Wednesday, January 10, 2007

Problem of the Day 1-11-07

No comments the last 2 days but many visitors are looking at these - I think! Feedback is critical for for me so I'd appreciate any suggestions. I'm thinking about having 2 a day, one for Gr 5-8 and one for Gr 9-12, but I don't know if I can get this going or maintain it!

Grade 5-8 Activity
Goals/Standards: Those relating to prealgebra, patterning, place value, factors, multiples, making conjectures, verifying, etc.
Class Time Required for Activity: 20 minutes

Your mission, should you accept it, is to discover the effects of inserting a 9 in the middle of a 2-digit number. You and your partner have 10 minutes to make your conjecture. You will start by collecting data from several 'sample' values and recording your results in a table. Mission Control (that's me!) will start the table for you: (scroll down to see it!)

Original #

New #









  • Continue the table on your own, choosing 7 more random values in the 30's, 40's,... through the 90's.
  • Look at the differences and formulate a rule for finding the differences using only the original numbers. Your rule may use any of the following: words, numbers, algebraic expressions.
  • Make sure you verify your conjecture (that is, thoroughly TEST it).
  • Be prepared to explain your 'theory' and demonstrate it. A student or your Mission Control Commander may throw a random 2-digit number at you. You will have to correctly compute the difference mentally in 3 seconds or less to receive one extra bonus point!

Now for the extension: Ask students to think about the following outside of class and submit their thoughts to you or the class in an electronic class forum, wiki, or however:
Is there a similar rule for inserting other digits into a 2-digit number or is NINE special? Show work or explain your method.


Mrs. Temple said...

I love the format of today's question. My HS kiddos like the zany stuff like Mission Control, but are too cool to act like they enjoy it :)

Keep it up!

Dave Marain said...

Thank you Mrs. Temple! I will try to continue this but it's very challenging to find the time. I see that this blog has now been discovered by accident on, so maybe others will now spread the word. There are other issues regarding a national math curriculum and addressing Professor Schmidt's concerns over a decade ago about a curriculum that is 'one inch deep and one mile wide' that are still critical for me. Stay tuned...

Mrs. Temple said...

hehehe - I am Druin on ILoveMath, but for my student blog, I go by my real name, hence why I posted a comment as Mrs. Temple. Sorry for the confusion!

Rex said...

Hi Dave

Hey, nice problem. We start back in a few weeks, and I will use this problem to review algebraic techniques.

Rex Boggs