FAQ: Struggling with Arithmetic

My son can’t stand long division or fractions. We had a lesson on geometry, and he enjoyed that — especially the 3-D shapes. If we can just get past the basics, then we’ll have time for the things he finds interesting. But one workbook page takes so long, and I’m sick of the drama. Should we keep pushing through?

Those upper-elementary arithmetic topics are important. Foundational concepts. Your son needs to master them.

Eventually.

But the daily slog through page after page of workbook arithmetic can wear anyone down.

Many children find it easier to focus on math when it’s built into a game.

Take a look at Colleen King’s Math Playground website. Or try one of the ideas on John Golden’s Math Hombre Games blog page.

Or sometimes a story helps, like my Cookie Factory Guide to Long Division.

Math Textbook Tips

Games are great for practicing math your child has already learned. But for introducing new concepts, you’ll probably want to follow your textbook.

Still, even with textbook math, there are ways to make the journey less tedious:

• Most children do not need to do every problem on a workbook page, or every page in a section. There is a lot of extra review built into any math program.

• You don’t have to finish a section before you work whatever comes after it. Use sticky bookmarks to keep track of your position in two or three chapters at a time. Do a little bit of the mundane arithmetic practice, and then balance that with some of the more interesting topics your son enjoys.

• As much as possible, do math out loud with a whiteboard for scratch work. Somehow, working with colorful markers makes arithmetic more bearable.

• Set a timer for math, and make the time short enough that he feels the end is in sight. I suggest no more than thirty minutes a day for now. And whenever the timer rings, stop immediately — even if you are in the middle of a problem.

The Timer Can Be a Life-Saver

Doing math in short sessions helped us avoid the emotional melt-downs my daughter used to have.

Thinking is hard work, and if I asked for too much, she would crash.

Because I sat with her and worked together every problem, I knew what she understood and when we could skip a problem. Or sometimes even jump several pages. Which meant that, even with short lessons, we still got through our book on time.

Arithmetic Is Like Vegetables

But as I said before, textbooks include a whole lot of repetition.

Too much repetition deadens the brain.

So we also took long breaks from our textbook program. Entire school-year-long breaks, just playing with math. Letting “enrichment” activities be our whole curriculum.

As healthy as vegetables are, you would never limit your son to eating just lima beans and corn.

Similarly, be sure to feed him a varied math diet.

For example, you can follow his interest in geometry beyond the standard school topics.

Explore tessellations, Escher art, and impossible shapes such as the Penrose triangle.

Building Lego scenes is a practical application of 3-D geometry. He might even want to try stop motion animation.

Talk about how math works in real life. Ponder the choices on John Stevens’s “Would You Rather?” blog or try some of the challenges at Andrew Stadel’s Estimation 180 website. Many of these require three-dimensional reasoning.

A Blogging Challenge

This is my second contribution to the blogging challenge #MTBoSBlaugust.

I’m aiming for at least one post each week. A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

Two posts down…

CREDITS: Frustrated Child photo by by Pixabay on Pexels.com. Penrose Lego by Erik Johansson via Flickr (CC BY 2.0). Homework Hands photo by Tamarcus Brown on Unsplash.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

FAQ: Forgetting What They Learned

“As we go through each lesson, it seems like my daughter has a good handle on the concepts, but when we get to the test she forgets everything. When I ask her about it, she shrugs and says, ‘I don’t know.’ What do you do when your child completely loses what she has learned?”

Forgetting is the human brain’s natural defense mechanism. It keeps us from being overwhelmed by the abundance of sensory data that bombards us each moment of every day.

Our children’s minds will never work like a computer that can store a program and recall it flawlessly months later.

Sometimes, for my children, a gentle reminder is enough to drag the forgotten concept back out of the dust-bunnies of memory.

Other times, I find that they answer “I don’t know” out of habit, because it’s easier than thinking about the question. And because they’d prefer to be doing something else.

And still other times, I find out they didn’t understand the topic as well as I thought they did when we went through it before.

No matter how we adults try to explain the concepts, some kids want to be answer-getters. They don’t want to do the hard work of thinking a concept through until it makes a connection in their minds. They want to memorize a few steps and crank through the lesson to get it over with.

In all these cases, what helps me the most is conversation.

My children and I always talk about our math. I ask questions like “What do you think? What do you remember? Can you explain the question to me? What are they asking for?”

And, whether the child’s answer is right or wrong, I practice my poker face. Trying not to give anything away, I ask, “How did you figure it out? Can you think of a way to confirm your answer?”

If you have preschool and elementary-age kids, read Christopher Danielson’s inspiring book and blog:

For middle school and older students, check out Fawn Nguyen’s wonderful collection of Math Talks. Be sure to read the “Teachers” page for tips and talking points:

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.”

