Friday, August 22, 2014

An Algebra Puzzle to Start The Year! Grades 6-10

As I posted on Twitter today (@dmarain)...

If I were to give you $50 we'd have the same amount. If you were to give me $50 I'd have 9 times as much as you. How much do we each have?

Submit your answer and solution via the Blogger Contact Form in right sidebar.
Other comments welcome.


1. This was not intended to be highly challenging. It might engage students early in the year and I designed it to be accessible to most.

2. The language is open to interpretation by design! We want students to feel some disequilibrium. But we don't have to resolve ambiguities. I let my students do that among themselves.

3. Before jumping into an algebraic solution, I would allow my students to experiment with numbers - call it "plug in" or Guess-Test-Revise. After all on standardized tests this is what many will do in spite of all the algebra we teach!

Friday, August 15, 2014

Never ASS-U-ME in Geometry: A Triangle Problem to Get Them Thinking!

Not quite back to school for most but the problem above might prove interesting to review some geometric/deductive reasoning.

For new geometry students, replace 'a' by a value, say 40, and ask them to fill in all the missing angles. Most should deduce that angle 5 = 50, but my educated guess is that many will assume b = 40, so
angle 5= angle 6 = 50 and angle 3 = angle 4 = 40. From there to angle 1 = angle 2 = 50, so
angle 2 + angle 3 = 90. QED!  Not quite...

Well, the '90' is correct but the reasoning is another story! So this is all about justifying, checking validity of mathematical arguments, sorta' like some of the Eight Mathematical Practices of the Common Core!

In fact, you might ask them to redraw the diagram, keeping the given conditions but making it clear that b does not have to be 40 and that Angles 3&4 also do not have to be 40!

Monday, August 11, 2014

My Rant on MathShare 8 yrs ago

Haven't looked at the Yahoo group, MathShare I moderated several years ago. Phased it out when I started this blog.

Best way to describe what appears below? How about, " The more things change, the more they stay the same." Sad, but this could've been written today, except I'm retired...

From MathShare

Here's a novel thought...
I'd like to start a thread to explore what seems obvious to all of my teachers and probably to you and all of your colleagues as well. Not one of the teachers in my department teaches skills in a vacuum as in 'kill and drill.' They demand that students take notes and practice with many exercises until the concepts/skills are set in place and then come back to it in another context later on. They ask many questions in class to explore a topic, deepen conceptual understanding and assess: 'Show me why the absolute value of (x-1) is not x+1! How can you demonstrate this is not always true. Turn to your partner and convince each other!"
Technology enhances all of this but technology, standards, standardized tests and a plethora of new reports from various curriculum groups and governmental agencies WILL NEVER LEAD TO IMPROVEMENT of learning in the classroom and you all know why!
It's time to stop the political rhetoric and address what is really going on in the classroom. Effective teachers have always been effective. These are teachers who ravenously explore new instructional strategies, read everything they can get their hands on and then decide what will work best for their students. They are not mired in the the past nor are they easily swayed by buzz words or glitz. They are open to change but they will never abandon FIRST PRINCIPLES of learning. They will always be here after all the experts are long gone. ISN'T IT TIME WE CELEBRATE THEM AND USE THEM AS THE TRUE MODEL OF EDUCATION. THEY ARE THE GOLD STANDARD! Their students certainly know the truth: "She was the hardest and most demanding teacher I ever had. But boy did I learn!"

C'mon – don't be afraid to share 'self-evident' truths!! After all, someone has to tell the emperor he is naked! Ok, my rant is done!
Dave Marain

Tuesday, July 29, 2014

45 Free SAT MATH Problems Tweeted in 21 Days! Enjoy!

Just Follow me at

Pls remember that all of these are based on actual SAT questions but are completely original and therefore subject to the Creative Commons License in sidebar. Essentially, use them for your students or for yourserlf but no commercial reproduction. Thanks...

Perhaps my favorite is one I tweeted today:

How many combos of 2 pizza toppings can be selected from 10 choices?
Note: S,P is same as P,S; P,P is allowed

(A)100 (B)90 (C)55 (D)54 (E)45

Respond with answer and solution via Contact Form near top of sidebar.

Monday, July 21, 2014


See them on my twitter feed at

Did you submit your solution to the Geometry Puzzle from 7-20-14 via the Contact Form?

Sunday, July 20, 2014

Best Geometry Puzzle Ever?

Sorry. To see it, go to my twitter account:
Click on the image and magnify  or print as needed. If any angle measures are unclear let me know in Comments.
1. Submit answer and solution using Contact Form in right sidebar of my blog. PLS DO NOT SUBMIT SOLUTIONS IN COMMENTS!
2.  Best solutions (not just answer) will receive recognition (you'll be known to the 3 people reading my blog!) and a download of my book.
3. Please include your full name, email, state/country, your connection to math (student,teacher,etc) and how you found my blog.

Sunday, July 13, 2014

Dozens of Free Common Core, SAT Practice Problems

I've been posting numerous challenge problems on Twitter of late, some with answers.
You can see these at

Teachers: Feel free to use these to irritate your students.
Students: Feel free to use these to irritate your teachers. Lol

If you want to check your answers to these or you disagree with my answers or if you have any questions, use the new Contact Form in the sidebar.

Tuesday, June 3, 2014

And the winner is...

Our winning submission for the June 1st Challenge came from


Kaleb is a freshman at Fort Kent Community High School in Fort Kent, Maine.

Congratulations Kaleb!

Here are his answers:
B)64, 16, 8, 4, 2