The Stenhouse Blog

Building a Fraction Number Line as an Ongoing Number Sense Routine (Math Monday)

Posted by admin on Nov 15, 2021 9:00:00 AM

Highlighting Ideas from Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3 by Jessica Shumway

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As students dive into their study of fractions and decimals, making a number line together as a class can be a useful routine for developing and deepening number sense.

In her book, Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, Jessica Shumway explores this routine which she calls the Organic Number Line.

 

“The Organic Number Line is one section of a ‘whole number’ number line; with it, you magnify the number line from 0-2. It is ‘organic’ because your students continuously add to it throughout the year. It is ever changing based on the experiences in your class” (72-73).

 

Jessica writes about the importance of beginning the study of fractions with many experiences with region (area) models and set models. “Children will need a variety and plethora of experiences with ‘fair share’ story problems. They need visual understandings of region models of fractional amounts (like pies, brownies, and pizzas) and set models of fractional amounts (like the fraction of crayons that are blue) as well as clear mental models of important benchmarks like halves, thirds, and fourths” (73).

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In Jessica’s classroom she began with a six-foot long piece of string stretched across some cabinets near her meeting area and cards labeled with numerals and pictures. To start, Jessica’s third graders worked together to place the half and whole benchmarks.

first number line

Over time the class added various region and set representations of these numbers, followed by adding the quarter benchmarks.

second number line

 

third number line

The real power of the Organic Number Line routine comes from continued conversations about fractions and decimals. To facilitate rich discussions around the placement of these and other cards on the number line, Jessica used some of these questions below:

Big Idea: Benchmark and Counting Sequences

  • Where does this number go on our number line? How do you know?
  • What numbers can you think of that go between ½ and 1. How do you know that number goes between these two benchmarks?

Big Idea: Equivalency

  • You said that 2/4 goes here with ½. Prove that 2/4 and ½ are equivalent.

Big Idea: The Whole and Parts of a Whole

  • Why does ½ go here and 1½ go over here?
  • Are this half and this half the same amount? (Show two models representing ½, each with a different whole.) Prove it!

Big Idea: Linear Model as a Tool

  • What on the number line helped you figure that out?

Big Idea: Region and Set Models

  • Here we represent ½ with this picture. 
    pic from 75
         Can you think of another way to show that number? (Students might show ½ as a set model           by showing 4 yellow leaves out of 8 leaves total or show ½ as a region model with a pizza                 cut into sixteenths, with 8 pieces gone.)

Big Idea: Doubling and Halving

  • What is half of that amount? Where does that fraction go on the number line?
  • How did you know that 2/4 goes in the same spot as ½?
  • How did you know that ⅛ should be halfway between ¼ and 0?

As the school year went on, Jessica found that students often referred back to the number line that continued to hang in their class. When her third graders grew winter wheat in the school’s garden, they made connections to the number line as they used measuring tools to keep track of the wheat’s growth. The Organic Number Line became a critical tool and model in the classroom and an ongoing way to make sense of fractions and decimals.

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Are you interested in getting started with the Organic Number Line routine? We’re making a free downloadable version of this section of Number Sense Routines available right here. And to read even more about Number Sense Routines by Jessica Shumway and check out related resources including a free study guide, you can go here.

 

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Topics: Math, #StenhouseMath