Math Matters

I don't know why, but October always seems like the longest month. Maybe its because we are eager to transition into the cooler months and are deep into the heart of the semester with the breaks for Thanksgiving and Winter holidays just out of reach. For what ever the reason, there's no better time than to try some new activities, games, and models to get kids engaged, moving, and all of us reenergized about learning math. Hopefully you'll find some inspiration here to keep you going through this long month. And if that doesn't work, go find something pumpkin spice and enjoy a quiet moment! :)

A facebook post from a friend recently sparked my thinking about how we model subtraction. Many of us learned the "take away' concept and would think to teach this method to students starting to think about subtraction. But as I pondered I realized there is more than one way to think about the concept of subtraction. One of these is indeed the idea of "take away" or removal of some given number of items from a set. The other is the idea of difference. As I wondered about teaching these two ways of viewing subtraction, I went instantly to a number line.

Lets use an example like 6 - 2 for the purpose of illustration. To model the idea of removal or take away, I would place a marker at 6 on the number line and then "take away" or move back toward zero, or the left, 2 marks to show how I might remove a quantity of 2 from the set of 6. With early learners I might even stack 6 counters above the 6 mark on the number line and then place 4 counters above the 4 mark to show how the number 4 has 2 fewer numbers in the set than the quantity of 6.

The second way is to think about subtraction as the difference between two numbers. Here I would model by placing a marker at the 6 on the number line and another marker at the 2 on the number line and then find the difference, or in this case the distance, between the two marks.

In either example the value is still 4 when you solve the problem using either model. I certainly would want students to start thinking about why both of these ideas have merit when it comes to subtraction - perhaps something for slightly older students to ponder with me.

All this subtraction thinking got me wondering about how these ideas work in integer subtraction. The key when subtracting integers is to also think about direction and not just movement on the number line. What are your ideas about how to take these models and apply them to integer subtraction?

Modeling is a critical part of the teaching process. Using visual models helps students get a clearer picture of the concept behind the topic being covered and makes learning deeper, easier to connect to other knowledge, and more interesting for students. Throughout the instructional modules of Edusmart, visual modeling also plays a key role and is prominent as part of the teaching process. While using the instructional module video, teachers can show how a concept is modeled, then pause and work additional examples as needed using our built in white board. You can also incorporate the available virtual manipuatives into instruction to provide even more clarity and model with students how the process might work in a hands-on way.

Click here for a sample of how Edusmart models the concepts of subtraction with integers, along with the interactive tools available, that can make your teaching, and your students' learning more conceptual.

If you are interested in learning more check out EduSmart Math today. And if you have questions or thoughts, please email me anytime!

Students often think that the math studied in class has little relevance to the larger world around them. I think its important to always help students see how math is "real world" by connecting the concepts and ideas we study to careers or tasks they can relate to. For integers this is typically connecting to ideas such as elevations which are given in integer values, golf is another easy way to talk about real life uses of negative values. In science students will study atoms and charges given in integer values and will also encounter the concepts of positive and negative force. Any way you can help students see relevance, the better off you are at engaging them in learning more.

In Edusmart Math, each unit/concept is paired with a Math in the Real World career video. For the concept of integers we meet an airplane stunt pilot who talks about how the instrument gauges work and how he uses integer values as he flies the plane. We connect this to an online interactivity, or a printable activity as needed, where students apply the ideas they heard in an application with airplane gauges. SO much fun and SO powerful for students!

For a quick way to engage students as an introduction to integer thinking, or maybe as a reflection at the start of an integer unit, have students ponder the concept of how a double negative in English works and how it affects the meaning of a statement. For example, what does the statement "I don't have no candy" really mean? Then have them make up a few of their own double negative statements and partner to discuss what they really mean. Extend their thinking from the language application to what a double negative in numbers will mean. As we subtract a negative number from a minuend, we begin to apply this idea in the use of the additive inverse. Show students how learning isn't limited to one subject area at a time!

Formative assessment comes in many forms but basically involves small tasks that help discover students' current understanding and diagnose any misconceptions during the course of learning. These tools allow us as teachers to make course adjustments so that by the end of the learning process, all students GOT IT!

Something good for integers might be Problems Without Numbers. In this task, students are given word problems with blanks where the numbers would go. Then students fill in numbers for themselves, all while making sure the problem makes sense. If you design it right, the numbers students select can really affect the rigor of the problem solving. the other plus in using this task is that it reinforces good problem solving and READING of the problem; something students can always use more work on. Click here to see a sample using integer word problems.

Math Cut Ups are the heart of what I love to do. This is because they are designed to be hands on, student friendly ways to engage students to do more math. No one wants to work problems on a boring worksheet. Math Cut Ups take the problems off the worksheet and make them interactive and more fun for students.

This month I'm featuring a a title keeping to our theme of integers. The activity ensures students get plenty of practice solving problems with integer operations, but rather than use a worksheet, students have more fun when you can make the activity hands-on. In this task students solve the problems on the cards and then find pairs of cards whose answers are opposite integer values. If you can't make a pair, then you may need to re-solve some problems and check your work.

Each package comes with 10 full sets of problem cards so that you can put students in small groups of 3 and have everyone engaged. There are 32 problem cards, 2 of which are distractor cards that do not make a matched set, just to up the rigor a big. All materials are pre-printed on colored cardstock. Each package is just $15 and comes ready to laminate, cut, and use!

Visit my square market page for purchasing or visit my full website for more titles and ideas. I also have a Facebook page, Twitter account, and a Pinterest page if you are interested in following me there.

Want to visit about Math topics, Math Cut Ups, or Edusmart Math? I be attending, exhibiting, or presenting at the following conferences in the coming months. Come learn with me!

K-12 Mathematics Specialist

Mathematics Enthusiast

Math Cut Ups creator

Edusmart Mathematics Director

Email: integralmathematics@gmail.com
Website: www.mathcutups.com
Phone: 214-471-5760
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Twitter: @mathcutups