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## Thursday, January 22, 2015

### Doesn't memory matter anymore?

Florida's FSA Mathematics Reference Sheets Packet (original is here)contains the conversions given here in each of its state tests from 4th grade through Algebra 2.

Doesn't memory matter anymore?  If Americans are to come out of public school knowing anything at all, shouldn't the list here be part of that knowledge?

This chart (along with others equally scary) are included in Florida tests, which tells me that students do not have to remember them. That means that you can be called successful in Florida schools without knowing any of them. That is scary.

The following is from the Common Core State Standards Initiative in its materials for 4th grade (The red is mine):

"Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ..."

Even Common Core is aware that some things just need to be known.
Is Florida the only state that thinks otherwise?

## Wednesday, January 21, 2015

I do not normally post twice in the same day, but here is number 2:

Here you will see two snippets from New York and Florida.

The first is from New York's Educator Guide to the Regents Examination in Geometry (Common Core) from November 2014.

The second is from Florida's Geometry End-of-Course Assessment Sample Questions.

Note that is you use 3.1416 as an approximation for π, your are evidently breaking the rules in both states.

To all those who have a good solid answer as to what should best be used. all I will say is I'll bet 355133  is as good as most (not all) people need.  Check it out.

### Be careful America. Carelessness is dangerous.

Below is a question from the August 2014 New York State Regents Exam in Integrated Algebra. Although it is multiple choice, I have left the choices out because they do not matter here.
Do you understand this question? If you do, you will recognize that it is written poorly.

You do NOT see the "parabolic path of a ball kicked by a young child". If you did, it would be in  two length based dimensions (a 3 dimensional perspective diagram might be going overboard...). The axis cannot be labeled as "time" if the graph is meant to represent a "path."

Below is an edited version of the problem that would have been fine.

## Tuesday, January 20, 2015

### Using polynomials to graph a circle

Drag the slider and you will see the red graph get a better and better approximation to the circle.
The x and y coordinates are calculated from polynomials, and those polynomials are changing as the slider is dragged.
Although this creation is made based on calculus and trig, the fact is that it can be appreciated by people who have no knowledge of either.

Carpe diem.

## Monday, January 19, 2015

### Look at the actual tests. Please do.

The above question is from the Regents Examination in Algebra I (Common Core) Sample Questions Fall 2013 (link to it from EngageNY's page here).

The big question to the test writers and test takers is this: what are the solutions if the quadratic formula is not used?

Some people may chuckle at this, but it seriously takes into question the skill level of the creators of the test. Admittedly, the method first taught in school is factoring, and that method will not work. However, completing the square will do an admirable job.

In addition, a quick graph on a graphic calculator (which students are required to have) would allow solvers to identify the roots to the nearest integer, then calculate the four choices to see what is reasonable.

Also, with a graphic calculator, one could  get a fairly decent decimal approximation and then calculate the choices to see which one "pairs up". I haven't worked with a TI calculator in a few years, but I can pretty much be assured that there are at least 2 or 3 ways of getting decimal approximations to roots (x-intercepts).

In general the question is misleading and poorly written. Imagine a student who is the master of calculators and quadratics who skips this question because they never liked the quadratic formula.

Below is a comparable question from the first of these tests (Regents Examination in Algebra I (Common Core) from June 2014)  that was actually used. See the difference? Much better.

## Thursday, January 15, 2015

### Just a beating heart...

As I explore more with GeoGebra, I envy those teachers who get to use it.
Just a little doodling here in anticipation of next month.
If you want to see how it was done, click here.

## Tuesday, January 13, 2015

### Give me your tired, your poor, Your huddled non-mathematicians, yearning to breathe free

Here we have a pentagon with 5 equal sides, and all its diagonals drawn in. This diagram is actually made up of pieces with 4 different lengths. One piece is colored for each of those length.
Your job, non-mathematician, is to divide the orange length by the red length, the red length by the blue length, and the blue length by the green length. You may drag the two labeled points wherever you want (make sure you can see the lengths!).

What do you notice? You are on your way to a mathematical discovery.

## Monday, January 12, 2015

### What if...................

Today has just been one of those days when I wonder what it would be like to be in the classroom with technology such as GeoGebra. For some reason, I think that Common Core would be promoting such technologies, but the testing that has grown up around it would be forcing me to forego such things. Who knows. Here is just a "doodle" from this morning. Enjoy.

## Monday, January 5, 2015

### Algebra 1 and pencils

The New York State Common Core Sample Questions for the Regents exam in Algebra 1 (Common Core) from fall 2013 (see it here) includes the following situation in question 12:

At an office supply store, if a customer purchases fewer than 10 pencils, the cost of each pencil is $1.75. If a customer purchases 10 or more pencils, the cost of each pencil is$1.25.

I find this question to be a microcosm of our society in the new millennium.  Overlooking the fact that a dozen pencils should cost less than two bucks, let's let the costs be as stated.

I need 9 pencils. Do I overspend and pay out $15.75 (eight times$1.75) or do I buy 10 for \$12.50 and just toss the one I do not need?  Do I waste money or waste product? (I use those last two words wisely.)

Which is the intelligent choice?

## Friday, January 2, 2015

### Regents Examination in Geometry (Common Core) Sample Items Fall 2014: Question 4 is BAD!!!!!

Here is question 4 from the Fall 2014 New York State Common Core Sample Questions for the Regents Examination in Geometry (Common Core) You can find it here.

Here is the sample solution.

This question is a RED FLAG!!  The question is misleading and the answer is wrong!!!

The answer assumes that the vertex of angle B is at the center of the circle. There is nothing in the statement of the question that stipulates this.  In point of fact, the angle can change depending upon exactly where in the circle that vertex is. Drag that vertex in the diagram below.

A major MAJOR point in any Geometry course is, and must be, that care must be taken about making assumptions based on appearance. Just because the vertex looks like it could be the center does not mean it is.