Ms. Z : Aha Moments

Showing posts with label Aha Moments. Show all posts

Why do I have to learn this? I am so lucky that 29 years in, I still have Aha's (or Alzheimer's).

sin75⁰ for example. My calculator does this Sh*t, so why should I? I know why, in one of those moments of clarity, because...if I never made you look at the sin75⁰ as the sin(30⁰ + 45⁰) and only let you use your calculator, you would never get to discover that the trig functions are not distributive. Mind blown, KaPow. I have TOLD the students over the years that the functions aren't distributive, but I have never delivered a reasonable reason for why they should care until now.

Another important reason I discovered for WHY Precalculus and Trigonometry students should find the exact value of sin75⁰ is because...I uncovered SO many misconceptions about adding radicals, I felt like a complete idiot that I had assumed a skill level that just wasn't there.

E.D. a student with a 95% average: (✓6 + ✓2)/4 = ✓8/4

V.C. a student with a 90% average: "I have no idea how to add ✓6/4 + ✓2/4

And on and on it went. I felt so lucky to have tripped on this little secret from students with A's and B's in Algebra 2. Phew.

For another time, why do so many students struggle with adding fractions? Anyone? Anyone?

We had a new seating chart in Geometry. I like to use ice breakers to warm the kids up, especially after a break. I sneakily chose this one: Think about your favorite destination in the United States. Share that destination with your "elbow" partner. But I had bigger, more devious designs for their answers.

I needed a lesson idea for unit analysis. I liked this one http://betterlesson.com/lesson/614611/dimensional-analysis from Betterlesson.com that I tweaked.

I asked a student who usually has ants in their pants to come up front and another pair of wigglers to come up also. I gave the antsy one the job of jumper and the wigglers as spotters. The idea was to have wigglers measure a vertical jump. Then I picked a volunteer to tell me their favorite destination, her house. Great. Go on Google Maps and tell me the exact distance in miles from our campus to your house. The question was "How many Ian jumps to Katie's house?" Going from centimeters per jump to miles. I was lucky that a smarty pants student wasn't as smarty pants as he could have been, because he asked Siri how many centimeters in a foot, not the entire distance. Phew. For the next part I let the students design a jumping activity--vertically or horizontally, to one of their destinations, had to go from centimeters to miles. For their partner's destination they had to use "strides in one trip across the room." As in there are how many Susie trips across the classroom to get to Imagination Island? Again from centimeters to miles. As it was raining, this was a great activity. The one stipulation was that they had to use the centimeter to foot conversion that smarty pants came up with.

The next morning I showed them this picture:

And asked what questions did they have?
Then I said to look over with their partners what questions could be answered knowing that the ball used 840,000 rubber bands and 1/4 bag of 3" rubber bands contains 460 rubber bands. Our calculations were way off, but we had a lot of fun and asked what could have led us astray.

Their homework was from a blog post I found on the MTBoS search engine Ms Z Teaches in Mathland
(Hey, that is my own blog post from 3 years ago, almost to the day!). Their job was to take something that they threw away, and measure it by length, area, or volume, determine how much it would be if every person in Windsor used the same amount, and make that amount TELL A STORY. So what if it is 1,000 miles long. Give us an exact location. Can the amount fit in our classroom, in the gym, fill Lake Tahoe? Students were exited to show me how far pieces of paper used lined up in a year (4,000 miles shy of the moon lined up end to end). Can't wait to see their illustrations!

Does this count as modeling?

About how kids are cheating these days next time.

Hope you have good times with your kiddos this year!

This post is inspired by my blogging buddy Christopher at Overthinking my teaching:

18 year old daughter going off to University in Washington D.C. this fall:

SB: MOM! Is this a 9 x 13 pan? (check pan on top of picture)

Me: OY VEY! Really, they are going to let you graduate with honors? Should I sue the school?

Daughter's first try top: Mom to rescue Bottom

SB: Oh Mom, You are sooooooooooo dramatic!

7th Block...yeah you read that correctly...block...put 28 mostly 9th grade Algebra 1 students in a basement room after three 95 minute block classes, lunch, and no air conditioning and you get...my favorite class of the day!

