Discovering Matrices

I wasn't sure if my Accelerated Algebra 2 kids would be able to "discover matrices", but I wanted to try.

I have taught matrices before - the boring direct teaching, here is the vocab, here are the operations, let's try it, you try it.

Then, I switched to a 3 day project on the computers.  Two days doing a webquest and one day of students presenting to the class.  This went well, but each year, I would feel like there were kids who were still confused.

So, I brought in the idea of "what you notice"?  Matrix Discovery Lab

When I was first designing it, I thought I had to do add, subtract, multiply, and determinants in one day.  Then, I remembered I had planned to do multiplication the second day.  So, I told the kids to do the first and third sheet.  All I told them was that we were starting matrices.  None of them had done or seen them before.

I showed them matrices of different dimensions with the dimensions written and asked, what do you notice?  Some noticed the brackets.  Some figured out the rows and columns, but without those vocab words.  They talked about the height and width.

Then, I gave them 2 addition problems that worked with the answers and one that was not possible.  They figured out why it did and didn't work and they figured out how to add the matrices.  They didn't have the vocab, so they said things like "add the upper left number plus the upper left number and put it in the upper left spot."

Awesome.  They were struggling a little bit to describe it without having the vocab, so they were seeing a need to know the vocab. 

Next up was scalar.  They saw that this looked like a distributive property.

Turn the page and next up is determinant of a 2x2. I gave them two examples, each with the answers.  I told them they could use their calculator.  They worked hard trying to figure something out.  I would say about 3 people in each class figured it out.  Finally, they were onto the 3x3 with answer.  Nope, they didn't figure it out. 

Then, we shared.  What did they figure out about the first few problems?  And, I gave them the vocabulary.  We worked our way through the worksheet, adding the vocabulary and important tips, like how and when.

When I got to the 3x3, they thought I was making it up.  I did the diagonals method.  I color coded it on the board and they got it. 

The usual questions came up, when are we going to use matrices, what is a real world problem with this, what is a determinant used for.  I hinted that they would soon love them.  We have already done 3 equations with 3 unknowns and I suggested that matrices might help us with that type of problem. 

It was a fun class. 

I am going to see what they can do with multiplication.  I am secretly hoping somebody may have already googled it.  I will see if they were curious enough to find out before I teach it.  I think if I was a student I would have done a sneak peek.

How I stifled creativity in math class....

I didn't mean to, really, I didn't.

Last week, in our 20 minutes after block, I had the Algebra 2 kids take out the big whiteboards and work in groups of four to do the four 4's problem.  I instructed them to try and create math equations using only four 4s and the operations to equal 0-25.  They got right to work and I heard some great conversations.  The whiteboards were great.  All four kids working all over the place.

Round 2: I learned that 20 minutes wasn't long enough to do all 26 equations, so I made changes.  I was only going to have my second class do equations totaling 0-20.  Okay.  Oh, yeah, and Back to School parent night is this Thursday, so I will keep a board to show parents. 

My mistake....to tell the kids.

Before I introduced the problem, I told the kids I want to keep one for back to school night.  Then, I explained the problem and they were slow to start.  They were afraid.  They felt they had to be neat and work in order.  I told them they didn't need to do it in order.  Only one person in each group was writing.  The others were thinking and sharing, but only one person actually writing.  They would carefully erase if they didn't get the next consecutive number. 

Oy, what had I done.  I told to forget it, dive in, be messy, work out of order, make mistakes.  Nope, they were too perfect. 

Live and learn.   Here are two examples:

 

By the way, all the groups got stuck at 19.  One boy came back after school to ask if he could use a factorial.  I said sure and he did it = 4! - 4 - (4/4)     At least he was still thinking about it.

Desmos.com Review

I borrowed the idea from Bob Lochel to have my Accelerated Algebra 2 students write a review of Desmos.com's online calculator.  We only used it once in class so far, but the kids loved it.  They wrote some great reviews.  I cut and pasted some into a google doc found here. 

If you haven't tried Desmos yet, what are you waiting for? 

We were looking at all the graphs we are going to be working with this year and added sliders to see the transformations. 

