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Last week, my colleague Kami Wenning and our math coach, McKenzie Zimmerman conducted an informal morning PD session on the site
Estimate 180. Kami has been using the site with her 3rd graders and the conversations around it have been astounding so they wanted to share the resource.
Estimate 180 is a website created by Andrew Stadel (@mr_stadel). According to his website, he is a middle school math teacher and coach. He began the site in October 2012 with estimating activities he uses with his students each day of the school year.
After the PD, McKenzie and I talked about how I could use this site She facilitated the class while I transcribed and listened to her language with students. She went through the 4 day Lego Estimations and I watched from the back of the room to learn what I could about how best to use this resource and to listen to and record my students' thinking. The goals for the lesson were from the math practice--explaining your mathematical reasoning and understanding someone else's math reasoning. So that was the focus of the talk over the four days.
The conversations across days went so far beyond the typical estimation activities I've seen. The way that the site is built, the learning builds from one day to another and kids have information to build from. The talk around numbers was incredible and the engagement was high. Knowing the standards so well, McKenzie was able to take advantage of the last day's conversation to create a number sentence with a number to solve for. I am finding that oral language and conversation is such a huge part of math learning and Estimate 180 definitely supports this.
There are so many amazing things about the Estimate 180 site. There is a huge variety on the site. So many math concepts are covered in the over 200 estimation activities on the site. In a few weeks, I am going to use a series of lessons designed around estimating height and I am looking at another that estimates the amount of money in coins. You can browse the site or search estimations based on math topic. I also love that these are multi-day activities that are built to help kids think across time and to use understandings from one day to solve the next day's challenge.
Mr. Stadel must think about estimation all day every day because so many of these estimations come from real, daily life and I think kids will start seeing estimation opportunities everywhere after a few weeks of these.
I loved this site so much that I just had to share. I am excited to jump into another estimation with my kids next week (Cheeseball Estimations) and see where the conversations go!
I have been reading lots of
math professional books as we've implemented Math Workshop in our district. This summer, I read
Well Played: Building Mathematical Thinking Through Number Games and Puzzles, Grades 3-5. This was a perfect read for me this summer as we move forward with Math Workshop. I love that Stenhouse provides such an amazing online preview on their site. I was able to dig in and know that I wanted to own a copy of this book. I know it is one I will revisit throughout the school year.
The book is more than just a set of games. As Kassia Omohundro Wedekind states in her Foreword,
"This is a book about math games and puzzles, but it is also a book about building communities of mathematicians who work together to problem solve, talk about math and figure things out."
The book begins with thoughtful chapters around the use of games in the math classroom. Early on in the book, the authors state, "...many students experience games or puzzles as fun activities or time fillers, but do not consider them as essential to their learning or as an important part of a lesson for which they are accountable." The authors go on to show us how to make games a more critical piece of our workshop and to help students have ownership of the games, their goals and the conversations they have while playing.
There is a great section about discussions and the authors give lots of practical tips for teaching kids to have productive conversations while playing game. There are so many examples of these conversations, questions that push thinking and ways to differentiate throughout the book.
Much of the book is organized in chapters by math concept and there are many games that support kids across levels and operations. The authors give great games and give great variations of several of the games. The games focus on engagement and problem solving and give kids ways to use math vocabulary throughout.
The games throughout the book are introduced in a way that you can really visualize how they might look in your classroom. Directions and materials are given as well as an example of how one teacher introduced the game in a real classroom. (The appendix is large and provides blackline masters for all of the games, directions, etc.) The game pages include Tips, What to Look For when observing kids play the game, Exit Card ideas and Extension of ways to change up the game.
An amazing resource for intermediate math teachers!
It's Math Monday!
for the Math Monday link up!
We were going to begin a big estimation problem (How Many Books Are There in Ms. Hahn's Classroom?), so I chose my math workshop opener from
Estimation 180 -- days 28-30, a sequence of toilet paper estimations. I knew exactly what I wanted to get out of this opener, and I expected it to be quick.
What I didn't expect what that my students would get mired down in a dis-remembering of what exactly perimeter, area, and volume are, and why the square footage fact we jotted down from the packaging shown in the answer of day 28 could not be used as the total length of the toilet paper on the roll on day 30. Maybe it's because we were talking about squares of toilet paper that their brains convinced them that square feet would be okay as a unit of length.
I let them struggle through misconceptions like squares and cubes are the same and you use 3D measurement for square feet. It was one student's tentative sharing of a rhyme she learned at her old school, "Perimeter goes around, but area covers the ground" that finally turned the tide away from the confident assertion of another student that square feet is a measure of length. You should have seen the lightbulbs go off above the heads. Boom. They had it back. Area is LxW (2D), volume is LxWxH (3D), and perimeter is S+S+S... (a measurement of length). Whew.
I've written often about the difference between leading the learning and following the learning. The importance of following is something I have to remember over and over again.
It's Math Monday!
for the Math Monday link up!
Dividing whole numbers by unit fractions and unit fractions by whole numbers are 5th grade standards. (CCSS.MATH.CONTENT.5.NF.B.7)
I've never taught division of fractions, but when you are struggling to understand something yourself, you often do a better job explaining it to someone else.
In my classroom, dividing fractions is all about pans of brownies.
If you have four pans of brownies and you want to divide them each into fourths, how many fourths will you have?
4 ÷ 1/4 = 16
You will have sixteen one-fourth-sized pieces to share with your friends.
