Did you know that there is a famous illusion associated with Lincoln’s “stove pipe” hat? The hat looks like it’s taller than it is wide, even when the height and width (including the brim) are the same. Let’s make a hat:

- Cut a circle with a radius of 5 1/2 inches.
- Cut a circle from the center of the first circle with a radius of 3 1/2 inches.

The smaller circle will form the tip of the hat, and what’s left of the larger circle will form the hat brim. If we had a rectangular sheet of paper of the right size, we could make the cylindrical part of the top hat.

]]>Mia drew a shape with exactly 4 sides.

It has 4 lines of symmetry.

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- Write 23 X’s on a piece of paper.
- On your turn you can erase or take away 1, 2, or 3 of the X’s.
- Turns alternate. You cannot skip your turn.
- The person who erases or takes away the last X wins.

I’ve always felt a connection to Punxsutawney Phil because my birthday is on February 2nd, the same day folks watch to see if Punxsutawney Phil sees his shadow! One year, I noticed:

- Phil’s height = 51.2 cm
- Suzanne’s height = 5′ 4″
- Suzanne’s shadow length at Gobbler’s Knob = 76.2 cm

Kelly was watching her favorite Winter Olympic event – the four-man bobsled. On each team a driver sits in front, followed by two teammates and the brakeman in the back.

The numbers 1 through 20 were assigned to the 20 athletes. The drivers wore numbers 1, 2, 3, 4, and 5.

Before the race Kelly studied the teams. Drivers 2, 3, and 4 were riding with brakemen 18, 15, and 20 respectively in three of the sleds. In another sled were 6 and 12, and in the remaining sled were 10 and 17.

Suddenly Kelly realized that if you added up the four numbers on each team, all five sums were the same!

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*Hidden Figures* twice now (and counting). The question my wife asked as we were leaving the theater is still haunting me:

“How much is the human race missing out on because the people with the genius ideas aren’t being heard, because of oppression?”

As a math educator, I’m so eager for people to see and discuss this movie. I want to hear what we are learning about what it means to do mathematics, about who can be good at mathematics, about what it means when we embrace new technologies and how that changes workers’ lives, about how racism and sexism manifest themselves in big and small ways, about what it takes to transform cultures, and more.

I’m especially eager for students in our math classrooms to get to think their way through *Hidden Figures*. There are a million lesson plans that could be written, and I know people like John Burke are encouraging teachers to collect them and share them in his post, “Let’s Start a Movement for Hidden Figures”

Here’s my first contribution, written for Philadelphia’s week of Black Lives Matter lessons. In this lesson, students play a game that my colleague Suzanne invented called Mission Control, in which they have to describe, using one-way communication, some mathematical object that their partners out in space have to recreate. It focuses on communication of math ideas (something Katherine Johnson worked on a much harder version of later at NASA, when she wrote papers about helping astronauts quickly calculate new trajectories on the fly, in time to change course and not get lost in space, when things go wrong), and also on seeing familiar objects in new ways when you’re forced to describe them under new rules (a very simple version of the problems Katherine Johnson was trying to solve when they knew what a basic orbital trajectory should look like but didn’t know of any calculations to plot it exactly).

My lesson also encourages students to reflect on their own lives and how their lives prepared them to be mathematical problem solvers, able to see things in new ways, cope with frustrations, share their ideas, etc. And then asks, ~~“How might the women in Hidden Figures have drawn on their life experiences as Black women to help them succeed in this moment of crisis?”~~ “How might the women in Hidden Figures have drawn on their life experiences to help them make mathematical and engineering and computing breakthroughs?”

(**Update**: after sharing with Black educators and asking for feedback I was told that for students without a lot of context to empathize with Black women, asking that general question was likely to lead to stereotypes, not more empathy and reflection. Carl suggested asking specifically about the movie characters, and Rafranz suggested adding more opportunities for students to reflect on their own identities and the impact of identity on mathematicians. Inspired by their work I also added links to Annie Perkins’s “The Mathematician Project” and NCTM’s “The Impact of Identity”)

Finding strength in the ways adversity has shaped us, and knowing those strengths serve each of us in our mathematical lives, is one of my takeaways from this movie. What’s yours?