Noticing and Wondering

I have two classes of Accelerated Algebra II, mostly sophomores.  One big class, one small class.  I showed them some equations and asked them to notice and wonder.  The two classes did it quite differently.  I thought I would share.

Disney Project - one of my favorites

Last year at this time, I created a Disney project for my Accelerated Algebra 1 9th grade classes.  It went better than I anticipated. My school has laptops, so they had those to do the research on.  I kept it simple and told them they would have a week to plan Disney.  Their final product is a power point shared with me.  They needed to have at least one math equation, graph, and table in their product.

That's about all I gave them.  (Check back later, I will attach the actual project but I left my school computer at school.)  Update: Here is the Disney Project

Then, we got into groups - they chose them because they would be working with these people.

Next, we brainstormed.  They had to ask me questions about planning the trip.  What did they need to know to plan it?

How will we get there?  I have five groups, so I did five different scenarios.  We live in MA.  One group is flying from Logan.  One group is flying from Providence, RI.  One group will drive the family car.  One group will rent a car.  And, the final group will drive the family car to Maryland, stay over night for free with a family friend and then fly from Maryland to Florida.  There were ooohs and ahhs, and laughs.

Where will we stay?  You have to stay in the park.

When are we going?  You are going Saturday, Nov 2nd - Sat, Nov 9th of this year.

Who is going?  A family of four, 2 adults, one 14 year old child, and one 8 year old child.

Then, they were stuck.  I let them think.  They finally came up with money - how much money do we get?  I gave them $8,000.  They liked it, thought it was good.

Then, we brainstormed what they would need to spend their money on and they did pretty good.  They even thought of parking at the airport.

They quickly got to work and the room was abuzz.

Some groups broke up the work - you do the travel, you do the food, you do the park tickets.  Some started with the travel and all researched different airlines or car rentals.  Some brainstormed in google docs, some on paper.  I loved it.

But, it was the conversations that were priceless:

Conversations heard while planning a trip to Disney: (directed to each other, not me)
"How many nights are we in the park?"
"Can we get a Prius?"  Heard in both classes.
"I did miles/hr.  What else do I need to do?"  
While looking a McDonald's menu, "I am going to save money."
"Can we use my dad's flight points?"
"Can one of the adults be a grandparent so we can get a senior discount."
"I'll get the park tickets.  You get the plane.  We will keep it on the cheap."
"Oh, the Chevy Spark gets $30 mpg."
They used google maps to see the trip.
"Let's camp." "No way, that's $54/night, way too expensive."  "No, that's the cheapest place in the park." - says the group who chose to fly first class.
"We're going to do buffet all day."
"This is so confusing.  How do adults do this?"
When they find the Disney packages and after pricing it separately - "Would it be cheaper to do the package?"
One group is dividing up the family - I'm the dad, you're the mom, etc.  They are "The Millers" and finding pictures of families on line.  "I can't find any good moms."
"How many nights can we stay in the park if we have to travel there and back?"
"Do I actually have to book the car?"  ME: NO!
"$3,000 per week for food - that's ridiculous!"
"Do we have to count the road trip back from Maryland?"  Ummm, yes!
"Can we rent a nanny?"
"When it says under 14 is that 14 year old an adult?"
"Southwest says 2 and over are adults, does that mean we have 4 adults?"

There were lots of giggles and they were really engaged.
Love it!  I only give them a week to do it because some of them would go way overboard.  I assign it now so I can have some nice projects for parent night next Thursday :)

I will try to remember to attach it tomorrow. 

Barbie Bungee - Why did I wait so long?

I think I have been reading about the famous Barbie Bungee for about 2 years now.  I don't know what I was afraid of - lack of time, mostly.  But, you know, just make time. 

I did Barbie Bungee today in two Accelerated Algebra 2 classes.  It was a hit.  They had already learned how to make scatterplots and determine lines of best fit.  Then they made their predictions.  After the activity, I used the Barbie data to introduce the correlation coefficient and how to do linear regression on the calculator. 

