I had about 20 minutes after a test today, and RIGHT before the test, a high school student in precalculus was confused about how to divide 2 fractions, and she couldn't remember the method: "do you multiply the top and bottom?" were words that came out of her mouth.

So. I thought I'd give the following short lesson on why the "flip and multiply" that they seem to spout works.

First I asked them the following questions:

Simplify: (7/3) / (4/5)

Then after they did that and checked, I asked them to discuss WHY it worked, and "my teacher said so" or some such thing wasn't an option.

Then we walked through the following 4 scenarios:

So to recap, it basically boils down to seeing how many groups of the denominator fit into 1 unit (that's where the "flip" comes from), and then how many 1's fit into the numerator, and then you combine the 2 numbers and MATH.

# Math Teacher Mambo

“What will you do with your one precious, wild life?” ― Mary Oliver

## Thursday, October 23, 2014

## Saturday, October 18, 2014

### Boring Ceiling. Fixed That For You.

Something needed to change. I could no longer stand the travesty that was my ceiling. How could we spend day in and day out under such a boring mess? How was learning taking place? How did we all not just fall asleep under the endless white scandal that was looming over our heads?

After searching the internet for ideas and finding an art teacher that had her kids paint black and white designs ON the tiles and realizing I didn't want to go THAT far, I came up with:

I am happy with the results. I still need more, as not all kids chose the opportunity. And as a side note ... for all the questions I get about bonus points, you'd think I'd be drowning under a pile of drawings, but, nope. Nada. I am not one for bonus points, and this was a rare instance, but, hah, go figure.

After searching the internet for ideas and finding an art teacher that had her kids paint black and white designs ON the tiles and realizing I didn't want to go THAT far, I came up with:

I am happy with the results. I still need more, as not all kids chose the opportunity. And as a side note ... for all the questions I get about bonus points, you'd think I'd be drowning under a pile of drawings, but, nope. Nada. I am not one for bonus points, and this was a rare instance, but, hah, go figure.

## Thursday, October 16, 2014

### Intermediate Value Theorem

I have never liked my unit as a whole for the Intermediate Value Theorem in Calculus. My explanations, I like, my homework and the time the kids spend thinking about it and then quickly forgetting it, I don't like.

I like this first page because the kids have to stop and process the whole IVTh and think about the parts and then analyze the parts and see what goes wrong. I heard some good discussion.

I like this second page because for 5 and 6 they then have to start the thinking process graphically on how to apply the IVTh. Then problems 7-9 are what I just used to do by themselves. Hopefully, this year after they've processed things, then 7-9 should go better. We will see.

In other news, apparently I make kids feel dumb - based on a conversation I had with a parent. Oy! They interpret how I talk to them as just expecting them to know things already. Of course it's an obvious logical conclusion on my part that "one kid" implies THE WHOLE CLASS. Go me! Because of this, I made the following handout, and we had a discussion, and I asked them to tape this in their notebooks (or staple it to their hearts) to remember:

**Attempt**this year:I like this first page because the kids have to stop and process the whole IVTh and think about the parts and then analyze the parts and see what goes wrong. I heard some good discussion.

I like this second page because for 5 and 6 they then have to start the thinking process graphically on how to apply the IVTh. Then problems 7-9 are what I just used to do by themselves. Hopefully, this year after they've processed things, then 7-9 should go better. We will see.

In other news, apparently I make kids feel dumb - based on a conversation I had with a parent. Oy! They interpret how I talk to them as just expecting them to know things already. Of course it's an obvious logical conclusion on my part that "one kid" implies THE WHOLE CLASS. Go me! Because of this, I made the following handout, and we had a discussion, and I asked them to tape this in their notebooks (or staple it to their hearts) to remember:

## Monday, October 06, 2014

### Trig Identity Match Up Activity

I'm on my quest to try different things for the Trigonometric Identities unit. They explored last class, and today I wanted to get them started on simplifying various trig expressions using identities. Here's what I did. I made

They're mixed up on the sheets, and there are FOUR total problems that start with the "squiggly" boxes, but I didn't tell them that first. I said they should look for 2 cards that pair up in such a way that they are ONE step away from each other either by an algebra law or by an identity. I did one example with them and took questions. Then they were on their way.

Since they sit at tables, and I didn't want to do different colors of sheets of paper (though I guess I could have), I had them draw dots in different colored pens (one per set) at the bottom right corner of their cards to avoid mix up.

