The Number Line in the Common Core

CONTENTS OF CURRICULUM UNIT 16.05.03

  1. Unit Guide
  1. Introduction
  2. Demographics
  3. Using rods and ten blocks to recognize lengths
  4. Using base ten blocks for addition and subtraction
  5. Recognize that the size of numbers can correspond to length on a ruler
  6. What is a fraction?
  7. Fractions on the Number Line
  8. Equivalent Fractions
  9. Teaching Strategies
  10. Classroom Activities
  11. Appendix A
  12. Appendix B
  13. Appendix C
  14. Appendix D
  15. Appendix E
  16. Appendix F
  17. Appendix G
  18. Appendix H
  19. Implementing Common Core State Standards
  20. Resources
  21. Endnotes

Moving from Rods to Number Lines to Understand Fractions

Kathleen Geri Gormley

Published September 2016

Tools for this Unit:

Recognize that the size of numbers can correspond to length on a ruler

The bars and trains students have been making do not have an intrinsic location in space, they essentially are just floating around until they are assigned an origin. Deciding on where the trains begin and assigning that place a value of 0 will create a number line. The number line will then give a standard exemplar for each length.  As students begin to measure a variety of items throughout the classroom, I will point out the connection between their trains and a ruler. I will make sure to encourage students to measure longer items as well to allow them to be accustomed to working with larger numbers. In preparation for larger numbers, I intend to create a 100 train by gluing ten “ten’s” pieces together. It is not practical to have every student have a “1000” train, however having one for the class to use will be invaluable, I will use a meter stick for actual measurement. This will allow students begin to formulate a visualization as well as a conceptual knowledge of the magnitude of the number 1000 in relation to 1. Students should independently discover the ease of using larger trains in measuring larger items. As they record their measurements, students should consistently say, “my item is so many cubes long.”  If they are two-digit measurements, I will have them report how many 10s and how many ones, and then state standard name of the length. Additionally, if they are three-digit measurements, I will have them report how many 100s, how many 10s and how many ones, and then state standard name of the length. This reinforces the importance of the unit used. Inevitably students will measure items that will not produce an exact whole number. Typically, students will report this as “about 21 units long”. A better description of this situation would be, “my object is between 21 and 22 units long.”. This language will naturally point out the need for numbers different from whole numbers in the realm of measurement.  This then will set up nicely the need for fractions and point out that fractions are not a combination of two different whole numbers but a number between two numbers.

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