Day 174: Guess My Rule

I put this up as the opener for algebra today:

Rule

A large chunk of students quickly jumped to “the previous number times two”.

That wasn’t my rule.

Then they shifted to +2, +4 +6…

That wasn’t my rule either.

Silence for about 2 minutes… Then a student asked “Is the next number 10?”

“That fits my rule” I replied.

This threw ’em all off… They dabbled around with different numbers for a bit, I had fun with it, especially when they pitched crazy numbers like 54, 81, and 1092, which fit my rule.

Eventually, they drifted into trying to find numbers that didn’t fit my rule… which is awesome problem solving.

This really is the heart of what I want to get at through all this factoring, solving, graphing and so on. To me math isn’t so much about memorizing or reproducing a certain skill, but more about taking what you know and tweaking it to solve some crazy problem you have never seen before.

That moment where you have abandoned all hope and try some crazy technique in a problem that you learned months or years ago, which ends up working is what I love about math. The struggle leading up to that moment; following hundreds of self-imposed rules and just sheer grit isn’t easy. It is even more difficult to learn and teaching it takes someone really special.

Everyday I try and very delicately move students towards that direction. With the hopes that maybe, at some point in their lives, in a situation that isn’t even close to math related, they will be able to use their critical thinking abilities, which took years to develop, to solve a difficult problem and experience that felling of having everything fall perfectly into place.

For me, that hope makes everyday worth it.

By the way… my rule was each number had to be larger than the previous. They went crazy over this, some nasty reverse psychology on my end: They automatically see something math related and dive into testing different equations and rules, when really the rule doesn’t require anything fancy. Credit. 

Day 159: Openers

This year I am really happy with the openers I give students each day. However, right now students are burnt out on estimating and visual patterns. I try not to repeat any single type of opener each week, but never seem to quite pull off the review/get-them-thinking about math sorta ones.

Whenever I pick an opener, I try and hit as many of these points as I can:

  • Low entry point so all students are engaged
  • Gets ’em thinking
  • Is relevant to the days lesson
  • Unfolds to become social
  • Takes under 10 minutes
  • Has some sorta aspect that allow students to self-correct

Today was a practice day on solving quadratic equations. Have a look at my opener:

Opener

I am in a weird limbo right now; I want to address misconceptions yet at the same time keep my students engaged because summer time is looming. Depending on how you look at these questions, the opener may hit on all the points above or miss ’em entirely.  In my classes, it produced maybe 50% engagement, while everyone else just wrote down everything down then filibustered.

Here are a couple a questions I have for everyone out there:

  1. On a typical day, what does your classroom look like during the first 10 minutes?
  2. If you have some sort of question on the board to start with, do you a) Have students share responses to the questions, b) Straight up show the answers/work, c) Work through the problems in front of the class, or d) Move on and collect them at a later time for grading.

I am surely overlooking some options for #2.

Maybe my methods are totally off.. Who knows? I am looking forward to some conversation/criticism.

Day 153: A Long Sum

I gave algebra this problem as an opener today.

Day153_1

One period was convinced it had to be one of these three possibilities.

Day153_2

The class was split into thirds when I took a poll on 1, 2, or 3. We talked about what x actually represented and decided to use x = 3 as a test value.

Students were surprised with their results after plugging 3 in for x. I kept saying “If only there were a way to add to over and over without having to do all that work”.

At time time of the year, students get so caught up in multiplying polynomials, finding GCFs, and dealing with exponents that they get tunnel vision and sometimes apply ideas in inappropriate situations. This opener helped put on the breaks.

Day 117: Estimates

Algebra is working on classifying polynomials. Today students dove into a note taking guide. This is the only one I will give all year. I am not quite sure how to approach this topic other than direct instruction. So… instead of lecturing at them I wanted to try having them read the book. It went okay.

I am excited about a sort of gallery walk activity that should go down tomorrow with classifying.

Today I opened all my algebra classes with this

Estimate

I love all the estimates over at Estimation180, however, these are at the top of my list.

Anytime I have high and low students engaged in a mathematical discussion is a win. I all students were into it for about 15 minutes at the start of the period today.

If you haven’t tried this set of estimates with your class…. You should.

Day 115: Clash of Calculators

Well, I bombed a lesson in geometry on geometric mean today. I went way too fast through the different similar triangles, tomorrow is a new day and another try at it. It is my first time through geometry so I am not as prepared in how to explain certain concepts. Whereas this is my third year through this portion of the algebra curriculum.

Anyways… I wanted to share one of my favorite openers (of all time).Calc_Opener

Last year I asked them which calculator is correct. This year I didn’t say anything and let them ask the questions.

We are working on exponents and there have been some good discussions over order of operations since T.I. calculators say -3² = -9 and iPhones say -3² = 9. A good extension on this opener is to ask what solution each calculator would spit out for another expression.

*I don’t remember where this image came from… if you have seen it before let me know and will give out some credit.