And please, if you read the lesson or use it with your students, let me know how it goes and how it can be improved! Here’s the link to the lesson: https://docs.google.com/document/d/1DSZGK-qL40ldZft5Lb-OTTNPOBIlGSR4G-Dek0ta91k/edit?usp=sharing

** Updates from the Community!**:

Melynee Naegele took this lesson and ran with it. She blogged about it, and also made Google Slides with nifty outer space backgrounds that you could use to present the lesson.

Norma Gordon has been collecting Hidden Figures resources in a Google Drive folder. She has links to other resources, NASA’s “Modern Figures” toolkit, and a lesson on Conversion Errors that’s full of the math of space travel.

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At a recent math conference, lunch was provided for the participants. To be sure that there was enough food for everyone, the kitchen staff made more lunches than there were people attending. In fact, the ratio of prepared lunches to people was 7:5.

Because they anticipated a large number of vegetarians at the conference, the staff made 2 vegetarian lunches for every 3 non-vegetarian lunches.

It turned out that the ratio of non-vegetarians to vegetarians at the conference was 3:4.

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This is off the top of my head… to me it feels like taking what I know from the Mathematical Practices, the Process Standards, others’ work on Habits of Mind, and trying to put it into a short, kid- and teacher-friendly list.

What do you think?

The next step is to connect these with some activities to get the kids doing and reflecting on these reasoning moves…

**Students who are ready to learn from problem solving, make and critique mathematical arguments, and apply their understanding to new problems do the following things:**

*Working on problems and applying their learning:*

- They read problem statements/scenarios multiple times and ask themselves: do I understand the story?
- They represent math scenarios in multiple ways, and understand other representations they don’t choose to use
- When faced with a problem that seems hard, they have ideas to try, like making a guess and seeing what happens, drawing a picture, using manipulatives, or estimating.
- If they aren’t sure, their go-to is NOT an algorithm or a process
- When they use an algorithm or a process, they ask themselves:
- Why did I do that?
- Does this answer make sense in the story?

- They check their work in different ways:
- Checking the story
- Solving the problem another way
- Using another representation
- Making sure their work is accurate
- Asking a friend to compare

*Reflecting, getting better, and learning from others:*

- After they have an answer, they are interested in other ways to solve the same problem
- When someone else shares a different approach, they pay attention to:
- Things that are similar
- Things that are different
- Things that don’t make sense, yet

- They ask questions to understand similarities, differences, and work through confusion
- They take notes on other people’s thinking, and mark up their notes to help them make sense and remember
- When they learn new ways to solve problems, they quickly try the new ideas out
- They ask themselves, “does this make sense?” and if it doesn’t, they ask a question
- They pay attention to processes and repetition in processes, in order to look for generalizations and shortcuts, and can explain why those generalizations or shortcuts make sense

*Being a good math community member:*

- They seek out collaboration and offer collaboration when asked
- They listen to ideas, and when they don’t understand or disagree, they ask a question
- They try to find common ground (I think we agree up to…)
- When there is a disagreement, they use definitions and assumptions to find the source of the disagreement (when you say this isn’t a rectangle, are you thinking that’s because it doesn’t have 2 long sides and 2 short sides?)

Our son Specialist Lee Alejandre wished us a “Happy New Year!” from his Army post overseas using his iSight camera and iChat AV connection. It was 12:01 am, January 1, for us in Philadelphia, PA, but it was 2:01 pm for him in Seoul, South Korea!

My husband and I were talking about the time zones. I looked on the web and found that Philadelphia is about 203 degrees of longitude west of Seoul. Once we realized that there are 360 degrees of longitude and there are 24 hours in a day, we understood why there is a 14 hour difference in time.

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