## Thursday, February 6, 2014

### Lesson 9 - Year 2

*Sorry there are no notes on this one!
Midget Spell
A dragon put a curse on you (one of the kids) that made your steps twice smaller every time you took a step. Can you get from this side of the room to the other, with your first step being half the way to the end of the room? Have the kids take turns and try it out and see whether they can get to the end of the room this way. At first though, have them make a prediction whether they will make it to the other side of the room.
Folding Paper
How many times can you fold a piece of paper in half? Try to fold it in half as many times as possible. Give each of the kids a piece of paper so they could each try it on their own. Compare results.
Folding Toilet Paper
After the kids have folded a normal piece of paper, now have them try to fold toilet paper (I am using a long ribbon) in half as many times as they can and see how the result differs from the number of times they could fold a normal sheet of paper. Again, before you start the activity, have them make predictions of what they think will happen. When they complete the activity, they should have an idea of how exponential growth can be very rapid, and that folding something in half one time already makes it twice smaller.
Splitting Pies
How do you split three pies for four people evenly? Draw three big “pies” on the board and have the kids try splitting them, and then counting what part of a pie every person gets.
Exploring Fractions
Draw circles, squares and other shapes on the white board and have the kids explore fractions. Don’t forget to explain what fractions are!
·         Are 2 out of 4 parts of a square equal to 1 out of 2 parts of an identical square?
·         If you have half of a square, and you a fourth more, how many parts out of 4 will you have?
·         If you have a pie, and you split it in half, and take one of the pieces, what fraction of the pie will be left?
·         What is bigger – one third or one half?
·         What is one half + one half?
·         What is one third + one third?
·         What about one third + one third + one third? Explain that when a fraction is x/x (same number for numerator and denominator) that means that it is a whole (1).
·         Explain that when the numerator is bigger than the denominator, it means that there are more pieces than what is available in one whole (1), which means that there is more than one of something.
·         If you split one half of a cake in half, what fraction of the cake would one of those pieces be?
·         What is 1/2 – 1/4?
Do all of these things on the white board (the kids can’t understand most of these unless they are visual).

Explore! If available, use something similar to these 3D Magnetic Fraction Shapes.
Play fraction Simon Says (half of you sit down, a third of you raise your right hand, etc)
Play opposite fraction Simon Says (if Simon says “a third of you sit down” that third has to not do that, but the rest of the kids have to do that)

If there is still time left, have the kids try to color this triangle with three different colors but no two same colors can touch (if there are lines connecting two circles, those circles can’t have the same color):

## Friday, December 13, 2013

### Lesson 8 - Year 2

GENERAL COMMENTS: This was probably one of the best classes I've ever had! :)

Talk to the kids about system thinking and ask them questions along the way.

Ask if anybody knows what a system is, if yes, ask them to explain to everybody else.
Nobody knew what a system was (except somebody who said that a system means electricity – which is an example, but not the definition of a system), so I just went on to the examples, so that they will learn along the way.

Suppose we have all the pieces to a car – the motor, the doors, the windows, the seats, the wheels – everything. If you throw these things in a heap, they won’t get up and drive. For this to become a system (the car) we need to connect these things to each other. When you have a real, built car, the different parts pass data to each other and regulate everything with sensors.

When one thing changes, the other parts know that and change as well in their own way. The parts are interconnected. That’s the difference between a heap of parts and a working system.

The kids are listening carefully.  I asked them whether a heap of parts from a car is a car. Half said yes, half said no. I asked a student who said “yes” why they thought so, and same with a student who said “no”. This was what a student who said “yes” said: “A heap of all the parts from a car is a car because all the pieces are already there and you wouldn’t need to add anything more to make it a car. All you would have to do is put the parts together, and that’s easy”. A child who said “no” said: “A heap of all the parts from a car is not a car because they are not working together and that’s what’s needed for the car to work”. That’s precisely the answer I was looking for. Working together, interconnected, and causing each other to do things, are major elements of a system. For some reason they thought it was very funny that a pile of parts from a car could get up and drive.

If a human’s body is ripped into pieces (legs, feet, hands, arms, head), will that be human? No, it will just be the pieces that a human body is made out of. For this to be a system, the parts have to connect and work together as a whole.

To check their understanding, I asked “who can now explain to everybody what a system is?” Nobody answered.  I just told you what a system was, all I’m asking you to do is repeat what I told you! “We forgot.” Forgot… I explained again, and then each of the kids in turn, explained what a system was in their own words. As you can see, it’s important to ask the kids to explain what they just learned because otherwise, (like in this case), we could’ve moved on through the lesson and I would never have known that they didn’t understand what a system was (and that’s mainly what this lesson is about).

