SAS MATH SUMMIT, 8/6/14 JENNIFER PARKER KATIE PHELPS Equal Sharing Problems – The Key to Conceptual Understanding Fractions
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SAS MATH SUMMIT, 8/6/14
JENNIFER PARKER
KATIE PHELPS
Equal Sharing Problems – The Key to
Conceptual Understanding Fractions
GETTING TO KNOW
EACH OTHER
•Turn and talk to your neighbor and
discuss the following:
•Would you rather be a fraction or a
decimal? Why?
TODAY’S OVERVIEW
•Using a Book Study: Why and How
•Sharing our Experience in Orange County
Schools with Extending Children’s
Mathematics
•Understanding sophistication of student
strategies
•Teachers sharing and analyzing student
work
PROFESSIONAL BOOK
STUDY GROUPS
By Sally J. Zepeda
Adapted from
PowerPoint created by
Carol Coudel and Vicki Kraner
Chapter 8
Teacher Study Groups,
Whole-Faculty Study Groups,
and Book Studies
WHY BOOK STUDIES?
Effective book studies support the
development of thinking around ONE
topic and refine instructional practice.
Our OCS goal: Refine how we think about
fractions and how we introduce them to
students.
Ultimately, it is a hope that this increased
understanding in an area will lead to
applying new ideas in classroom practice.
REASONS TO USE BOOK STUDIES
Ownership
Teachers are in charge of their
own learning, so they more likely
to take into their classroom.
Relevance for the individual and a
support network for the group.
REASONS TO USE BOOK STUDIES
Peer Interaction
Frequent opportunities for the
sharing of ideas.
Professional conversations and
support during times of change.
A group of teachers who want to
better meet the needs of students.
FORM A BOOK STUDY GROUP
It is recommended that meetings:
Last no more than 1 to 1 ½ hours
Be held at the same time of the day
Be held in the same room and building
Foster the responsibility to try new
ideas and practices
(Makibbin & Sprague, 1991)
OUR STRUCTURE
3rd-5th grade teachers
Student teachers, interventionists, support staff also
invited
Meet for 1 ½ hrs each month
Meet at the same school
Teachers agree to read a certain amount of chapters
and try certain problems
Bring work samples from students to share and
analyze
Teachers offered CEUs/stipends for their work!
READ AND DISCUSS THE BOOK
Real experiences and student work is the focus of
discussion when the book is related to classroom
practices.
Book study members need the opportunity to:
Share insights
Ask tough questions
Learn from the perspectives other members
READ AND DISCUSS THE BOOK
Encourage members to keep
reflective notes.
Bring these reflections to book study
meetings.
For our study, we bring reflections
and samples of student work.
EVALUATE THE BOOK
Follow-up is needed to implement changes in
practices. Type of support our members need:
Peer coaching
Ongoing discussion
Action research
Lesson study model
Book study as a job-embedded form of
professional learning does not begin
and end with the reading of a book.
EXTENDING
CHILDREN’S
MATHEMATICS
Exploring
Fractions
And
Decimals
PART 1: WAYS STUDENTS
THINK WHEN SOLVING EQUAL
SHARING PROBLEMS.
6 children are sharing 4 candy bars
so that everyone gets the same
amount. How many candy bars can
each child have?
TIME TO SOLVE:
HOW MIGHT A STUDENT SHOW A
SOLUTION TO THIS PROBLEM?
DEVELOPMENT
OF STUDENTS’
THINKING
STUDY/UNDERSTAND STUDENT
WORK
What do you notice? What stands out?
What is an example of a more basic strategy? What
makes it basic? What does the student who created
the strategy seem to understand?
What is an example of a more advanced strategy?
What makes it advanced? What does the student
who created the strategy seem understand?
Four kids want to share 10 hotdogs
so that none are left over. If they
share fairly, how many hotdogs
should each kid get? Prove your
solution with pictures, numbers,
and/or words.
HOW MIGHT A STUDENT SHOW A
SOLUTION?
Three children want to share 7
candy bars so everyone gets the
same amount. How much would
each child get? Prove your solution
with pictures, numbers, and/or
words.