But what if you you share 15 of those one-fourth-sized pieces and realize you forgot to share with 4 other friends?
If you chop a one-fourth-sized piece into four pieces, what size of piece will each of those friends get?
1/4 ÷ 4 = 1/16
They will get a tiny little piece, but at least you didn't completely forget them!
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| Creative Commons photo from Wikimedia Commons |
It might not happen so much for primary teachers, but I am humbled on about a weekly basis by students in my 5th grade math class who are smarter than I am.
Case in point, this pizza problem. Do whatever you need to do to enlarge that picture. The work you will see there is flat-out brilliant.
In this problem, a class has won the PTO's pizza party for bringing in the most Boxtops For Education™. Each student gets their own personal pizza and eats a different fraction of the pizza. They eat thirds, fourths, eighths, twelfths, and sixteenths. The challenge was to put the fractions in order from greatest to least to find out which student(s) ate the most pizza, and then find out which table group ate the most pizza.
The pair of students who made this poster demonstrate two different ways to create equivalent fractions with a common denominator of 48: the "Bring to 48" table at the top in the center of the page, and the longer version on the right side of the page. (I didn't teach them either of these methods. They came up with them on their own. Brilliant, right?)
On the left side of the poster, they show their work finding an equivalent fraction for each of the children in the problem. They add each column to find out which table group ate the most, and they put all of the fractions/students in order (below the "Bring to 48" table in the center of the page).
Differentiation is important. While these two were engaged in solving this problem and demonstrating their work on this poster, I was working with a group of students who still can't independently make equivalent fractions in order to add and subtract with an unlike denominator. Others in the class were working on solving the pizza party problem, but they never got to the demonstration stage, or else their demonstrations were not nearly as elegantly organized.
I am joining Mandy at
Enjoy and Embrace Learning for Math Monday.
I had been struggling with an authentic reason to introduce Google Presentation to my students. I needed a time when we would collaborate on a presentation rather than each student doing his/her own. And I needed a way for collaboration to happen without students revising each other's work.
When we were working on irregular volume in math, I found a way to use Google Preso! I created a slideshow with a page for each student and shared it to their Drives. I demonstrated how to use the drawing tools to make rectangular prisms. Their job was to first build two rectangular prisms using manipulatives, then combine them into one shape, and finally represent them and solve for volume on their slide. If they got finished early, they could add an additional slide and tell the three most important things about volume. For the sake of privacy, I have taken the students' names out.
I am joining Mandy at
Enjoy and Embrace Learning for Math Monday.
Franki has resolved to join Alyson Beecher's Nonfiction Book Challenge in order to stretch herself to read more nonfiction. I'm going to stretch myself in a different direction and try to focus on what's working (or not working) in my 5th grade math workshop.
This week (in between a snow day and a windchill day) we began working towards a deep understanding of division. Our standards in 5th grade do not require students to be able to do long division with the algorithm. We will be exploring multiple strategies for division.
Mandy wrote this week about
the importance of play. What I discovered was the importance of manipulatives...even for fifth graders.
Students were in groups of 4 or 5 on the floor in the meeting area. Each group had different manipulatives (beans, dominoes, pattern blocks, tiles). We modeled what addition looks like (combining groups) and what subtraction looks like (starting with a big group and taking some away from it).
Then we moved to modeling multiplication, which was surprisingly hard for them. After I gave them a problem to model (3x4), they realized/remembered that they needed to make equal groups or an array. We spent a lot of time thinking about what a multiplication problem SAYS -- "Three TIMES" tells you will be repeating a process three times, or making three groups.
Modeling division was as challenging as modeling multiplication. We started with a problem that they could easily solve with mental math so that they could check to make sure their model made sense (22 ÷ 2). Knowing that partial products is one of the first strategies we'll work on once we move to paper-pencil, I also gave them problems like 68 ÷ 5 so we could talk about efficient ways to share 68 into 5 equal groups rather than counting one by one. (Starting with 10 in each of the five groups, for example, and then sharing the leftover 18 into the 5 groups.)
Our math block is cut 10-15 minutes short by related arts, which we have actually come to love, because we can come back to our work and share, or students can complete an exit ticket or formative assessment that will inform my instruction for the next day. I gave each student a sheet of notebook paper and asked them to draw a model for 19 ÷ 3 and then write three things they know about division. What an eye opener! I've got a group of 5-6 who modeled 19 x 3, and another 4 or so who modeled 19 ÷ 3, but didn't demonstrate complete understanding by giving an answer. There were students who could model, but not write anything they know about division, and there were students who could write three things about division but not model.
So, now it's time for differentiation. I need to get some students to that deep understanding of what division means (modeling), and I need to move others along to applying that understanding to various strategies! This is the tricky part! This is the FUN part!
The first few days of math are always so interesting as I listen into conversations. On the third day of school, we used our math time to do a "Numbers About Me" project. I've seen this often on Pinterest and blogs and wanted to make sure we started the year thinking about math in our world. It was an interesting conversation as their eyes lit up each time they realized the things in their lives that involved numbers. They were simple things but making the connection to math made for a good conversation. We combined this with self-portrait work and the kids had a great time creating themselves with their Numbers About Me information.
*Please note that the 3rd boy in the top row made himself wearing an "I Love Mrs. Sibberson" shirt. Hysterical. Gotta love 3rd grade :-)
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