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.
Students transition from numerical expressions to algebraic expressions in topic B as they learn why and how to use variables to represent unknown numbers and quantities. Students learn to precisely define variables as values with units and to identify constraints on variables. When representing mathematical and real-world descriptions with algebraic expressions, students use common conventions and recognize how subtle variations in wording indicate different meanings.
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.3: Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values.
5.AT.8: Define and use up to two variables to write linear expressions that arise from real-world problems, and evaluate them for given values.
I can...
Write algebraic expressions to represent descriptions involving addition and subtraction.
Write descriptions of algebraic expressions involving addition and subtraction.
Lesson at a Glance
In this lesson, students reason about the ages of three siblings when given clues about the siblings’ ages. Then students evaluate numerical expressions, recognize repeated patterns, and write algebraic expressions. When given algebraic expressions involving addition or subtraction, students evaluate the expressions for different values of the variable and write descriptions of the expressions. In pairs, students sort descriptions based on whether the descriptions describe addition or subtraction. Then partners write algebraic expressions to represent the descriptions. This lesson formally defines numerical expression, algebraic expression, and equivalent expression and adds new mathematical definitions for variable and expression.
I can...
Write algebraic expressions to represent descriptions involving addition, subtraction, multiplication, and division.
Write descriptions of algebraic expressions involving addition, subtraction, multiplication, and division.
Lesson at a Glance
Students begin this lesson by reasoning about two similar but different algebraic division expressions. In a Whiteboard Exchange, students transition from writing numerical expressions to writing algebraic expressions. Students learn to write multiplication and division expressions efficiently by using common conventions. For example, students learn to write the product of 3 and x as 3x. Students write algebraic expressions to represent descriptions and write descriptions of algebraic expressions for multiplication and division expressions and then for expressions with multiple operations.
This lesson formally defines the terms term and coefficient.
I can...
Define variables precisely.
Write algebraic expressions involving addition and subtraction to represent real-world situations.
Lesson at a Glance
In this lesson, students recognize that the size of a quantity is unclear without the units of the quantity. Students apply this understanding when they define variables precisely, including defining units, and write algebraic expressions to represent real-world situations. Students participate in the Co-construction routine and define a variable to represent one quantity in a situation. They determine the necessary operation and write an algebraic expression that represents another quantity in the situation. Working with a partner, students complete problems that involve writing addition and subtraction expressions from given situations and writing situations that can be represented by given algebraic expressions. This lesson introduces the verb define.
I can...
Write and interpret algebraic expressions involving multiplication and division that represent real-world situations.
Lesson at a Glance
In this lesson, students represent a variety of real-world situations with algebraic expressions. Students choose whether to represent situations with multiplication or division, and they discuss how a situation can be represented by both operations. Through discussion and partner work, students define variables, identify constraints on variables, write and compare algebraic expressions, and interpret the meanings of coefficients. Finally, students use the Co-construction routine to contextualize an algebraic expression.
I can...
Write algebraic expressions with two terms to represent real-world situations involving addition and multiplication.
Lesson at a Glance
In this digital lesson, students make predictions about the cost of a ride to various destinations. Students are given feedback about their predictions as the car drives to the destination and as the miles and cost are revealed. After several predictions, students decide that they need more information to write an expression for the total cost of the ride. Through an interactive, students use a table to describe the rideshare situation with words and then write an expression to represent the total cost of the ride. Students then look at different real-world situations and write expressions to describe the situations. Finally, students compare verbal descriptions of the expressions they wrote.
Use the digital platform to prepare for and facilitate this lesson. Students will also interact with the lesson content and activities via the digital platform.
If student computers or devices are not available, use the alternate version of this lesson.