## 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.

## Math Curiosity

Image by:  Samana

Here’s a typical elementary multiplication math problem:

John has 5 buckets with 10 tomatoes in each bucket.  How many tomatoes does John have in all?

To be honest … there’s nothing really wrong with the problem, but there are different ways to teach multiplication.  To me, this type of problem, although it could happen outside of the classroom, seems extremely scripted.  I’ll tell you a quick story about one of my math lessons from last week.

Last week I was given the opportunity to teach second and third grade students multiplication.  I find that when students are able to explore their own curiosity regarding math, they are often more intrinsically motivated to learn.  I’ve attempted to create a classroom environment that promotes math curiosity.  After introducing students to the idea of multiplication, I showed the students the video below.

After watching the video, I posted a few follow up questions on the whiteboard.  The class had a thorough discussion foru about 15-20 minutes regarding the mistakes made by some of the actors in the video. Students where asked to answer the questions below in collaborative groups and eventually communicate their answers to the class.  Here are a few of the questions:

1.  What math vocabulary terms did you hear/watch in this video?

2.  Did you see any math mistakes?  If so, where?

3.  Could some of the mistakes be prevented?  if so, how?

4.  What was done correctly?

5.  How can you prove that your answer to a multiplication problem is correct?

6.  What can we learn from this video?

Overall, I thought this was a great supplement to a multiplication lesson at the elementary level.  Integrating technology and asking thought provoking questions gives students opportunities to follow their curiosity.