# 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!”

# Spoons Full of Beads (Age 8)

## The Activities

1. Topic: Estimation. Book: Betcha by Murphy. In this book two friends estimate the number of various objects, e.g. cars on a block, people on a bus. It ends with guessing the number of jelly beans in a large jar.
2. Topic: Estimation. Guess how many beads will fit on each of three different spoon sizes. First the kids guessed by just looking at the spoon. Then we piled on the beads, and I let them make a second guess based on the beads on the spoon. Then we counted to see how many there really were.
3. Topic: Building. Next I gave each kid the small size of spoon and challenged them to fit as many beads on the spoon as they could.
4. Topic: Charts. Each kid tracked a different attribute of a Pokemon: color, height, hit points, number of abilities. We flipped over 10 random Pokemon cards and each kid updated their chart. Then we looked at our charts and predicted how the chart would change when we add in the next 10 Pokemon cards.

## How did it go?

We had four kids this week, and it was a rowdy but good-natured circle. Several kids got off topic at various points but they generally came back on track after some warnings from me. This morning was my daughter’s 8th birthday party, and she had come home completely exhausted and grumpy. I was quite worried she would want to sit out circle again, but she actually did ok, though she was gigglier than usual.

#### Estimation

The kids all enjoyed the book, and played along making their own guesses. The spoon activity was also fun. It was a bit tough to get kids to actually make their guesses, but once they were written down, everyone enjoyed helping to put the beads on the spoon and counting the beads to see who was closest.

We started with the medium sized spoon, and they realized the smaller one would hold fewer, and the bigger one more. Their second guesses (after seeing the beads on the spoon) were generally more accurate than the guess based just on the spoon.

The kids were not satisfied that I had really gotten the maximum number of beads on each spoon, so I gave them a chance to do better. I gave each kid a small-sized spoon and we sat on the floor piling beads on the spoon.  Initially we had gotten 30 beads on the spoon. I managed to get 39 on during this activity, which is one more than the 38 that had fit on the medium sized spoon. Two other kids got 34 and 36 beads. At first my daughter was messing around and giggling but eventually she got quite serious and managed to get 41 beads on her spoon, beating me by two.  The last kid never really tried and mostly threw beads around the room or put them in pockets.

#### Pokemon Charts

4 of the 5 kids are obsessed with Pokemon Go, so last week David promised them a Pokemon activity. We thought making charts of various Pokemon attributes would fit into this lesson because we could predict the attribute distribution after some Pokemon to the chart. However, this turned mainly into a looking at Pokemon and making tally marks activity. Not sure how much we really learned here, but the kids enjoyed it.  Two kids did notice that their attributes were closely related: nearly every pokemon with 40 or fewer hit points is also shorter than two feet.  We also noticed that nearly every Pokemon card has two attacks. A few have one attack, and none seem to have three or more attacks.

# Shrinking Ears (Age 6)

## The Activities

1. Topic: Size. Book: The Biggest Fish by Keenan. This is a simple book about a town that has a contest to see who can catch the biggest fish. The kids loved the drawing of a fish as big as a school bus.

2. Topic: Measurement, Graphs, Differences. We used ribbon to measure the kids’ wrists, ear, hand, foot and height. We compared the measurements to last year’s.

3. Topic: Estimation, Graphs, Counting. We guessed how many steps it would take to get from the kitchen to different parts of the house. Then we counted it out and compared the answer to our guesses.

•  First each kid made a guess and counted it out, to different destinations.
• Next, we each made a guess for a farther away destination (the front door), and then counted it to see who was closest. Each kid computed how far off their guess was.
• Finally, we counted how many baby steps it would take to get to that destination.

## How did it go?

This is the one year anniversary of the younger kids circle.  It was also the first circle in 4 weeks, due to Christmas vacations.  The kids had lots of energy, and were excited to see each other after so long.

#### Body Measurement

The kids were all really excited to find out who had the biggest feet/wrist/ ear.  It was a bit chaotic during the measurment phase. Another parent helped, but there was still lots of noise and excitement. Eventually everyone got their new ribbons glued down to their sheets.

As usual, there was a fair amount of measurement error. One girl’s ear appeared to have shrunk since last year 🙂

The kids were especially excited to see who was the tallest. My son won that competition by being one centimeter taller than the next kid. Interestingly, the smallest kid in circle grew the most — seven centimeters since last year. No one else grew more than five centimeters.

The kids had trouble answering, “Which measurement of yours changed the most in the last year?” They all wanted to answer whichever was their biggest measurement, even if it hadn’t changed much.

