ALEX Resources

   View Standards     Standard(s): [MA2019] (6) 7 :

7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

[MA2019] (6) 16 :

16. Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

This video lesson introduces distributive property. Students recall the use of rectangle diagrams to represent the distributive property and work with equations involving the distributive property with both addition and subtraction.

   View Standards     Standard(s): [MA2019] (6) 7 :

7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

[MA2019] (6) 16 :

16. Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

The purpose of this video lesson is to apply the distributive property to situations where one of the quantities is represented by a variable, as in 2 (x + 3) = 2x + 2 • 3. Students use rectangle diagrams to represent these situations, reinforcing the idea that the work with expressions is an extension of the work with numbers. They see that the distributive property can arise out of writing areas of rectangles in two different ways, emphasizing equivalent expressions as two different ways of writing the same quantity.

   View Standards     Standard(s): [MA2019] (6) 7 :

7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

[MA2019] (6) 8 :

8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

a. Use factors and multiples to determine prime factorization.

In Module 2, Topic D, students think logically about multiplicative arithmetic. Students apply odd and even number properties and divisibility rules to find factors and multiples. They extend this application to consider common factors and multiples and find the greatest common factors and least common multiples. Students explore and discover that Euclid’s Algorithm is a more efficient way to find the greatest common factor of larger numbers and see that Euclid’s Algorithm is based on long division.   

   View Standards     Standard(s): [MA2019] (6) 7 :

7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.

[MA2019] (6) 8 :

8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

a. Use factors and multiples to determine prime factorization.

[MA2019] (6) 15 :

15. Write, read, and evaluate expressions in which letters represent numbers in real-world contexts.

a. Interpret a variable as an unknown value for any number in a specified set, depending on the context.

b. Write expressions to represent verbal statements and real-world scenarios.

c. Identify parts of an expression using mathematical terms such as sum, term, product, factor, quotient, and coefficient.

d. Evaluate expressions (which may include absolute value and whole number exponents) with respect to order of operations.

[MA2019] (6) 16 :

16. Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive.

In Module 4, Topic D, students become comfortable with new notations of multiplication and division and recognize their equivalence to the familiar notations of the prior grades. The expression 2 × b is exactly the same as 2 · b and both are exactly the same as 2b.  Similarly, 6 ÷ 2 is exactly the same as 6/2. These new conventions are practiced to automaticity, both with and without variables. Students extend their knowledge of the greatest common factor and the distributive property from Module 2 to expand, factor and distribute expressions using new notation (6.NS.B.4). In particular, students are introduced to factoring and distributing as algebraic identities.  These include:  a + a = 2 · a = 2a, (a + b) + (a + b) = 2 · (a + b) = 2(a + b) = 2a + 2b, and a ÷ b = a/b.