Students split numbers in area models, expand and factor expressions with variables, and use the distributive property for a cost story and mental math.
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Splitting 8 × 57 into 8 × 50 and 8 × 7 on a rectangle shows students why a(b + c) = ab + ac works. They draw the same kind of split for six products. Page 2 moves to variables: six expressions to expand, two with a negative number outside the parentheses, such as −2(5k − 4), and four to factor, including 18x + 12. A story about 6 art kits has students write the cost both ways. The answer key accepts any correct area-model split.
Watch item 9, −3(a + 6): students often write −3a + 18, applying the negative to the first term only. Have them write −3 × a and −3 × 6 as separate steps first.
On the factor items, students often pull out a common factor that isn't the greatest, such as 3(6x + 4) for 18x + 12. Ask whether the two terms left inside still share a factor.
Ways to adjust the three parts for different students.
Each one is checked against the official document. Where the resource covers only part of a standard, the note says so.
Students split a number into parts, multiply each part and add the results (area models, the art-kit cost problem and the times-99 trick), which is the distributive property. Grade 7 does not name expanding expressions with letters such as 5(x + 3), which makes up Part 2.
Students find the greatest common factor of two terms and write it outside the brackets, for example 18x + 12 = 6(3x + 2). Only four items use this skill, and lowest common multiples are not covered.
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