Florida B.E.S.T. MA.8.AR.1.3

Math8th GradeGenerate equivalent algebraic expressions.

The Standard

Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students find the greatest number and variable factors shared by two terms. They pull out that factor and use the distributive property to write an equivalent product.
What Mastery Looks Like: A student can rewrite 12x² + 18x as 6x(2x + 3). They can explain why 6x is the greatest shared factor and verify by distributing.
Common Misconceptions: Students may factor out only the number and ignore shared variables. They may subtract exponents instead of using the smaller exponent, or stop before finding the greatest common factor.
How to Assess It: Exit ticket: Factor 18x³y + 24x²y² completely, then distribute your answer to check it.

Lesson moves

Give students factor cards for 12x² and 18x, then have them remove shared cards and write the remaining product.
Ask: Why is 6x the greatest common monomial in 12x² + 18x? Students justify the coefficient and variable exponent.
Create matching cards with two-term expressions, factored forms, and distractors; pairs race to make correct matches and verify by distributing.
Sketch adjacent rectangles with areas 12x² and 18x sharing height 6x, then find and label their combined width.

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