# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic B: Special Notations of Operations
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).

Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic C: Replacing Letters and Numbers
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).

Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic D: Expanding, Factoring, and Distributing Expressions
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.

Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic E: Expressing Operations in Algebraic Form
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.

Subject: Mathematics (6)
Title: Grade 6 Mathematics Module 4, Topic F: Writing and Evaluating Expressions and Formulas