Discern Patterns

Posted on by Denise Gaskins

I’m almost done rewriting the Standards for Mathematical Practice into student-friendly language.

They say mathematics is the science of patterns. So here’s…

Math Tip # 7: Discern Patterns.

  • Look for patterns in numbers, shapes, and algebra equations.
  • Notice how numbers can break apart to make a calculation easier.
  • Number patterns morph into algebra rules.
  • Adapt math situations to make the structure clear. (For example, by adding new lines to a geometry diagram.)
  • Step back from a situation to see it from a new perspective.
  • Try to find simpler patterns within complex equations or diagrams.
  • Not all patterns continue forever. Test your patterns. Can you trust them?

Continue reading Discern Patterns

Say What You Mean

Posted on by Denise Gaskins

Continuing my project of rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP6…

Math Tip # 6: Say What You Mean.

  • Words can be tricky, so watch your language.
  • Label drawings and graphs to make them clear.
  • If you use a variable, tell what it means.
  • Care about definitions and units.
  • Pay attention to rules (like the order of operations).
  • Use symbols properly (like the equal sign).
  • Understand precision. Never copy down all the digits on a calculator.

Continue reading Say What You Mean

Math as a Verb

Posted on by Denise Gaskins

Here’s the full quote:

I like to play games. Almost any type of game.

I also like to play math.

If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

—John Golden
Yes, Playing Around

CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

Master Your Tools

Posted on by Denise Gaskins

As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP5…

Math Tip # 5: Master Your Tools.

  • Collect problem-solving tools.
  • Practice until you can use them with confidence.
  • Classic math tools: pencil and paper, ruler, protractor, compass.
  • Modern tools: calculator, spreadsheet, computer software, online resources.
  • Physical items: dice, counters, special math manipulatives.
  • Tools for organizing data: graphs, charts, lists, diagrams.
  • Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.

Continue reading Master Your Tools

Look Beneath the Surface

Posted on by Denise Gaskins

So, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s the fourth installment…

Math Tip # 4: Look Beneath the Surface.

  • Notice the math behind everyday life.
  • Examine a complex situation. Ignore the parts that aren’t relevant.
  • Pay attention to the big picture, but don’t lose track of the details.
  • Make assumptions that simplify the problem.
  • Express the essential truth using numbers, shapes, or equations.
  • Test how well your model reflects the real world.
  • Draw conclusions. Explain how your solution relates to the original situation.

Continue reading Look Beneath the Surface

Know How to Argue

Posted on by Denise Gaskins

You may remember, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

My kids loved to argue. Do yours?

Math Tip # 3: Know How to Argue.

  • Argue respectfully.
  • Analyze situations.
  • Recognize your own assumptions.
  • Be careful with definitions.
  • Make a guess, then test to see if it’s true.
  • Explain your thoughts. Give evidence for your conclusions.
  • Listen to other people. Ask questions to understand their point of view.
  • Celebrate when someone points out your mistakes. That’s when you learn!

Continue reading Know How to Argue

W.W. Sawyer’s Rules of Mathematics

Posted on by Denise Gaskins

“In the beginnings of arithmetic and algebra, the main purpose is not to get the pupil making calculations. The main purpose is to get him into the habit of thinking, and to show him that he can think the problems out for himself.

“Pupils ask ‘Am I allowed to do this?’ as if we were playing a game with certain rules.

“A pupil is allowed to write anything that is true, and not allowed to write anything untrue!

“These are the only rules of mathematics.”

—W. W. Sawyer, Vision in Elementary Mathematics

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

Inspired by Sawyer’s Two Rules

I love this quote so much, I turned it into a printable math activity guide. I hope it helps inspire your students to deeper mathematical thinking.

Here’s the product description…

Join the Math Rebellion: Creative Problem-Solving Tips for Adventurous Students

Take your stand against boring, routine homework.

Fight for truth, justice, and the unexpected answer.

Join the Math Rebellion will show you how to turn any math worksheet into a celebration of intellectual freedom and creative problem-solving.

Help your students practice thinking for themselves as they follow the Two Rules of the Math Rebellion: “A pupil is allowed to write anything that is true, and not allowed to write anything untrue! These are the only rules of mathematics.”

Find Out More

Free Number Sense Resources from Steve Wyborney

Posted on by Denise Gaskins

If you teach children in the primary grades, you’ll enjoy this new series from the wonderful Steve Wyborney. Every day for the rest of the school year, Steve will post a new estimation or number sense resource for grades K–8 (or any age!) at his blog:

“This is my way of providing support and encouragement – as well as bringing math joy to your classroom… I’m going to stick with you all year long.”

—Steve Wyborney

Click to visit Steve’s blog

Don’t Panic

Posted on by Denise Gaskins

As I mentioned last Saturday, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s the second installment…

Math Tip # 2: Don’t Panic.

  • Don’t let abstraction scare you.
  • Don’t freeze up when you see complex numbers or symbols.
  • Break them down into simpler parts.
  • Take each problem one step at a time.
  • Know the meaning of the math, how it relates to the “real world.”
  • But if it gets in your way, ignore the “real world” situation. Revel in the abstract fantasy.

Continue reading Don’t Panic

Never Give Up

Posted on by Denise Gaskins

Have you read the Standards for Mathematical Practice? Good idea in theory, but horribly dull and stilted. Like math standards in general, the SMPs sound as if they were written by committee. (Duh!)

I’ve seen several attempts to rewrite the SMPs into student-friendly language. Many of those seem too over-simplified, almost babyish.

Probably I’m just too critical.

Anyway, I decided to try my hand at the project. Here’s the first installment…

Math Tip # 1: Never Give Up.

  • Fight to make sense of a problem.
  • Think about the things you know.
  • Ponder what a solution might look like.
  • Compare this problem to those you solved in the past.
  • If it seems too hard, make up a simpler version. Can you solve that one?
  • If one approach doesn’t work, try something else.
  • When you get an answer, ask yourself, “Does it truly makes sense?”

Download the poster, if you like:

What do you think? Would this resonate with your students?

What changes do you suggest?

You can find the whole SMP series (eventually) under the tag: Posters.

Update: I Made a Thing

I had so much fun making these posters that I decided to put them into a printable activity guide. It includes the full-color poster shown above and a text-only version, with both also in black-and-white if you need to conserve printer ink.

Here’s the product description…

Join the Math Rebellion: Creative Problem-Solving Tips for Adventurous Students

Take your stand against boring, routine homework.

Fight for truth, justice, and the unexpected answer.

Join the Math Rebellion will show you how to turn any math worksheet into a celebration of intellectual freedom and creative problem-solving.

This 42-page printable activity guide features a series of Math Tips Posters (in color or ink-saving black-and-white) that transform the Standards for Mathematical Practice to resonate with upper-elementary and older students.

Available with 8 1/2 x 11 (letter size) or A4 pages.

Check It Out