Monday, September 7, 2015

Math Tip Monday: Ideas for Teaching Number Sense

Happy Monday!  K's Classroom Kreations and I are happy to welcome you to our Math Tip Monday. This month we are focusing on Ideas for Teaching Number Sense. I'm excited to share with you some ways I use number lines to help students to understand numbers. Some of the games I play came from our Math series, Investigations, but I've been using similar number line activities for years.

Start With, Get To...

I use number lines in a lot of different ways. The most basic being a visual aid to counting. But as a second grade teacher, I don't want my students to only know how to count from 1 to whatever.  I want them to be able to count on and to count back starting from any number.  One way we do this is to play the Start with, Get to Game. When we play this game, I use two clothespins, one of which I've marked with green tape and the other I've marked with red tape.  I also have a number line that I keep on my board with magnetic tape. I have a student draw a number from a basket. That number is our "start with" number and we mark it with the green clothespin.  Another student draws a number from the basket and that's our "get to" number. It's marked with the red clothespin.  We then determine whether we are counting forwards or backwards.  A third student uses my pointer as the whole class counts starting with green and ending with red.  The students always enjoy the game and it's a quick and easy way to get kids comfortable with counting on and counting back.

Since it's still early in the school year, I don't have a picture of this activity yet, but here's a representation. In this illustration, we would count from 5 to 16. I usually play 1 to 3 rounds of this game as a math warm-up.

Guess My Number on the Number Line

My students are already loving this game. It's another great warm-up activity. The first time we play, I am the leader of the game.  I secretly choose a number (for example, 11) and tell the students that the number I'm thinking of is between 1 and 20.  I have a nice laminated number line, so we use an expo marker to mark those numbers. I then start taking guesses. If a student guesses 5, I tell the student that was a great guess, but my number is greater than 5. The guesser then would come up to erase the arrow pointing to 1 and draw an arrow pointing to 5. Then I ask another student to guess. They guess 10.  Again, I tell the students that it was a great number, but my number is greater than 10. So that student comes up, erases the arrow pointing to 5 and draws an arrow pointing to 10. I point out to students that "Now we know the number is between 10 and 20.  The next guess is 18. I tell the student it is less than 18.  He/she moves the arrow from the 20 to the 18. And so on.  Finally, a student guesses 11. That student then excitedly becomes the leader. To keep the game honest, I always have the leader secretly write down their number on a post-it before we start.  Here are some pictures from some of our rounds after students learned the game.

What's really cool about this game is that we are learning number sense and math vocabulary - greater than, less than, and in between - while at the same time, students are learning to be math leaders and feel successful. I usually play about 3 rounds of this, keeping track of who won the last round so they can be the leader the next time we play. Of course as the year goes on, we use different parts of the number line - for example, "My number is in between 55 and 80."

Hopping on the Number Line

Floor number lines are great for this activity because the kids are moving and engaged. I've also used a small frog figure to hop on the whiteboard. When I taught first grade, we would use the floor number line to hop forward to review counting, again starting from and getting to different numbers. Students would stand by the start number and then hop forward counting 5, 6, 7, 8, 9, 10... We would also hop backward (I had to stand close to help students who had difficulty with balance as they hopped backward. LOL).  It's also a fun way to practice skip counting by 2s or 5s (10s are a little too far apart).  

Now that I'm in second grade, I also use this strategy to help students with the counting on or counting back strategies when adding or subtracting. The number line provides a great visual and students understand that they count the hops and then see what number they "land" on.  

You can make a floor number line pretty easily. Use adding machine tape, pieces of construction paper taped together, or a line of tape on the floor with laminated numbers taped next to it. Another option is to move outside. Draw a number line on pavement using sidewalk chalk. Whatever works for you.

The Empty Number Line

The empty number line has been a revelation for me. I'll talk more about that in a future post that deals with addition and subtraction.  For number sense, it's a great tool for thinking about skip counting, which builds the foundation for mentally adding and subtracting larger numbers, in addition to building understanding of number patterns. You don't need an actual number line or any other resource to use it. Just draw a line - no numbers - on the board.

Then write the starting number under it.

Whatever pattern you're practicing, you then would write the next number. I usually have the kids tell me what to write or do it themselves. Draw an arrow to show the hop.

Continue the pattern, showing the hop to each successive number.

You can use the empty number line to practice skip counting from any number using any number pattern: 3,6,9,12,15... or 25,35,45,55,65... or 100, 200,300,400... It's a tool you can use to learn/practice any number pattern. This is also building the mental math skills our students need in order to be efficient mathematicians. Once the kids know how this works, they are easily able to use this strategy on their own, to show their work, to solve problems in their math journals, and to demonstrate their thinking.

Rounding on an Empty Number Line

This is not actually part of the second grade curriculum in my state, but I wanted to mention it. Students become much better at understanding the concept of rounding when you use a number line to model and practice it. No tips or tricks to memorize, just which number is it closest to. I'm going to refer you to an expert for information on this one. Math Coach's Corner has an excellent post on Rounding on an Open Number Line. (By the way, an Open Number Line is the same thing as an Empty Number Line.) If this is part of your curriculum, I encourage you to check it out. 

So that's it. I use the number line in multiple ways throughout the year. My students know that it is a tool mathematicians use often to solve problems or to show their thinking.  I hope you will be able to use some of these ideas in your own classroom. Do you have any other ideas for using a number line? Please share them in the comments below. 

Thanks for checking out our Math Tip Monday Blog Hop.  I hope you'll visit some of the other blogs below to gather some more great ideas for teaching number sense.

Next time, we will be sharing ideas for teaching basic addition and subtraction.

I hope you have a great week!


  1. I love the games with Investigations and all of your number line ideas! We are doing the giant floor number line this week!

  2. I would like to try the number line game. I can do that with my 1st and 2nd graders. I think they will love it!

  3. I really like your idea with hopping on the number line on the floor. I've been thinking of setting something like that up, but I haven't got around to it yet. You've inspired me to get on that! Thanks for the ideas!