Vermont Math Leadership Council

the view from my porch

Vermont has a new education organization - Vermont Math Leadership Council - thanks to Julie Conrad, Tracy Watterson and others for getting it off the ground. Thanks to me we have a blog with the easy URL vermontmathleadership.org. Thanks to Tim Whiteford, there is a bunch of great posts on the blog! Check it out. We’d like to get more material from more voices on this blog and increase our readership. Anyone can join the organization. Our next meeting is January 29, 2014.

I was about to post something here on my blog about the new Institute of Education Sciences Educator’s Practice Guide called Teaching Math to Young Children. But then I saw that Tim beat me to it by posting about the very same thing on the VMLC blog. So, read his post here.

What I like about this publication is that it helps both rookies and veterans understand how best to work with young children and math. There are clear, specific recommendations that are easy to follow and a selection of easily usable games and ideas that illustrate the concept.

Whereas we often encounter activities or lessons and need to figure out what math we’re really going for, this resource communicates the math goals clearly and first, then hands us the activity to use.

Estimation Jars

Today I’m creating Estimation Jars for Math Night at John J. Flynn Elementary School. This is always a highlight at Math Night and it’s fun to watch kids at work on their estimate. I have one jar full of Rolos (there is something appealing about the gold wrapping), a smaller jar containing Skittles, and a very small jar with unpopped popcorn.

This year, I plan to accept all estimates within a reasonable range for each jar and then randomly draw a winner. That’s different than past Math Nights when the person who estimated the number closest to the actual number won the jar. I am hoping this helps promote a more correct understanding of estimation, with the goal being to produce a reasonable estimate, not to land on or closest to the exact number.

It is a good idea to have a few jars containing different sized objects so students can think about how the relative size of the objects affects the number that fit in a space. Ongoing math explorations can be done using estimation jars outside of an event like Math Night. Here is an excellent write-up and video about how classroom teachers can use estimation jars with their students, with a focus on the all-important concepts of doubling and halving.

What must be and what can't be

Have you heard of KenKen puzzles? They are logic puzzles like Sudoku but with an extra element of math calculation. They are great challengers for people of all ages and abilities, since there is such a great range of levels of difficulty. I’ve given them to students, teachers, and friends. 


My dad first introduced them to me. He must have discovered them when they showed up in the New York Times on the same page as the crossword puzzle. He does them in pen, with many cross-outs. The answers to the previous day's puzzles are always there, but they are unnecessary. You know when you've got it right.

I have figured out how to do KenKen puzzles and can do an OK job, especially with the easier puzzles. I want to be better than I am now, so I know I need practice. My dad and mom are visiting me in Vermont this week, so I decided to see if I could get some help with my KenKen chops.

Here is my dad’s advice to me: “First you look at the arithmetic, put in some candidate numbers. Then you start looking for what must to be and what can’t be. Remember to see the whole puzzle even as you work on the pieces. Don’t quit. Keep looking for what must be and what can’t be. If you look at it a little bit you will see it. If you get really stuck, go pour yourself a glass of Pinot Noir or something and the answers will become evident.”

Dad is all about creative problem-solving perseverance, which means he is down with the Math Common Core without knowing it. I was stuck on the harder of the two New York Times puzzles today but he freed me with one little tip. I filled in the rest of the numbers almost as fast as I could write. The tip went something like, “This has to be a 5 and that can’t be a 5 so it must be a...”.

KenKen puzzles are great for young mathematicians. My youngest KenKen student was in first grade. I think most first graders are too young, but she nailed it. I like giving out packets that start with the easier 3x3 grids and are limited to addition and subtraction, and then progress to larger grids with multiplication and division. Most students can quickly find a just-right puzzle and dive in.

The best part of this story is that the marvelous Phia S., a student entering fifth grade, loves KenKens so much she decided to write her own. Here is a photo of the treasured book of KenKen’s given to me by Phia. 

Phia's amazing KenKen book

So, enjoy your summer and take your KenKens (and Pinot if you are of age) to the lake or wherever you might be relaxing. The New York Times publishes two a day on the crossword page (they always include the directions) and more online. Cheers!

A Pickle

There are some interesting new websites out there. One is called Math Pickle. Shannon Walters, C.P. Smith Library Guru, alerted me to this one. So far, I like most of what I’ve seen on this site, although the layout is a bit clunky. Dr. Gordon Hamilton presents activities for students based on math problems dating back several decades to mathematicians like Issai Schur and Lothar Collatz. His decision to put young Vi Hart on the same page as some of the older mathematics greats is a good sign. Math activities are presented via video, and include footage of real students. I’m less impressed with Dr. Hamilton’s philosophizing about the way math should be taught in a video entitled “Let’s Abolish Elementary Mathematics”, even though I agree with most of what he is saying.

