### Trigonometry, Geometry, Cheating and A New Semeter

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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

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!

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!