Sixth Grade · Math · week 17

Using the distributive property with sums

Use the GCF and the distributive property to rewrite a sum of two numbers as a product, and expand a product back into a sum.

The distributive property connects multiplication and addition: a × (b + c) = (a × b) + (a × c). You can use it in either direction - to expand a product into a sum, or to rewrite a sum back into a product.

To rewrite a sum like 18 + 24 as a product, find the GCF of the two numbers (here, 6), then divide each number by the GCF and put the results inside parentheses: 18 + 24 = 6 × (3 + 4).

Check your work by multiplying back out: 6 × (3 + 4) = 6 × 3 + 6 × 4 = 18 + 24. If it matches the original sum, the rewrite is correct.

📋 For the teacher

Teach it (10–15 min):

Connect this directly to last week's GCF skill - rewriting a sum as a product IS an application of the GCF.
Always check the rewritten form by multiplying back out; it should rebuild the original sum exactly.
Show both directions, expanding and rewriting, side by side so they see they undo each other.
Point out this is the same tool that will soon simplify algebraic expressions like 6x + 9.

Talk about it:

How does finding the GCF help you rewrite a sum as a product?
How can you check that you rewrote a sum correctly?
How does expanding a × (b + c) undo the rewrite?

Mastery looks like: They find the GCF of two numbers and use it to rewrite their sum as a product, and can expand a product back into a sum to check.

Common stumbles: Dividing only one of the two numbers by the GCF; using a common factor that is not the GREATEST one.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →AdditionSee groups combine — with counters, blocks, and the number line.try →

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →

Records attendance + 15 min of Math for this learner.

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