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.

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.

Math Warmups

Lately, we are experimenting with math warmups in elementary school classes. Today, I tried one on a fourth grade class. I think someone else tried the same warmup in a fifth grade class, so I will have to ask them how it went.

Math warmups take just 5 to 10 minutes at the start of math class. For maximum effect, they are done every day or almost every day. With math warmups, it is possible to teach specific skills related to number sense. Lots of math gurus talk about these, including Sandi Stanhope and Bob Laird from the Vermont Mathematics Initiative, Marilyn Burns, Cathy Fosnot, etc. etc.

Here’s the one from today:

4 x 8 =
8 x 4 =

8 x 3 =
4 x 6 =
2 x 6 =

1 x 6 =
½ x 6 =
¼ x 6 =

I asked the students to solve these mentally and write the answers. I didn’t want anyone to struggle, so, if they didn’t know it, I just told them or had another student tell them the answer. I encouraged students to use what they knew from the previous equations to help them find answers without the usual calculation.

When asked what they noticed, students were able to share that they saw the commutative property in action (without using that vocabulary word) and could see halving and doubling relationships.

For example, 8 x 3 and 4 x 6 both equal 24, and that 4 is half of 8 but 6 is double 3. When you double something then halve it, you are back to where you started.

Getting down to the series of _ x 6 was interesting. Students noticed the pattern of the 6 staying the same while the other factor kept getting reduced by half. By the time they got down to the fractions, they were able to use their knowledge of the properties of multiplication to help them through a potentially difficult task. These students haven’t yet studied much about multiplication of fractions, but were able to do it easily.

I am thinking in the future it might be fun to try a number times ¼ and let students work back up to one through doubling if necessary to assist them in solving the equation without an algorithm.

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.