In module 4, students work with numerical and algebraic expressions and equations. First, they learn that exponents represent repeated multiplication, evaluate powers with whole number, fraction, and decimal bases, and use the order of operations to evaluate numerical expressions. Then, students learn why and how to use variables to represent unknown numbers and quantities. They write and evaluate algebraic expressions and use properties of operations to generate equivalent expressions. Students reason about and solve single-variable, one-step equations, and they understand the meaning of a solution to an equation or inequality. At the end of the module, they revisit ratio relationships and write and graph equations in two variables, identifying independent and dependent variables in real-world situations.
In topic C, students write and identify equivalent algebraic expressions. Students use the distributive property to write products as sums or differences, to factor algebraic expressions, and to combine like terms.
6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor.
6.C.6: Apply the order of operations and properties of operations (identity, inverse, commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property) to evaluate numerical expressions with nonnegative rational numbers, including those using grouping symbols, such as parentheses, and involving whole number exponents.
6.AF.1: Evaluate expressions for specific values of their variables, including expressions with whole-number exponents and those that arise from formulas used in geometry and other real-world problems.
6.AF.2: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them.
6.AF.3: Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.
I can...
Write and identify equivalent algebraic expressions involving multiplication and division by using the properties of operations.
Write algebraic expressions that represent real-world situations.
Lesson at a Glance
This lesson begins with students working with a partner to write and evaluate multiplication and division expressions that represent real-world situations. Students write terms efficiently by using as few factors as possible and learn to write terms as products of their factors. In a class discussion, students explain that terms written with as few factors as possible allow for efficient evaluation. In a game of bingo, students identify equivalent algebraic expressions.
I can...Use the distributive property to write the product of two factors as a sum or difference.
Lesson at a Glance
In this lesson, students consider rectangles made up of two smaller rectangles. At first, both side lengths of the rectangle are known; later, one side length is unknown. Students write two expressions that each represent the area of the new rectangle formed: one that is a product of two factors and one that is a sum of two products. They write two expressions that each represent the area of one of the smaller rectangles: one that is a product of two factors and one that is a difference of two products. Students use the distributive property to show why the expressions are equivalent. In pairs, students complete several sequences of problems to practice using the distributive property to write equivalent expressions.
I can...Use the distributive property to write a sum or difference as the product of two factors.
Lesson at a Glance
In this lesson, students are given an expression with two terms that represents the area of a large rectangle composed of smaller rectangles. They write expressions to represent the side lengths and areas of the smaller rectangles. Working in pairs, students determine different numbers of treat bags that can be made from a given number of lollipops and candies. Using the distributive property, students write multiple expressions as products of factors, with each expression being equivalent to a given expression. Students progress to using the greatest common factor and the distributive property to factor expressions written as both sums and differences.
I can...
Add and subtract like terms by using the distributive property.
Write an algebraic expression that represents a geometric situation.
Lesson at a Glance
In this digital lesson, students write several expressions that represent the total area of a rectangle and explain why the expressions are equivalent. Students use area models to make connections between using the distributive property to write expressions and adding and subtracting like terms. Students then write expressions from information about angles and their measures and use the distributive property to add like terms.
Use the digital platform to prepare for and facilitate this lesson. Students will also interact with lesson content and activities via the digital platform.
If student computers or devices are not available, use the alternate version of this lesson.
I can...
Write equivalent expressions by using the properties of operations and combining like terms.
Write algebraic expressions that represent real-world situations.
Lesson at a Glance
In this lesson, students write equivalent expressions by applying the distributive property to expand expressions before combining like terms. Students identify equivalent expressions. Students write and evaluate algebraic expressions that represent real-world situations. With a partner, students use the Co-construction routine to write a real-world situation that can be represented by a given expression.