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The eight units in Investigating Number Sense, Addition, and Subtraction (Grades K-3) support the development of such fundamental topics as place value, compensation and equivalence, addition and subtraction on the open number line, and the efficient use of the five- and ten-structures.

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.

Grades K–3

– Overview Book
– Unit Books
– Read-Aloud Books
– Resource Guides
– Online Resources
  • Sequence of Instruction
  • Landscape of Learning
  • Samples
  • Buy Now
  • Young Mathematicians At Work book and CDs

    Grades 3–5
    Grades 4–6