# Boxes of Math are here

I and dozens of families across the US, Canada, and England had a blast with the Summer of Math last summer, and now I’m gearing up for the school year version: Boxes of Math.

Starting small with a single option for kindergarten and first grade (five- and six-year-olds, roughly), Boxes of Math will have some overlap with last summer’s Summer of Math, but are targeted at this more narrow age range and the math they’re learning in school.

• A small welcome and introductory shipment before the New Year

• A box for counting and patterning in mid-January

• A box for shape study in late February

• A box for number structures and operations in late March/early April

Each box will have a book, one or more things to get your hands on, and a newsletter with ideas about fun ways to play and to continue the learning in your everyday lives.

## Why Boxes of Math?

Inside these boxes are things that help create conversations. They get children thinking about the most important ideas of elementary math.

A few of the objects that will fill the boxes of math.

Most children who struggle with math later on aren’t familiar with these ideas. They know facts by rote, but not in relation to each other. Or they cannot retain the facts because they see no relationships. They can name triangles, but don’t see all polygons as made out of triangles. They can count large numbers of objects fluently, but they don’t notice whether these objects are arranged in rows and columns.

Those are the things this website is all about.

Struggling or not, all children benefit from exercising their math minds through play and conversation.

Boxes of Math offers children and caregivers opportunities to play, experiment, and talk in ways that bring these ideas to life. Noticing rows and columns is a natural outcome of playing with pattern machines. Playing with 21st Century Pattern Blocks is an extended exercise in putting shapes together and taking them apart.

The target outcome of Boxes of Math is children (and families) with a similar relationship to math as they have to literature. They talk about it, see it in their world, and use it to understand their lives in richer, more beautiful ways than before.

# How Many? An invitation to #unitchat

Make Math Playful is an unofficial slogan here at Talking Math with Your Kids. An important part of play is that there is not one right answer. Through Which One Doesn’t BelongI showed a way to make geometry playful. Now with How Many? I’m working on a way of making counting playful.

The idea has grown out of the TED-Ed video I did a while back, and the more I play with it, the more I see it in the world around me. My goal is to help parents, teachers, and especially children see it too.

Most counting tasks tell you what to count. Whether it’s Sandra Boynton’s adorable board book Doggies, or Greg Tang’s more sophisticated The Grapes of Math, the authors tell you what to count—or even count it for you.

How Many? is a counting book that leaves possibilities open and that seeks to create conversations. Creativity is encouraged. Surprises abound.

The premise is simple. Every page asks How Many? but doesn’t specify what to count. Each image has many possibilities.

An example. How many?

Maybe you say two. Two shoes. Or one because there is one pair of shoes, or one shoebox. Maybe you count shoelaces or aglets or eyelets (2, 4, and 20, respectively). The longer you linger, the more possibilities you’ll see.

It’s important to say what you’re counting, and noticing new things to count will lead to new quantities.

Another example. How many?

A few possibilities: 1, 2, 3, 4, 6, 12, 24, 36. What unit is each counting? Maybe you see fractions, too. 2/3, 4/6, 3/4, 1/12….others? What is the whole for each fraction? The number 3 shows up more than once—there are three unsliced pizzas, and there are also three types of pizza. Are there other numbers that count multiple units?

All of this leads to two specific invitations.

Let me come talk with your students.

(It turns out my schedule filled very quickly, and I’m no longer seeking new classrooms to visit right now—thanks to everyone for your support!)

If you are within an hour of the city of Saint Paul and work with children somewhere in the first through fourth grades, then invite me to come test drive some fun and challenging counting tasks with your students. I have set aside November 17 and 18 and hope to get into a variety of classrooms on those two days. Get in touch through the About/Contact page on this blog.

I’ve been using, and will continue to use and monitor, the hashtag #unitchat, for prompts and discussion of fun and ambiguous counting challenges. Post your thoughts, your own images, the observations of your own children or students, and I’ll do likewise.

How Many? A counting book will be published by Stenhouse late next year.

# Birthday Chocolate

Today is my birthday. Griffin (12 years old) gave me three chocolate bars as a gift. He gave me candy because he is deeply aware of its value in life. He gave me dark chocolate because he knows it’s my preference.

He is frequently disturbed by how slowly I eat these gifts of candy he gives me.

Here’s how my after-work greeting went this evening.

Griffin (12 years old): Happy birthday, Dad.

Me: Thanks.

G: One thing I’ve noticed about you is that you eat the candy I give you incredibly slowly.

Me: I know. But actually I ate half of one today.

G: Half of a bar, or half of all the bars?