What else is a system?
Nobody could think of anything, so I gave some examples (by asking them some questions).

Examples:
Before giving an example, I asked the kids a question – “do you think a friendship is a system” There was a loud chorus of “No!!” Well then. Let me explain;
·
Ohh…. Now we get it. “Yess! A friendship is a system! How could we not understand earlier”

·         A family is a system – when a child behaves badly, what do the parents do? The parents get angry, right? – The family members’ behaviors are connected and change when others’ behaviors change. If a child behaves well, the parents are happy, and might praise the child. This is also a system.
D.: “That makes sense. If I don’t behave well, my parents get angry also”

Also, there is a loop here: The child behaves badly, the parents get angry, the child starts to cry and behave worse, the parents yell more, the child behaves even worse, the parents yell even more, until… the child smiles and starts to behave. Then it starts to go the other way – the parents smile, the child calms down, the parents calm down, and everything settles back down. This isn’t a very balanced system because to stop the family from getting into a worse and worse mood, something opposite has to happen (the child starts to behave better) for the loop to start going the other way.
“Interesting... so a lot of things are systems – that’s cool!”

Let’s play a game (‘Yay! A game!)– all of you (kids) come and stand in a circle, holding hands. When I do something, you do the same (slightly raise a hand), the next person does the same, then the next, the next, etc, until it comes back to me and again I slightly raise a hand (because that’s what the previous person did), and everyone in the circle continues to slightly raise their hands until their hands are so high that we can’t go any higher and the system breaks. Do the same thing with a negative feedback loop – slightly lower hands until everyone’s on the ground, and again, the system breaks.
They had a lot of fun with this, especially with breaking the system at the end and pretending to die – ok. This system is obviously not balancing.

Here are some more examples of systems:
·
Imagine a forest with only wolves and bunnies. When there become less bunnies, there become (ask - more or less?) wolves. When there become more bunnies, there become more wolves (why?). But when there are more wolves, there become less bunnies, and there become less wolves. So this is a balancing system.
We discussed this for a while, and the kids seemed to really enjoy it. “When there are less bunnies, there are… more wolves because they want to eat” “No! When there are less bunnies there are less wolves because there is less to eat” – correct. Katya, if we didn’t feed you for a day, would you grow more or less? “Less…oh” So now we agree that when there are less bunnies there are less wolves.
Me: “But when there are less wolves are there less or more bunnies?”
Kids “The same amount!”
Why? “Uh…?”
Me: “When there is less wolves eating the bunnies, do there become more or less bunnies?”
Kids “Less bunnies because there is nobody eating them.”
Me: “What? So when there aren’t any wolves hunting you, you die? Why?”
Kids: “OOPS! We meant to say more bunnies”
Me: “But when there become more bunnies, do there become less or more wolves?”
Kids: “Less because there is nothing to eat”
Me : “But when there are less wolves there are more bunnies, right? So there become more wolves again… or no?”
Kids: “Yes because there are more bunnies to eat and when there is more to eat, the wolves can lay more eggs in their nest!”
The parents were sitting on the couch and laughing so hard… J
Kids : “What’s wrong?”
Nothing…
Anyways, it was a very interesting discussion.

Can you think of any systems in your body?

Kids “Our heart! It beats and regulates. It doesn’t just suddenly beat really fast or really slow. It’s making sure that it’s at the right speed. Except when we run. For some reason, when we run, our heart beats very fast. Also our heart is a system because it makes us have blood…”
Me: “That’s one example. Let me give you a few more;”
·
When you breathe in, you don’t just continue breathing in until you burst, right? Your body regulates that you take in the same amount of air as you breathe out.
“We never thought of that…” So is that a system? “Yes.”
·
When it’s hot outside, your body temperature doesn’t just keep increasing and increasing until you boil, right? Your body regulates your body temperature- when it’s cold outside, and your temperature starts to drop, your body warms you up and raises your temperature. When it’s hot outside, your body cools you down. This is another example of a balancing and self-regulating system.
When it’s 0 degrees outside (C°), do you freeze into an icicle? When it’s hot outside, do you melt like a sugar cube? “Oh… so our body keeps us cold, or warm…Yay!” “So that’s a system too… there is a system inside my own body… wow!”

In systems, there are many different processes that regulate and balance the systems.
Let’s play the same game as we just played except that every person has to do the opposite of what the person before them just did (I start with slightly raising my hand, the next person does the opposite- lowers their hand, the next person raises, and the system stays balanced).

