The Importance of Number Lines

Do you use a number line in your classroom?
If you're like most, you've probably said the phrase "use your number line"  to students struggling with math at least a few times day day!

But the number line is SO much more than a simple tool to help students count forward or backward! Numberlines and horizontal thinking are mentioned throughout the Common Core State Standards.  Thinking horizontally is probably more important than any of us ever thought! Today, I'd like  to show you a few examples of what you can do on a number line and in turn stress how important it is to use number lines in early education!
First, let's get a definition straight. This is called an open number line.

 You'll notice two arrows on each side, demonstrating that numbers continue in both directions forever. You'll also notice that this number line doesn't have any numbers.... yet!!

 Number Line Warm Up
Let's start with a great math lesson warm up- draw three numbers out of the bag, and place them on the number line. How close should the numbers be? How far apart? Are two of the numbers
closer than the other? Next, place a "?" on the number line. What number might be represented by the "?"

Addition Samples
Addition is another wonderful way to think about the number line. Start at any given number and add logical pieces of the second addend until you arrive at the sum.  Let's try 127+ 213.

I started with 127. Since I'm only 3 numbers away form 130, I decided to add three ones next.  From there, I counted two groups of 100 and a group of ten. The sum is 340.

I could have broken up the "chunks" of 213 in a variety of ways. I might have also decided to start with the largest added, 213, and add 127. The beauty in this is that there isn't one set way of using a number line, so students are free to solve the problem in any way that makes sense to them!

Subtraction Samples
Can I subtract on a number line too? Let's check it out and try 340- 127.

 Since my number will get smaller, I'll start with the largest number and place it on the right of my number line. I can subtract any number, any amount of numbers, so long as it equals 127.  I've chosen to subtract according to place value, so I'll subtract a group of 100, two groups of 10, and 7.  Again, there are multiple ways you might choose to subtract- there's no single path to the difference!


Multiplication Samples
The number line is great for representing groups.  We'll start with an easy one,  3x5 ( three groups of 5). Here, you can see that I'm creating three groups, with five in each group, by "jumping" the number line in groups of 5, for a total of 15.

This works no matter how high the numbers! What would 17x25 look like? 17 groups of 25 would take too long, so I decided to chunk in groups of 4. Since 4 groups of 25 make 100, I'll show four groups of 100- this makes 400, or 16x25. Since the problem asks for 17x25, I'll add one more group of 25, for a total of 425. Again there are multiple ways of arriving at 425, and I encourage you and your students to create multiple ways to solve the same problem!

Division Samples
Yes Virginia, there is a way to divide on the number line! How many groups of 25 are in 425?

I start with the total, 425. If I take away 4 groups of 25 (100), then I'm at 325. I'll take out three more groups of 100 ( 4 groups of 25), which gets me to 25. If I take out one more group of 25, then I've arrived at 0. This tells me there are no remainders. How many times did I take away 25? A total of 17, so 425 divided by 25 must equal 17.


Our number line fun doesn't have to end here. Number lines will play an important role in fourth grade fraction studies as well. I'd like to encourage ALL elementary, starting with Kindergarten, to incorporate a number line into your "toolbox of strategies." If students understand how to manipulate number lines in early elementary, they're more likely succeed in higher elementary math with number line strategies as well.

So what's next?
Check out some of my favorite number line resources to use in your classrooms!

Number Line Freebie Resource- click here!

Number Line Nightmare-  a fun Halloween themed activity where students Gr.k-2 use a number line to order various pumpkin numbers- click here!

           Number Line Math Meetings and Center Activities grades K-1

   The number line is one of the most beneficial daily exercises you can add to your morning meeting. This one simple tool assists your students in building a strong foundation in number sense!
    Use this tool 5 minutes a day during your morning meeting to increase your students' number sense! Activities and cards focus on numbers 0-20.
 Click here to get yours!

Active Participation for Emerging Communicators

The first thing that we must consider is that communication is the number one way for students to actively participate in academic activities. Communication is in part how we all learn, and teachers need to be able to communicate with students in order to understand how they think and where they struggle. We also have to consider that students communicate on different levels. There are students that can expressively communicate to participate in activities. There are students that may have 1 or 2 strategies down that are reliable for them to convey their messages. Then, there are students that mainly communicate through signaling behaviors (e.g., pointing, touching, one word comments, etc.). The emerging communicators are why I am blogging about active participation. Here are some ways to work towards active participation: 

• Have expectations that the student will communicate. Let them know you are interested. 
• Look for opportunities in every activity that you do with them. 
• Pause when you are waiting for a response. Count to 10 to give them time to process and respond. 
• Expand on what the student is saying by adding your own thoughts. ("I smell tacos in the cafeteria. They smell good!")
• Avoid sentences that begin with "tell me" or "show me". These can be threatening to the student.
• Use the students modes of communication when interacting with them (e.g., pointing, signing words, etc.)
•  Avoid yes and no questions. It is not motivating for students to communicate when they feel pressured to reply with the correct response. 
• There is nothing wrong with telling a student that you did not understand what they were trying to communicate. Try to help them find ways to clarify. 

I hope you find this post helpful, and I'd love for you to add to it! Please leave a comment to share other ways to encourage active participation! 

Tasha
A Tender Teacher for Special Needs 

Fabulous Freebies on the Fifteenth!

Hard to believe that its already the middle of September!

I've linked up with Molly at Lucky To Be In First for her Fabulous Freebies on the Fifteenth! 