#### House Measurement

The kids all enjoyed guessing how far it would be to their target. Some of the kids were very strategic when taking their steps, taking smaller and smaller steps at the end, if necessary.

We all guessed how far it would be to the front door. The guesses were 19, 29, 30, 31, and 44. It took us 21 steps to get there.  Each kid then computed how far off their guess was, using our chart.

We had just a few minutes left in circle, and the kids were all joking about taking tiny baby steps, so I decided we would try it out. I picked a kid who had pretty regular baby steps, and then we all counted together as she walked to the front door. It took 115 steps, which was an excitingly big number to the kids.

# Furry Monsters Hate Raisins (Age 5)

## The Activities

1. Topics: Arithmetic, Counting: Book: Math for All Seasons by G. Tang.  We read about half the pages, solving each problem.
2. Topics: Combinations, Venn Diagrams, Attributes: The kids made pumpkins using 2 different kinds of eyes, 1 kind of nose, and 2 kinds of mouths, each with 2 orientations (right-side up or upside-down) — download templates here.  The goal was to make as many different pumpkins as possible.  After that, we made Venn diagrams with attributes like “Half-circle Eyes” or “Upside-down Mouth”.
3. Topic: Logic: We solved several Halloween-related logic story problems.  We’ve done this activity before with this circle, but this time we did all seven puzzles instead of just three.
4. Topics: Estimation, Counting: We have a small plastic skeleton bucket (about the size of a baseball).  One at a time, I filled the bucket with several different types of item: glass beads, paper clips, etc.  For each item type, he kids all guessed how many there were in the bucket, and then we counted as a group.

## How Did It Go?

We had four kids this week.

#### Math for All Seasons

The kids liked counting the items.  I don’t think they ever did the clever counting methods until after I suggested it.

#### Pumpkin Combinations

The kids did a pretty good job coming up with different pumpkins.  I taped each one to the wall after checking whether it was different.  There were a few duplicates which we fixed by turning one of the parts upside down (since we were using glue sticks, this was easy to do).  They ended up making 18 of the 32 possible pumpkins; they didn’t get blocked, they just got tired of making pumpkins.  Around this time, one of the kids started to get distracted and remained that way for the rest of this activity and the next as well.

The Venn diagrams went pretty well — they weren’t all that great with the overlaps, but they understood the idea.  We did a three-circle Venn diagram, and they did alright with that as well.

#### Halloween Logic

I still helped them some, keeping things moving, but they were much faster than last time we did this (in March).  They were more likely to guess and fix things later, and they understood all the clues right away.  So we were able to get through all 7 of the puzzles.  Two of the kids (including the distracted one) thought the clue “Furry monsters hate raisins” was hilarious.

#### Skeleton Estimation

They guessed low every time, except for a guess of 90 for small plastic acorns when the answer was 36.  In general I’ve found that they almost always guess too low.  They were particularly far off for paper clips (largest guess was 60, answer was 179).  They enjoyed counting the items as a group.

# Secret Numbers and Secret Shapes (Age 5)

## The Activities

1. Topic: Attributes, Estimation: Book: The Case of the Missing Zebra Stripes by Time-Life Books. This book has about 10 chapters all about different zoo-themed math activities. We did the first two chapters today.
2. Topic: Number Line: I have a number board that shows the numbers 1 – 100. I covered up numbers on the board and asked the kids which number was missing. Then I covered up 3 or 4 numbers in a row, and asked the kids.
3. Topic: Number Line, Number Guessing: Each kid picked a secret number between 1 and 100. The other kids took turns guessing the number. The secret kid would say whether their number was higher or lower than the number the kids had guessed.
4. Topic: Spatial Reasoning. One kid used pattern blocks to make a shape, out of sight of the other kids. Then the kid described the block arrangement, and the other kids tried to match.

One kid’s shape.

## How did it go?

All 5 kids attended today. We had a picnic for all the families after circle, so some of the kids were a little wild during circle. But overall it was a good circle.

#### Zoo Math

The first task was to estimate how many flamingos there are in a picture.  The kids initially guessed between a couple hundred and ‘ten hundred and twenty’.  I had one girl put her hand on the page, and counted that 10 flamingos fit under her hand. Then we found that it takes 15 of her hands to cover the page.  That means there could be 150 flamingos.  I then asked the kids for their final guess, and despite the estimation we had done, several kids still guess a couple thousand. The answer was 130.

