I am thrilled to have Chris Shore take over the newsletter this week to share about his experiences with Clotheslines. This week's newsletter has been translated into Spanish (bit.ly/TTMspanish46) by Ed Campos, Jr. Make sure you check it out and tell him thank you on Twitter.
A person’s ability to think mathematically has far more to do with their number sense than with their ability to study and memorize formulas and procedures. Number sense is the capacity to think flexibly, efficiently, and accurately about numbers. One of the great methods in teaching number sense is the open number line, which is a number line with no or few given benchmarks.
I’m currently working extensively with this open number line concept using an instructional tool know as the Clothesline. The Clothesline is a dynamic number line (string) on which students can actually move the values and benchmark (folded cards).
For example, let’s say we ask students to place the following three fractions: 1/2, 1/3, 1/4
Typically, students will use only 0 and 1 as benchmarks, then many will often inaccurately place the fractions in the following order:
This misconception offers a great opportunity to discuss how when something is divided into more and more equal parts, each part gets small. For example, 1/2 of a pizza is a bigger slice than 1/4 of the same size pizza.
Once the order of the fractions is correct, students are prompted to properly space the fractions. While students frequently find the proper spacing for one-half and one-fourth, one-third challenges them. Is it closer to the fourth or the half? There are several strategies for determining this, from converting to decimals (0.25, 0.33..., 0.50), finding a common denominator (3/12, 4/12, 6/12) or proportional reasoning (three thirds equals exactly one).
As a parent at home working with the number line with your child, you don't need to try to do the teacher’s job. Simply share aloud how you think about these numbers. We math teachers call these “number talks,” and it is one of the most effective ways you can support your child’s learning of mathematics.
If you are interested playing with the Clothesline or simply the open number line on paper, you can find free resources on clotheslinemath.com