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RED CLAY CONSOLIDATED SCHOOL DISTRICT
4th – 6th Partnership Institute
Building a Conceptual Understanding of Fractions:
A 4th Through 6th Grade Partnership
A CALL TO ACTION
"These Standards are not intended to be new names for old ways of doing business. They are a call to
take the next step."
Common Core State Standards for Mathematics
RCCSD
District Mathematics Department
Jodi Albers, Supervisor of Mathematics Lou Mingione, Secondary Mathematics Specialist Eric Shane, Elementary Mathematics Specialist Shirl Ellison, Elementary Mathematics Specialist
Participants
23 District Schools 15 Elementary 8 Secondary
Institute of Higher Education
University of Delaware, MSERC
Janice McCarthy Val Maxwell
Instructional Technology Coaches
Karen Ammann Vicki Green
Funding
Delaware Department of Education
$122,600
4th – 6th Partnership
Institute
RCCSDINVESTED PARTNERS
EXAMINING THE DATA
Count Pre
AssessmentPost
Assessment Change
Total 128 11.53 13.30 +1.77
0 - 9 39 7.59 10.92 +3.33
10 – 15 74 12.57 14.05 +1.48
Mathematical Knowledge for Teaching Survey (MKT)
RCCSD
FRACTIONAL UNDERSTANDING
“The coherence and sequential nature of mathematics dictate the foundational skills that are
necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and
negative fractions). The teaching of fractions must be acknowledged as critically important and
improved before an increase in student achievement in algebra can be expected.”
National Mathematics Advisory Panel
RCCSD
GOALS
• Explore what educators need to know and be able to do in order to effectively instruct students in the area of fractions using visual models, number talks, and additional research-based strategies.
• Examine and reflect on research that explores best practices for teaching the essential ideas that students must grasp about fractions.
• Examine and implement rich mathematical tasks that align to CCSSM.
• Explore the understanding of rigor within CCSSM through the development and implementation of model lessons.
RCCSD
A TYPICAL DAY IN THE INSTITUTE
• Formulated Norms• Conducted Exit Ticket Summary• Reviewed Homework• Participated in a Team Builder• Examined the Common Core State Standards• Examined the Standards for Mathematical Practices• Engaged in Rich Mathematical Tasks• Participated in a Book Study• Enhanced Smarter Balanced Assessment Items
RCCSD
PARTICIPANTS
167 total participants• 72 fourth grade teachers• 67 fifth grade teachers• 26 sixth grade teachers• 84 participants from Title I buildings• 8 participants from special schools
RCCSD
PARTICIPANT STRUCTURE
• 167 Teachers• 4 Cohorts• 6 Teams per Cohort• 8 players per team (maximum)• At least 2 fourth, 2 fifth and 1 sixth grade
teacher per team• No more than 1 person per building per
team
RCCSD
RESEARCH
• Developing Effective Fractions Instruction for Kindergarten Through 8th Grade Practice Guide
RCCSD
RESEARCH
• Putting Essential Understanding of Fractions into Practice in Grades 3-5
RCCSD
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
CCSSM
Domains from Grade 3 to Grade 7:• Number and Operations – Fractions • Ratios and Proportional Relationships
RCCSD
Progressions Documents for the Common Core Math Standards
ICEBERG RCCSD
CCSSM
• The Standards for Mathematical Practices• Reasoning abstractly and quantitatively• Construct viable arguments and critique the
reasoning of others
RCCSD
CCSSMDelaware Department of Education
RCCSD
Mathematical Practices Student Dispositions Teacher Actions to Engage Students in Practices:
Reasoning and Explaining
Reason abstractlyand quantitatively
• Create multiple representations• Interpret problems in contexts• Estimate first/answer reasonable• Make connections• Represent symbolically• Talk about problems, real-life situations• Attend to units• Use context to think about a problem
• Develop opportunities for problem-solving strategies• Give time for processing and discussing• Tie content areas together to help make connections• Give real-world situations• Demonstrate thinking aloud for students’ benefit• Value invented strategies and representations• More emphasis on the process instead of on the
answer
Construct viablearguments andcritique thereasoning of others
• Ask questions• Use examples and counter examples• Reason inductively and make plausible arguments• Use objects, drawings, diagrams, and actions• Develop ideas about mathematics and support their
reasoning• Analyze others arguments• Encourage the use of mathematics vocabulary
• Create a safe environment for risk-taking and critiquing with respect
• Provide complex, rigorous tasks that foster deep thinking
• Provide time for student discourse• Plan effective questions and student grouping• Probe students
SMARTER BALANCED
• The Four Mathematical Claims• Concepts and Procedures• Problem Solving• Communicating Reasoning• Modeling and Data Analysis
• Enhancing the Technology-Enabled questions
RCCSD
SBAC – GRADE 5 MATHEMATICS
Mr. Jones will cut 6 identical loaves of bread into pieces that are loaf each.
Part A
After he cuts the 6 loaves, how many pieces will Mr.
Jones have? Show your work using numbers, words, and/
or pictures.
pieces
RCCSD
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
MRI – MARILYN BURNS
Which fraction is greater?
or
How did you decide?
RCCSD
Session 1: Equivalence and Comparison
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
Book Study RCCSD
Session 2: Addition and Subtraction
Putting Essential Understandings of Fractions into Practice - NCTM
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
CMP2Connected Mathematics Project
RCCSD
Session 3: Addition, Subtraction, and Multiplication
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
NUMBER STRING RCCSD
Session 4: Multiplication, Division, and Ratios
CONTENT FOCI
The Institute • Session 1: Equivalence and Comparison• Session 2: Addition and Subtraction• Session 3: Addition, Subtraction, and Multiplication• Session 4: Multiplication, Division, and Ratios• Session 5: Ratios
RCCSD
CMP2Connected Mathematics Project
RCCSD
Session 5: Ratios
MEASURING IMPACT
• Mathematical Knowledge for Teaching• District Created Walkthrough Tool• PLC Minutes• District Coach Observations• Anecdotal Information
RCCSD
FEEDBACK
What made learning easy or hard for you today?
• Group work with our tables is nice. • It is always great to work cooperatively.• I am in an awesome group!• Discussions within the group was easy.• Great group I work with!• Collaboration with teammates made it easier.• Staying in groups produced a lot of responses. At
this point we are getting comfortable with each other and can share at will.
RCCSD
