Multiplication and the Meaning of the Factors

Author: Great Minds, as featured on EngageNY

  • Description
  • Files

What we like about this set of lessons


  • Uses repeated addition as an entrance point (not an ending point) for students learning the meaning of multiplication as equal groups (3.OA.A.1)
  • Devotes significant time to understanding the concept of multiplication as opposed to the operation of multiplication
  • Starts the year right away with major work of the grade, and begins the journey towards an important fluency expectation (3.OA.A.2)
  • Connecting repeated addition number sentences to multiplication number sentences gives students opportunities to look for and make use of structure (MP.7)

In the classroom:

  • Uses multiple concrete representations and visual models to make the mathematics explicit
  • Prompts students to share their developing thinking and understanding (Student Debrief and throughout lessons)
  • Provides opportunities and suggestions for differentiation
  • Gives formal and informal opportunities for teachers to check for understanding

  • Making the Shifts

    How does this set of lessons exemplify the instructional Shifts required by CCSSM?

    Focus Belongs to the major work of third grade
    Coherence Builds upon second grade work with equal groups of objects (2.OA.C.4) and lays the foundation for much of the work in third grade

    Conceptual Understanding: primary in these lessons (3.OA.A.1)

    Procedural Skill and Fluency: secondary in these lessons

    Application: secondary in these lessons (3.OA.A.3)

  • Additional Thoughts

    It's important to note that these sample lessons are the first in a 21-lesson unit called Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10. It is not intended for students to meet the full expectations of the grade-level standards addressed in these lessons through only these two selected lessons. These sample lessons lay a strong foundation for the work that is to come in third grade. 

    The structure of these lessons and the unit/curriculum overall have some interesting aspects to highlight. The units make explicit the coherence within the fully developed curriculum. Each topic (a set of lessons) is connected to prior learning and also points to the next lesson that follows in the learning progression. Within individual lessons, there are a number of components that add to their strength including daily fluency practice, variety in questioning techniques, and daily opportunities for students to debrief about their learning.

Supplemental Resources