Once they got as many pairs as they could, and I mentioned that depending on a variety of things they may not get pairs. Then I said they could try to find a "triple" pair for their remaining lone cards. After some time for this, then I asked if they can "pair up" the pairs to get a set of four .... Ultimately, I then said, or they noticed the "squiggle" cards, and we got to the point that there are FOUR separate problems, that each start with a squiggle card, so see if you can set up 4 different strings of "one steppers".

**this set**of 2 sheets for every student, put it on colored paper, and then made them cut them up (my first class) when they started.They're mixed up on the sheets, and there are FOUR total problems that start with the "squiggly" boxes, but I didn't tell them that first. I said they should look for 2 cards that pair up in such a way that they are ONE step away from each other either by an algebra law or by an identity. I did one example with them and took questions. Then they were on their way.

Since they sit at tables, and I didn't want to do different colors of sheets of paper (though I guess I could have), I had them draw dots in different colored pens (one per set) at the bottom right corner of their cards to avoid mix up.

Once they got as many pairs as they could, and I mentioned that depending on a variety of things they may not get pairs. Then I said they could try to find a "triple" pair for their remaining lone cards. After some time for this, then I asked if they can "pair up" the pairs to get a set of four .... Ultimately, I then said, or they noticed the "squiggle" cards, and we got to the point that there are FOUR separate problems, that each start with a squiggle card, so see if you can set up 4 different strings of "one steppers".

During all this they had their "

**notes**" on pink paper that they were going to eventually tape in their notebooks.
This all took about an hour or so to give them think time, and not everyone was successful with all of them, but we came together as a class and talked it out and got the 4 sets of problems, and celebrated any successes they had. Some problems had 7 steps, some 6, some 4. Then students taped the notes in their books, and we copied down 2 of the problems into their notes with "reasons". Hopefully, this will aid in their homework tonight where they have to do a string of one steps for each problem.

## Friday, October 03, 2014

### Trig Identities

We have started our unit on Trigonometric Identities in precalculus. Every year is going to be THE YEAR where it all comes together nicely, and the sun comes out and the birdies chirp and the kids embrace their Identities. Yes. It will happen. Chirp. Chirp.

I took some extra time at the start of the unit this year for them to

**explore**instead of me walking them through things and them nodding their heads pretending to understand.
This took most of a block period (2 pages), and it was a nice refresher of a few things:

* proof rules from geometry

* fraction rules for adding/dividing

* exponent rules

Hopefully, the extra time we spent will be worth it in the end as we skip and hop through solving/simplifying various equations/expressions involving trig.

## Friday, September 26, 2014

### Learning is Hard

Students are learning to solder in Digital Electronics. I let them tinker and figure a lot out for themselves. I do give them tips, and we had a safety discussion, and we saw a soldering video and we talked some more. But basically, once they have the kits, they have to jump right in to something they are not comfortable with.

There are casualties.

Hopefully, this is not a symbol on how they feel inside.

There are casualties.

Hopefully, this is not a symbol on how they feel inside.

## Monday, September 15, 2014

### Basic Derivative Rules

Last year our school got "schooled" on Kagan strategies, and one I liked was "Quiz Quiz Trade". I used that today for about 10 minutes for my calculus students to help each other learn some basic derivative strategies for monomials.

They always struggle if there are radicals or x's in the denominator or fractional exponents. I have tried in the past to get them to rewrite the f(x) first as ax

Quiz Quiz Trade to the rescue. They get practice, and they have to explain, and they have another student helping them, and they want to understand. I think it helped this year, since I had less questions when they started their homework.

Here is my

They always struggle if there are radicals or x's in the denominator or fractional exponents. I have tried in the past to get them to rewrite the f(x) first as ax

^{b}. But after they nod their heads "yea yea", they go back to messing up.Quiz Quiz Trade to the rescue. They get practice, and they have to explain, and they have another student helping them, and they want to understand. I think it helped this year, since I had less questions when they started their homework.

Here is my

**template**for cards that looked like this:`Quiz Quiz Trade Rules:`

` `

`You have to model this and keep an eye on them and move them along.`

`1. You raise your hand high when you need a new partner and you search for `

` another hand and you pair off.`

`2. You greet each other with eye contact (social skills)`

`3. One person holds their card, question side facing partner.`

`4. The quiz-ee tries to answer it.`

`5. If correct, you praise the quiz-ee (social skill).`

`6. If wrong, you give hints on how to get to answer .... until answer correct, `

` then praise.`

`7. The quiz-ee is now the quiz-or and does 3-6.`

`8. When both done, TRADE. and go to 1.`

` `

` `

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