# 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.

### (2) I can work with numbers and symbols.

• I know how numbers relate to each other.
• I’m flexible with mental math. I understand arithmetic properties and can use them to make calculations easier.
• I’m not intimidated by algebra symbols.
• I don’t rely on memorized rules unless I know why they make sense.

### (3) I value logical reasoning.

• I can recognize assumptions and definitions of math terms.
• I argue logically, giving reasons for my statements and justifying my conclusion.
• I listen to and understand other people’s explanations.
• I ask questions to clarify things I don’t understand.

# Two Ways to Do Math

There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else — but persistent.

— Raoul Bott

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Raoul Bott, via The MacTutor History of Mathematics archive. Background photo courtesy of Swedish National Heritage Board (CC BY 2.0) via Flickr.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

# 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.

# Math Teachers at Play #70

[Feature photo above by David Reimann via Bridges 2013 Gallery. Number 70 (right) from Wikimedia Commons (CC-BY-SA-3.0-2.5-2.0-1.0).]

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 70th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of 42+ links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 70th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

# One Right Way

What’s really neat about mathematics is that even when there’s only one right answer, there’s never only one right way to do the problem.

— Herb Gross

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Herb Gross, via Math as a Second Language. Background photo courtesy of kristos_b (CC BY 2.0) via Flickr.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

# A Good Problem Requires Dreaming Time

A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some “dreaming” time.

— Howard Eves

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Today’s quote is from Howard Eves, An Introduction to the History of Mathematics. Background photo courtesy of Brenda Clarke (CC BY 2.0) via flickr.

Get monthly math tips and activity ideas, and be the first to hear about new books, revisions, and sales or other promotions. Sign up for my Tabletop Academy Press Updates email list.

# Math Teachers at Play #66

[Feature photo above by Franz & P via flickr. Route 66 sign by Sam Howzit via flickr. (CC BY 2.0)]

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!

## Puzzle 1

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.