Space for All Learners

In my ongoing quest to find great math resources on Twitter (not hard), I started following Steve Wyborney (@SteveWyborney). Steve is a math teacher and coach in Oregon. He has been posting high quality math activities immediately usable by elementary teachers. I will share a few of them here.

Teachers often struggle with math tasks that feel just right for some students but not others. Steve’s activities are accessible by a wide range of learners in the elementary grades. They provide access points for many but also opportunities for challenge within the realm of grade-appropriate number sense, place value understanding, and additive or multiplicative reasoning.

Provide Massive Space to Notice

Steve has created this subitizing/number patterns video that teachers can show to students, pausing at a certain spot to allow thinking and noticing. It couldn’t be much easier. He provides a printable page to give to students. Simple to try, powerful results.

The Maze Hundreds Chart

Watch Steve’s video of ideas for how to use this resource. Then you can get the interactive powerpoint slide he created and try it with students. I can’t get it to work on a Chromebook, so you probably need a computer with Powerpoint installed.

Also try The Green Light Hundreds Chart and The Animated Multiplication Table.

These are simple tools, already frequently used in elementary mathematics, but often without the kind of exploration and reflection encouraged by Steve.

If you explore Steve’s blog, I’m on a Learning Mission, you will find lots more high quality instructional strategies as well as tools that are immediately usable with students.

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.

The Powers of Ten

Lee Orlando, fifth grade teacher, kindly contributed this article.

Our Bridges November calendar focuses on decimals and "base-ten fractions," and we've been having some good discussions around the nature of decimal numbers.

Yesterday, we were ordering some numbers that included whole numbers and mixed numbers (expressed as decimals)... one student confidently announced:  "3 is greater than 33.45 because any decimal is smaller than a whole number."   The salient feature for this student was the decimal point, and she was working under the misconception that whenever you see a decimal point, the number is automatically smaller than any whole number.  Just that comment alone kept the students talking and debating for quite a while!

I also did a quick formative assessment: Instead of giving students decimal numbers already arranged appropriately (in a column) in order to add/subtract, I simply gave them the numbers and had them arrange them in order to add (there were four numbers). Perhaps you can guess what many students did. They applied their understanding of place value of whole numbers (ones, tens, hundreds, etc, lining up the numbers from right to left) and totally disregarded the decimal point.  Here were all these decimal numbers, neatly lined up as if they were whole numbers, with the decimal points totally misaligned. These were students who have been adding and subtracting decimal numbers in our weekly math computation practice, but when given the numbers separately - not pre-arranged in a column - their lack of conceptual understanding about decimals and their values was completely transparent.

All this has led to lots of discussions about the power of zero which we had already explored in our Great Wall of Base Ten, but which was now coming back in light of decimal numbers.  I have been digging up some cool resources around this, including this awesome video which you may already know: "The Powers of Ten."

http://www.powersof10.com/film