What Are Mixed Numbers?

I just discovered a fascinating fact: In some places in the world, mixed numbers apparently don’t exist.

So that made me curious about my blog readers:

  • Did you learn about mixed numbers in school?
  • Do you ever use mixed numbers in daily life?
  • Are your children learning to work with them?

And if you DO know mixed numbers, can you simplify this mess:

[If you enjoy dry math humor, the answer is worth the work.]

Continue reading What Are Mixed Numbers?

Printable Activity Guides

Since my publishing house opened its online store last month, I’ve been busy stocking the shelves with printable math activities for all ages.

It’s a fun collection of low- or no-prep ideas for playing math with your kids.

And it’s still growing. I’m pouring through old notes of my favorite projects from years of playing math with the kids in our math clubs and homeschool co-op enrichment classes, looking for ideas.

Which One Will You Try?

We’ve kept our prices as low as possible to fit struggling family budgets — less than a cup of coffee at my favorite cafe, back when we could still go out for a sweet, creamy cuppa.

Just go to our online store and click the “Printable Activity Guides” button to check out all the mathy fun.

Someday, I hope to combine these books into a creative math “uncurriculum” for homeschoolers. Stay tuned to this blog for more news about that. Eventually…

Make Sense of Math

So, I decided to rewrite the Standards for Mathematical Practice into student-friendly language.

Here’s the final installment…

Math Tip # 8: Make Sense of Math.

  • Use the patterns you discover to help you solve problems.
  • Don’t get lost in the details of a problem. Look for general truths.
  • Apply common sense to math situations.
  • Think about how different things are similar.
  • Think about how similar things are different.
  • Remember that your mind is your most important math tool.
  • Pay attention to your thinking process. What patterns do you find there?

Continue reading Make Sense of Math

Discern Patterns

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

Exciting New Homeschool Math Program

Homeschooling friends, check out this new homeschool math program that’s fun, rigorous, and engaging — a delightful, hands-on course that helps parents (and their children) understand math.

Introduction to Cuisenaire Rod Structures Course

I had the privilege of previewing this class as Sonya and Lacy put it together. I highly recommend it to anyone who struggles with math, or who wants to take a non-traditional approach.

By focusing on making sense of number relationships, and by teaching algebra before arithmetic, this course provides a stress-free path to rich mathematical mastery.

And for all they provide, including weekly live workshops and a slew of printable math journal pages that prompt deep thinking, the price is a steal!

Continue reading Exciting New Homeschool Math Program

Say What You Mean

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

Master Your Tools

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

FAQ: Playful Math for Older Students

My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

Here are a few ideas to get your older children playing with math…

Continue reading FAQ: Playful Math for Older Students

Look Beneath the Surface

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

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