Here is all my stuff set up for Barbie:

If you notice the white circles with numbers, those are paper plates that I cut the middle out of.  When my husband and I were practicing Barbie Bungee, he was having a hard time seeing where her head actually went, so he wanted something flat so he could "hear" her head hit...voila the paper plates.  I bought my little boxes from Staples this summer and they were perfect for little boxes of rubber bands. 

Another note, I had a skirt on today to wear, but realized I would be standing up on a table - so don't wear a skirt.  I realized this in time at home to change.

Here are some kids doing it:

I did take a video but can't figure that out yet.  We did have one group who named their Barbie Simone.  Poor Simone lost her head (literally).  I bought really cheap Barbies.  Another one lost her leg. 

It was awesome!  I got to finally have fun with my students in a way I got to know them. 

I highly recommend you try it.

Taco Carts, Marshmallows, Venn Diagram Elephants, and Name Tags

Not necessarily in that order.

It is Thursday and it has been a great week.  I thought I would share.

First, we did whiteboarding with Dan Meyer's 3 Act Taco Cart.  I loved it.  I did it in my Accelerated Algebra I class.  I didn't have to tell them the Pythagorean Theorem.  I didn't have to tell them to divide by the rate.  They figured it out.  It had a great entry point and the kids were hooked.  They made their guesses and went to work.  Here is one board. You can see their guess of "Dan" in the middle and the 4 students' work:

jjjjjj

 In my Accelerated Algebra 2 class, rather than just review the different types of numbers, we used the whiteboards to make a Venn Diagram.  This one isn't quite right, but hey, we learned from our mistakes.  The "I" for irrational numbers turned into a squiggly little animal and then the group "saw" and elephant and went for it.  We did R for Real Numbers, Q for rational, I for irrational, Z for integers, W for Whole and N for Natural numbers.  It was a great discussion.  Some didn't know the difference between natural and whole.  Some didn't know what an integer was (insert gasp).  Some asked what they were if they weren't real numbers, ahhhhh, coming soon to a math room near you. 

jk

I used the name tags with noticing and wondering statements.  From this blog:  Name tags  We folded a paper in half the hot dog way, wrote their name on one side and other side was divided into three days on which to write "I notice...." and "I wonder...."  It went so wonderfully, beyond my expectations.  First, voila, I have a name tag.  I wasn't even considering those benefits to the first week of school, duh!  And, second, it really got the kids noticing and wondering.  They really struggled with it at first.  I am glad I did it for three days because they did get better.  Some things they wrote:

"I notice this room is really hot.  I wonder if it will always be this hot."  Me - No, in the winter, we will be wearing scarves and mittens.

"I notice a large tv.  I wonder what it is for."  Me - Back in the old days, we would hook a vcr up to it, then teachers got computers, and we might be savy enough to hook our computers up to it, but now we have computers and projectors so we don't need the tvs.  They used to project the students making announcements too but we don't do that anymore either.

"I notice catapults in the room.  I wonder if we will use them."  Me - Yes, we will be launching M&Ms soon.

"I notice lots of inspirational posters around the room."  Me - Thank you for noticing.  I love being surrounded by them.

And, finally, the Great Marshmallow Challenge.  I did this with my group of 8 seniors in Futures Math Class.  (They are pulled out from a regular class scenario.)  They did awesome.  We had 2 groups of four.  One group went really tall and it bent over right away.  The other group tested it midway and got it to work.  Then, doubled it in height and it started to bend, so they squished it down some and voila.  

There were some leaders, some frustration, some competitiveness, lots of conversation and smiles and laughs and work!

We watched the TED talk after and had a conversations.

Here are some pictures.

What a great week.  And, tomorrow is Friday, which brings along Barbie Bungee!!!!!!
Thanks to the mathtwitterblogosphere!

 

Graphs & Transformations on Desmos

I have been borrowing a lot from math blogs and twitter but I finally had some time to put something together myself.  Granted, it is built off of someone else's ideas, from here:  Notice and Wonder Equations

Instead of direct teaching all the equations and how they are transformed, I want to use desmos.  Oh, such cool sliders!  So, I typed this up and included noticing, reflection, and prediction.  Here you go: 
Graphs and Transformations on Desmos

I was so excited I am typing this during prep period.  Off to lunch duty.

