[TMWYK] – Sizes of Numbers

As a math teacher, I understand and enjoy the importance of building mathematical reasoning skills and a strong number sense. I try every day to share this with my students in class. I’m also a parent, so I get to share this with my kids at home as well. Luckily, my interactions with the MTBoS online community provided me the opportunity to connect with Christopher Danielson and his work regarding talking math with kids. As a parent, I want to give my children every opportunity to be successful with their learning, and making it a point to engage in mathematical talks with my three-year old daughter has been a very satisfying experience.

Meet Callie, my daughter.

Callie

I thought it’d be nice for you all to put a face with the name. Plus, regardless of my inherent bias, I think she’s pretty cute. Anyway, Callie and I like to talk about numbers, different ways we use numbers, and the sizes of numbers. She is currently fixated on the number and quantity of 3 because, of course, she’s three years old. For example, if I ask her how much of something she wants (cookies, stickers, etc.), she defaults to “3, because I’m three years old!” I’m trying to get her thinking about different sizes of numbers (quantities), thus being able to compare and order them. Following is a conversation Callie and I had, which gives a glimpse as to where she currently is in her understanding of numbers, quantities, and sizes. I’ll be updating this adventure in future posts as we progress with our understandings.

Me: Callie, finish up your game. You have to go to bed in 20 minutes.
Callie: How about I go to bed in a hundred minutes?
Me: 100 minutes is too many. It would be much too late for you to go to bed.
Callie: Then how about 10 minutes?
Me: Would you rather go to bed in 10 minutes or 20 minutes? Which do you think is longer?
Callie: Oh. 20 minutes.
Me: Is there another amount of minutes that’d you prefer?
Callie: 30 minutes.
Me: Why is that?
Callie: Because 30 is bigger than 20.
Me: How do you know that?
Callie: Because 30 is the biggest number in the world!
Me: Are you sure? Can you count past 30?
Callie: 31, 32, 33…

At this point, I felt the conversation heading off to goofy-sleepy land, so I made a note to revisit this soon. I think our next conversation will use a unit other than time to see if their are different results.

These conversations with my daughter have made me reflect on why I enjoy being a teacher: I like talking math with kids.

[Math Task] – What’s Your Blood Type?

Some upperclassmen were discussing blood types in our study hall the other day, and they asked me to search for what types of blood were compatible as well as what the most common blood type is in the United States. What we found was quite interesting, and as I was perusing the information, I kept thinking that the information would make for a nice math task. Here is some information that I found:

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I think on their own, these could spark some interesting questions from students that could then be spun into engaging math tasks. There was also some other information that I can see as more challenging extensions:

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My question to our MTBoS community is “What would you do with these? What sort of tasks could you build around this information? Would it be engaging to students?” I Look forward to discussing ideas in the comments.

[All images and information courtesy of Scott & White Healthcare.]

Algebra. It’s Everywhere. So Get Rid of Algebra Class.

Algebra. It’s everywhere. So let’s get rid of algebra classs.

Pennsylvania (where I teach) has made it the capstone math requirement for graduation. I’m going to argue that algebra shouldn’t even be its own course, but rather a set of tools to learn in conjunction with other courses (I’m looking squarely at you geometry). We try to shoehorn algebra practice into other courses already, so why shouldn’t they become a little more integrated and create a need for algebra? Below is exhibit number 1. Feel free to argue at will.

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Billions and Billions

I got some math teaching inspiration the other day when I was sitting at a traffic light staring at the ubiquitous McDonald’s sign, the one that reads “Billions and Billions Served,” one like this:
mcdonalds4

This sign made me wonder, “Just how many are billions and billions? Over one billion? Over two billion? When would it be appropriate to use billions and billions?” It was a fun internal debate, and I wondered whether students would find this perplexing as well. It seems like it could lead to an interesting conversation involving large numbers, orders of magnitude, etc. What could you do with this? I’d love to hear your ideas.

Here is a post regarding the history of the numbers of McDonald’s and following are some more McDonald’s signs that I found on the internet:

0808mcdonalds
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mcdonalds2mcdonalds-hamburgers-over-99-billion-served-wingsdomain-art-and-photography
247 Mcdonalds sign

Sly Fox, Level Up

In my continuing addiction of turning my kids’ television shows into teachable and learnable moments, I present to you the “Sly Fox” game, first seen on Peppa Pig. The game works like this: One person (pig in the cartoon) stands with their back towards the other participants. The others try to sneak up (like a sly fox) on this person, who at any moment can turn around and catch the “foxes” moving. If this happens, the not-so-sly fox has to return to the starting line. The winner is the first person to reach the “fox hunter” and then becomes the new “fox hunter.”

My daughter asked to play this game with her adaptation of having her mother and I close our eyes while she was sneaking up on us. When we opened our eyes, she would stop moving (well, as much as an almost 4 year old can stop moving). I thought this was a pretty good abstraction of the game for her to devise, but I took the opportunity to “level up” this game and add some thinking, reasoning and decision-making for her. Here is my adaptation:

  • The “sly fox” can only START moving when he or she sees a thumbs-up signal.
  • The “sly fox” can only STOP moving when he or she sees a palm-up stop signal.
  • The “fox hunter” is allowed to throw up other signals, such as different fingers and numbers of fingers, as well as the tricky thumbs-down signal.

How’d it go? It had mixed results, but my daughter generally liked our adaptations. She had no trouble starting on the thumbs-up signal and stopping on the palm-up signal. What was a challenge for her, and I could see her thinking through this, was whether she should START moving if she didn’t see the stop signal or STOP moving if she didn’t see the start signal. I tried to explain that regardless of what state she was in (moving or stopped), the thumbs-up could only START her and the palm-up could only STOP her. This seemed a bit to much for her at her age, but we’ll continue to play and see how we progress with our thinking and decision-making skills.

Pro Tip: Be careful which signals you decide to use. These are kids after all.