Two recent problems.

Ok...this was a mathcounts problem that we could not get for several days.   We finally were albe to find a few ways to solve it.  Do not scroll down to the hint, unless of course you would like to see the hint.  I will not post the solution.

Hint: draw a line from H to I, and then another line from D to F.  Go after it with some right triangle trig!

Problem #2

Then here is another photo of a problem I do not have a solution for.  Why should vehicles that get better gas mileage get to park closer to Best Buy?

So I like to hang around 101questions.com.  Dan Meyer has inspired me to look for sharper hooks, often in images or video.  Most importantly they make students care.  I use quite a bit of his three act problems.  

Which problem would you rather discuss?

Dan Meyer and INDY NCTM regional conference 2014

Great conference.   Go to experience Dan Meyer and one of his three acts live.  Here he is...super tall by the way, over 6'4".  Fun problem.  Interesting discussion on how to find the most exact area of a circle.   Is it easier to measure the diameter of a circle or the radius?

Fractal Forest

Fractals can be quite a lot of fun.  They often encourage students to explore patterns and create their own patterns.  They are fit for STEAM.  

Each week I have the sixth grade for a period called Problem Solving.  We have been working on fractals....both two dimensional and three dimentional.   Here is my board after we tried to make fractal trees.

Here is a picture of a Brocoflower...one of my students brought it in to share.  It was found at the local farmers market.  We fiddled with this  guy so much in class I decided not to eat it.  Seems a great combination...broccoli and coliflower? 

Student Reference Sheets and ISTEP

What we give students.

Indiana just published a new math reference sheet.  I do not know which part of this sheet bothers me the most.
1) The odd mix of volumes of solids, with inconsistent use of "B", for the area of the base.  But wait, look at the formula for a cone, here the area of the base is spelled out.  I think this takes away from the general understanding of how we can go about finding the volume of a solid.  Maybe it is just me.

2) Just the abc's of Pythagorean Theorem.  We need more here, it falls short of the story it tells about all triangles.  

3) What are those = signs doing with those conversions!!  The only one that is correct is 1inch=2.54cm.  Precision indeed!!

I am all for leveling the mathematical playing field by giving students the formulas on SAT, ACT, ISTEP, ECA exam....But what Indiana is giving the students is ambiguous, not true, and vague.
Here it is.

A Day of Math Pd

I really thought today was going to be great!  I had put together a presentation and activities for the k-5 math teachers in the building on problem solving.  It was bad.   Lots of silence, very little participation,and energy.  What went wrong?   I swear the problem we all worked was excellent, the resources we used to find good problems were great, and the reflection we all did on what makes a good problem was relevant and worthwhile.  I do not know.

   

This is not the first time I have done in-service for other math teachers and came out wondering what just happened.   I think part of it is my expectations.  Just because I think I have put together a brilliant PD, does not mean others will think it is.....especially if it not for math teachers.   I have been surprised in the past. It is important for me to look through the eyes of an elementary teacher, where Math is important, but does not take up the day.  So i thought I had that covered today.  I thought wrong.

Ugh.  I feel like  I just taught a poor lesson, but I am not sure why it was bad?  At least when I am teaching I know what I could have done to improve the lesson.   Teaching adults is not as easy as teaching children.  I know children.

1st POST: Why am I here? The Proof

So I have been wanting to start a blog.  Here it is.   The past few years I have been going to blogs to reflect and get ideas from other math teachers.  I want to record some of those travels.... a blog is like a photo album of teaching.  A record.  Maybe someone will come here and learn something or get inspired.

I teach at The Hasten Hebrew Academy of Indianapolis.   This is a small private jewish day school on the north side of Indy.  I am the head of the middle school and teach mathematics to children in grades 4-8.  My classes include 6th grade math, Pre-Algebra, Algebra, and Geometry.

Blogs are full of ideas for new activities and good problems to solve.  This past month I have been introducing proofs to my Geometry class.  The book seemed too prescribed and dull.  There is almost nothing in the book to help students understand what a proof is.....and very little variety beyond two column geometric proofs.  I was able to gather some good thoughts on how to present my students some great ideas about proofs.  John Benson, a former colleague I used to teach with in Evanston, had some great ideas on his blog, Angles of Reflection.  This blog has the best general math teaching advice.

As I hunted around and found great ideas for helping students see the power of proof.  Students really enjoyed these WORDs activities.  They saw how a set of rules could be made for us to follow.  Deductive reasoning became a fun game, a logic puzzle.

We then looked at proofs that we could not solve.  When I heard my students explain what they needed to do in order to solve I felt like progress had been made.   Then we looked at proofs that were deceiving, ones they lead you down the wrong road.  Here are some examples.

I will have to wait and see if this helps create a foundation in "proof in geometry" as we will me doing proofs all year long