# Math Matters

## Math Cut Ups Edition, Volume 12 October 2015

## Make October FUN-tober!

## Focus Topic - Integer Operations

### Modeling Subtraction

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?

### Conceptual Modeling with EduSMART

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!

#### Bingo

#### War

#### Zip, Zilch, Zero

### Integers in the Real World?

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!

### Integers in English?

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 Featured Title: Integer Operation Opposites

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.

### Upcoming Conferences

#### Texas ASCD Annual Conference

#### Rio Grande Valley CTM 50th Annual Conference

November 7, 2015

#### Conference for the Advancement of Science Teaching (CAST)

November 12-14, 2015

### Kelli Mallory, Ed.D.

Mathematics Enthusiast

Math Cut Ups creator

Edusmart Mathematics Director

**Email: **integralmathematics@gmail.com**Website: **www.mathcutups.com**Phone: **214-471-5760**Facebook: **facebook.com/Math-Cut-Ups-155205867883398/timeline/?ref=hl**Twitter: **@mathcutups