I like the Graceful Tree Conjecture as a means of practicing subtraction with third graders and the Collatz Conjecture for fourth graders. These are captivating problem-solving activities which are an excellent way to encourage students to work together, discuss different strategies, practice skills, check their work, and have fun. I would also try the magic cauldrons addition game for second graders. Teachers will find Math Pickle a useful site for finding new activities for math class and getting a thorough explanation of how to use them.

Caine's Arcade

My dear friend, Rachel Wynne, sent me the link to this wonderful video. Nine-year-old Caine designed and constructed an entire arcade out of cardboard. He taped calculators onto the front of the games so he could validate pin numbers using the square root function. So cool. Rachel, thank you for thinking of me and Jim when you saw this. Caine is an inspiration to us all.

Plus Ten, Plus One

Here’s a simple question: What is ten more than 73?

Based on students’ responses, we learn something about their understanding of place value and our base ten number system. They might know it right away. They might have no idea and no strategy for figuring it out. They might want a paper and pencil in order to use a written algorithm, or they might count on their fingers. If their response isn’t quick and correct, they are poised to make an important conceptual leap.

There are many tools to help students understand place value and base ten. These include arrow cards, hundred charts, ten frames, and more. Here is a favorite from Sandi Stanhope and Loree Silvis. We’ve been using it in various classes and with individuals. It’s fast, easy, and you can carry it around in your back pocket (literally).

Rebekah Thomas, ELL and Math Teacher Extraordinaire and soon-to-be Vermont Mathematics Initiative graduate, shows you how here. Thank you, Rebekah!

Math and the iPad

 

I have a new iPad and I’m looking for good math apps.

Lee Orlando has a new iPad, too. She loves trying new things and is already way ahead of me on using the iPad in math class. This is from a recent email:

This weekend I bought an adapter for my iPad so I can hook it up to the LCD projector, and I also got a wireless keyboard.  Today, I went into school to try it out.  It was so cool to see the iPad screen projected and to sit at the back of the room (or any place in the room for that matter) and see the text appear.

This was soon followed by another email:

I just found some awesome free apps for the iPad.  All are from "Mathtappers" and the three that I downloaded involve placing numbers (including rational numbers) on a number line and finding equivalent fractions.  All games are designed for three levels of play.  I've been trying them out at each of the levels, and they get pretty challenging at the highest level.  However, the easiest level is well within the ability of fifth graders.

...these apps look like a great way to engage students in a whole-class warm-up activity/discussion.   I had made up my own number line activity using a sketching app that I have... the kids' attention level goes WAY high when they get to come up and draw on the iPad!  Getting that adapter for the LCD projector may have been the best investment I have made in a long time.

Later, I ran into Lee at school and she showed me how she’d photographed a piece of graph paper to use as the background of her sketching app, so that students could draw arrays and fractions with the aid of the grid. What a great idea!

I hunted around a bit and found some other useful apps. My favorite so far is Sketchpad Explorer. If it’s been awhile since you contemplated the Pythagorean theorem, you’ll enjoy the Getting Started screen, which allows you to drag right and non-right triangles around to see the theorem in action.

The real fun, though, comes when you touch the little book icon in the lower left corner of the screen. Choose “Elementary Mathematics” and Sketchpad Explorer presents you with a suite of eight activities involving symmetry, triangles, fractions, decimals, multiples, and volume. There is even a logic game which gives less than and greater than clues to find an unknown number. Sketchpad Explorer’s creativity and nice, clean graphics are appealing. At first glance, there seems to be a wealth of resources and lesson ideas for teachers on the website. I can’t wait to try these with students.

Who Has?

Sidewalk card game by Lewis Hine

Who has played the Who Has game? I have. It’s a really good one, because it keeps all students on their toes.

Basically, you print up a bunch of index cards and hand them out to the class. If you’ve got 30 cards and 22 students, give extras to some of your stronger students. Choose a student to read their card. The game will go around the room until you are back to the first card.

Who Has? can be played with cards for any topic or subject area. There is a nice collection of Who Has? cards for different math activities on the excellent Mathwire website.

I’m going to specifically recommend two of them: More or Less and Place Value. I’ve encountered many students, even in the upper elementary grades, who do not fully understand place value. I think these Who Has? decks might help. Let me know if you try them.