Bird Family Question

During small groups today, I verbally gave my third graders the following question that I so skillfully made up in a few seconds.

Suppose there are 40 bird families in Tucson. A bird family consists of a Mom Bird, a Dad Bird, and 2 kids birds. 18 bird families fly away to Phoenix. How many kid birds are left in Tucson? 

Allow me to list the mathematical practices that this task required:

MP1 Make sense of problems and persevere in solving them
MP 2 Reason abstractly and quantitatively
MP 3 Construct viable arguments and critique the reasoning of others
MP 4 Model with mathematics
MP 5 Use appropriate tools strategically
MP 6 Attend to precision
MP 7 Look for and make use of structure
MP 8 Look for and express regularity in repeated reasoning

Huh. I honestly didn't know I would list out all eight. Oh well! If the shoe fits...

My group of three girls made me so proud! They're getting used to (finally!) my persistent questioning and demands that they represent their work in multiple ways. With little prompting, here are some pictures of what they came up with.

Student A (we'll call her Jessica) ended up drawing 22 circles to represent a "family." She then drew four dots to represent each bird and crossed out the adults since my initial question only required her to find how many kids were left.

Similarly, Student B (let's say, Anna) showed represented the situation similarly, but didn't even draw the two "adult" dots since she said they didn't matter. She had more difficulty counting the two dots, so she grouped the families to keep track of how many bird kids she was counting.












Lastly, Student C ("Danielle"), was able to identify the first step as "subtraction," but struggled at first with picturing the situation. She came up with "22" but couldn't identify if that was bird of bird families. After a group discussion, she decided that there were 22 bird families left. In order to figure out how many kids that was, she made the chart and continued it onto 3 whiteboards (not pictured).

Conceptual Teaching and Learning of Math

Ramblings: When I was a wee undergraduate student, I was a research assistant to a math education professor. My thesis had a title with words like "novel," "linear relationship," and "student thinking."Basically, for a year I was immersed into the idea that conceptual understanding is paramount in math education. And I totally drank the Kool-Aid. A professional goal I set for myself most ears is to try and incorporate as much conceptual understanding into each lesson as possible. However, with district and state tests, sometimes it can be very overwhelming to teach students conceptual understanding, make sure that develops into fluency, ensure students able to apply said concepts to new situations, and teach test-taking strategies. It is so exhausting. Huh, I just realized this whole spiel wasn't even related to what I wanted to post about: an excellent problem I did with 3rd grade. I guess I just needed to vent! Here begins my real post:

Last week, I started reading Principal Actions: Ensuring Mathematical Success for All, which is a National Council of Teachers of Mathematics (NCTM) publication. Of course they promote this conceptual understanding of mathematics and encourage giving students real-world scenarios, letting them experience a "productive struggle," work collaboratively and solve the problem in many ways. I gave my 3rd graders the following problem from the book:

There's going to be a talent show and the principal wants to set up 7 rows with 20 chairs in each row, and possibly an aisle down the middle for people to walk. How many chairs should she order to be pulled out of storage? 

I didn't print this out and give this to them on a worksheet. I had a small group of 3 students (of similar ability levels) and gave them the question verbally. They were to tell me how they thought they could solve it before they started to write it on individual whiteboards. I was SO impressed with what they came up with. Between the three of them, they were able to represent the situation with a picture, counting by 10s, counting by 20s, and with a multiplication equation. It even concluded with two of the students representing the solution in various ways after I kept questioning.

This activity reminded me that it is not too difficult to incorporate conceptual-based tasks into your day. This one was about 10-15 minutes and it let me spend time with 3 students while the rest were on computers working independently on subtraction fluency. The students enjoyed this, and I can't wait for Monday to pull a new group of 3 students to see how they wow me.

Happy weekend!

Disclaimer (not sure if I need one or not): I am NOT affiliated in any way with NCTM. I just enjoy reading the book and have learned a lot!

Which One Doesn't Belong?

I found a new website and I fell in love with it! Found it last night whilst scrolling through teacher Instagrams and tried it out today. It's called Which One Doesn't Belong?

You HAVE to visit it. Here. It has a variety of figures and it can be used to encourage talking about mathematics in the classroom. Initially, I was thinking it would be an excellent warm-up for my high schoolers, just to get them thinking and comfortable since there are no right or wrong answers. Then today, I was working one-on-one with one of my 1st grade ELL students and I thought I should show him this. He was very interested. I showed him the following image from the website:



I asked him "Which one is different?" and it took him some time to realize there wasn't a right or wrong answer. We went through each box and he said how each one was "different."
The 1st graders responses, roughly translated:
Top left - upside-down
Top right - not a triangle
bottom left - slanted
bottom right - looks like a ramp

How amazing is that?? What an excellent discussion! Then he was ready for more. He really wanted a numbers one, so we did this next:

Responses:
Top left - 3 digits
top right - only box with a 6 in it
bottom left - only one digit
bottom right - if you had the digits together, you get 10.

I thought I was dreaming when my student then asked how we could add 73 and 16. Umm, you want to learn how to do double-digit addition because of mere curiosity? Absolutely, let's learn! And that's how my day started. It was very nice and I'll definitely return to this website for many years.

The Magic of "I have/Who has?"

High School Math is my jam. I'm comfortable with it. I studied it in college. Some might even say I'm not bad at it! However, this year I deviated and am at an elementary school with a seriously misleading title of "Instructional Specialist." Some of my new responsibilities include testing coordinator, computer lab dweller, teaching English to ELLs, and 3rd grade math and reading interventionist (but not at the same time). I have been immersed in a world of "bubble mouths," sight words, and place value charts.

My 3rd grade reading intervention group is working on the first 100 sight words, so I stumbled across an "I have/Who has" game. I fell in love! So of course I had to make my own. And they had to have a theme. And that theme was dinosaurs. I was both pleased and surprised that my students were suddenly so interested in sight word practice. Naturally, I had to make a contest out of it. If they could get through the chain of 24 words in under a minute and 30 seconds, I would bring them in a treat. After three weeks, they have succeeded!

The pro: They want cupcakes so I get to have cupcakes on Friday!
The con: They want cupcakes so I have to frantically make my way to the Walmart Bakery on Friday at 8:07 am.

Here is a low-quality picture of a few of my cards I made... AND LAMINATED!

For those of you unaware, here is a summary of "I have/Who has?"

1. Each student gets a card. I had a small group so in my case, each student got six cards.
2. Someone has the "beginning" card, so cleverly labeled "start here!"
3. They read the card, which then ends with "who has..." and then a word.
4. All students listen to see if they have their word. The student who does have the word reads their card.
5. This chain continues until the end card, which reads something along the lines of "the end."
6. Copious amounts of learning occur.

My stint in an elementary school is over halfway over, but I'm excited to bring this sort of practice into an Algebra class next year!

And you can download these cards here for your own personal collection!

Wishing a happy rest of the week to everybody!