Fraction Sense
Fran Gibson
Welcome and Introductions
• Please share the following information
about yourself:
– Name
– Position and School District
– Experience with California’s Common Core
State Standards
– One thing that you would like to learn from
today’s presentation
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Norms
We all agree to:
• Learn about mathematics
• Work together
• Implement what we learn
We will all work to:
• Learn
• Be Cooperative
• Be on Time
• Be Flexible
• Be Forgiving
• Be Responsible
• Be Respectful of Others
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Please turn all
cell phones to
off or silent and
refrain from
text messaging.
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Learner Outcomes
Today we will…
• Explore CCCSS that focus on naming, equivalence,
comparing and ordering fractions on the number line.
• Develop an understanding of how fraction
understanding progresses across grade-levels.
• Discuss implications of this structure on teaching
with the current mathematics textbook.
• Identify starting points for beginning implementation
of CCCSS.
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Number Line Activity
With a partner:
• Solve the 12 problems on your set of cards.
• Discuss the strategies used and identify the
concepts, skills, and procedures needed to solve
each.
• Order number lines in increasing order
of difficulty.
• Be ready to justify your choices.
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Instructional Implications
Teacher as Practioner
• As you watch the following two videos, keep the
following questions in mind:
– What strategies did the students use?
– How did it compare to the strategies you used as
adults?
– What did the students understand?
• Be prepared to discuss and share out some of your
thoughts.
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Video Example 1
Video Example 2
Looking for the Big Mathematical Idea
With a partner:
• Summarize, in as short a statement as you can, the
“BIG” mathematical idea that these problems
represent.
• Investigate the Number and Operations – Fractions
cluster and standards and determine how the
problem supported the content of the cluster.
• Be ready to share your ideas with the larger group.
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Cluster Progression
On your own…
1. Using the “Number and Operations–Fractions” handout,
pick one cluster within the domain for each grade level
and read the standards.
With your tablemates…
2. Discuss the following questions:
– What do you notice?
– What big ideas are repeated or similar?
– What is different?
3. Be ready to share out with the entire group.
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Fractions on a Number Line
On your own…
1. Draw a number line, locate and identify 2/5.
With your tablemates…
2. Discuss the following questions:
– What process did you use to do this?
– Could you use this process for any fraction?
Why?
3. Be ready to share out with the entire group.
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Equivalent Fractions- Part 1
With a partner:
– Using the same number line, identify and mark
4/10.
– Discuss the following questions.
• How many pieces are in the whole now?
• Did you use the same process? How was it the same?
How was it different?
• Are the two marked fractions equal?
• How can you be sure?
– Be ready to share out.
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Equivalent Fractions- Part 2
3/7 = ?/28
• How can you determine the number of
28ths that would be equivalent to 3/7 using
the process from the previous activity?
• Share out solutions and strategies
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Summarizing the Big Idea
3/7 = 12/28
• Thought Process:
– Three pieces that are broken into four equal
pieces making twelve pieces.
– Seven pieces that are broken into four equal
pieces making twenty-eight pieces.
• What arithmetic problem could be used to
get the number of pieces for the
numerator? For the denominator?
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Fraction Families
On your own…
1. Make a list of fractions that could be built from thirds, based on
our understanding of fraction equivalency on the number line.
2. Think about the following questions:
•
•
•
Would sixtieths be on this list?
How many equal pieces would each third be broken into to make sixtieths?
How would you describe the family of fractions that can be generated from
thirds?
With your tablemates…
3. Discuss your responses to the previous questions.
4. Build fraction families for halves, fourths, and sixths.
5. Discuss whether or not the description you found with thirds
still applies.
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Comparing and Ordering Fractions
With your tablemates…
1. Compare these two fractions: 5/8 and 5/11,
without computing.
2.
•
•
•
2.
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Discuss your reasoning to determine:
Which is bigger? Which is smaller?
Which is closest to ½?
Which is closest to 1?
Be ready to share out with the entire group.
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Practice Comparing Fractions
On your own…
1. Using relationships, not common denominators,
compare the fraction pairs in your notebook.
2. Think about the following:
– What generalizations can you make about comparing
fraction size?
– What strategies did you use?
– How do you know you are right?
With your tablemates…
3. Discuss how you might get students to the same
kind of exercise.
4. Be ready to share out with the entire group.
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Conceptual Thought Patterns for
Comparison
• Read through the conceptual thought patterns
for comparison in your notebook.
• Highlight key words or phrases.
• Partner up with others and discuss the following:
– What kinds of questions do you ask your students
to help you understand their thinking about
fractional relationships?
– What are some instructional implications inherent
in these thought patterns?
• Be ready to share out your thoughts.
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Debrief of Conceptual Thought Patterns for
Comparison
What are the key ideas in each of the
thought patterns?
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•
More of the same-size parts
•
Same number of parts but parts of
different sizes
•
More and less than one-half or one
whole
•
Distance from one-half or one whole
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Which Fraction is Greater?
On your own…
1. Using the problem set in your notebook,
determine which fraction in each pair is
the greatest using one or more of the conceptual
thought patterns.
2. Next to each pair of fractions, indicate the thought
pattern or patterns you used.
3. Be ready to share out with the entire group.
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Debrief of Which Fraction is Greater?
Explain the thought process you used to determine which
fraction in each pair was the greatest.
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
4/5 or 4/9

7/12 or 5/12

4/7 or 5/7

3/5 or 3/7

3/8 or 4/10

5/8 or 6/10

5/3 or 5/8

9/8 or 4/3

3/4 or 9/10

4/6 or 7/12

3/8 or 4/7

8/9 or 7/8
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Connect to the Curriculum
• Investigate how your text uses the number
line for fraction instruction.
• How might you use what you have learned in
this session to enhance your lessons?
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Resources
 Websites
◦ Common Core Standards: www.corestandards.org
◦ California Common Core Standards: Visit the
California Department of Education’s Common
Core State Standards Web page at:
http://www.cde.ca.gov/ci/cc
• The standards
• Frequently asked questions
• Additional resources
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Reflection
• Complete the prompts on the
Notebook page.
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Feedback Form
• Complete and submit the Feedback Form included
in the back of the Notebook.
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