Sunday, April 20, 2014

A Common Core Alg Activity Using Desmos - Piecewise Linear Functions and Squares

 This is my first attempt to use Desmos, the outstanding free online graphing calculator (and a free iPad app). I'm sure many of you have been utilizing this powerful resource. There are already many available teacher samples you can use.


 Let me know if you can view the graph (you may have to adjust the window slightly). More importantly, what do you think of the activity and do you see its potential for deepening understanding of algebra?

 If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar. 175 problems divided into 35 quizzes with answers at back and DETAILED SOLUTIONS/STRATEGIES for the 1st 8 quizzes. Suitable for SAT I, Math I/II Subject Tests, Common Core Assessments, Math Contest practice and Daily/Weekly Problems of the Day. Includes multiple choice, case I/II/III type and constructed response items. Price is $9.95. Secured pdf will be emailed when purchase is verified.

Tuesday, April 15, 2014

Another Common Core Rant - not a video...

While I agree with the concerns of many parents that over-testing is damaging to children and subverts the purpose of education, I don't believe that the Common Core has set the bar too high, at least in math, my area of expertise. I know from direct experience with children that we can expect far more thinking of them than is commonly held. That is the Core Belief of my blog.

The problem is that teachers have not received the necessary preparation and the testing has been rushed and lacking in quality control.

We're trying to set the bar higher for children without raising the bar for those responsible for implementing these changes. That is irresponsible at best and criminal at worst.

Saturday, April 5, 2014

Developing Fraction Sense Using Egyptian Fractions

This MathCast describes a procedure for writing proper fractions as a sum of unit fractions, e.g., 5/6=1/2+1/3. This exploration is appropriate for Gr5 on up.A simplified form of the Greedy Algorithm.
Watch "Developing Fraction Sense Using Egyptian Fractions" on YouTube:
I'm experimenting with embedding these MathCasts directly into my blog post, however, the audio may not come out right. May work on your computer but not your tablets or smartphones. Please let me know. If there is a problem you can just click on the link to YouTube.

Sunday, March 30, 2014

A Data-Based Percent Problem for the New SAT and Common Core

The MathCast below is a more sophisticated % problem which requires processing several pieces of data expressed in percent form. Students have to make sense of the information and  develop a model to represent the data. Both a tree model and a table/spreadsheet approach are demonstrated.

These are the kinds of data-based applications which will become a central theme of the newer assessments from PARCC, SBAC and the College Board.

Sorry, you'll have to watch the video to see the problem but I'll give you a glimpse:

70% of the left-handed students surveyed were boys...

Watch "SAT/Common Core Data-based Percent Challenge" on YouTube - SAT/Common Core Data-based Percent Challenge:

Also, pls let me know if these MathCasts are blurry.

Monday, March 24, 2014

40% of 9th graders play sports...Math Challenges for the Old/New SAT and the Common Core

David Coleman of the College Board has stated that ratios, percents, etc., will be an important focus of the new SAT, particularly in an applied setting.The MathCast below demonstrates a classic medium-hard percent word problem which should continue on all of our "new" assessments.

Watch "40% of the 9th grade... Percents,New SAT and…" on YouTube-40% of the 9th grade... Percents, the New SAT and…:

I encourage all my readers to offer constructive criticism re both the content and the technology of these videos and suggest topics/problems for future MathCasts.

Wednesday, March 19, 2014


A hard adjustment for parents/educators who were raised as I was on traditional algorithms. Of course, understanding the rule for multiplying fractions DOES NOT mean students should use this to get the result.

Teaching conceptually is fundamental to the Mathematical Practice Standards of the Common Core. BUT this should be BALANCED with traditional methods. Current thinking is that the way we learned may be far more efficient but it leads one to think of math as just a set of meaningless rules. Kind of like a "black box." I see the need for both.

After watching this MathCast you'll probably conclude this is way too confusing for students not to mention adults! Just remember, some of that confusion results from sloppy drawings and carelessly worded explanations. I'm definitely guilty of both!

Watch "SHOWING one-third of three-fourths vs Traditional" on YouTube -

Sunday, March 16, 2014

5^(2x)=4; Find value of 5^(3x-1) Non-Calculator SAT-Type

These types of more challenging exponent problems requiring strong manipulative skills will probably not go away on the New SAT!
And on the NON-CALCULATOR section!

You have to watch the video to see the solution!

Watch "5^(2x)=4; Non-calculator exponent SAT-Type Problem" on YouTube - 5^(2x)=4; Non-calculator SAT-Type Problem:

Saturday, March 8, 2014

4% of 8% of 16x is what % of 2x? New SAT, Common Core and Percents, Pt.1

A classic SAT math challenge that will probably not go away on the new SAT coming in 2016. And just imagine if calculators are not allowed for this!

Watch "4% of 8% of 16x is what % of 2x? New SAT, Common Core and Percents Pt 1" on YouTube -