GROCERIES, STAMPS, and
MEASURING STRIPS
INTRODUCTION and EARLY
DEVELOPMENT of MULTIPLICATION
Presented by:
BARBARA BROWN, Grapeland ISD
JANE DICKSON, Magnolia ISD
MAURA ROACH, Centerville (Trinity) ISD
LISA SMITH, Coldspring-Oakhurst CISD
SUSAN BOHAN, ESC 6 TRC-M Project Director
ABOUT the AUTHORS
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FRANS van GALEN
Researcher and developer of
mathematics at the
Freudenthal Institute in the
Netherlands.
Coauthor of Dutch math
programs for the primary
levels.
Coauthor of Mathematics in
Context, a program for middle
school mathematics.
Developer of internet math
games and puzzles.
CATHERINE T. FOSNOT
• Professor of Education and
Director of Mathematics , City
College of New York.
• Author and coauthor of many
books and articles on
mathematics education, most
recently, the YOUNG
MATHEMATICIANS at WORK
series and the accompanying
professional development
materials funded by NSF.
• “Significant Contribution”
award.
YOUNG MATHEMATICIANS at WORK
• Describes and illustrates what it means to do and learn
mathematics.
• Provides strategies to turn classrooms into math workshops
that encourage and reflect mathematizing.
• Examines ways to engage and support students as they
construct math strategies and big ideas.
• Defines and provides examples of mathematical modeling
relative to context.
• Describes how to strengthen performance and portfolio
assessment.
• Emphasizes teachers as learners, facilitators, and
mathematicians.
CONTEXTS for LEARNING
MATHEMATICS grades 3 - 5
INVESTIGATING MULTIPLICATION and DIVISION:
1. GROCERIES, STAMPS, and MEASURING STRIPS:
Early Multiplication
2. THE BIG DINNER: Multiplication with the Ratio
Table
3. MUFFLES’ TRUFFLES: Multiplication and Division
with the Array
4. THE TEACHERS’ LOUNGE: Place Value and
Division
5. THE BOX FACTORY: Extending Multiplication with
the Array
GROCERIES, STAMPS, and
MEASURING STRIPS
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UNIT OVERVIEW
Day 1: INSIDE THE GROCERY STORE
Day 2: POSTAGE STAMPS
Day 3: DESIGNING YOUR OWN STAMPS
Day 4: HOW LONG? HOW TALL?
Day 5: THE CITY CENTER
Day 6: MEASURING STRIPS
Day 7: MORE MEASURING STRIPS
Day 8: WINDOWS & NUMBER LINE MYSTERIES
Day 9: THE BAKER’S TRAYS & MORE NUMBER LINE MYSTERIES
Day 10: PATIOS, STICKERS, & REFLECTIONS
Reflections on the Unit
Appendixes A - Q
THE LANDSCAPE of LEARNING
BIG IDEAS
STRATEGIES
MODELS
THE LANDSCAPE of LEARNING
BIG IDEAS
• Unitizing
• Repeated addition can be regrouped
• The distributive property of multiplication (over
addition and over subtraction)
• The commutative property of multiplication
• The place value patterns that occur when
multiplying by the base
THE LANDSCAPE of LEARNING
STRATEGIES
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Using repeated addition
Skip Counting
Doubling
Using partial products
Using five-times and ten-times
Doubling and halving
THE LANDSCAPE of LEARNING
MODELS
• Open number lines
• T – chart or ratio table
• Arrays
INSIDE the GROCERY STORE
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Developing the Context
Supporting the Investigation
Preparing for the Math Congress
Facilitating the Math Congress
Reflections on the Day
Assessment Tips