OK, parents: Three people shake hands with each other, without repeating. How many total shakes will there be?
Answer: three.
Now what about a group of four people?
That answer would be six total non-repeated shakes.
Betsy Ross Arts Magnet School sixth grader David Couvertier (pictured), who loves math, did pretty well with this.
Couvertier (pictured) was one of 50 kids and their parents who tackled questions like these at Betsy Ross Thursday night at a CMT (Connecticut Mastery Test) workshop run by the school system’s pre-K to 12 math coordinator Ken Matthews, part of an ongoing effort to involve parents more in their children’s education.
(Matthews is pictured at the top of this article with Ross parent and 5th grade John Martinez School teacher Genevive Goubourn.)
While you read the rest of this article about Matthews’ Math Prep road show, try to figure total shakes for a group of five, then six people. Now, how many total non-repeated shakes in a group ten people? You’ve already been given a hint.
And can you devise an algebraic formula to illustrate this “circular permutation”? Answers are provided at the end of the article, and your posted responses will be graded.
This challenging math brain teaser was (pardon the pun) merely the hands-on warm-up exercise to help orient kids — and especially, their parents who want to help them — to the considerable demands of the three one-hour CMTs to be administered in March.
Matthews brings energy, wit, and M&Ms, otherwise known as math manipulables, to his presentation. (They make for tasty teaching about triangles.) He had another large crowd Wednesday night at the Fair Haven Middle School, and he is only the tip of the math teaching and test-prep iceberg moving throughout the New Haven Public Schools system.
His shows are needed, Matthews said, because the CMTs are far tougher than the testing for fractions and decimals that characterized rote math teaching in generations past.
“Circular permutation used to be taught in high school, maybe even in college. Can middle school kids do it? You bet. We just did it here together.”
Each K-8 school, he said, has a math coach.” Some 30 in all travel from class to class helping teachers teach and pulling out kids to assist them as the class moves through the curriculum.” Sometimes these coaches conduct sessions like this for their schools on their own.
Matthews’s presentation is part of the activities of the central Board of Education’s outreach to parents under a program called the Parent Academy. It’s organized by Patti Avallone (pictured with the arriving Sal Festa family), a former teacher of the year and now parent outreach coordinator.
There are dozens of such activities initiated, also, she said, by the school themselves. Some schools have even purchased test prep computer software for their kids.
The handshaking exercise was evidencethat although there might be a lot of teaching to the test, if it it’s taught well and entertainingly, strong long-term learning happens too.
Matthews went on to ask groups of parents working with their kids to build a 5×5×5 triangle, that is with five M&Ms, which had to be “kissing,” on each side. They they were to build various other M&M triangles — so you couldn’t be eating all of them.
He elicited from the kids “equilateral” and “hypotenuse,” and he taught the Latin derivations of the names. Then he asked the students and parents to build triangles whose sides contained three, five, and 11 kissing candies. When no one could do it, he taught that no triangle can be built unless the length of the two shorter sides add up to at least the length of the longest; otherwise the structure collapses.
Parents were cued into the three types of questions on the math CMT: computation, open-ended queries that require a written explanation or defense, and grid questions. Grid questions have the kids writing the answer on the top of the grid they work with. “If the answer is “15,” he said, “and the child gets it right, but places the “15” to the right of the decimal point, then it’s scored as wrong. We all need to help them with such things.”
Parents (like John Lewis and his son John Lewis, Jr., a seventh-rader at Ross) were urged to monitor at least a half hour’s work with their kids on math every night. If they themselves do not know enough high school math, they were encouraged to talk to the teachers to learn themselves. “Confidence is really key,” said teacher Goubourn. Matthews concurred. “If your child is not getting something, go the teacher immediately to clear it up. Don’t let it linger.”
Also recommended was to have analog clocks in the house. “You can learn patterns from analog clocks; digitals are no help,” Matthews explained. Cooking with kids and doing measurements was also encouraged; likewise, doing the monetary math during store transactions. And, of course, reading with kids. “Reading” is correlated, he said, “with good scores in math as well.”
For other upcoming Parent Academy activities around the CMT and more, contact Patti Avallone at this email address. And check out the Parents Corner on the Board of Ed website.
Answers Revealed
Oh, the answers to the hand shaking questions: A group of five shaking would produce ten shakes; a group of six, 15 shakes; and ten shakers would produce 45 non-repeated shakes. The pattern discerned, Matthews taught, would be to multiply the number in the group by one less than that number – so 10 shakers X 9 = 90. Then you have to eliminate shaking the same person twice, so you divide by 2, which gets your 45. Seems to work, but you come to it through a combination of actual shaking hands and looking for patterns.
The formula would be n(n-1) divided by two. Thus, said Matthews, the kids and parents at Betsy Ross reprised Isaac Newton’s discovery (or re-discovery) of algebra.
Now. Extra credit: What patterns do you see in the following: 9, 18, 27, 36, 45, 54,63, 72, 81,90?
Right, the nines times table, but notice each set of two numbers always adds up to nine.And if you set them up vertically, you could see the ones digit decreases by one, whereas the tens digit increases. David Couvertier thought these things pretty nifty.
For previous installments in the Independent’s series on parental involvement in local schools, click on:
Brandon Aims For The Blue Shirt
Night-Shift Waitress Hangs Up Apron
Dad Meets The Teachers. All Of ‘Em
Ms. Lopez Moves Brandon’s Seat
Night-Shift Waitress Gets Xena To Class On Time
Fifth-Graders Get “Amistadized”
Board of Ed To Parents: Get Involved!
Task Force Hones Plan for Kids
The New St. Martin DePorres Comes Home
Good-Bye Recess. Hello Take 10.
