The intelligent use of technology

The other day a student asked me “why can’t I just punch the whole quadratic formula, with the numbers into it, into my calculator?”.  Of course you can, but there’s some subtle ways that we write mathematical formulas that you have to be very detailed about when you put them in the calculator.

What I’ve seen students do is say out loud “negative b plus or minus the square root of b squared minus four a c all over two a”, and that’s the way they type it into the calculator. So if a is 1, b is -2, and c is 3, they proceed thusly;

-2 + √ -2^2 – 4*1*3 / 2*1 Enter
Then they do it again with a negative in place of the first positive, since they do understand the ± notation.
(Note that ideally they would use (-(-2) + √ ( (-2)^2 – 4*1*3 ) ) / (2*1) Enter.)

I’m trying to come up with a good learning opportunity to address this.

Probability Bingo

I used this activity to review before a test at the end of our “Probability and Data Management” unit. It covers probability up to and including grade 9, in terms of expectations from the Ontario Ministry of Education. The questions are quite difficult – more difficult than the ones on the actual test! Students were allowed to use calculators during the bingo game. There are two sets of bingo cards in PDF, so each student’s card is unique.

Probability Bingo overview
Probability Bingo presentation
Bingo Cards (set 1)
Bingo Cards (set 2)

Grade 7/8/9 Data Management

The NCTM publication “Navigating through Probability in Grades 9 to 12” has an interesting data management activity called “One-Boy Family Planning”. Using the Chinese “one-child” family planning policy from 1979, students are asked to imagine that the policy says that families can have “one boy” rather than “one child”. A die is used to simulate the birth of a boy (odd numbers) or a girl (even numbers). Students run 20 simulations and track how many “children” are born before a boy occurs in each of the 20 simulated families.

I am using this activity as a make-up activity for students who didn’t do well in our initial data management and probability unit. Since the activity requires them to pool their data with other students, the attached document includes data for nine fictional students. The table can be selected, copied, and pasted into Excel. Students can also receive BTT10 marks for their use of Excel in creating the tally charts and graphs.

My data for you to use as you wish: oneboydata.doc

Link to the NCTM book to purchase:

Shaughnessy, Michael. Navigating Through Probability in Grades 9-12. Reston, VA: National Council of Teachers of Mathematics, 2004.