ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] (6) 14 :
14. Write, evaluate, and compare expressions involving whole number exponents.
[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.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic B: Special Notations of Operations
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-b-overview
Description:

In Module 4, Topic B, students experience special notations of operations. They determine that 3x = x + x + x is not the same as x3, which is x times x times x.  Applying their prior knowledge from Grade 5, where whole-number exponents were used to express powers of ten (5.NBT.A.2), students examine exponents and carry out the order of operations, including exponents. Students demonstrate the meaning of exponents to write and evaluate numerical expressions with whole-number exponents (6.EE.A.1).



   View Standards     Standard(s): [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) 17 :
17. Determine whether two expressions are equivalent and justify the reasoning.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic C: Replacing Letters and Numbers
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-c-overview
Description:

Students represent letters with numbers and numbers with letters in Module 4, Topic C. In past grades, students discovered properties of operations through example (1.OA.B.3, 3.OA.B.5). Now, they use letters to represent numbers in order to write the properties precisely. Students realize that nothing has changed because the properties still remain statements about numbers. They are not properties of letters, nor are they new rules introduced for the first time. Now, students can extend arithmetic properties from manipulating numbers to manipulating expressions.  In particular, they develop the following identities: a times b = b times aa + b = b + ag times 1 = gg + 0 = gg divided by 1 = gg divided by g = 1, and 1 divided by g = 1/g.  Students understand that a letter in an expression represents a number. When that number replaces that letter, the expression can be evaluated to one number. Similarly, they understand that a letter in an expression can represent a number. When that number is replaced by a letter, an expression is stated (6.EE.A.2).



   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.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic D: Expanding, Factoring, and Distributing Expressions
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-d-overview
Description:

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 · = 2a, (a + b) + (a + b) = 2 · (a + b) = 2(a + b) = 2a + 2b, and a ÷ b = a/b.



   View Standards     Standard(s): [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.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic E: Expressing Operations in Algebraic Form
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-e-overview
Description:

In Module 4, Topic E, students express operations in algebraic form. They read and write expressions in which letters stand for and represent numbers (6.EE.A.2). They also learn to use the correct terminology for operation symbols when reading expressions. For example, the expression 3/(2x - 4) is read as “the quotient of three and the difference of twice a number and four.” Similarly, students write algebraic expressions that record operations with numbers and letters that stand for numbers. Students determine that 3a + b can represent the story “Martina tripled her money and added it to her sister’s money” (6.EE.A.2b).  A Mid-Module Assessment follows Topic E.



   View Standards     Standard(s): [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) 18 :
18. Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true.
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic F: Writing and Evaluating Expressions and Formulas
URL: https://www.engageny.org/resource/grade-6-mathematics-module-4-topic-f-overview
Description:

Students write and evaluate expressions and formulas in Module 4, Topic F. They use variables to write expressions and evaluate those expressions when given the value of the variable (6.EE.A.2). From there, students create formulas by setting expressions equal to another variable. For example, if there are 4 bags containing c colored cubes in each bag with 3 additional cubes, students use this information to express the total number of cubes as 4c + 3.  From this expression, students develop the formula t = 4c + 3, where t is the total number of cubes. Once provided with a value for the amount of cubes in each bag (c = 12 cubes), students can evaluate the formula for t:  t = 4(12) = 3, t = 48 + 3, t = 51. Students continue to evaluate given formulas such as the volume of a cube, V = s3 given the side length, or the volume of a rectangular prism, V = lwh given those dimensions (6.EE.A.2c).



ALEX Classroom Resources: 5

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