The next chapter was a mystery about a new animal joining the zoo.  We got clues like: “The animal shares a trait with snakes, ostriches, and robins”.  The kids needed help to know that those animals all lay eggs. They were able to figure out the next two clues, that the animal was furry and had webbed feet.  None of them knew what animal that must be, but were able to pick out the platypus when looking a set of possible animals.

The chapter was followed by several “Odd One Out” puzzles, some of which were easy for the kids and some harder.  The kids were happy to all give their own theories. For example for the numbers “10, 11, 20, 30” one girl felt the 10 didn’t belong because it was smallest, which other kids thought 11 didn’t belong because it didn’t end in a 0.  One girl was especially good at articulating why something didn’t belong “I think the elephant doesn’t belong because the others are all birds”.

#### Number Lines

All the kids were pretty good at figuring out the missing number when just one number was covered, although a couple kids still got 68 and 86 confused.

Covering three numbers in a row was much harder.  A few kids would answer the first missing number, even if I was pointing at the second or third covered box.

After we did a few round of this, the kids all wanted to cover the board with the number tiles in order.  I handed out three numbered tiles at a time to the kids, who searched for the proper place to put them. Most of the kids were quick at this, though one boy still did exhaustive search to find where to put ’21’. He didn’t have a sense of whether 21 is a big or small number.  The kids were all excited to see who would be lucky enough to get the ‘100’ tile, but didn’t cry when someone else got it.

#### Number Guessing

Each kid got a chance to think of a number between 1 and 100. Then the other kids would try to guess it, and the secret kid would say whether their number was higher or lower than the guess.

The kids with the secret number were all pretty good at knowing whether to say higher or lower.  Only one kid got confused, and he seemed to understand after I took him aside and showed him where his secret number was on the board.

The kids loved to pick high numbers. 89, 90, 99, and 100 all got chosen.  The guessing kids were not good at binary searching for the numbers.  I helped them by pointing out that the number must be less than X, but they would still sometimes guess things higher than X.

#### Shape Description

Two weeks ago David had described shape arrangements, and the kids were very good at recreating the shapes.  This time the kids took turns making a secret arrangement, and describing it to the other friends.  They were actually all pretty good at describing their shapes, although sometime they weren’t precise enough so the friends would have different variations.

# 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.

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!

# Spooky Halloween Programs

## The Activities

2. Topic: Programming, Functions:
 The functions: Scream { ___Print “B” ___Do 2 times { ______Print “O” ___} ___Print “!” } Ghost (Box_X) { ___Print “I saw” ___Print Box_X ___Print “ghosts!” } AfraidOf(Box_X, Box_Y) { ___Print Box_X ___Print “ is afraid of “ ___Print Box_Y }

The programs:

 Print “Lisa shouted” Scream Do 4 times { ___Scream } Ghost(799) Print “Siddarth said” Ghost(10) Print “Rachel said” Ghost(“scary”) Print “Elsa said” Ghost(“Anna”) AfraidOf(“Lyle”, “zombies”) AfraidOf(“Carol”, “fairies”) AfraidOf(“Witch”, “Lucy”) Print “Corey said” Ghost(20) Print “The ghost said” Scream AfraidOf(“Corey”, “ghosts”)
3. Topic: Maps, Spatial Reasoning, Logic:Fill in a map of a treat-or-treating neighborhood based on the following clues.
1. Each house is the same shape and size as your house.
2. Directly to the West of your house is the Witch’s house.
3. The Zombie house is 2 houses West of the Witch’s house.
4. Olaf’s house is across the street from the Zombie’s house.
5. Elsa’s house is directly South of the Witch’s house.
6. The pumpkin house is directly East of your house.
7. The Spider house is on the very West end of the South side of the street.
8. 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.
9. The Goblin is between the Zombie and the Witch.
10. The skeleton is directly across the street from the Spider.
11. Next to Elsa’s house is a Graveyard that takes up two houses.
12. The Ladybug’s house is right next to the Butterfly’s.
13. The Fairy can fly right across the street to the Ladybug’s house.
14. The Wizard’s house is East of the Fairy’s.
15. Anna’s house is next to Elsa’s house.

The empty neighborhood map.

4. Topic: Estimating: How many of various objects fit inside a small skeleton bucket?  One of the items were Smarties candies, and the closest kid got 5 Smarties, and the other got 4.

The estimating skulls.

## How did it go?

We had 5 kids at circle this week. We did Halloween-themed math.  Everyone was excited to get a (tiny) candy treat at the end.

