options: Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Activity
In this activity students continue the work of generating equivalent expressions as they decide where to place a set of parentheses and explore how that placement affects the expressions.
Launch
Arrange students in groups of 2. Tell students to first complete both questions independently. Then, trade one of their expressions with their partner. The partner’s job is to decide whether the new expression is equivalent to the original or not, and explain how they know.
Student Facing
Diego was taking a math quiz. There was a question on the quiz that had the expression
\(8x - 9 - 12x + 5\)
. Diego’s teacher told the class there was a typo and the expression was supposed to have one set of parentheses in it.
Where could you put parentheses in
\(8x - 9 - 12x + 5\)
to make a new expression that is still equivalent to the original expression? How do you know that your new expression is equivalent?
Where could you put parentheses in
\(8x - 9 - 12x + 5\)
to make a new expression that is not equivalent to the original expression? List as many different answers as you can.
Student Response
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Anticipated Misconceptions
Students may not realize that they can break up a term and place a parentheses, for example, between the 8 and
\(x\)
in the term
\(8x\)
. Clarify that they may place the parentheses anywhere in the expression.
Activity Synthesis
Questions for discussion:
“How can you write the original expression in different ways with fewer terms?” (
\(\text-4x-4\)
,
\(\text-4(x+1)\)
,
\(4(-x-1)\)
)
“Where did you place the parentheses to create an equivalent expression?”
“Share other ways you placed parentheses and the resulting expression with fewer terms.”
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary.  Include the following terms and maintain the display for reference throughout the unit: parenthesis. The display should include examples of how to create equivalent expressions using parentheses by breaking up the components. Be sure to emphasize how the placement of the parentheses affects the expression.
Supports accessibility for: Memory; Language
Speaking, Writing: MLR8 Discussion Supports.
When students interpret the new expression they receive, ask students to press their partner for more details in their explanations by challenging an idea, or asking for an example. Listen for, and amplify language students use to describe how the parentheses influence the resulting expression with fewer terms. This will help call students' attention to the types of details and language to look for to determine if an expression is equivalent to another or not.
Design Principle(s): Maximize meta-awareness; Support sense-making


correct_option_index: 3