Me: Half of one bar. And then maybe I’ll have another half tomorrow.

G: Oh brother.

Me: And since I know 3 divided by 1/2 is 6…

G: You ate one-sixth of it.

Me: And it’ll last me 6 days.

Having arrived home a bit chilly and damp from the bike ride in the 45° rain, I went downstairs for a shower and he returned to his iPod.

## So What Do We Learn?

I haven’t written a lot about this boy recently because he is in a phase of rejecting everything the adults around him care about. All adolescents go through some form of this. He is doing it with gusto.

In any case, the groundwork we’ve laid in the early years has paid off. When math is useful for his purposes, he will use it. Here, he wanted to prove his point that I am a painfully slow candy consumer. That made it important to clarify that I had not eaten half of my candy, but only half of one bar of candy.

We play around with units like this frequently. It has contributed to both children’s place value understanding, as well as their fraction work.

## Starting the Conversation

Ask frequently about the units that are attached to the numbers in your lives. When you’re cooking, ask, Should we use 3 eggs or 3 dozen eggs? Ask about how many pieces of candy a pack of Whoppers is at Halloween.

Look at these pictures—one at a time—and ask How many? Challenge yourselves to find different numbers, and different units. (For example, there are 15 avocado halves, 7.5 avocados, 8 pits, 7 holes, and 1 cutting board).

# What Math Looks Like

I’ve been working on some presentations, and I’d like to share with you some images I’ve collected and made along the way, without further commentary. Enjoy.

# Which One Doesn’t Belong? is in print!

I am delighted to announce that Which One Doesn’t Belong? A Better Shapes Book is in print and shipping from Stenhouse Publishing this week.

I’ll be at Math On-A-Stick at the Minnesota State Fair August 25 through Labor Day. Stop by for a selfie and to get your copy signed!

(Note: The books are not for sale at the fair—nothing is for sale at Math On-A-Stick.)

# Help wanted: Math On-A-Stick

We are almost ready for Year 2 of Math On-A-Stick at the Minnesota State Fair. Last year’s favorites are back. We have a few delightful new exhibits.

And we need help.

The fair is a bit more than a week away, and we have several shifts that still require volunteers.

If you are in a position to help, please do. Here’s how:

• Bring a friend.
• Recruit, recruit, recruit.
• Email your colleagues (and neighbors and students and….?)
• Forward this post to everyone you know!
• Tell your spouse he/she is gonna need to rally for the cause.

Here are dates and times we especially need help:

Sunday, Aug. 28 5:00—8:15 p.m.

Monday, Aug. 29 2:15—5:15 p.m. and 5—8:15 p.m.

Wednesday, Aug. 31 8:45 a.m.—11:45 a.m., 2:15—5:15 p.m. and 5—8:15 p.m.

Thursday, Sept. 1 11:30 a.m.—2:30 p.m., 2:15—5:15 p.m. and 5—8:15 p.m.

Friday, Sept. 2 11:30 a.m.—2:30 p.m. and 2:15—5:15 p.m.

Saturday, Sept. 3 11:30 a.m.—2:30 p.m. and 2:15—5:15 p.m.

Sunday, Sept. 4 8:45 a.m.—11:45 a.m., 2:15—5:15 p.m. and 5—8:15 p.m.

Monday, Sept. 5 (Labor Day) 2:15—5:15 p.m. and 5—8:15 p.m.

Email me if you have any questions: mathematics.csd@gmail.com

Need help visualizing Math On-A-Stick? Check out our photo album from last year.

Or watch this video.

Or read this post from last year’s Fair.

Whatever you can do to help spread the word, all of us involved in making Math On-A-Stick happen thank you!

# On helping children to love math

Some version of the following comes through my email Inbox every so often.

My daughter does not like maths. How can I ignite the passion for maths? She’s 8 and I feel she’s got to learn the importance of maths but how can I do it?  A teacher told her Maths is not for everyone and she believes it. Help!

Here is a version of my standard response.

Your story strikes close to my heart.

You may well know that girls are much more likely to get these kinds of messages from teachers than boys are, and they are much more likely to internalize these messages, as their teachers are much more likely to be same-gender role models.

It is all heartbreaking.

And I’ve seen these forces first-hand this year with my 9-year-old daughter. Her teacher said to her in a parent-teacher conference, “Your mind is better with words than with numbers, isn’t it?”

This, despite extensive evidence that she is a super creative mathematical thinker. A significant fraction of that evidence is documented on my blog, Talking Math with Your Kids.

With my own children, I have taken the perspective that “loving math” or even “appreciating its importance” may not be reasonable goals. Instead, being able to see math in their lives, and becoming competent mathematicians is.

