## Sunday, October 4, 2015

### COMMON CORE: LINKING MEAN AND CENTER OF MASS

Posted by Dave Marain at 12:08 PM 0 comments Links to this post

## Wednesday, August 26, 2015

### Common Core Desmos Activity for Algebra 2 and beyond

Click on graph to see the activity!

Set viewing window: -5<=x<=5

Also, it's better to manually animate the tangent lines by dragging the point or the slider!

Just a simple demo of the power of Desmos to build interactive Investigations for our math students.

Posted by Dave Marain at 3:41 PM 0 comments Links to this post

## Thursday, July 30, 2015

### Balanced Learning is not Blended or Flipped

***BALANCING*** PROCEDURAL LEARNING and CONCEPTUAL UNDERSTANDING.

Oh, Dave, you're so 90s, 80s,70s,... You just don't get it, Dave....

Posted by Dave Marain at 7:53 PM 0 comments Links to this post

## Tuesday, July 28, 2015

### Modeling - What Algebra Looks Like on the New SAT/PSAT and the Common Core

P(t)=M-k(t-20)², 0≤t≤20.

Initial population:356

Max pop'n:500

Estimated population after 10 yrs?

Answer: 464

Should some background be developed BEFORE exploring with technology or AFTER or something in between?

Posted by Dave Marain at 9:20 PM 0 comments Links to this post

## Saturday, July 25, 2015

### 37 not 42 the Answer to The Meaning of Life? A Common Core Investigation

37x13=481

37x22=814

37x14=518

37x23=851

1/27=0.037037...

Posted by Dave Marain at 6:31 AM 0 comments Links to this post

## Monday, July 20, 2015

### Parabolas, NEW PSAT/SAT and the Common Core

As posted on twitter.com/dmarain...

SHOW: The line with slope 1 intersecting y=-(x-h)²+k at its vertex also intersects at (h-1,k-1).

COREFLECTIONS

How would you modify this to make a grid-in or multiple choice question? A question similar to this appears on the published practice NEW PSAT. It is one of the last 3-4 questions on the grid-in with calculator section and was rated "medium" difficulty. I would rate it as more difficult! I recently tweeted the link for this practice test but easy to find on the College Board website.

Do the parameters h,k discourage use of graphing software?

Does the student need the equation of the line to solve the linear-quadratic system? Why does (h-1,k-1) have to be on the line? Then what?

What will be your source of questions like this for your students?

Posted by Dave Marain at 1:11 PM 2 comments Links to this post

## Saturday, July 18, 2015

### Median = Geometric Mean? A Common Core Investigation

As tweeted on twitter.com/dmarain...

J noticed that for an arithmetic sequence like 3,7,11,15,19 the median equals the arithmetic mean. In this case, the median and "mean" are both 11. She found this was well-known and not too difficult to prove.

She wondered if there was an analogous rule for geometric sequences like 2,4,8,16,32. Instead of the arithmetic mean she tried the geometric mean:

(2•4•8•16•32)^(1/5) which equals 8, the median. VERIFY THIS WITHOUT A CALCULATOR!

Unfortunately her conjecture failed for a geometric sequence with an even number of terms like 2,4,8,16 in which the median equals 6 while the GM = 4√2.

(a) Test her conjectures with at least 4 other finite geometric sequences, some with an odd number of terms, some with an even #.

(b) PROVE her conjecture for an odd number of terms.

Hint: If n is odd then a,ar,ar²,...,ar^(n-1) would have an odd # of terms. Why?

(c) How would the definition of median have to be modified for an even # of terms?

COREFLECTIONS

How much arithmetic/algebraic background is needed here?

Arithmetic sequences more than enough for middle schoolers to explore? Geometric too ambitious?

PROOF too sophisticated for middle schoolers? How would you adapt it? We are trying to raise the bar, right?

Posted by Dave Marain at 7:12 PM 2 comments Links to this post

## Sunday, July 12, 2015

### Tangrams Forever...

Posted today on twitter.com/dmarain...

Math educators K-14 have used tangrams for creative activities and to make learning "fun" but the underlying mathematics is rich. Whether you cut out the 7 pieces and rearrange to re-form the original square or a cat or a swan it's all math! Enjoy!

Posted by Dave Marain at 10:02 AM 0 comments Links to this post