Lesson 2

Factor Pairs

Lesson Purpose

The purpose of this lesson is for students to learn the meaning of factor pairs by building rectangles with a specified area.

Lesson Narrative

In grade 3, students learned that a factor is a number being multiplied by another number. For instance, when we multiply 3 and 5 to find the total in 3 groups of 5, or to find the area of a rectangle that is 3 units by 5 units, the 3 and 5 are factors. In this lesson, students learn that a factor pair of a number \(n\) is a pair of whole numbers that multiply to result in \(n\). For example, 3 and 5 a factor pair of 15.

Previously, students made sense of multiples of a number in the context of area: they built and drew rectangles with given a side length and reasoned about their area. Here, they use the same context to make sense of factor pairs. Students build and draw rectangles with a given area and reason about their side lengths. Students then analyze the rectangles that the class has drawn in a gallery walk. They make observations about the side lengths of the rectangles and consider whether all possible rectangles have been drawn for each area. In these activities, a rectangle with 3 rows and 2 columns is considered the same as a rectangle with 2 rows and 3 columns.

Math Community

Tell students they will have an opportunity to revise their “Mathematical Community” ideas at the end of this lesson, so as they work today they should think about actions that may be missing from the current list.

  • Engagement

Learning Goals

Teacher Facing

  • Find side lengths of different rectangles with a given area.
  • Understand that each side length of a rectangle is a factor of its area.

Student Facing

  • Let’s learn about factor pairs.

Required Materials

Materials to Gather

Materials to Copy

  • Centimeter Grid Paper - Standard

Required Preparation

Activity 1:

  • Each of the 8 groups needs tools for creating a visual display.

CCSS Standards

Building On


Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

Which question asked during the synthesis gave the most information about students' understanding of the learning goal for the lesson? What did you hear or see that made you feel this way?

Suggested Centers

  • Can You Build It? (3–5), Stage 2: Multiple Rectangles (Addressing)
  • Can You Build It? (3–5), Stage 1: Rectangles (Supporting)
  • Capture Squares (1–3), Stage 7: Multiply with 6–9 (Supporting)

Print Formatted Materials

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Additional Resources

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