The Field Trip

When I taught second grade in CPS, I had students choose where they wanted to go on a field trip. Students decided to go to the Planetarium, the Museum of Science and Industry, Lincoln Park Zoo, and Shedd Aquarium. I had decided to provide subs for the students and this is what the distribution looked like:

Group #1 [Planetarium]

- 3 subs

- 4 people

Group #2 [Museum of Science & Industry]

- 4 subs

- 5 people

Group #3 [Lincoln Park Zoo]

- 7 subs

- 8 people

Group #4 [Shedd Aquarium]

- 3 subs

- 5 people

Now the question that was on everyone's minds when we returned the next day was:

WAS IT FAIR?!?

So, today, I decided to make my fourth grade students decide if on that day five years ago:

1) Was the distribution fair - did each person in each group get the same amount?

2) How much of a sub did each person get, assuming the pieces were cut equally?

Phew. My fourth graders went to work today! Oh, and did I mention that today was the first day of our fraction unit?

Some big ideas that will be discussed tomorrow in our math congress are:

- fractions can be seen as division

One student was able to find the pattern right away and didn't have to draw pictures to decide the amount each student from each group got.

- fraction equivalence

This partnership used connecting cubes called this amount 4/5.

This partnership used connecting cubes and called the amount 16/20.

- what to name a piece

Do you see the misconception that we'll address tomorrow?

1/2 + 1/10? I love it!

Students worked on a draft first, figuring out all of their math. I walked around at this point, lifting the work that students were doing, or addressing some ideas that students were using, but confusing. Then as students finished their rough drafts, they then began to work on their stand-alone posters [posters must speak for themselves w/ clear mathematical thinking] that will be critiqued during our gallery walk tomorrow!

I love me some Cathy Fosnot! I can't wait to see what our gallery walk and math congress will bring tomorrow! Stay tuned...

Math Journals!

Math has been a struggle this year. So as I thought about what my students needed, I thought about last year. What was I doing differently this year that might be affecting the learning?

And with that came an "AHA!" I wasn't using a math notebook as I normally do! So, even as late as we are in the year (Quarter 4 to be exact), I introduced math notebooks to my friends! On the left side of the page, we write down: 1) Learning Goal (before the lesson), 2) What I Know (before the lesson), 3) What I Learned (after the lesson), 4) Proof (after the lesson), and 5) Reflection (after the lesson).

The Proof is something that they have to prove based on what the lesson was that day. For example, "Show the differences between a polygon, a nonpolygon, and a regular polygon." Students would then have to either draw or write the differences between these three categories. Reflections will help students reflect on the process as well as some content!

Here are some student examples!

Hopefully taking notes and making foldables will help students remember the knowledge/skills learned!

The Best Buy

In June, I had an awesome opportunity to learn how to teach math from the incredible Kara Imm. She is a staff developer from Math in the City and taught middle school and high school math in her years as an educator. I could go on and on about how much I love learning from Kara and how she's changed the way I approach teaching math to fifth graders! However, I will spare you these details and talk about the math we did the past couple of days.

Before we dive into the math though, I'd just like to say that I had about twenty teachers from my district come into my room and observe my teaching and Kara's conferrals, as well as observe my students, so that we could do a whole lot of learning in our debrief. I was really excited about learning from the feedback of my colleague, but it wasn't until I started launching the lesson that I got really nervous. I mean, I saw the usual twenty-five faces of my students in anticipation of the lesson. But in addition to those lovely faces, I saw the eyes of twenty adults watching my every move. I'm prettttttty sure my face was flushed pink!

Anyway, enough about me! How about that math now? :)

Students were given this context to begin:

I noticed that Target and Babies 'R Us sold the same brand of baby food, but had different bargains. Target sold 12 jars of this brand of baby food for $15 while Babies 'R Us sold 20 jars of the same brand for $23.

I then informed students that I was trying to figure out which one was the better buy and sent them off to do the math.

Whoa, what an entrance into our fractions unit!

Here are some of the posters that students made to show their thinking:

Whoa, did you catch what some students were doing in the first poster? They dealt out the money amongst the jars in order to find the price of one. Did you catch a misconception in the second poster? Some students were able to do long division, but were unable to name out what the "R3" represented. What about the last poster? What do you notice here? They didn't have to start from the beginning once they found the price per unit at one store. They knew that they could compare the pricing of 20 jars at Target to the 20 jars at Babies 'R Us instead of finding the price per unit!

Trust me. This math isn't easy. I know I'm asking my students to do some hard work! But most of them are showing me what grit looks like in math and I am truly impressed! Keep it up, fifth grade rockstars!

Box Factory

What do you remember about learning math in elementary school? I remember sitting in a desk facing the chalkboard and all the desks were lined up in rows. I also remember that a lot of the work was whole-class and a lot of worksheets and a lot of quiet think time! I also remember my dad sending me to Sylvan Learning Center and other after-school math programs and/or tutors and doing a lot of skill drills and rote memorization.

Now imagine this: a classroom where students are working in groups of three or four, collaborating on a problem/project at hand. They are in discussion and using manipulatives (the 1' by 1' by 1' tiles on the floor or the 1" by 1" by 1" connecting cubes) to solve the different questions brought to their attention. The classroom has a slight buzz to it from all the conversations occurring at once and all students seem to be engaged in the task at hand.

Those seem to be completely two different pictures of a math class!

To introduce volume, our school curriculum uses Cathy Fosnot's Box Factory. I think that this is a fabulous way to get kids thinking about volume and surface area (and even multiplication) without even mentioning those specific math-content vocabulary words!

Students explored these questions on different days:
1. I have 24 items and I want to send them to a friend. How many different boxes are there and what are the dimensions? How do you know that you have all the possibilities?

2. How much cardboard is needed to make all the different boxes we found in the first question?

3. I have three different-sized boxes: small (2 by 2 by 2), medium (3 by 3 by 3), and large (4 by 4 by 4). How many items does each box hold and how much will the packaging cost if the cardboard costs 12 cents per square unit?

4. How many 4-inch by 4-inch by 4-inch boxes will fit into a cardboard shipping box that is 4 feet by 6 feet by 4 feet? How many of a smaller 2-inch by 2 -inch by 2-inch box would fit into the same shipping box?

Whoa! Now that is some different math from when I was in fifth grade! I remember getting the equation for finding volume that didn't completely make sense to me! Now it makes sense!

Here are pictures of our learning walls that students created on the last day, reflecting on what they learned throughout the Box Factory unit!

Now after this unit was over, I actually did have to go to the FedEx store to ship a box of running gear to a friend in New York City. And guess what I saw when I got there that made me chuckle?!?!

When I showed my students this picture, one delightful student asked, "Are you going to make us do some math with these boxes?!?!"