I had the pleasure of spending an entire day visiting with each grade level at one of the schools in our district. We discussed assessments (huge issue that needs to be tackled - on another post!), math guidelines and teaching philosophy. We discussed the important role CPA plays in our Singapore approach to math and introduced the use of a number line at each grade level by asking them to solve an addition or subtraction problem using the number line. It was a challenge for the teachers, but they revealed an "aha" moment on their face once I showed them how to utilize this tool that we all have access to.
The use of a number line has been used for many years, but most of us are only familiar with the traditional number line with the whole numbers already in place. But what is an empty number line? Research supports its use as a graphic organizer that supports students understanding of numbers and improving mathematical performance by shifting the focus from merely a classroom tool for instruction to engaging students in the learning process.
Kindergarten -
Children can start out by locating numbers on the number line that teacher or student calls out, they could also point to a number and say the number aloud for recognition, or use it to skip by twos, fives, and ten!
I have seen the use of Ziploc baggies for practicing addition problems. Place problem index cards inside the baggie to store. When students have time to practice, they can grab a bag and go! The baggie has the number line written close to the zipper in a permanent marker and the zipper moves along the number line to help solve the problem. One could also write the answer or show the moves on a number line on the back of the card - this helps students to check their own work and allows teachers to assist with other students while practice is occurring.
Another idea I have seen is a number line taped to the students' desks (which I recommend for each grade level) and a pipe cleaner or piece of string with a bead threaded on it secured above the number line. The bead serves as the marker for "jumps".
A human-sized number line can be taped to your floor or painted on your playground. Students can then be used as the markers as a fun way to practice addition and/or number recognition!
First Grade
1.OA.2, 1.NBT.4, 1.NBT.6
Using two colors of beads, string ten of each color and alternate. The color beads leads to students to thinking in "tens", helps students to use mental math to solve problems, and allows students to perform addition and subtraction on the beads by using jumps and not counting the beads.
You can have students manipulate the beads by:
- counting by tens both forwards and backwards
- locate a number on the line (not by counting each bead, but by looking at the groupings of ten and then adding on!) etc...
Be sure to check out Megan Mutchmor's research on the use of the empty number line and the progression with activities.
2nd Grade
By second grade students should have an understanding of the base ten system and be able to make connections to the number line. Here is a packet from the Math Learning Center with some excellent activities to get your students using an empty number line to solve addition and subtraction problems.
3rd Grade
3.NBT.2, 3.NG.2, 3.MD.1
By the time students reach the third grade they should understand that a fraction is a number that appears on the number line! We can also use the number line to determine elapsed time and add and subtract numbers. The use of the number line supports the use of mental math - which is a foundation
to Singapore math.
We are learning to add/subtract numbers like 178+225 by decomposing them into friendlier numbers - the number line is an excellent tool to support this mental math strategy.
4th Grade
4.NF.4, 4.NBT.3, 4.NF.2
Now that students have had several years to experience the number line in a variety of ways, they can be successful at comparing fractions, adding/subtracting fractions, multiplying fractions, and rounding decimals (or whole numbers).
Use a visual fraction model to represent 3/6 as the product of 3 x 1/6
5th Grade
5.NBT.7, 5.NF.2, 5.NF.4, 5.NF.7
But why do I need to line up the decimal point when I add decimal numbers? Students haven't developed the underlying number sense needed to understand why, but if you show them how to solve problems on the number line they are able to see that decimal numbers are less than a whole!
number line generator
Click on the image for a site with a number line generator - great for use on Promethean Board!
This site has number lines that you can download and print here.
Some of the information and images provided can be found through the research performed through the Department of North Carolina Public Schools