## Number Line Concepts

Image by:   D. Rizzuti

Lately, I’ve been having conversations with colleagues regarding how to communicate number line concepts in the classroom.  Specifically, I’ve been giving examples of how understanding number lines may lead to a more stable mathematical foundation. In the past, my class has created various products related to the number line.  My original inspiration came from this number line below.

The project in this post emphasizes the idea that percents, fractions, mixed numbers, and decimals are all related  This basic understanding helps develop number sense skills.  Here are the generic steps for this project:

• Students cut out percents, decimals, percents, and fractions out of the template
• Students draw a number line on a piece of construction paper
• Students glue/tape each number on the number line

Here are a few sample photos (click to enlarge):

The project seems simple, right?  Well … it took about 20 minutes for the cutting, coloring, and gluing.  I then facilitated a classroom discussion after the number lines were presented.  The math curiosity (I really like that term) and discussion that followed the project seemed beneficial.  It’s truly amazing to see what type of concepts can be discussed when observing the number line through a variety of lenses.  Our conversations touched on the concepts of absolute value, positive/negative numbers, fractions and mixed number conversions, addition of negative numbers, and place value.  In fact, the math conversation lasted 30+ minutes.  Having these types of “math chats’ with third graders was a phenomenal learning experience.  All of the concepts discussed will be introduced later in their academic career, and hopefully I gave my students a quick preview to what is to come.

## Unlock the Number Line

Image by:  Tratong

It’s becoming more evident that the Common Core initiative is running at full throttle. Keeping that in mind, I’m now finding myself exploring different methods to introduce fundamental math concepts and create lessons that emphasize number sense skills. These number sense skills are especially needed at a young age and often influence how students perceive / achieve in math later in their academic career.

Having students explain their mathematical thinking is a big focus next school year.  By asking appropriate questions, teachers are able to analyze and give feedback in real-time to best meet the academic needs of each student.  After researching math strategies and participating in a variety of CCSS workshops this summer, I’ve concluded (at least partially) that the number line can be utilized for many math objectives at the elementary level.

Teachers that model the mathematical problem-solving process find that it’s beneficial. The visualization of a numer line can be useful, whether it involves the concepts of measurement (elapsed time), percents (finding discounts), algebra (inequalities) or fractions (computation).  A number line can be useful in solving problems related to any of the above concepts.  If the idea of utilizing a number line to solve math is introduced via classroom instruction, it may be beneficial to give examples of how it’s used outside school as well.

So.. how did you use a number line today?

## The Real Number Line – In Practice

Image by:  Samana

A little while back I wrote a blog post about how the typical math number line needs an upgrade.  You can find that post here.  I thought and still think that the general math number line that is introduced at the elementary level needs to be enhanced.

I believe that students should encounter all types of numbers on a number line. Students should find whole numbers, decimals, square roots, fractions, percentages, mixed numbers, etc.  Of course, the concept needs to be age appropriate .  So, in my last post I wrote about how students should understand the real math number line.  In theory it sounded like an idea that could be put into practice.  I decided to find out how the theory looked in practice.  I asked students to create a math number line with multiple components. This activity fit in well with the decimal and fraction unit that I’m currently teaching.  I gave each student learning group a sheet like the one below and a specific number range (like numbers 3 – 6).

Every student worked on this project in a cooperative group. Through this experience, I believe the students had a unique opportunity to learn about the many different ways that numbers can be represented.  See below for examples.

Overall, students were engaged and thoroughly enjoyed the activity.  At the end of the project, I facilitated an informal plus/delta chart and the feedback was generally positive.   While students were in their cooperative groups I overheard them debate the differences and similarities of fractions, square roots, decimals, improper fractions, and mixed numbers on the number line.  It was a great learning experience and definitely a project I’ll put in the plan book for next year.

Disclaimer (unfortunate but necessary) : The thoughts and opinions expressed in these pages are my own, and not necessarily the opinions of my employers.