Category Archives: News

Which Poster Doesn’t Belong?

(Cross-posted from Talking Math with Your Kids)

Two and a half years ago, I was developing Which One Doesn’t Belong? (before Stenhouse had signed on to publish it). I went on a tour of elementary classrooms to talk with K—5 students all around the Twin Cities about these collections of shapes. I learned a tremendous amount of course, and much of that learning went into the Teacher Guide (which Stenhouse convinced me needed to exist).

I learned a lot, and I also noticed something.

Most of those classrooms had some form of shapes posters on the walls. Triangles, rectangles, squares, and rhombi were proudly and prominently displayed so that students would be surrounded by correct geometry vocabulary. Most of those shapes posters had something important (and unfortunate) in common with the shapes books in the school library and in the children’s homes.

There were rarely squares on the rectangle poster. All of the triangles were oriented with one side parallel to the ground, and most of them were equilateral. Sometimes the shapes had smiley faces. You and I know that a triangle is still a triangle, no matter its orientation. I can assure you not all elementary school children know this. While the vocabulary is good on your standard shapes poster, the math is not. (I decided not to link to examples—you can do your own search and report back if you find my claims exaggerated.)

This summer, Stenhouse is helping all of us to fix this. You can now preorder Which One Doesn’t Belong? shapes posters.

Poster images

They come as a set of eight, with an insert in the spirit of the Which One Doesn’t Belong? Teacher Guide to help you facilitate student thinking and classroom conversation as they hang in your classroom.

1. Which SQUARE doesn’t belong?

2. Which RECTANGLE doesn’t belong?

3. Which RHOMBUS doesn’t belong?

4. Which HEXAGON doesn’t belong?

5. Which TRIANGLE doesn’t belong?

6. Which POLYGON doesn’t belong?

7. Which SHAPE doesn’t belong?

8. Which CURVE doesn’t belong?

These posters are filled with good mathematics. Consider the triangle poster on top of the pile. The triangle in the lower right is the only right triangle. The one in the upper right is the only equilateral triangle. The one in the upper left is the only isosceles triangle (or is it? do equilateral triangles count as isosceles?) The one in the lower left is the only one you can’t build out of the triangle in the lower right. Students will notice side lengths, angle measures, orientation, composition and decomposition, and more properties of triangles. Some will complain that not all of them are triangles (“too pointy” or “doesn’t have a bottom”). These posters let you and your students sit with—and play with—these ideas over a period of weeks or months.

So as you plan your back-to-school classroom organizing and decoration, I hope you’ll consider making space on your walls for these posters. And I definitely hope you’ll share your students’ ideas here and on Twitter.

Available for pre-order now. They’ll ship in early August.

A quick plug for Estimation 180

Estimation is more than rounding.

Most of the time we don’t teach this, but it is.

Tabitha (8 years old) had a homework assignment the other night that asked her to imagine she had $100 to spend in a catalog, and to make a list of things she would like to buy from that catalog. She found the latest American Girl catalog and got to work.

There was a table to fill out with three columns.

  1. Description of item
  2. Actual cost of item
  3. Estimate

A couple minutes later she asks, What’s the estimate if it costs five dollars? Should I write $5.01?

She has discerned that estimate means write down a number that is not the exact value.

But that’s not what estimation is about at all. Estimation is about finding a number that makes sense, and not worrying about whether it’s the exact value or not.

The image below seems to be going nuts on the Internet today (despite my exhortations to the contrary! Oh, Internet! When will you learn to listen to me?)


“Is this reasonable?” is a great estimation question. Rounding is one way to answer the question. But if a kid can quickly find a number that makes sense and it happens to be a precise number, then we probably haven’t asked a good estimation question. Rather than mark it wrong because the kid didn’t round, we should ask this kid a more challenging question next time.

What does a good estimation question look like? What would be more challenging?

I’m glad you asked.

Estimation 180. Thinking of a number that makes sense is much more interesting when you have to bring your knowledge of the world to bear.


Is 75 inches a reasonable answer for the difference between the father’s height and the son’s? Is 75 centimeters reasonable?

Oh! And here’s the first in a nice sequence about numbers of pages.

New year, new job

If you’ve been following along (and honestly, I cannot imagine how anyone could possibly have time to do so!), you are under the impression that I’m on sabbatical leave this year.

There has been a change of plans.

I’ve taken an unpaid leave from my college and am spending the bulk of my professional time on curriculum development work at Desmos as a (nearly) full-time teaching faculty member.


The job actually involves almost no sitting on small children.

Our team is growing (Do you know any awesome designers? Send them our way, please!) We have a lot of great stuff in the pipeline. I’m delighted and grateful for the opportunity to work with this amazing team. It’s well known that I’ve been working with them on an extracurricular basis for some time now (>1.5 years), and this has made the transition super smooth.

I am especially fortunate to be able to set aside a portion of my professional life for ongoing projects that are outside the scope and focus of Desmos (although they are certainly consistent with the overall Des-mission of more and better mathematics for all learners!) I’ll spend a couple mornings a week in a kindergarten most of this school year, for example, and Which One Doesn’t Belong is still slated for a 2016 release from Stenhouse. (We still need to sort out Math On-A-Stick for next summer, but that’s a year away.)

Help Wanted: Math on a Stick

The following is cross-posted from Talking Math with Your Kids.

I want to tell you about a vision of a beautiful thing, and I want to ask you to help make it happen.


Math on a Stick logo by Emily Bremner Forbes, who makes beautiful things. Many thanks, Emily!

Math on a Stick will be an annual event at the Minnesota State Fair (12 days of fun ending Labor Day!) that engages young children (4—10 years old) and their caregivers in informal mathematics activity and conversation using the Fair as a context.