My newest forever freebie is a Counting with Bundles of Ten puzzle. 

This is one of my favorite puzzles, as it allows students to think in multiples and understanding that a bundle also means a group of ten! Set up is easy for teachers too- just print, cut a part, and your center is ready to go!

Stop on by the Molly's blog to grab my puzzle freebie along with other great resources!  Remember to thank the creators by taking a moment to leave some feedback! 

The Classroom Reveal

          School is in full swing, and I have been very busy putting my classroom together, planning activities, and getting to know my class of precious 2nd grade students.  I thought I would feature a few photos to help you all see what I have been doing in the classroom!

I used 6 crates and 2 settee cushions that were on sale at Pier 1 to create a reading corner.  There is a rug with a couple more pillows to the side of this reading corner.  Four children fit on this comfortably.

This is above our main reading area.  It is a space for kids to put post-it notes about their favorite book from the week.  My plan is to have kids post a note each Friday stating I like __________ because ________________.  We started this last Friday and I was impressed with the reasons that the kids gave.  Some of them just said a generic "I like it because I just do," so we will continue to work on this!

This is above all of our books.  I worked at a teacher supply store for a bit during undergrad and still had these monkeys.  My previous job was a Spanish teaching job.  I traveled to various classrooms and didn't have my own, so this is the first time I was able to put these monkeys to use!  The font I used in my classroom is called "Tequila Sunrise" at www.dafont.com.  I know the name isn't classroom appropriate, but I really like the font!  

Of course, I just had to use my awesome book basket labels to label my classroom library.  I used one of the blank labels included in the book basket label set to label our classroom "reading buddies."  My kids take turns reading to their buddies during independent reading time.

    

                      

 Our class has started a postcard collection.  I have a world map and a U.S.A. map up in our room.  On facebook, I asked friends and family to send me postcards of the places they live and also to think of our classroom when they travel to new places!  The kids are so excited when they receive new postcards.  I have photocopied the postcards to make them into a little book.  The kids refer back to these cards during writing time and are having fun writing back to our friends.  I stapled the originals up.  I also stapled a map blank print-out of these maps and have been having kids color in states and countries when we receive a postcard.  This is fun!

And of course, I couldn't resist buying this adorable inflatable monkey from Party City.  It was only a dollar!

There are so many other things I would LOVE to do in my classroom, but I just didn't have the time and/or money.  I am already looking forward to setting up my classroom next year, when I will already have a lot of the materials I need to make my classroom look awesome. 

We always welcome any other tips or suggestions for making the classroom an awesome place to live, learn and grow!

:-)    Kenzie

The Learning Highway presents.....

INTERACTION!

Interact with us! 

Periodically, we will pose a question or discussion topic to our wonderful readers and followers.  This week, our topic is:

In the comments section below, please post photos or talk about an amazingly awesome area of your classroom.  We will choose our favorite response to win in a giveaway of items from Christine Cadalzo and Kenzie's Treehouse!

You may enter for the next three weeks.  After those three weeks, we will choose a winner!  This will be a regular feature for the weeks that we post.  

May the luck be with you!

:-)  Chris and Kenzie

Pssst...... be sure to also check out the fall linky party below.  There are several fun fall activities, many of which are free. Link up your fun fall activities from your TpT store or blog! Kenzie's Five Little Pumpkins Fact Family Story is down there too!

All Things Fall Linky Party!

It's Time for Place Value!

It's that time of year again! Place value is one of the many reasons I LOVE teaching math. It is critical that our students gain a firm foundation of place value number sense in their early elementary years. I believe its the "magic key" that unlocks the true meaning of any number!

So what activities do you create that allow your students to discover and explore the power of place value? I'd like to share a few of my favorite place value activities with you!

Place Value Blocks
Just about every classroom teaching place value will use a set of these manipulatives to represent the ones, tens, hundreds, and thousands.  Visually they're easy for students to understand, as it is easy to see that the values of each block increases by ten.

To ensure your students are working on mastering the place value concept ( and not mastering the manipulative), mix it up a bit! Use something different to represent the tens, like a crayon perhaps. Use a post it note to represent a hundred's block. It is important students see that the place value system works, no matter what tool I use to represent the various amounts.

Stacking Cups
Stacking cups together is another great way to represent place value! Each cup represents one place value. Turn the cups to create different numbers in standard form. Create the expanded form of a number by pulling the cups apart!

Place Value Cups, Standard 

Place Value Cups, Expanded

 Place Value Cards
This is a set of cards I created a few years ago for my students. Each value possible is represented
(0-9, 0-90, 0-900). To create a number, students stack the cards on top of one another. This is a great way for students to see that the "7" really has a value of "70," as the value is revealed when we pull the cards apart and find the expanded form and value.  Click here to get a set for your own classroom!

Review, Review, Review!

Students need LOTS of opportunities for practice! That's why I've created so many place value centers, games, and class activities on place value!  My latest game, called "The Powerful Place Value" board game, gets students thinking about the value of various digits, standard and expanded form, and working as a team to complete "team challenge" tasks! I tested this new game out with a local group of second graders, and it was a major hit! Get your own 1st grade game board here  and a 2nd grade edition here!

The Powerful Place Value Board Game, Gr. 2 edition

Need Place Value Activities?

Check out my Place Value Games and Centers Bundle Pack !
** All place value activities mentioned in this blog article are on sale now through the end of September!

So how do you teach place value? Please take a moment to share your strategies with us!

Best wishes,

Tabitha