Having fun getting to know my students

I was trying to find out who did this originally so I could give them credit, but I can't find the person.  I changed the end a little bit.  Autobiography

Today was our 2nd day of classes and the kids handed in their "autobiography".  I loved reading through them. 

I learned that most of my 14 and 15 graders have lived in our town for all of their lives.  Most of them do sports, a whole variety.  I have the accelerated math students so most of them like math. 

They had a hard time with the "write a sports play by play of math class."  This one was my favorite:

"He started with addition and subtraction.  He hit a homerun on timed quizzes.  The ball was turned over to algebra and they started to run trick plays.  He was confused at first, but then he figured them out and tackled every play.  He has still yet to meet an opponent that has beaten him."

They want to learn about: quadratics, graphs, calculus, sig figs, how to open their locker, and functions, LOL.

Here are two pictures about what they don't like about math.  Two different people in two different classes:

These were two more favorites.

And, one more: (what do you want to learn this year)

First Day of School and Bucky the Badger Explains it all

I had my first day of school yesterday after a busy month of August preparing for it.  It went very well.  I had a packed agenda and didn't get to 31-derful in my Accelerated Algebra 1 classes but I did in my Accelerated Algebra 2 class with just 10 minutes left in the class.  They worked in pairs and I had three pairs succeed!
    But, more importantly, I opened with the Bucky the Badger 3 Act by Dan Meyer.  I did it in both levels of Algebra 1 and 2.  I prefaced by explaining what a three act was and that I got to meet Dan Meyer in person and how I hope to use more of them in my classroom.  We listened to the first act about this football mascot having to do pushups for each football score.  One game, the team scored 83 points, and the question becomes, how many push ups did Bucky have to do?  They listened, they were interested. 
      Now, I asked them to guess.  Just quickly guess.  Don't do any math, don't write anything down, just guess.  They were uncomfortable.  Was I for real?  They shifted in their seats.  They looked up in the air.  They looked to see if anyone else was writing anything.  It was hard for them to take a chance and maybe be "wrong".  I moved them along quickly to - pick a number you know is too high and a number you know is too low.  They wrote all of these in their notebooks.  I asked for some of their predictions and wrote them on the board. 

    We moved on to Act 2.  What information do they need to know?  They answered - how many points for a touchdown, how many for a field goal, do they always make the extra point, how many touchdowns and field goals were scored, were there any safetys scored, and finally, what was the order that it all happened in.  Act 2 shows the answers and they were off to work.  I encouraged them to work with their neighbor and to have some discussion.  It was fun to watch them work and listen to their thought processes.  Some worked by adding horizontally, some did a 2 column table, some a 3 column table, some were totally clueless, but slowly worked through each score.  Some lumped the 7 touchdowns together and figured out that that wouldn't work.  There was a group of 2 boys where one came out to 1 number too high and the other boy was 1 number too low.  Interesting. They were persevering (a good math practice).  They didn't want to give up.  They wanted to figure it out.  I gave enough time for most of them to do it.  Some of them found their small calculation mistake or they found out the mistake to what they were doing.  A bunch of them figured out a pattern - imagine that!  I shared the different ways I saw students working.  In the future, I will let them share, but I was quickly running out of time. 

    In Act 3, I shared the answer.  I didn't get into the bit about the "was it really the same badger", but I did ask them about their guesses on the board and a little intro to "what do you notice?"  They were all too low and all around each other.  I asked them if they were indeed uncomfortable making the guesses in the first time and they quickly answered yes.  They don't want to guess.  They want to do the calculation and get it right.  I am going to show them it isn't just about getting the right answer but all the different ways the problem can be solved.  I extended the problem by having them think about if order mattered.  Would it have been a different number of pushups if they 2 field goals were scored first in the game?  I got a mixed batch of answers and asked them to think about that later that night.

   They were persevering, finding patterns, having a math discussion, finding and fixing mistakes, estimating, and problem solving.  I loved it and I think they did too. 

    Now to get ready for day 2.  Thank goodness I had today off.  I went math supply shopping on my day off and practice playing with Barbie bungee.