don’t know whether it was one or two kids figuring it out and the others copying.  But from a few times I came over a little early, it looked like many of them were working independently.  They were able to choose shapes based on just the name (including hexagon and trapezoid), to get the right number of each shape, and to follow complex instructions like “Take two white diamonds and put them so each one is touching both the square and the hexagon”.

#### Dice Jumping

They continue to love this activity.  I had a bunch of different kinds of dice; the kids have mostly caught on that they should choose the die with the most number of sides each time (so they can jump as much as possible).  I had two different kids choose one die each, a third choose jump or clap, and a fourth role the dice, which helped keep everyone involved.  The most number of times we had to jump was 35; counting past 20 is kind of slow for them, so most of them jumped 70+ times.

#### Hidden Letters

The kids enjoyed this quite a bit, and only needed help a couple of times.  They understood the idea of covering half of a reflected letter in order to see the original letter.  One note is that although some letters are part of other letters (e.g., F and E), each letter is present by itself, not as part of another letter.  One tricky case was the reflected U, which they thought was a W.

#### Coordinate Drawings

This is the second time we’ve done this; they were quite a bit better than last time.  All of the kids were able to make progress on their own this time, and several were noticeably faster than last time.  Most of the kids still made a mistake or two.  One interesting thing is that the kids had trouble telling what the pictures actually were; for example, one kid couldn’t tell it was a car until I told them, but then when they showed it to their mom, she knew it was a car right away.

# Where Is The Potty?

## The Activities

1. Topics: Numbers, Place Values: Book: Earth Day — Hooray! by S. Murphy.
2. Topics: Numbers, Place Values: Using Base Ten Blocks, we practiced going from Base Ten Block representations of numbers to the numerical form, and vice-versa.
3. Topics: Addition, Subtraction, Games: We played Math Dice Jr.  Each round, you roll 1 12-sided die and 5 6-sided dice (2 of them with only numbers 1-3) and then try to make the number on the 12-sided die using the numbers on the 6-sided dice using addition and subtraction.  We had a small modification where each player could only match one set of dice per round.
4. Topic: Maps: We happen to have architectural drawings from the remodel of our backyard, so we all went outside and found things on the map.  Then, I made an overhead view of the first floor interior, and I had the kids find and draw various pieces of furniture and other things on their maps.

## How Did It Go?

We had 4 kids this week.

#### Earth Day — Hooray!

A nice introduction to place values for 4-digit numbers.

#### Base Ten Blocks

The kids were a bit better at this than the last time we did this, half of them are fairly solid and the other half still need more practice.

#### Math Dice Jr.

The kids were all in pretty different places with this game, ranging from coming up with the answer right away every time to mostly just getting it when the die matched the number exactly.  That’s why I introduced the rule that each person could only get one match each time, and also once each kid got to the finish line they watched until (all but one of) the other kids finished.  This worked out fine, the kids who were finished were still mostly interested in watching.

#### House Maps

This activity also had a pretty big range of abilities, but not in the same order as the dice game.  One of the kids had a pretty decent handle on how to read a map, and when drawing objects got the exact right spot most of the time.  The other kids were much spottier — they could do reasonably well on getting the right room, but within the room had a lot of trouble finding the right spot.  The kids definitely enjoyed running around outside.  They were good at looking at textures (such as the stone-paved part of the backyard), but the spacial layout was much harder.  Any talk of bathrooms was extremely funny.