We started with the premise that it sort of sucked to be us...and we rock! The basement is empty, everyone is gone. We watch the feet of athletes and the "lucky" students departing campus before we even start our warm- up ( our windows are below ground). But guess what? We get to make noise! No one yells at us or sends us notes to be quiet! We hoop and holler about...MATH! We shout out answers! We eat lollipops and take teeny tiny breaks.

Today I was moving the students along this line of thinking:

So we did three old and one with a new twist together. They were getting it.

I stopped them and said, there is a story about why we study this kind of equation, and not mentioning it to you would be really mean on my part and would lead all of you into thinking Algebra was just smushing a bunch of numbers around (I said an exercise in futility, but I think I lost them).

So I told them the good ol' yarn about how it takes me 5 hours to paint the livingroom by myself because I am easily distracted and how it only takes my husband 3 hours because he is concrete sequential...Then we saw the POWER in doing a job together! The students were actually impressed...which led to a discussion about the alternative economy and what they could do to earn money (I said offer your neighbors to vacuum for $5 per room, or $10 to load the dishwasher and wipe down the sink after dinner). I also told them about the water treatment plant and how some liquid is pumped in and others are pumped out at different rates. (hence the possible minuses in the equations)

They WANTED to know how long it took Dom's uncle to replace the clutch on his '74 BMW by himself when it took Dom 8 hours by himself and took them 3.5 hours together. One of my squirrelly 9th graders (who will be repeating Algebra 1 next year) and who is beginning to think like a Sophomore said, "hey, I get this, this is kinda fun."

May not be a 3 Act yet...but it was still a powerful afternoon.

My Student, A, is a nice kid. This doesn't say all there is to say about A, but it says a lot:

He mostly pays attention...he is a bit of a clueless wonder in Algebra, although his arithmetic skills are super strong. He is affable and wants to do better. He does an entire page of work...and it is all incorrect. My main theory about A. is that he comes from a family where he hasn't been shown how to study, that he is just under-exposed to "how to do school."

When Fawn Nguyen says Do These Two Things, you better listen, and here's why:

I was telling my students a story (1. Do talk to your students about yourself)
about how I spent my Saturday morning having breakfast with a bunch of fellow nerds at the Sonoma County Math Council's Breakfast. It was a rare lecture, usually we get to the business of getting dirty in some math activity. John Martin is an amazing lecturer, funny, light, thoughtful, inspiring...he must be from Midwest originally, he is just so nice. His talk was on the Golden Ratio, and he was giving a shout out to Fibonacci along the way. In addition to explaining a rather elaborate way to convert miles to kilometers using Fibonacci Numbers that only a mathematician can appreciate, he went on to show us that the 100th Fibonacci Number is in the quintillions! This is just astonishing to me! So I shared my astonishment with my students.

~~Alex~~ A, thought it was astonshing too. Before you look at the picture below and really absorb the profroundity of what is happening here, re-examine the picture above:

Powerful image. We see so clearly what is right and now I have to ask myself what is wrong with A's picture and what can I do about it?

(PS, the next class is right before lunch and the kids are STARVING) A girl in front busts out a package of seaweed (we are from Sebastopol after all) and you know what...the ratio of length to width in those sheets is 1.55, intersting, eh?

Thanks John for the inspiration...and a little pat on my back for spending my glorious Saturday morning...in mathland.

Oh and anyone have a better title for this piece?

1. Ross, a student with an IEP, Grade 10, repeating Algebra, making a little more progress than last year. Very quiet.
Students are in Part 1 of a Diagnostic Teaching Lesson ALA Phil Daro.
The problem is "What is the longest pencil that can fit into an 8"by 4" by 3" pencil box?"

The class has read the problem together. The students have had 80-90 silent seconds to put some of their initial thoughts about the problem on their papers. The students get to ask any clarifying questions before we begin working in partners to solve the problem. Quiet ol' Ross raises his hand and asks, "It that the measurement from the exterior or interior of the box?" That guy got at least 50 virtual pieces of candy.

2. D. Gr 9 whom I caught fighting with boxing gloves on in the Safeway parking lot across the street from school during the first week of the school year, is now passing all of his classes and is trying very hard to catch up in Algebra. I picked up a textbook off the ground near his desk. Me: I can't stand when a textbook is on the floor. D: I know all books are precious, they are the reason we are here, why would anyone show such disrespect? (Me: with big cartoon bubble, really, my bad ass D, just said that...oh my happy heart!)

