Half of our students were missing from this month’s homeschool teen math circle, but I challenged the three who did show up to wrap their brains around some large numbers. Human intuition serves us well for the numbers we normally deal with from day to day, but it has a hard time with numbers outside our experience. We did a simple yet fascinating activity.
First, draw a line across a page of your notebook. Label one end of the line $20 (the amount of money I had in my purse), and mark the other end as $1 trillion (rough estimate of the US government’s yearly overspending, the annual deficit):
Where on that line do you think $1 million would be?
Go ahead, try it! The activity has a much greater impact when you really do it, rather than just reading. Don’t try to over-think this, just mark wherever it feels right to you.
The kids were NOT eager to commit themselves, but I waited in silence until everyone made a mark.
Okay, now, where do you think $1 billion would be?
This was a bit easier. Once they had committed to a place for a million, they went about that much farther down the line to mark a billion.
Hooray for September 25th — it’s Math Storytelling Day!
Celebrate Math Storytelling Day by making up and sharing math stories. Everyone loves a story, so this is a great way to motivate your children to play around with math. What might a math story involve? Patterns, logic, history, puzzles, relationships, fictional characters, … and yes, even numbers.
Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest.
By tradition, we start the carnival with a couple of puzzles in honor of our 66th edition.
Let the mathematical fun begin!
Our first puzzle is based on one of my favorite playsheets from the Miquon Math workbook series. Fill each shape with an expression that equals the target number. Can you make some cool, creative math?
Click the image to download the pdf playsheet set: one page has the target number 66, and a second page is blank so you can set your own target number.
Both of my homeschool math circles (one with preschool-1st grade, and one with teens) thoroughly enjoyed the month-long problem solving course this summer, and we expect the new one to be just as much fun. Will you join us?
As with most of the Moebius Noodles courses, Maria and Yelena have adapted the activities for all ages from toddlers to adults. Where young ones go on a scavenger hunt for pretty snowflakes and cool truck wheels, older kids build bridges from multiplication to symmetry, spatial transformations, and proportions.
Visit the registration page to sign up no later than September 8. The main course activities will happen September 9th through 22nd. Expect to spend about two hours a week.
Now is the accepted time to make your regular annual good resolutions. Next week you can begin paving hell with them as usual.
Yesterday, everybody smoked his last cigar, took his last drink, and swore his last oath. Today, we are a pious and exemplary community. Thirty days from now, we shall have cast our reformation to the winds and gone to cutting our ancient shortcomings considerably shorter than ever. We shall also reflect pleasantly upon how we did the same old thing last year about this time.
However, go in, community. New Year’s is a harmless annual institution, of no particular use to anybody save as a scapegoat for promiscuous drunks, and friendly calls, and humbug resolutions, and we wish you to enjoy it with a looseness suited to the greatness of the occasion.
For many homeschoolers, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2013 Mathematics Game!
Our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I planned to set up a static display showing some of our projects, like the fractal pop-up card and the game of Nim, but the students voted to do a skit based on the logic puzzles of Raymond Smullyan.
We had a small class (only four students), but you can easily divide up the lines make room for more players. We created signs from half-sheets of poster board with each native’s line on front and whether she was a knight or knave on the flip side. In the course of a skit, there isn’t enough time to really think through the puzzles, so the audience had to vote based on first impressions — which gave us a fair showing of all opinions on each puzzle.
The 2012 Purple Comet! Math Meet is a free, on-line, team competition for middle and high school students around the world. Every team needs an adult supervisor. Homeschoolers are welcome and should register under the Mixed Team category.
As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn ﬁrst? How hard should they work? Should they even “work” at all? Should we push them, or just let them be?
There are no correct answers to these questions, and Zvonkin deals with them in classic math-circle style: He doesn’t ask and then answer a question, but shows us a problem — be it mathematical or pedagogical — and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.
This book is not a guidebook. It does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. On the other hand, if you are interested in running a math circle, or homeschooling children, you will ﬁnd this book to be an invaluable, inspiring resource. It’s not a “how to” manual as much as a “this happened” journal. … Just about every page contains a really clever teaching idea, a cool math problem, and an inspiring and funny story.
For our homeschool, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2012 Mathematics Game!
Rules of the Game
Use the digits in the year 2012 to write mathematical expressions for the counting numbers 1 through 100.
You must use all four digits. You may not use any other numbers.
The MathCounts Club Program provides enrichment activities and puzzles for 6th-8th grade math clubs within schools — and homeschool groups may join, too! Participants receive a free Club in a Box Resource Kit, which includes the Club Resource Guide, two game boards to accompany one of the meeting plans, 12 MathCounts pencils, and a MathCounts tote bag for the coach. (Apparently they had good intentions, but they didn’t follow through. My box had no tote.)