  • Parents will push children on a protractor swing so that together they can notice the angles and fractions of a circle the children travel through.
  • Parents and children will use beautiful tiles to make shapes and intriguing patterns.
  • They will comb the fairgrounds looking for groups of many different sizes, asking questions such How many mini donuts are in a bag?, How many sides does the Agriculture-Horticulture building have? and Why is it so hard to find a group of 17?
  • They will notice the rotational and reflection symmetry in a wide variety of plants and flowers, then copy these symmetries by making a paper flower to take home.

Math on a Stick has four components:

  1. The Math-y Midway
  2. The Garden of Symmetry
  3. The Number Game
  4. Visiting mathematicians and mathematical artists.

Find out more about each of these below.

The major question now is whether Math on a Stick happens for the first time this year or next. The organizing body is the Minnesota Council of Teachers of MathematicsThe Math Forum is by our side. Max Ray and Annie Fetter from the Math Forum plan to come to Minnesota to help run the event. The Minnesota State Fair and Minnesota State Fair Foundation love the idea. We just need to convince all parties that it is possible to pull this off in the coming three months, and we need to locate the funding to make it happen.

Your Call to Action

We’ll need help with three things:

  1. Volunteer hours this summer, before the Fair
  2. Volunteer hours during the Fair
  3. Funding

Of course I expect that most who heed this call will hail from the great state of Minnesota, but I encourage others to consider scheduling a visit. This will be a wonderful event, and the Minnesota State Fair is truly a grand spectacle.


Before the Fair, we’ll need help finding and creating the things that will make the event go.

During the Fair, we’ll need help staffing the event. It runs 9 a.m. to 9 p.m. August 27—Sept. 7. We’ll have have about four shifts a day and we’ll require multiple people staffing each shift.

If we get Math on a Stick up and running this summer, one of our first orders of business will be to establish our volunteer website. Please check your summer calendars, pencil us in, and keep an eye on this blog for more information.


If you (or someone you know, or an organization you are involved with) are in a position to help fund Math on a Stick, get in touch with the Minnesota State Fair Foundation to let them know you’d like to help make this happen. Our overall budget is on the order of $20,000.

The specifics

Here are specifics on the four components of Math on a Stick.

The Number Game

The major activity at Math on a Stick is The Number Game. Adapted for math from the Alphabet Forest’s Word Game, children and parents are challenged to find groups of every size 1—20 at the fair. Examples: A corn dog has 1 stick, a cow has 4 legs, the Ferris Wheel has 20 carts.

Players receive a form they carry with them around the fair to record their findings, and can return with a completed form to claim a ribbon. Additionally, players can email, tweet, and post to Instagram, their Number Game fair photos. These are curated by Math on a Stick volunteers and posted to a public display that resets each day so that collectively State Fair attendees recreate daily a new visual answer guide to the Number Game.

The Math-y Midway

A protractor swingset, tables with fun tessellating tiles, and images from Which One Doesn’t Belong? and a (forthcoming) counting book to play with and discuss.

The Garden of Symmetry

Flowers are grown in planters along a path. As you walk from one end of the path to the other, you pass flowers with increasingly complex symmetry. Grasses (with one line of symmetry) are near one end. Irises are a bit further along (with three rotational symmetries), and sunflowers are near the far end (with MANY symmetries). Visitors to the Garden of Symmetry are invited to carry a tool consisting of two small mirrors taped together to investigate symmetries in the garden and the interpretive signage.

Visiting mathematicians and mathematical artists

An activity area is set aside for a daily visit from a mathematician or mathematical artist. Each provides engaging, hands-on math activities during a scheduled period each day. We will draw upon talent from Minnesota, as well as nationally (budget allowing).

For full details on the event, have a look at our Math on a Stick white paper.

Hit me in the comments with any questions you have.

Get in touch with me through the About/Contact page on this blog.

Please help us build this thing. It’s going to be great!

Building a better shapes book

Just a quick note here for the folks who are (a) not on Twitter and (b) not following Talking Math with Your Kids.

I created a shapes book for all ages. The digital version is free for now. Details are in this post over at TMWYK.


New Desmos lesson(s)

You should seriously go check out Polygraph. Four versions of a delightful and challenging game:

  1. Lines
  2. Parabolas
  3. Rational functions
  4. Hexagons

The hexagons will be familiar to long-time readers of this blog.

Screen shot of hexagons

I have run the parabolas version in College Algebra, and the hexagons version in my Ed Tech course. It was a huge hit both times—lots of conversation happened both electronically and out loud in the classroom. It’s a ton of fun.

I am especially pleased with the rational functions version. It makes for challenging work—even among the mathematically astute Team Desmos in recent trial runs.

Read the Desmos blog post on the matter if you like.

[News] A new project

Back in the spring when the Letter to Jack was a hot item, I took to Twitter to wonder why there was no Common Core Math for Dummies. One thing led to another, I proposed it to Wiley and now you can expect it in the spring.

Audience is parents, and this may appear in the title (Common Core Math for Parents For Dummies is the working title). It goes for the big picture in each of the grade levels, K—8.

The For Dummies format is pretty rigid but there will be no mistaking authorship. A few sample section headings (and the grades where they will appear) to whet your appetite:

1st grade. Saying bye-bye to key words

1st grade. Understanding the importance of ten

2nd grade. Why units matter

2nd grade. Place value

2nd grade. More about place value

2nd grade. Seriously. Place value.

4th grade. Multiplication: What is it and why not just memorize the facts?

5th grade. Standard algorithms: Doing things “the old-fashioned way”?

6th grade. Dividing fractions—More fun than you’d think!

6th grade. Area: It all goes back to rectangles

8th grade. Congruence and similarity: Two kinds of sameness

Catch you all later. I have some writing to do!

I’ll keep you posted.