3. Daughter is going to American University in the fall and will be in the University College Program for International Relations. Makes me happy in so many ways, just two are that AU is one of the most racially diverse colleges in the US, and AU is ranked the highest for their study abroad programs. (not happy at all about price, but they threw us a 20% bone...that will surely help, and Grandma, and Grandpa, and us, and her...we'll figure it out baby girl!)

First week back from Spring Break is always daunting, don't you think? Kids are feeling the hints of summer freedom, they forgot that the "F word" is factoring, not the expletive, and the STAR is looming.

And it is also an interesting time for a maturity growth spurt for my Freshman Algebra students.

On Wednesday the third day back:

Student 1 to Student 2: I am so going to tell Mrs. K. (their 8th grade Algebra Teacher) how much I hated taking all those notes but now I am SO glad I have them so I can figure out how to do this stuff.

Okay, I'll admit I was so butt hurt. Really. But then I got to thinking about it. Now they want to learn it. Why now, and why are they not using their interactive notebooks? Because maybe now they are motivated. Maybe now, they see big picture and they see the math in context, not just as a set of procedures. Does the SAT or a Physics textbook problem set say, "For this problem you will need to set the quadratic equal to zero and then you need to take out the GCF?" Of course I summarized for the students in a flipbook what it means to factor, but I don't give them a problem set with each step illuminated for them. I just keep repeating, "remember the flipbook we made about factoring? Read the first page!"

What do you think?

First Day on the Job at Las Brisas School in Chacraseca, Nicaragua

I used to think when my students graduated from their local town high school in Windsor, California, they should be handed a one way bus ticket to an unknown destination with their diplomas. Now, however, after spending 10 days double digging twenty-three 4' x 12' vegetable beds in a RURAL school in the 2nd poorest country in Latin America, I have changed my mind. If you want students to get behind their own success, send them into the rural communities in developing countries whose fertile land was stripped by the agro-industrialists and left to rot when the prices of their commodities dropped.

The program I had the privilege of chaperoning 14 High School students on is Global Student Embassy (GSE), a youth leadership program that emphasizes sustainable food and reforestation projects in Latin America. GSE partners with Students for 60,000, to build schools and provide the school families with a sustainable means of feeding themselves. We worked at Las Brisas, a fairly new school to 150 students (yes, they are all housed in that those four rooms) in Chacarseca, Nicaragua, 45 minutes by bus from Leon. (The American engineer who has designed and in overseeing the installation of bringing running water to the school, rides his Honda 650 motorcycle to the location in just 20 minutes). The school is accessed by 2-3 kilometers of paved road before one goes bouncing and bumping down 8? 10? 12? kilometers of rutted, rocky, dirt road. Students arrive at the school by bike, on foot, motorcycle, or horseback.

So what is the connection to getting students behind their own success and that one bus ticket?

We GET 7.5 hours of school per day. We GET 4 years of English, 4 years of Math and Science, and 4 years of Social Studies, not to mention the opportunities for 4 years of language study, AP Art, AP Sciences, PE, Jazz Band, Digital Photography, Dance, Leadership, Ceramics, and Drama.

Students in rural Nicaragua go to school, if their parents can afford giving their children the day away from the farm for 4 to 5 hours per day. They take Spanish, English, Math, and Science. Some get PE and a Practical hour during the week.

After 4 back breaking days of pick axing, mixing concrete, and weeding, my 14 students are MOTIVATED to do whatever it takes to go to college. They see the power in giving themselves choices, including the choice to do more than serve, but learn how to help those who have fewer choices achieve independence and have the opportunity to choose the direction of their lives too.

I am so inspired by my students and the twenty-something leadership team. These young men and women actively serve as amazing role models to the students. Between the four leaders, they have 4 Bachelor's Degrees and 3 Master's Degrees and are passionately finding ways to heal and sustain the Earth. (They range in age from 24 to 29.)

Final Bed. That building in the background houses the Boy's and Girl's (and teacher's) restrooms, concrete pit toilets.

Back to the homework, school work connection. These kids met some amazing Nicaraguan youth whom had skills our students were floored by. And now they are ready to come home with a new appreciation of the gifts they have been given, including the opportunity to do their homework.