— Christopher Danielson

Playful Ways to Learn or Review Math

Games are a great way to practice math. Check out these (free!) math games for all ages:

And if you have elementary-age children, here are a few grade-level tips to help them learn (and remember) math concepts:

Credits: Girl in field photo by SOURCE Hydration Systems and Sandals technology via Flickr. (CC BY 2.0) Nigerian classroom photo by Doug Linstedt and young girl studying by pan xiaozhen on Unsplash.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

I’ve been working on my next Playful Math Singles book, based on the popular Things to Do with a Hundred Chart post.

My hundred chart list began many years ago as seven ideas for playing with numbers. Over the years, it grew to its current 30+ activities.

Now, in preparing the new book, my list has become a monster. I’ve collected almost 70 ways to play with numbers, shapes, and logic from preschool to middle school. Just yesterday I added activities for fraction and decimal multiplication, and also tips for naming complex fractions. Wow!

Gonna have to edit that cover file…

In the “Advanced Patterns” chapter, I have a section on math debates. The point of a math debate isn’t that one answer is “right” while the other is “wrong.” You can choose either side of the question — the important thing is how well you support your argument.

Here’s activity #69 in the current book draft.

Have a Math Debate: Adding Fractions

When you add fractions, you face a problem that most people never consider. Namely, you have to decide exactly what you are talking about.

For instance, what is one-tenth plus one-tenth?

Well, you might say that:

$\frac{1}{10}$  of one hundred chart
+ $\frac{1}{10}$  of the same chart
= $\frac{2}{10}$  of that hundred chart

But, you might also say that:

$\frac{1}{10}$  of one chart
+ $\frac{1}{10}$  of another chart
= $\frac{2}{20}$  of the pair of charts

That is, you started off counting on two independent charts. But when you put them together, you ended up with a double chart. Two hundred squares in all. Which made each row in the final set worth $\frac{1}{20}$  of the whole pair of charts.

So what happens if you see this question on a math test:

$\frac{1}{10}$  + $\frac{1}{10}$  = ?

If you write the answer “$\frac{2}{20}$”, you know the teacher will mark it wrong.

Is that fair? Why, or why not?

CREDITS: Feature photo (above) by Thor/geishaboy500 via Flickr (CC BY 2.0). “One is one … or is it?” video by Christopher Danielson via TED-Ed. This math debate was suggested by Marilyn Burns’s blog post Can 1/3 + 1/3 = 2/6? It seemed so!

Today we have a guest post — an exclusive tale by Sasha Fradkin and Allison Bishop, authors of the new math storybook Funville Adventures. Enjoy!

Funville Adventures is a math-inspired fantasy that introduces children to the concept of functions, which are personified as magical beings with powers.

Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. Some Funvillians have siblings with opposite powers that can reverse the effects and return an object to its original state, but other powers cannot be reversed.

In this way, kids are introduced to the mathematical concepts of invertible and non-invertible functions, domains, ranges, and even functionals, all without mathematical terminology.

We know about Funville because two siblings, Emmy and Leo, were magically transported there after they went down an abandoned slide.

When they came back, Emmy and Leo shared their adventures with their friends and also brought back the following manuscript written by their new friend Blake.

Once again, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the run-up to Christmas.

Including an especially-tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar home pages.

For Primary Students

Easier activities for elementary and middle school.

Math puzzle fun, plus a printable coloring page.

When you get to the Nrich website, click a number to go to that day’s math.

For Secondary Students

Activities for middle and high school.

Each day features a challenge from the Short Problems Collection.

When you get to the Nrich website, click a number to go to that day’s math.

“This year we’ve decided to bring you some of our favourite Plus videos. There’s nothing more soothing that a bit of fascinating maths, explained by a fascinating mathematician, that doesn’t even require you to read stuff. Happy watching!”

When you get to the +Plus Magazine website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

One link becomes live each day — so come back tomorrow and discover something new!

Christmas Meta-Puzzle

Or try your hand at the biggest mathematical mystery of them all — and save Christmas for Alex, Ben, and Carol!

Santa’s lost his memory, and the elves are cursed to alternate between lying and truth-telling. It’s up to you to piece together the clues and figure out which presents go where.

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.

“Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

Check Out These Cool Math Sales

I’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math.

You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

Sale price is \$30 from December 2-15.

But Wait, There’s More

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

Stock Up on My Playful Math Books

Finally, if you’ve been wanting to pick up a paperback copy of Let’s Play Math or some of my game books, or maybe a set of dot-grid math journals, I’m currently offering a discount on bulk orders.

Bundle ANY assortment of titles. Stock up on books for your family, friends, or homeschool group.

• 2–4 books: 15% discount off retail prices
• 5–9 books: 25% discount
• 10–19 books: 35% discount
• 20+ books: 35% discount, and free Continental U.S. standard shipping or the equivalent discount off other shipping options

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

Do You Know of Any Math Deals?

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.