?
HOW MIGHT A STUDENT SHOW A
SOLUTION?
Jameka and Keisha both had the
same size pizza. Jameka cut her
pizza into eight equal slices and ate
three pieces. Keisha cut her pizza
into four equal slices and ate two
pieces. Who ate more pizza? Use
pictures, numbers, and/or words to
explain your answer.
HOW MIGHT A STUDENT SHOW A
SOLUTION?
SHARE
AND
ANALYZE
STUDY/UNDERSTAND STUDENT
WORK
Find a strategy that you are having difficulty
understanding and discuss it with other teachers.
What information do you need from the student to
better understand the strategy?
Is there strategy that appears the most? Why do
you think so?
PART 2: MORE EXAMPLES
OF STRATEGIES
WHAT ARE POSSIBLE STRATEGIES (FIGURE 1-17)
FOR SOLVING EACH OF THESE PROBLEMS?
There are 4 large sub sandwiches at a party. 10
students want to eat all of the subs and they
want to get exactly the same amount. How much
sub can each student have?
3 friends were at a Mexican restaurant. They
were feeling hungry, so they ordered 5 burritos to
eat. They want to share the burritos equally.
How much will each friend get?
5 friends are at the same restaurant and not as
hungry. They only ordered 3 burritos to share
equally. How much will each friend get?
THERE ARE 4 LARGE SUB SANDWICHES AT A
PARTY. 10 STUDENTS WANT TO EAT ALL OF
THE SUBS AND THEY WANT TO GET EXACTLY
THE SAME AMOUNT. HOW MUCH SUB CAN
EACH STUDENT HAVE?
THERE ARE 4 LARGE SUB SANDWICHES AT A
PARTY. 10 STUDENTS WANT TO EAT ALL OF
THE SUBS AND THEY WANT TO GET EXACTLY
THE SAME AMOUNT. HOW MUCH SUB CAN
EACH STUDENT HAVE?
3 FRIENDS WERE AT A MEXICAN
RESTAURANT. THEY WERE FEELING
HUNGRY, SO THEY ORDERED 5 BURRITOS TO
EAT. THEY WANT TO SHARE THE BURRITOS
EQUALLY. HOW MUCH WILL EACH FRIEND
GET?
5 FRIENDS ARE AT THE SAME RESTAURANT
AND NOT AS HUNGRY. THEY ONLY ORDERED
3 BURRITOS TO SHARE EQUALLY. HOW
MUCH WILL EACH FRIEND GET?
3 CHILDREN WANT TO EQUALLY SHARE 6 ½
PEANUT BUTTER SANDWICHES, WITH NO
LEFTOVERS. HOW MUCH CAN EACH CHILD
HAVE?
3 CHILDREN WANT TO EQUALLY SHARE 6 ½
PEANUT BUTTER SANDWICHES, WITH NO
LEFTOVERS. HOW MUCH CAN EACH CHILD
HAVE?
PART 3: GENERAL FORMAT
FOR WORKING WITH YOUR
STUDENTS
HOW TO USE THESE PROBLEMS IN
YOUR CLASSROOM- CGI GENERAL
STRUCTURE:
Introducing the Problems:
Pose problems without showing students how to
solve them (read multiple times to younger
students).
If needed, talk through or act out what is
happening in the story so students can picture
the situation.
HOW TO USE THESE PROBLEMS IN
YOUR CLASSROOM- CGI GENERAL
STRUCTURE:
Problem Work-time:
Listen to your students explain how they solved
problems (you can ask for two different ways to
solve a problem).
If a student cannot solve a problem:
You can make the numbers/relationships simpler
You can have the student listen how another student
solved the problem
HOW TO USE THESE PROBLEMS IN
YOUR CLASSROOM- CGI GENERAL
STRUCTURE:
Problem Share-Out:
Choose 2-3 students to explain their strategies to
the rest of the class.
Start by sharing least abstract to most abstract
thinking.
This supports working with students to listen to each
other.
This shows different strategies (some more advanced)
that are possible
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