To start, here are some fun facts about the number 41:
- Starting with 41, if you add 2, then 4, then 6, then 8, etc... you would get a string of 40 prime numbers in a row!
- 41 is also a Centered Square Number, which means that it is the sum of two consecutive squares -- 42 and 52, in this case. Can you figure out how this picture relates to the Center Square Numbers, and use the picture to explain why all Center Square Numbers are 1 (mod 4)?
- If you substitute 41 into n for the quadratic expression x2 - x + n, then the expression will evaluate to be prime for all integer values of x = 0, 1, 2, ..., n-1. There are only 6 such values for n, and they're called the "Lucky Numbers of Euler." 41 is the greatest of these lucky numbers.
- One molecule of Penicillin G has 41 atoms.
- On very special occasions in the UK (such as when President Obama visited the Buckingham Palace or when a royal birth takes place), a 41-gun salute is used to mark the occasion.
- In their 1996 album Crash, the Dave Matthews Band recorded a song called "#41." It was the most performed song on their tour that summer.
Caffeine Coquette has written a nice commentary on why we should not be praising children for counting well. Even though her piece is intended for an audience educating young children, there are lots of parallels in the higher grades.BASIC ALGEBRA AND GEOMETRY
Tracey Mansted offers a beautiful collection of methods to introduce young students to new math concepts while keeping away from the drill and kill.
Bon Crowder presents some fun ways to incorporate cuisenaire rods into coordinate-plane math and also how to teach math while crossing the street!SECONDARY MATHEMATICS
Sue Downing tells us a fun story about a few kids who know how to ask the right questions when given a bad math problem.
Denise over at Let's Play Math forwarded a post written by one of her students, reflecting on why a0 must equal 1 using exponent rules as justification.
Guillermo P. Bautista, Jr. uses the properties of a tessellated parallelogram to illustrate angle relationships within a single parallelogram.
Alex Washoe (whose blog is about birds) uses some neat examples from nature to illustrate how animals and humans can do complicated mathematics in the blink of an eye based on instincts alone. It's nice to know that pigeons can figure out the Monty Hall problem faster than I can.MISCELLANEOUS
In his series called Engaging Math Activities for the Summer Break, Alexander Bogomolny presents a type of shuffling algorithm and asserts that the algorithm will terminate. Also check out his other activities for ideas on fun ways to introduce new concepts.
John Cook points out that there exists an elegant theorem regarding nonzero terms of a polynomial and the number of distinct roots. He also recommends a short video from Dr. J illustrating some real-world examples of statistics.
In case you haven't already seen this, Kate Nowak presents a good problem that can generate a lot of questions and different approaches. It's a nice rich problem you can keep in the back of your pocket, because it is tied to various concepts but would still work well as a standalone task.
The latest in his Mathematics in the Real World series, David Wees presents a connection between families and math.
Ashli Black writes a brilliant tip on how to use Jeopardy-style slides to drop hints on which mathematical concepts are intimately interconnected. Are your students thinking fast in order to beat you to the punchline of the lesson?
Erlina Ronda presents how to use repeated patterns to introduce the Pascal's Triangle and its connection to counting.
Since I am a sucker for systems of instant feedback, I recommend reading Bowman Dickson's guest post on Sam Shah's page about modeling with integrals in GeoGebra. Bowman has since written a series of guest blog entries, and you should definitely check them out! I met him over the summer at a teacher program; he is an excellent teacher with some fresh ideas.
From my own blog, I am going to plug some resources we developed at the Park City Math Institute over the summer for assessing your implementation of the 8 Mathematical Practices of the Common Core State Standards. Both the rubric and the supplemental document are still just drafts, but I hope that you will find them useful as you think about modifying your instruction in the new school year.
VISIT OUR SISTER CARNIVALS
Gary Antonick presents a fun, interactive puzzle on eliminating equilateral triangles, and links it nicely to the idea of questioning in mathematics.
Terrance Banks shares a few tips on planning for the first days of school. Another place you can look for first-day ideas is over at the MS Math Wiki.
Edmund Harriss shares the specs on how to build a hexayurt dome. If you teach Geometry, you can start by asking your students to create the nets from scratch, using only compasses and straight edges. You might be surprised how difficult it is for kids to figure out spatially where to construct the next polygon in the 2-D net.
Lucas Allen shares his frustration with the media as he reflects on the question, "Are some kids just born bad at math?"
Not to get all commercial-y on you (This post is not sponsored, I promise!), but it looks like Microsoft Mathematics 4.0 is free and has some neat features, such as 3-D graphing.
...And that sums up this issue of Math Teacher at Play! I hope you have enjoyed these articles. The next edition of the carnival will be hosted at Math is Not a Four Letter Word, due to come out on September 16, 2011. Submissions must be relevant to either students or teachers of preK-12 mathematics. Old posts are OK, but due to the large amounts of readers, please do not submit an article if it has already appeared in a previous edition.