From Numberphile: “Some stuff about Pi, the ‘celebrity number’. This video features maths-loving author Alex Bellos and Professor Roger Bowley from the University of Nottingham.”
Did you notice the error? It was supposed to be “a”…
The Math Student’s Manifesto
[Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]
Note to Readers: Please help me improve this list! Add your suggestions or additions in the comment section below…
What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.
(1) I can make sense of problems, and I never give up.
- I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
- I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
- I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
- I like to compare my approach to the problem with other people and hear how they did it differently.
2015 Mathematics Game
[Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both via Flickr (CC BY 2.0, text added).]
Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!
For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.
Rules of the Game
Use the digits in the year 2015 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
- You must use all four digits. You may not use any other numbers.
- Solutions that keep the year digits in 2-0-1-5 order are preferred, but not required.
- You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
- You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
- You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.
My Special Variations on the Rules
- You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
- You MAY NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.
December Advent Math from Nrich
[Feature photo (above) by Austin Kirk via Flickr (CC BY 2.0).]
Click on the pictures below to explore a mathy Advent Calendar with a new game, activity, or challenge puzzle for each day during the run-up to Christmas. Enjoy!
Advent Calendar 2014 – Primary
Advent Calendar 2014 – Secondary
Math Debates with a Hundred Chart
Wow! My all-time most popular post continues to grow. Thanks to an entry from this week’s blog carnival, there are now more than thirty great ideas for mathematical play:
The latest tips:
(31) Have a math debate: Should the hundred chart count 1-100 or 0-99? Give evidence for your opinion and critique each other’s reasoning.
[Hat tip: Tricia Stohr-Hunt, Instructional Conundrum: 100 Board or 0-99 Chart?]
(32) Rearrange the chart (either 0-99 or 1-100) so that as you count to greater numbers, you climb higher on the board. Have another math debate: Which way makes more intuitive sense?
[Hat tip: Graham Fletcher, Bottoms Up to Conceptually Understanding Numbers.]
(33) Cut the chart into rows and paste them into a long number line. Try a counting pattern, or Race to 100 game, or the Sieve of Eratosthenes on the number line. Have a new math debate: Grid chart or number line — which do you prefer?
[Hat tip: Joe Schwartz, Number Grids and Number Lines: Can They Live Together in Peace? ]
Fractions: 1/5 = 1/10 = 1/80 = 1?
[Feature photo is a screen shot from the video “the sausages sharing episode,” see below.]
How in the world can 1/5 be the same as 1/10? Or 1/80 be the same as one whole thing? Such nonsense!
No, not nonsense. This is real-world common sense from a couple of boys faced with a problem just inside the edge of their ability — a problem that stretches them, but that they successfully solve, with a bit of gentle help on vocabulary.
Here’s the problem:
- How can you divide eight sausages evenly among five people?
Think for a moment about how you (or your child) might solve this puzzle, and then watch the video below.
What Do You Notice?
Reblog: Solving Complex Story Problems
[Dragon photo above by monkeywingand treasure chest by Tom Praison via flickr.]
Over the years, some of my favorite blog posts have been the Word Problems from Literature, where I make up a story problem set in the world of one of our family’s favorite books and then show how to solve it with bar model diagrams. The following was my first bar diagram post, and I spent an inordinate amount of time trying to decide whether “one fourth was” or “one fourth were.” I’m still not sure I chose right.
I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:
Cimorene spent an afternoon cleaning and organizing the dragon’s treasure. One fourth of the items she sorted was jewelry. 60% of the remainder were potions, and the rest were magic swords. If there were 48 magic swords, how many pieces of treasure did she sort in all?
[Problem set in the world of Patricia Wrede’s Enchanted Forest Chronicles. Modified from a story problem in Singapore Primary Math 6B. Think about how you would solve it before reading further.]
How can we teach our students to solve complex, multi-step story problems? Depending on how one counts, the above problem would take four or five steps to solve, and it is relatively easy for a Singapore math word problem. One might approach it with algebra, writing an equation like:
… or something of that sort. But this problem is for students who have not learned algebra yet. Instead, Singapore math teaches students to draw pictures (called bar models or math models or bar diagrams) that make the solution appear almost like magic. It is a trick well worth learning, no matter what math program you use …
![x - \left[\frac{1}{4}x + 0.6\left(\frac{3}{4} \right)x \right] = 48](https://s0.wp.com/latex.php?latex=x+-+%5Cleft%5B%5Cfrac%7B1%7D%7B4%7Dx+%2B+0.6%5Cleft%28%5Cfrac%7B3%7D%7B4%7D+%5Cright%29x++%5Cright%5D++%3D+48&bg=ffffff&fg=303030&s=0&c=20201002)
[Click here to go read Solving Complex Story Problems.]
Update: My New Book
You can help prevent math anxiety by giving your children the mental tools they need to conquer the toughest story problems.
Read Cimorene’s story and many more in Word Problems from Literature: An Introduction to Bar Model Diagrams—now available at all your favorite online bookstores!
And there’s a Student Workbook, too.
Reblog: The Handshake Problem
[Feature photo above by Tobias Wolter (CC-BY-SA-3.0) via Wikimedia Commons.]
Seven years ago, our homeschool co-op held an end-of-semester assembly. Each class was supposed to demonstrate something they had learned. I threatened to hand out a ten question pop quiz on integer arithmetic, but instead my pre-algebra students voted to perform a skit.
I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:
If seven people meet at a party, and each person shakes the hand of everyone else exactly once, how many handshakes are there in all?
In general, if n people meet and shake hands all around, how many handshakes will there be?
Cast
1-3 narrators
7 friends (non-speaking parts, adjust to fit your group)Props
Each friend will need a sheet of paper with a number written on it big and bold enough to be read by the audience. The numbers needed are 0, 1, 2, 3, … up to one less than the number of friends. Each friend keeps his paper in a pocket until needed.
Math Playtime With Blocks
Feature video by Stuart Jeckel via youtube.
DO Try This at Home
And ask questions!
- What do you notice?
- What do you wonder?
- Will the pattern continue?
- How can we know for sure?
Algebra for (Almost) Any Age
Fawn Nguyen’s Visual Patterns website just keeps getting better and better. Check it out:
In addition to the 115 puzzle patterns (as of this writing), the site features a Gallery page of patterns submitted by students. And under the “Teachers” tab, Fawn shares a form to guide students in thinking their way through to the algebraic formula for a pattern.
How can you use these patterns to develop algebraic thinking with younger students? Mike Lawler and sons demonstrate Pattern #1 in the YouTube video below.
Denise Gaskins' Let's Play Math 