A school (or homeschool group) may choose to participate in the Club Program, the competition or both programs. Since these programs can complement each other, any school that registers for the MathCounts competition automatically gets the Club in a Box Resource Kit, too.
(n!)! = a factorial of a factorial, which is not the same as a multifactorial
n!! = a double factorial = the product of all integers from 1 to n that have the same parity (odd or even) as n
n!!! = a triple factorial = the product of all integers from 1 to n that are equal to n mod 3
[Note to teachers: The bonus rules are not part of the Math Forum guidelines. They make a significant difference in the number of possible solutions, however, and they should not be too difficult for high school students or advanced middle schoolers.]
Tomorrow, September 23, is the equinox — when night and day are equally balanced (or would be, if the sun appeared as a point, rather than a disc). If we lived on the equator, the sun would appear directly overhead at noon and would cast no shadow. Therefore, it’s a great day to perform Eratosthenes’ experiment of measuring the earth:
As I was preparing for Wednesday’s Homeschool Math Club Games & Activities meeting, I remembered my old math calendars and thought, that would be a fun activity to offer. So I pulled up the files and discovered that the days of the week matched perfectly. What a cool coincidence!
So in case you missed the math calendars last year, or in case it’s been long enough that your children have forgotten, here are the “new” versions:
A few years ago, I had several (potentially) future engineers in our homeschool math club, and we enjoyed the challenge of MathCounts and AMC puzzles — but the current crop of local homeschool students is another story.
Last year’s contest-based club meetings dwindled to one student. Even before the recent MathCounts rulechanges, I knew I needed a new plan. The final straw was Kitten, whose moaning complaint that she “hates math” has begun to drive me crazy.
… After taking all concerns into account, a compromise was crafted that would grandfather in homeschools and virtual schools that participated in the 2009-2010 program year to allow them to participate on teams in this year’s Competition Program. All new homeschool and virtual school participants must abide by the new eligibility rules that require those participants to register only as individuals. This compromise was brought to the MATHCOUNTS Board of Directors and approved unanimously.
Therefore, for the 2010-2011 school year, all homeschool and virtual school groups that registered for the MATHCOUNTS Competition Program either as teams OR individuals during the 2009-2010 program year will be allowed to register teams or as individuals for the upcoming 2010-2011 program year, following all of the 2009-2010 requirements for participation.
I try to avoid ranting on this blog, but I’m deeply disappointed. My students always enjoyed the team aspect of working/suffering together. I don’t know if any of them will be willing to participate as individuals.
If you’ve been thinking of starting a math club, here’s a good model:
People have this notion that math is about getting a right answer, and the testing really emphasizes that notion. And that’s such a bad way to approach math because it makes it scary.
When you look at little kids, they pose their own questions. They say, “Ooooh, what’s bigger than a million?” And they think about things their own way. At school, the teacher poses the questions, and the students answer their questions. Schooling is not a natural environment for learning.
Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking Number of players: any number Equipment: deck of math cards, pencils and scratch paper, timer (optional)
I’m afraid that Math Club may have fallen victim to the economy, which is worse in our town than in the nation in general. Homeschooling families have tight budgets even in the best of times, and now they seem to be cutting back all non-essentials. I assumed that last semester’s students would return, but I should have asked for an RSVP.
Still, Kitten and I had a fun time together. We played four rounds of Tens Concentration, since I had spread out cards on the tables in the library meeting room before we realized that no one was coming. Had to pick up the cards one way or another, so we figured we might as well enjoy them! She won the first two rounds, which put her in a good mood for our lesson.
I had written “Prime numbers are like monkeys!” on the whiteboard, and Kitten asked me what that meant. That was all the encouragement I needed to launch into my planned lesson, despite the frustrating dearth of students. The idea is taken from Danica McKellar’s book Math Doesn’t Suck.
Use the digits in the year 2010 to write mathematical expressions for the counting numbers 1 through 100.
All four digits must be used in each expression. You may not use any other numbers except 2, 0, 1, and 0.
You may use the arithmetic operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial). You may also use parentheses, brackets, or other grouping symbols.
You may use a decimal point to create numbers such as .1, .02, etc.
Multi-digit numbers such as 20 or 102 may be used, but preference is given to solutions that avoid them.
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.
[Note to teachers: This rule is not part of the Math Forum guidelines. It makes a significant difference in the number of possible solutions, however, and it should not be too difficult for high school students or advanced middle schoolers.]