#### Programming with Functions

This went really well this week.  Everyone loved the Halloween-themed programs, and again they loved having their names in the programs.

Yesterday we bought a laminator and laminated our programming worksheet, so the kids could erase their programs when they finished.  The kids all enjoyed using dry-erase markers to trace their programs.

The was a slight drama at the beginning because four kids all wanted a green marker, but we only had two.  So I took away both green markers.  The kids moved on quickly and chose new markers.

The first program was:

Print “Lisa shouted”
Scream

I asked the kids if they knew the command ‘Scream’ and they said no.  So I got out the sheet with the 3 function definitions and we all looked at the commands for scream.  The kids all successfully traced through ‘Scream’.  2 kids did it on their own.  The other 3 got it after I helped them.

The next few programs involved the Scream function, and everyone understood it easily.  Kid A loved predicting what the output would be, like shouting “Boo! Boo! Boo! Boo!” for

Do 4 times {
___Scream
}

Kid B started to write ‘Scream’ a few times, but I reminded her that she needed to do the commands in the Scream function instead.

Next I gave the kids:
Ghost(799)

Everyone wondered what the 799 meant.  We looked at the definition of the Ghost funciton, and I showed them how it tells them to put 799 in Box_X.  The kids did this, and then were able to complete the steps in Ghost.

When we got to
Print “Luke said”
Ghost(“scary”)

several of the kids were unsure whether it was legal to put “scary” in Box_X, but I assured them that was right.

Next was:
AfraidOf(“Sanjay”, “zombies”)

The kids were all excited by the word “zombies”.  I asked if they knew how to do this program.  I explained that AfraidOf tells you where to put each word.  The first should go in Box_X and the second in Box_Y.  After the kids assigned the variables, they had no trouble finishing AfraidOf.

Kid B several times still made the mistake of writing “AfraidOf” instead of following the steps in Afraid of.

The next program was:
AfraidOf(“Witch”, “Lyle”)

I think every kid got tricked and put Lyle in Box_X, instead of Witch, but I said again that the first word has to go in Box_X so they fixed it.  They all thought this was a funny program.

Finally I gave them the big program:

Print “Corey said”
Ghost (20)
Print “The ghost said”
Scream
AfraidOf(“Corey”, “ghosts”)

3 kids did this completely independently.  One kid needed a tiny bit of help.  The fifth kid needed a bit more, because she kept forgetting which line to go to in the main program after finishing a function.  So I held my finger in the main program to help keep track.

Kid C was extremely efficient at these programs.  She didn’t mess around at all, and was obviously working hard to try to finish first every time.  Kid A did quite well.  Kid D understood it all, but somehow took longer to trace through than other kids.  Kid B and Kid E needed a bit of one-on-one help to complete some of the programs.  Everyone seemed to enjoy the programs, and were excited to see what came next.

 My daughter at work on the hardest program. My daughter’s finished program.

#### Trick-or-Treat Maps

I gave everyone a map with a street and one house on it.  Then I started reading the clues.  At first the kids didn’t understand that the houses had to be right next to each other, but once they understood that, they were pretty good at drawing 4×4 squares on graph paper.  Kid Aunderstood every clue right away, and again worked hard to be first on each.  She would quickly draw her house, and then ask me how to spell the name.

The other 4 kids started to embellish their houses, drawing a pumpkin on top of the pumpkin house, for example.  Kid B had some trouble understanding the difference between “across the street” and “at the other end of the street”.

The clue “The zombie house is 2 houses West of the Witch’s house” was a bit tricky because they didn’t know whether to leave 2 empty houses or 1 one empty house.

The trickiest clue was “Next to Elsa’s house is a Graveyard that takes up two houses.” Kid A immediately realized that only one side of Elsa’s house had space for the graveyard.  Kid B started to say that she didn’t know which side of Elsa’s house to put the graveyard on, but then she noticed suddenly that it would only fit in one place.

One kid’s finished map.

#### Estimation

First we did the blue glass beads. The kids guesses ranged from 15 – 20.  Then Kid A peeked at my answer sheet and announced that the top two numbers were 38 and 30.  Kid B changed her guess to 38, and Kid C guessed 30.  So I skipped the yellow acorns which had 30 inside.

Next I brought out the paper clips.  The kids guessed between 40 and 100, but the answer was 204.

Finally I brought out the Smarties, and told them the winner gets an extra piece.  The guesses were between 100 and 598.  The answer was 160, and the closest kid was Kid B who was 66 off.