Of course I would love for my children to love math, just as I would love for them to love reading. But I can’t enforce those emotions. What I can do is infuse my children’s everyday world with shapes, patterns, and numbers just as I infuse their world with words and stories.

This blog is full of concrete examples of opportunities for this. The post about hot chocolate is probably the simplest and clearest example of how parents can make simple changes to support their kids’ developing mathematical minds.

I would also recommend spending some time reading the research posts. There’s a lot of useful and interesting research work going on in math education right now, especially as it pertains to elementary-aged children, parents, and math.

Please don’t hesitate to reach out if there is anything further I can do to support you and your daughter.

I wish you both the best!

Christopher

# Tessalation: A great new book

Tessalation is a terrific new picture book by Emily Grosvenor. The story involves a little girl whose mother needs a bit of peace and quiet, so sends her outside to play. While outside, Tessa (get it?) notices shapes fitting together without gaps everywhere she looks.

I helped sponsor Tessalation on Kickstarter this spring, and our hard copies arrived last week. Naturally Tabitha (9 years old) and I read it together right away.

Here are some of the things Tabitha, Griffin (11 years old) and I noticed and discussed while reading it, and afterwards:

• The turtles are delightful.
• While they are somewhat different turtles from the ones we’ve played with around the house for the last year, they have an important characteristic in common—two noses and two tails come together in both tessellations.
• There are tessellating leaves that look an awful lot like some shapes I’ve made and we’ve played with a number of times. We saw kites and hexagons and triangles in the leaves just as we have in the pink quadrilaterals below.
• We wondered whether this object counts as a tessellation. (It’s not from the book, but Tessa set a great example for us to notice and ask about tessellations in our world.)

All in all, Tessalation is perfectly aligned with the Talking Math with Your Kids spirit. It creates a richly structured and playful space for parents and children to notice things and to converse. The language is fun. The images are beautiful. Tabitha and I highly recommend it.

Quick notes: Tessalation will be a component of August’s Summer of Math box. It’s not too late to sign up! Also, we’ll soon have a Tessalation/Tiling Turtles combo pack available. You can order the book right now from Waldorf Books, and e-books from Amazon.

# Ceiling fan arithmetic

Summer has arrived in Minnesota, and that means we alternate between warm days where we open the windows and run the ceiling fan, and hot days where we close everything up and run the air conditioning (a luxury, btw, that our 1928-built home only got about five years back).

Not our ceiling fan.
Image credit: Brian Snelson (CC-BY 2.0)

Tabitha is naturally curious about how the ceiling fan works. In case you don’t have experience with them, or yours works differently from ours, here are the basics: There is a switch on the wall—just like a light switch—that powers the fan. Then there is a chain hanging from the fan itself that affects the speed. There are four settings controlled by the chain—High, Medium, Low, and Off.

By the time this conversation takes place, Tabitha and I have already explored a variety of ceiling fan questions, such as If the fan is off, should you pull the chain to turn it on, or head over to the light switch? and How many times can I pull the chain before my parents tell me to stop playing with the fan?

On this day, I ask Tabitha to flip the wall switch to turn on the fan, which she does. She then starts to stand up on the couch to reach the chain. I ask why.

Tabitha (9 years old): I want to see if it’s on high.

Me: But how will you know? If you pull the chain it will slow down, but that’s what it always does. So how will you know whether it was on high to begin with?

T: Well, it doesn’t always slow down, otherwise how would it ever be on high?

## So What Do We Learn?

There is some very deep math going on here.

Tabitha and I are playing with properties of modular arithmetic, but she (and you) don’t need to know the specifics. Things that go in cycles are all examples of this kind of math.

The classic example is time. You could say that later times have bigger numbers. 4 is later than 3; 12 is later than 9. This is just like my claim that every pull of the chain slows down the fan. Both of these claims are only sort of true. Three in the afternoon is later than 11 in the morning, despite having a smaller number. If the fan is on low and you pull the chain twice, it’ll be on high.

People study these things in great depth in the field of Modern Algebra, and the ideas are useful in all sorts of places.

## Starting the Conversation

Play with a ceiling fan. Talk about staying up all night. Notice together that weird things happen when the fan is in the off position, and at midnight and noon. Wonder aloud whether 12 o’clock is like zero (and if not, what is?)

Play around with basic facts in this ceiling fan environment. If it’s on high, how many pulls to turn it off? If it’s on low, how many to get it to medium? I just pulled the chain three times and now it’s on low—where was it before? Etc. Challenge the child; have the child challenge you.

Stay cool!