In this Grade 5 Eureka Math lesson from Chapter 26, students learn to interpret and evaluate numerical expressions using the language of scaling and fraction division. They practice translating word-form expressions into numerical notation — such as "twice the sum of" or "half the sum of" — applying order of operations and parentheses correctly. The lesson also reinforces dividing decimals and partitive fraction division as foundational skills for understanding how expressions scale quantities up or down.
Section 1
Translating Grouping Phrases with Parentheses
Verbal phrases like "the sum of," "the difference between," or "the product of" indicate that the operation and its numbers should be grouped together using parentheses. This group is treated as a single value within the larger expression.
Section 2
Translate Numerical Expressions into Verbal Phrases
To translate a numerical expression into a verbal phrase, identify the operations and their order based on PEMDAS. The operation performed last often forms the main structure of the phrase. Use grouping words (e.g., "the sum of," "the quantity," "the difference between") for operations within parentheses or those that must be performed first.
Section 3
Evaluate Multi-Step Expressions with Fractions and Decimals
To evaluate a multi-step expression, follow the order of operations (PEMDAS):
Section 4
Matching Expressions to Word Problems
To match a numerical expression to a word problem, analyze the problem to identify the quantities and the sequence of mathematical operations. The correct expression will use numbers, operators, and parentheses to model the exact structure and order of events described in the problem.
Expand to review the lesson summary and core properties.
Section 1
Translating Grouping Phrases with Parentheses
Verbal phrases like "the sum of," "the difference between," or "the product of" indicate that the operation and its numbers should be grouped together using parentheses. This group is treated as a single value within the larger expression.
Section 2
Translate Numerical Expressions into Verbal Phrases
To translate a numerical expression into a verbal phrase, identify the operations and their order based on PEMDAS. The operation performed last often forms the main structure of the phrase. Use grouping words (e.g., "the sum of," "the quantity," "the difference between") for operations within parentheses or those that must be performed first.
Section 3
Evaluate Multi-Step Expressions with Fractions and Decimals
To evaluate a multi-step expression, follow the order of operations (PEMDAS):
Section 4
Matching Expressions to Word Problems
To match a numerical expression to a word problem, analyze the problem to identify the quantities and the sequence of mathematical operations. The correct expression will use numbers, operators, and parentheses to model the exact structure and order of events described in the problem.