They loved the fact that everybody kept raising and lowering their hands and the system still didn’t break and continued to stay balanced.

Cause and effect are important elements of a system. When one thing happens, the other parts of the system change depending on what just happened.
For example, where are the causes and effects here;
·         The boy laughed because his friend told him a funny story
·         The teacher was tired of the students because they were behaving badly
·         The girl tripped because her shoe lace was untied, and she got hurt.
One of the girls gave a lecture to the girl who tripped because her shoelace was untied. J

Now that you know what a system is, can you think of any more?
·        Take a break for systems and do a fun activity;
Take a huge loop of yarn (the size of half a room) and ask the kids to hold it at any place (make sure that there is nothing else in the room or at least a lot of space!) Then tell them to close their eyes and that if they peeks, the game will not work and they will have to sit out. Then, tell them that with their eyes closed, they have to make a square with the yarn (they are allowed to communicate with each other). Try it multiple times and see what happens!
·         We only had a couple of minutes to play, but it came out very funny with everybody tangled. Almost all of them were cheating (their eyes were open) and they still couldn't make a square (or even get untangled). :)

Continue playing with the Handcuff Puzzle for 5-10 minutes and then show the kids the solution. If there is still time left, play Othello.

## Friday, November 8, 2013

### Lesson 6 - Year 2

Introduce the concept of x as an unknown
3 + ? = 5 How do we call ? in math? How can we solve this?
What about ? – 2 =4

The kids can easily solve these, but they can’t explain how they do it “We have done a lot of these in school already so we know the answers” Me: “But what if I gave you one that you haven’t already solved, then how would you solve it?” Kids: “We know how to do all of them (equations) already so you won’t be able to give us one that we don’t know!” Hmm… Anyway, since they can’t explain, life examples are always good. They have to learn that if the equation starts “balanced (equal on both sides)” then if they do the same operation to both sides then the balance will stay (because they didn’t think so at first).

Show with a problem:
*pretending that all apples weigh the same, all bananas weigh the same, all oranges weigh the same
“If you had a scale with an apple and an orange on each side, and it was balanced, then if I take an orange off of each side, will it still be balanced?” Kids: “NO! Of course not!” Well, we’ll need to work on that…

2 apples and 1 orange on one side of a scale, 3 oranges on the other side in this example, are 2 apples equal to 2 oranges? How do you know?
Play with a balance scale and small cubes – taking the same amount away from both sides
Come back to the problem and try it again with new understanding and do a couple more of the same type
By the end of this part of the lesson, the kids should understand that if you take the same amount (of the same thing) away (or add the same amount) to/from each side of an equation, it will stay equal. If the kids still don’t understand, have them do a few more equation examples of the same type, and let them experiment with adding/subtraction amounts from each side and checking if it still stays equal. That should most likely be enough for them to understand.

Try a few substitution problems:
What is apple + apple + apple if apple = 2?
What is orange + apple + banana if orange = 2, apple = 3, and banana = 4
With those same numbers, what is 2 apple + 3 orange?
This is pretty easy and not too interesting but it is good practice and will be useful later on when it gets a lot more complex.

Show the kids a “magic trick” and have the kids figure it out and then do it themselves (every person should get a turn)
Take 10 cards- lay them down slowly one after another until your partner says stop. When they say stop, show them the card that you were going to put down next but haven’t put down yet  (and DON’T LOOK AT IT YOURSELF), and then put that card on top of all of those cards that you have already laid down. Then, put that stack of cards under the rest of the 10 cards (whatever’s left). Find your partner’s card.
I used cards that had pictures on them
The kids thought that it was amazing and said that they will show it to all their friends J The trick is really just that you count how many cards you put down before your partner said stop, and then you subtract that number from ten, and the number of cards that you go through from the top of the deck will be that number. Example: Let’s say you put down 3 cards and then your partner said stop. You know that you are showing them the fourth card. 10-4=6, so after putting the cards you have already put down+your partners card under the rest of the pile, you count 6 cards from the top, and that card will be your partner’s. It actually involves more math than it seems like, and for a kindergarten-age child, is pretty complicated. Anyways, it’s an activity that the kids are enthusiastic to do, and that in itself is already very goodJ.

Handcuff puzzle- escape!
I made the handcuffs out of rubber bands tied together with yarn.
They LOVED it! They were completely tangled up with their partner, stepping under and over the string (and of course giggling). After a couple of minutes, the parents got involved, wanting to try it themselves, and trying to help their kids (and not succeeding). J I asked if they wanted me to show them the solution, and the parents said that “no”, they would need to think about it for another week until next class, and then, after they get to play around with it, then I can show them the answerJ. It was a complete mess. This is really an awesome activity.

