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 A, students write, interpret, and evaluate numerical expressions. Students learn that exponents represent repeated multiplication, and they evaluate powers with whole number, fraction, and decimal bases. Through an exploration of the hierarchy of operations, students learn the conventional order of operations and then apply it to evaluate numerical expressions.
6.C.5: Evaluate positive rational numbers with whole number exponents.
I can...
Evaluate expressions with addition and subtraction.
Lesson at a Glance
In this lesson, students begin by playing a game in which they roll dice and add and subtract the numbers they roll to get a score closest to the number 13. Then, by using interlocking cubes to model expressions with addition and subtraction of three terms, students find that the answer is not always the same if they rearrange the numbers or operations in expressions. Students also realize that performing the operations in a different order does not always result in the same answer. Thus, students conclude that they should add and subtract numbers from left to right to be sure their answers are correct. In pairs, students evaluate more complex expressions with addition and subtraction of more than three terms.
I can...
Evaluate expressions with multiplication and division.
Lesson at a Glance
In this lesson, students begin by playing a game in which they roll a die and multiply or divide the numbers they roll to get a score closest to the number 13. Then, by using interlocking cubes to model expressions with multiplication and division, students find that the answer is not always the same if they rearrange the numbers or operations in the expressions. Students also realize that performing the operations in a different order does not always result in the same answer. They conclude that they should multiply and divide numbers from left to right to be sure their answers are correct. In pairs, students evaluate more complex expressions with multiplication and division of multiple numbers. This lesson introduces the dot operator for multiplication.
I can...
Write numerical expressions by using exponential notation.
Lesson at a Glance
In this digital lesson, students explore repeated multiplication by observing patterns found in the Sierpinski triangle and the Sierpinski carpet. Students use these patterns to write numbers in expanded form and then with exponential notation. Then students identify and interpret how the base and the exponent affect the magnitude of the number. By analyzing graphs and tables, students compare two money situations involving repeated addition and repeated multiplication. Students then apply their understanding of exponential notation by using exponents to express the prime factorization of a number. During the lesson, students are reminded of the terms exponent and power. This lesson introduces the terms exponential notation and base.
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.
I can...
Evaluate numerical expressions written in exponential notation.
Lesson at a Glance
This lesson begins with a paper folding activity in which students model mathematical situations by using exponents. Then students use geometric models of squares and cubes to write expressions in exponential notation for the area of each square and the volume of each cube. In a Whiteboard Exchange, students evaluate numerical expressions with squared and cubed numbers. Students evaluate powers with whole number, fraction, and decimal bases. Lastly, students work in pairs through three sets of exponent challenge activities.
This lesson introduces the terms squared and cubed.
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Identify the relationships between operations and apply those relationships when evaluating expressions.
Lesson at a Glance
Students begin this lesson by determining which diagram represents a given numerical expression. Through teacher-led and partner discussion, students explore why multiplication and division occur before addition and subtraction in the order of operations. Students examine how grouping symbols affect the order of operations and how fraction bars can serve as grouping symbols. Students identify and correct errors in work for evaluating expressions.
I can...
Evaluate numerical expressions with exponents by using the conventional order of operations.
Lesson at a Glance
To begin the lesson, students use five different digits to complete an order of operations puzzle that involves exponents. Students explore and then explain why powers are evaluated before multiplication, division, addition, or subtraction. With a partner, students evaluate expressions with exponents, grouping symbols, and all four operations. Students learn about various types of grouping symbols and examine how changing the location of parentheses in an expression can change the value of the expression. To conclude the lesson, students use the Critique a Flawed Response routine to identify and correct mistakes in order of operations work.