Rectangle with GCF

Students and I worked on factoring a trinomial that had a common factor.  Notice that the common factor need not come out of the product first as is often demonstrated.  In the top example, you see that the common factor means that there are two duplicate rectangles to be considered.  In the bottom left, we showed that there are at least two correct ways to factor correctly.  In the bottom right, we see a student who factored out the 2 at the start. 

three related

Two students and I used our skills to factor three polynomials using tiles and grids.  Notice that the rectangles are the same “shape” for all three. For more information and practice on the is method, see the video below.

 

 

Mind=Blown!

Posted: October 30, 2015 in Uncategorized
Tags: ,

stretch example

mindblownOne of my students posted this example of a vertical stretch and wrote the words “wider and taller”…and I said, “wait a sec!”

Usually a vertical stretch makes the graph look taller and “thinner”; but, when I thought about this, it seems that we usually look at graphs where the curves face inward (toward the axis of symmetry or some other center-ish axis).  I  am thinking of a parabola,  a cubic, or a sinusoidal function.  Here however, the curves open away from the center and thus the vertical stretch gets wider.

Notice how some equations are written in vertex form, others are in standard, and others are in factored form.  Bravo, Paige!

sweeny design2sweeny design

Sookochoff’s Calculator Valentine

Here are the functions that will graph a heart in a window with an x-max is 10, x-min is -10, y-min is -7, y-max is 7).  To input the forward slash use the divide key and to input the inequality signs, press 2nd Math.  To use this as a learning opportunity, reflect on how one might graph a circle and a line and how I used these to make a heart.  Also, in the curly brackets, I have restricted the domain of the semi-circles and the lines.  Think about what you know about domain restrictions and how this is working here.  To see the effect of the domain restrictions, try viewing the graph without the domain restrictions.

Math 30-1 students, ask yourself how I used transformations of a circle to make the first four functions.  Look below to understand better how to graph a circle.

All students: compare the Pythagorean Theorem to the functions that graph a circle.  A semi-circle with radius 3 can be graphed with y=sqrt(9-x^2) which comes from 3^2=x^2 + y^2.  Check out some youtube videos about how to graph a circle (a set of points equidistant from a given point.

More for All:  can you graph an arrow through this heart using y=mx+b?  Happy Valentines, everyone.

Challenge:  Can you figure out how to get rid of the extra bits of line at the bottom?  Or can you adjust the window so that the lines are only visible where you want them.

This video, the first in a series from the Hypotenmoose Kitchen, will guide you to build a paper kit from which we can learn much about fractions.

Merry Christmas everyone! I have some friends who write songs and I think this one is funny. It is about Canadian curler, Brad Gushue.

But the math connection for me is also fascinating. How does one create enough interest so that a video goes viral. And what does the graph of the viewing pattern look like.  Here is an interesting article about that. I will post this video’s statistics over the next few days. The chorus is fun to sing.  If you watch on a desk top or laptop, you will see the words. :)

In the last week before winter break, it is tempting to let the curriculum go a little, to kick back and enjoy my students without my mathematical lens. NOT! For me, there is much more pleasure in going deeper into curriculum. If there is something to let go of, it is the “schoolishness” of some math that we do.  In the video below, I was able to revel in one of my favorite topics: factoring polynomials.  This method, based on thinking of products as area and factors as dimensions, was taught to me by Dr. Tom Kieren, an exceptional scholar and educator.

I would like to see this kind of factoring in all our high school classrooms.  It demonstrates three features of a well chosen algorithm:  transparency, error resistance, and memorability.

What could be better than a challenging math activity each day of December!  I wish I could have embedded it here, but alas, this link will have to do.

This one is for Secondary Students:  http://nrich.maths.org/10472.

And this one is for Primary:  http://nrich.maths.org/10473.

These are great launching pads for parent/child interaction.