In this lesson, students analyze and interpret images of discrete objects (connecting cubes) and discrete tape diagrams in which each unit is visible. These diagrams are precursors for more abstract tape diagrams that are used in future lessons.
Students also make connections between the multiplicative comparison language and multiplication equations. For example, they interpret “15 is 3 times as many as 5” as \(15 = 3 \times 5\) or \(15 = 5 \times 3\).
In this unit, the convention of representing the multiplier as the first factor in equations is used. Students may write the factors in any order. In later lessons, students write division equations to represent multiplicative comparisons using their understanding of the relationship between multiplication and division.
This lesson gives students an opportunity to make sense of each equation and how it relates to a corresponding image or diagram (MP2).
Activity 2: Diagrams to Solve Multiplicative Comparison Problems
- Interpret different representations of multiplicative comparison (situations, diagrams, and equations).
- Let’s make sense of representations of problems with “times as many.”
Materials to Gather
|Activity 1||20 min|
|Activity 2||15 min|
|Lesson Synthesis||10 min|
Teacher Reflection Questions
- How Close? (1–5), Stage 6: Multiply to 3,000 (Addressing)
- How Close? (1–5), Stage 5: Multiply to 100 (Supporting)
- Five in a Row: Multiplication (3–5), Stage 2: Factors 1–9 (Supporting)