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?

What about apple+apple-apple+banana?

 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.)