1. Fractions: Teaching with Understanding Part 3

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
What do you know about a number line that goes from 0 to 4?
Draw a number line on a chart paper. Get to proportional reasoning as well as sequential.
1. Equal distance between whole number
Who in here is a first grade teacher – how do your kids draw a number line? Don’t pay attention to intervals; label as sequential reasoning
2. There are numbers between 0 and 1. How do you mark them? On your slate draw a number line that shows fourths. Shoulder partners tell each other what they know about ¼. 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. On your slate draw another number line from 0 to 1 that shows fourths.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?
Proportional to the unit is defined. Can do it easily when the unit is defined. (equal intervals)

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.
Students have trouble integrating the visual (line) model and the symbols necessary to define the unit. The symbols can act as distractors.
Students don’t always understand that the numbers associated with the points on a number line tell how far the points are from zero.
Researchers “hypothesize” as long as partitioning and unpartitioning are difficult for children, number line representations of fractions may not be easily taught.

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.
Using fractions as number to fractions as units as length.
Scan picture on pg. 48 on Bits and Pieces 1

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.