Lesson 2: Expanding Binomials: FOIL & Area Models

• How do we multiply two binomials?
• What does FOIL stand for?
• Why does the area model work?
• How can we check our answer?

Binomial, FOIL, First, Outer, Inner, Last, expand, area model

CCSS.MATH.9.A.SSE.A.2

Description: Students learn two methods to expand binomials: FOIL (First, Outer, Inner, Last) and area models. The area model uses rectangles divided into sections, helping students visualize why we get three terms. Students practice both methods and see they produce the same result. Purpose: To develop procedural fluency in expanding binomials and conceptual understanding through visual models. DOK Level: 2-3 (Application)

• Start with area models: More visual and concrete than FOIL
• For struggling learners: Use binomials with simple coefficients (x + 1)(x + 2)
• For advanced learners: Include binomials with larger coefficients or negative terms
• Step-by-step cards: Provide FOIL steps in order with color-coding

• Observation: Can students use area models correctly?

• Worksheet: Expand 5 binomials using area models

• Practice: Expand 4 binomials using FOIL

• Check-your-work: Verify expansion using substitution (plug in a number)

• Area model templates (drawn rectangles)

• Algebra tiles for area models

• FOIL step-by-step cards (color-coded)

• Practice worksheets (with visual supports)

• Resource: Desmos "Binomial Expansion"