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:

Using base ten blocks for addition and subtraction

Now that students have made a connection between number and measurement, students can use base ten pieces to carry on this process as place value is uncovered as well as reinforcing procedures for adding across decades. They can do this by combining “trains” of base ten blocks. Suppose they want to add two two-digit numbers. Students can create a representation of the first two-digit number using base ten pieces and place the piece end to end to make a “train” of blocks with a given length. We will adopt a standard form for such trains, with the 10-rods on the left and the ones blocks on the right. Similarly, they will make a second train for the second addend. Next they will place the second train at the end of the first train. We will observe that the combined train is not in standard form, and will discuss what to do to put it in standard form. Students will then physically rearrange the pieces of the combined trains, grouping the tens pieces together on the left side and the ones cubes to the right, keeping the pieces, tens and ones, all grouped together without any gaps in a train. This movement exactly represents the symbolic procedures that many students have memorized and many have not assigned conceptual knowledge to yet. Students will make a train using base ten pieces to represent the expression: 24 + 17.

24+17= (20 + 4) + (10 + 7)

= 20 + (4 + (10 + 7)) = 20 + ((4 + 10) + 7) = 20 + ((10 + 4) + 7)) = 20 + (10 + (4+ 7))

= (20 +10) + (4 + 7) = 30 + 11= 30 + (10 + 1) = (30 + 10) + 1=

40 + 1= 41.

Students rearranged the trains of tens and ones. Once this was accomplished, they then saw they had eleven “ones” pieces and could make another ten train. Trading in ten of these “ones” pieces for a ten piece parallels the procedure for the algorithm. Students will notice that the rearranged and regrouped train is the same length as the first train, which may not be evident in this diagram. The final train exhibits the answer in standard base 10 form.

Comments:

Be the first to comment on this unit!

Add a Comment

Characters Left: 500

Unit Survey
Feedback