ALEX Classroom 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) 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.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 10 :

10. Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators.

[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 this interactive activity, students will be led through steps to add and subtract fractions with unlike denominators. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught in the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.