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:

Classroom Activities

Activity One- Investigating Measurement

Essential Question: What will you do when an object measures in between two whole numbers?

Enduring Understanding: Students will be able to use rods to measure a variety of classroom objects. Students will be able to generate measurement data. Students will understand that a fraction is a number on the number line.

Procedure: Students will be given an assortment of rods in varying lengths.  These rods could be Cuisenaire rods, base ten blocks, or any other type of manipulative that can be put together to form chains. Students will locate up to twelve classroom objects to measure.  Students will focus on making chains of blocks and determining the lengths of the objects. The objects will include both lengths that are whole numbers of units and lengths that are not whole numbers of units. I will lead students in discussions about the lengths of their objects inquiring whether or not the length is nearly a whole number or between whole numbers.  I will frame their responses to say, “My pencil is more than 7 units and less than 8 units.”. This will focus the students thinking to realize that there is a need for some type of unit in between the whole numbers. A sample recording sheet can be found in Appendix A.

Assessment: Exit Ticket- In your journal, answer the following prompt: What do we do when we measure something and it is in between two whole numbers?

Activity Two-Multiple Models of Fractions

Essential Question: What is a fraction? How can I use a number line to understand fractions?

Enduring Understanding: Students will be able to use multiple representations for fractions, including pictorial representations of the set model, circular model, area, model, and number line.

Procedure: Using our interactive math journals, students will create visual representations of unit fractions. As students move between the various representations, they will need to construct an understanding the relationship between the models.  We will focus on unit fractions with denominators of 2, 3, 4, 6, and 8. Students will complete the worksheet located in Appendix B.

Activity Three-Equivalent fractions

Essential Questions: How can I find equivalent fractions? How can I show equivalent fractions using different models?

Enduring Understanding: Students will be able to understand what makes a fraction equivalent. Students will be able to find an equivalent fraction.

Procedure: Using paper strips that are equal in length, students will create fractions strip models. One strip will remain unfolded to represent one whole. Then students will color each of the remaining strips a different color, there is not a specific color scheme that must be followed I will choose primary colors. Students will color a strip blue and then will fold the strip in to two equal parts and label each part 1/2 and cut the strip on the fold. They will follow this procedure of coloring, making folds, labeling, and cutting for each unit fraction in our lesson; 1/3,1/4,1/6,1/8,1/12. I chose to use these fractions because we can investigate many equivalent combinations with these. After students create their fraction strip models they will investigate finding equivalent fractions and complete the worksheet in Appendix C. Students will then use their math journal to place equivalent fractions on a number line. Using their fraction strips, students will partition one number line at a time with two different fractions. (A sample of this activity can be found in Appendix D, however many more variations of this activity can be completed.) Students will discover equivalent fractions and will label the lengths on the number line.

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