## Numberless Word Problems

As I mentioned yesterday, my new book includes links to online resources to help you play with word problems. So this week, I’m sharing a few of my favorites.

Today we examine a time-tested method to help kids reason about math: Leave out the numbers.

First up, there’s Brian Bushart’s numberless problem bank for young students. Then we’ll look at Farrar Williams’s modern revision of a math teaching classic with problems for upper-elementary and middle school students.

Have fun thinking math with your kids!

### Word Problem Bank

Word problems are commonplace in mathematics classrooms, and yet they regularly confound students and lead to frustrated teachers saying things like:

• “They just add all the numbers! It doesn’t matter what the problem says.”
• “They don’t stop to think! They just start computing as soon as they’re done reading the problem.”

Brian Bushart offers a collection of ready-to-go slide presentations that walk through the steps of making a word problem make sense.

### Math With No Numbers

Discover Farrar Williams’s book Numberless Math Problems: A Modern Update of S.Y. Gillian’s Classic Problems Without Figures, available in ebook or paperback.

Williams writes: “In order to answer the question, they’ll have to explain it, because the problem doesn’t give you anything to calculate with. The only way to answer is by explaining your process. See how sneaky a numberless problem is? It makes students really think about the process of solving the problem.”

“When students face a word problem, they often revert to pulling all the numbers out and “doing something” to them. They want to add, subtract, multiply, or divide them, without really considering which operation is the right one to perform or why.

“When you don’t have numbers, it sidesteps that problem.

“For students who freeze up when they see the numbers, this can be a really good way to get them to think about their process with math.”

—Farrar Williams, Math With No Numbers

CREDITS: Feature photo (top) by saeed karimi via Unsplash.com.

## Multiplication Escape Room Game

Ashly Latham, a student of the math-game superhero John Golden, has created an escape room game for third-grade students learning multiplication.

What fun!

## What Is Multiplication, Anyway?

At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:

What IS multiplication?

“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.

I can’t give a definitive answer.

Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.

Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”

—James Tanton, What is Multiplication?

### For Further Study

You may also enjoy these posts from my blog archive:

## Memorizing the Times Table: A Life Skills Approach

Continuing on my theme of times table facts, here’s the inimitable James Tanton:

“If our task is to memorize this table, please make it about mathematics — about thinking your way through a challenge, and what can I do to make my life easier.”

### For Further Study

You may also enjoy my blog post series about working through the times tables, paying attention to mathematical relationships (and a bit of prealgebra) along the way.

Click the button to see the whole series. Scroll down to the first post to go through it in order.

## Only Three Facts to Memorize

A comment from a friend got me playing around with multiplication. I found a few videos from some of my favorite math people, so I’ll be sharing over the next few days.

Here’s one from Sonya Post of Learning Well at Home. Also, Sonya just hosted Playful Math Education Carnival #143, which is well worth your time to explore!

“When students have to drill multiplication facts, it’s frustrating, unproductive and it makes them hate math. A better way to master the multiplication table is work on the skills that allow students to multiply quickly and efficiently.”

### Doubling and Halving

Making doubles and halves are a great foundation for all sorts of math.

Do you ever play the doubling game with your children? One player picks a starting number, and then you take turns doubling it until your mental math skills run out. How far can you go?

Or try the halving game: One player chooses a starting number, and you take turns cutting it in half. How tiny can you go?

As Sonya demonstrated, these skills help your child master their multiplication facts. And they are fantastic preparation for exponents and logarithms, too!

## What Are Mixed Numbers?

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

• 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.]

## New Printable Puzzle Books: Diffy Inception

The best way to practice math is to play with it—to use the patterns and connections between math concepts in your pursuit of something fun or beautiful.

Diffy Inception puzzles have their own symmetric beauty, but mostly they are just plain fun. Students can practice subtraction and look for patterns in the difference layers.

I just published four new activity books to our online store:

Notes to the teacher include puzzle instructions, game variations, journaling prompts, and more. Plus answers for all puzzles.

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

My publishing company runs this online store, so you can find all my playful math books there — including an exclusive pre-publication ebook edition of my newest title, Prealgebra & Geometry: Math Games for Middle School. Click here to browse the Tabletop Academy Press store.

## 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.

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!

## More Dover Samples

“Without mathematics you can’t do anything! Everything around you is mathematics. Everything around you is numbers.”

—Anna Claybourne, I Can Be a Math Magician

Dover Publications sent out a new email today with fun coloring and craft samples. And several puzzles from I Can Be a Math Magician: Fun STEM Activities for Kids by Anna Claybourne.

Enjoy!