Contexts for Learning Mathematics, Level 1 by Catherine Twomey Fosnot.
Contexts for Learning Mathematics, Level 1

Contexts for Learning Mathematics, Level 1

Investigating Number Sense Grades K-3

By Catherine Twomey Fosnot

Contexts for Learning Mathematics is a rigorous classroom resource that makes use of a math workshop environment to bring the Standards for Mathematical Practice to life. The Level 1 (grades K–3) package includes eight classroom-tested units (and supporting resources) that use rich, authentic contexts to promote understanding and ensure the development of a positive growth mindset.

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This product is part of the series:  The Context for Learning Mathematics Series

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Full Description

Learn more about the complete Contexts for Learning Mathematics resource at

Contexts for Learning Mathematics (CFLM) uses rich, authentic contexts provide a backdrop for fostering a positive growth mindset through:

  • the use of mathematical models as thinking tools
  • tenacious problem solving
  • the reading and writing of mathematical arguments and justification

Flexibly designed, CFLM units can be used to enhance your teaching, supplement your curriculum, or differentiate instruction. Each unit stands on its own, presenting a two-week sequence of interconnected investigations, games, and minilessons created to support key math topics.

Investigating Number Sense, Addition, and Subtraction (Grades K–3) is the first level in the Contexts for Learning Mathematics series. This package includes eight flexibly designed units for enhancing your teaching, supplementing your curriculum, or differentiating your instruction. The units in this package include:

  • Bunk Beds and Apple Boxes (Early Number Sense)
  • Organizing and Collecting (The Number System)
  • Beads and Shoes, Making Twos (Extending Number Sense)
  • The Double-Decker Bus (Early Addition and Subtraction)
  • Measuring for the Art Show (Addition on the Open Number Line)
  • Trades, Jumps, and Stops (Early Algebra)
  • Ages and Timelines (Subtraction on the Open Number Line)
  • The T-Shirt Factory (Place Value, Addition, and Subtraction)

Each unit can stand on its own, presenting a two-week sequence of interconnected investigations, games, and minilessons created to support the development of key topics in addition, subtraction, and place value.

Along with the units books, this package includes an Overview Book that provides a deeper dive into the content, strategies, and overall philosophy specific to these grade levels, eight Read-Aloud Books that set the stage for learning, three Resource Books containing strings of related minilessons for supporting instruction throughout the year, and access to Digital Resources that include extensive professional learning support.


Investigating Number Sense, Addition, and Subtraction (K–3) is organized around eight classroom-tested units.

Bunk Beds and Apple Boxes: Early Number Sense
by Catherine Twomey Fosnot
In Bunk Beds and Apple Boxes children learn about compensation and equivalence within the context of a pajama party during which eight excitable girls confound their babysitter by continually changing places on their bunk bed and also in a grocery store where a grocer arranges apples in different-sized trays. The arithmetic rack is introduced as a model for exploring part-whole relations.

Beads and Shoes, Making Twos: Extending Number Sense
by Madeline Chang and Catherine Twomey Fosnot
Beads and Shoes, Making Twos uses the context of walking hand in hand in two lines to explore doubles and even or odd numbers. A story about designing necklace patterns using two colors of beads creates a context for exploring the relationship between doubles and skip-counting and invites students to work with groups as units.

The Double-Decker Bus: Early Addition and Subtraction
by Maarten Dolk, Nina Liu, and Catherine Twomey Fosnot
The Double-Decker Bus, the story of a little girl’s efforts to count the passengers on fast-moving double-decker buses, introduces students to the benefits of using the five-structure to quickly calculate quantities. The arithmetic rack, whose beads mirror the organization of seats on the buses, provides a model for solving addition and subtraction problems.

Organizing and Collecting: The Number System
by Nina Liu, Maarten Dolk, and Catherine Twomey Fosnot
In Organizing and Collecting the hopelessly disorganized Masloppy family’s efforts to keep track of their things create a context for investigating place value patterns and efficient ways to count with five- and ten-structures. As the unit progresses, children develop place value and addition strategies.

Measuring for the Art Show: Addition on the Open Number Line
by Catherine Twomey Fosnot
Measuring for the Art Show builds on children’s early addition and measurement strategies within the context of preparing labels for an art show. The open number line is developed as a model for recording children’s addition and subtraction strategies.

Trades, Jumps, and Stops: Early Algebra
by Catherine Twomey Fosnot and Patricia Lent
In Trades, Jumps, and Stops, the equitable distribution of funds from the Masloppy piggy bank to finance a family trip introduces big ideas and strategies in algebra, including using substitution to examine for equivalence and using associative and commutative properties to make equivalent expressions. The double number line is used as a model for understanding exchange and equivalence.

Ages and Timelines: Subtraction on the Open Number Line
by Catherine Twomey Fosnot
Ages and Timelines begins with the story of eight-year-old Carlos’s visit with his great-grandfather. Carlos’s fascination with his great-grandfather’s beautiful silver hair, and the time it will take him to grow a similar mane, initiates a family-wide investigation into age differences. The context of age differences and the open number line model support the development of subtraction strategies.

The T-Shirt Factory: Place Value, Addition, and Subtraction
by Catherine Twomey Fosnot
Students revisit the Masloppy family in The T-Shirt Factory as Grandma Masloppy launches a lucrative T-shirt business. This context and follow-up simulations highlight place value, regrouping, equivalence, and systematic exchange. As the unit progresses, standard addition and subtraction algorithms are explored, and the concept of place value is developed to four places.

Companion Resources

Common Core Math Standards crosswalk to the CFL Math series