an empson approach to teaching fractions in a 3 rd grade class
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An Empson Approach to Teaching Fractions in a 3 rd grade Class. A fraction project based on the research of Empson and Levi conducted by Mr . Joe Bysiek, 3 rd grade teacher, and Dr. Gayle Millsaps and Diana Underwood - PowerPoint PPT PresentationTRANSCRIPT
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An Empson Approach to Teaching Fractions in a 3rd grade ClassA fraction project based on the research of Empson and Levi conducted by Mr. Joe Bysiek, 3rd grade teacher, and Dr. Gayle Millsaps and Diana Underwood****Slides marked new were added since the original presentation, for a Professional Development Project for Crown Point Community Schools.
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Empson and Levi, 2011• Susan Empson and Linda Levi have developed a method
for teaching children fractions across grades K-6.• Their method is based on research observing children’s
learning of fractions in K-6 classrooms.• It builds on the work of the Cognitively Guided Instruction
working group that documented children’s learning of whole number sense and operations.
• Their approach encourages students to build meaning for fractions through solving and discussing word problems.
• They articulate a learning progression of students’ strategies for solving fraction problems that are indicative of students’ growth in understanding fractions.
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A TRUE UNDERSTANDING ***NEW
Third Grade Problem:You have 4 sticks of butter. It takes ¾ sticks of butter to make a cake. How many cakes can you make?
YOU TRY
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One third graders solution ***NEW
Work Explanation
5 1/3…..You can make 5 cakes and then you have one of the fourths of the three fourths needed so that’s a third of another.
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Mr. Bysiek’s Learning Goals• Students understand that unit fractions are defined as equal parts of
a unit whole—i.e., 1/3 is one part of a unit whole broken into 3 equal parts.
• Students understand how fractions relate to a unit whole—what is ¾? 5/4?
• Students understand that a numerator and denominator that are the same equal one whole—3/3=4/4=5/5=1
• Students understand that the bigger the denominator the smaller the pieces—1/4 > 1/5.
• Students begin to develop an understanding of equivalent fractions—1/2=2/4=4/8 or 1/3=2/6.
• Students know how to add fractions with like denominators, and higher students can add unlike denominators—1/4+1/4+1/4=3/4 or ¼+1/2=3/4.
• Students begin to understand multiplying of unit fractions by whole numbers—3x1/4=3/4.
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Fair Share Example problem• A teacher gave 4 sandwiches to 3 children to
share. If the students shared the sandwiches equally, how many sandwiches would each child get?
Answer: ________________sandwiches Work:
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Students’ thinking one
• One student is working on how to share • Another is thinking how to add thirds
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Students’ thinking two
• One student is working on how to share• Anther student is seeing one whole and a piece
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Class Discussion
Here students begin discussing which is correct. Questions are asked if both are fair. As they agree, a discussion is started about how much each person would get. Is it the same? How do you name it? Can they both be right?
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Multiple Groups Example Problem• There are 6 children and I want to give them
each ¼ of a twizzler. How many twizzlers do I need? _____twizzlers
• Show Work:
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Students’ thinking one• ¼+ ¼ + ¼ + ¼ + ¼ + ¼ = 6/4 • ¼+ ¼ + ¼ + ¼= 1 and ¼ + ¼ = 2/4 • ¼ + ¼ + ¼ + ¼ =1 and ¼ + ¼ = ½
• Here a powerful discussion occurs with who is really correct? Is it fair each way? Does everyone get the same amount?
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Students’ thinking two• This student says 6. Even though it is not the
correct answer, the student is still working on sharing fairly. A powerful discussion can be used and discuss what to do with the extra ¾ of each twizzler.
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Fraction Equivalency and order problems
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Ordering problem one• Jen and Robert got into an “argument” of who ate
more. Jen ate 1/4 and Robert ate 1/5. Who ate more? Why do you think that?
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Students’ thinking one• One child states ¼ gets more because you are
sharing with less pieces.• Another child says states the smaller the
denominator the bigger the pieces, because you are sharing a candy bar with less people.
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Students two thinking• 1/5 because five is a bigger number. Here a
powerful discussion arises. The student is asked to show what each person would get and gets an “ah ha” moment.
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• 3 kids each get 4/3 candy bars. How many candy bars do they have all together? _____________Candy bars
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Students’ Thinking One• One student after drawing a
picture adds them together. • Another student has multiplied
them
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Students’ Two Thinking
This Student Realizes that 4/3 is 1 1/3 because 3/3 equals a whole
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Fifth graders’ explanations on equivalency ***NEW
Discuss Mr. Li’s class solutions of a problem.
Pages 123-125 of Empson’s Extending Mathematics
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Can you figure out which one is greater WITHOUT a common denominator? ***NEW
2/7 or 2/11
3/5 or 9/11
9/10 or 6/7
95/100 or 70/75
Taken from Empson’s Extending Children’s Mathematics p138
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Key Findings• Empson’s approach allows more students to make
sense of fractions and how they relate to whole numbers.
• More students are able to achieve the fraction learning goals for 3rd grade than with traditional approaches.
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Day 2 ***NEW• Review what a fair share problem is• Break into groups and create grade level
problems• Solve select problems together as a group
and discuss, how it meets Marzano’s scales.
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Day 3 ***NEW• Review what a multiple group problem is• Break into groups and create grade level
problems• Solve select problems together as a group
and discuss, how it meets Marzano’s scales.
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Day 4 ***NEW• Review what a “Problems for Fraction
Equivalence and Order” are• Break into groups and create grade level
problems• Solve select problems together as a group
and discuss, how it meets Marzano’s scales.