### Lesson 5 - Year 2

 Move three matchsticks to make 5 triangles

Warm up:

This was a good warm-up even though it’s pretty easy (all you need to do is move either the left or right triangle to the top (so that two of its vertices would be touching the two other triangles’ vertices). I set up a couple of these so that the kids could work in pairs. Then, I had a pair come up and explain what they did. At some point, the kids had the right solution, but they didn’t understand that it was the right solution because they thought they only made 4 triangles (they didn’t count the big one).

When I was walking to the Orange Village, I met 5 parents. Each parent had three children. Each child had a friend with them. What was the minimum number of people walking to Orange Village?
After a bit of thinking and discussing, they realized that the “I” could’ve been the only one walking there (since everyone else could be walking the other way)
1)
Pretend that a policeman came and told you that someone stole a gold chain from a museum. Facts:

- There are only three people who could’ve done it- Max, Dima, and Sasha (they could’ve done it together with one of the other suspects but those are the only people that could’ve done it)

- Max never does anything bad without Dima

- Sasha can’t drive (let’s say they got there by car)
Was Dima involved?

Thinking…discussing…arguing… After a couple of minutes, they thought of some possibilities of what could’ve happened;
1)      If Max did it, then Dima did it also – in that case, Dima did it
2)      If Sasha did it, then someone would have to be with him because he can’t drive, so it could either be Max (who would be with Dima) or only Dima, which, in both cases, involves Dima
OR…
3)      Dima did it alone, in which case, well… Dima did it.
Deep thinking… “These seem to be no other options except the ones we thought of, and in all the ones we thought of, Dima was involved…” Suddenly the kids’ faces brighten up “Now the policeman knows who to arrest! Ha!”

Play mancala with paper plates and poker chips (that way it is more “hands on” because it bigger than the usual mancala game board)
Very fun, and it involves math and strategy. We slip up into teams- two kids with me, three kids against us. The kids took turns moving, and we played a couple rounds, and mixed up the teams (the kids liked it, but they soon got tired of it).

Make a rectangle out of these pieces (solutions are included in white/gray):

They played around with these for a little while, and solved it, afterwards announcing that since they solved it one way already there was no point in continuing (oh well.)

## Tuesday, October 22, 2013

### Lesson 4- Year 2

1)      A car is driving down a road. Draw the graph, and tell the story.
 Minutes past Distance (miles) from the house 1 1 2 2 3 5 4 7 5 7 6 8 7 9 8 9 9 9 10 5 11 3 12 0

We drew a graph for this on the white board. The story they told went like this- “for the first 2 minutes the car was driving slowly because there was a police car behind it. Then, the police car drove away in the other direction. The car sped up because there was the parent had to get a child to day care. Then for the 4th and 5th minute, the car wasn’t moving because it stopped at the day care and the parents was talking to the instructor. Then the parent drove to the store, and bought a few things, so the car stood in place, and then started driving home. In 3 minute, the car was home.” I had them think about what it means when the time is changing but the distance isn’t (I made a mistake of making it in miles, because none of the kids knew what miles were).
2)      The temperature in the Arctic changes over the week. Kids: make a graph, explain how the temperature is changing.
 Day 1 3 Day 2 5 Day 3 9 Day 4 9 Day 5 9 Day 6 6 Day 7 0
They can’t draw the graph on their own yet, but they can plot the points and connect them with line segments. Ask: “If the temperature changes, but the day doesn’t?” “What if the day changes but the temperature doesn’t?”

3)      Dima, Sasha, Max, and Katya have different pets. Each of them has a kangaroo, a squirrel, a cat, or a bird. Who has which pet? Make a table.
Clues:
§  Dima has a pet that has feathers.
§  Sasha and Katya have pets that don’t start with the first letter of their name.
§  Max’s pet and Dima’s pet have to be kept apart because Max’s may eat Dima’s.
I had the kids draw a chart and put Xs were things can’t be and color the square in when there is surely something there (find the intersection of the name and the animal). It was a good problem for building charts.
4)      There are two villages- one always lies, one always tell the truth. They visit each other sometimes. You come into a village, but you don’t know which one it is. You ask a villager walking by “do you live in this village?” Make a chart of possible answers/liar/truth-teller/lying village/truth-telling village.

They got kind of confused by this one because there were many options of what the villager could answer, but it was still a good exercise for them to think about.

http://www.education.com/worksheet/article/smiley-sudoku-second/
http://www.education.com/worksheet/article/kenken-puzzle-second-1/