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Understanding and Using Fractions on a Number Line

Learn how to represent and compare fractions on a number line, using reasoning strategies. Explore the standards related to fractions and practice ordering fractions based on their size.

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Understanding and Using Fractions on a Number Line

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  1. CCSS-M: Fractions Part 2

  2. We are learning to: • Represent fractions on a number line • Use reasoning strategies to order and compare fractions • Read and interpret the cluster of CCSS standards related to fractions Success Criteria: • Clearly explain and provide examples for specific CCSS-M fraction standards

  3. Number Line Model 0 4 What do you know about a number line that goes from 0 to 4?

  4. Standard 3NF2a Make connections between activity and the standard 3NF2a. On your Standards Interpretation Sheet rephrase this standard and provide an example. Share with your partner.

  5. 0 1 On your slate draw another number line from 0 to 1 that shows fourths. Mark ¾ on your number line. Explain to your shoulder partner how you marked ¾.

  6. Standard 3NF2b On your Standards Interpretation Sheet rephrase this standard and provide an example. Share with your partner.

  7. Sequential & Proportional Strategies Draw two number lines from 0 to 4. Use whole numbers & fractions to show parts on the number line. # line 1 show sequential reasoning # line 2 show proportional reasoning Is it harder when you have to mark fractions? Why?

  8. Explain Ken’s thinking?

  9. Explain Judy’s thinking?

  10. On your slate, draw a number line from 0 to 1. Use proportional thinking to place and on the number line.

  11. Matt’s Thinking .

  12. Equivalency Place the whole fraction strip that represents 0 to 1 on a sheet of paper. Draw a line labeling 0 and 1. Lay out your fraction strips, one at a time, and make a tally mark on the line you drew. Write the fractions below the tally mark. Look for patterns to help you decide if two fractions are equivalent.

  13. Which fractions are equivalent? How do you know?

  14. Standards 3NF3a & 3NF3b On your Standards Interpretation Sheet rephrase this standard and provide an example. Share with your partner. Do the same process for 4NF1.

  15. Standard 3NF3d & 4NF2 On your slate, provide an example of comparing fractions as described in this standard. Share with your partner.

  16. Compare Fractions by Reasoning about their Size More of the same-size parts. Same number of parts but different sizes. More or less than one-half or one whole. Distance from one-half or one whole (residual strategy–What’s missing?)

  17. Ordering Fractions • 1/4, 1/2, 1/9, 1/5, 1/100 • 3/15, 3/9, 3/4, 3/5, 3/12 • 24/25, 7/18, 8/15, 7/8

  18. Ordering Fractions Write each fraction on a post it note. Write 0, ½, 1, and 1 ½ on a post it note and place them on the number as benchmark fractions. Taking turns, each person: Places one fraction on the number line & explains their reasoning about the size of the fraction.

  19. Ordering Fractions 3/8 3/10 6/5 7/47 7/100 25/26 7/15 13/24 17/12 8/3 16/17 5/3

  20. Reflect Summarize how you used reasoning strategies to compare and order fractions based on their size.

  21. Standard 3NF3d & 4NF2 On your Standards Interpretation Sheet rephrase this standard and provide an example. Share with your partner.

  22. Translating the Standards to Classroom Practice Discuss the progression of the standards we did today. Is the progression logical? Discuss how the standards effect classroom practice. What will need to change?

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