options: Understand and apply properties of operations and the relationship between addition and subtraction.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

Work with equal groups of objects to gain foundations for multiplication.

Rewrite rational expressions.

Work with addition and subtraction equations.

Understand properties of multiplication and the relationship between multiplication and division.

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Generate and analyze patterns.

Solve systems of equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Use polynomial identities to solve problems.

Understand the connections between proportional relationships, lines, and linear equations.

Interpret the structure of expressions.

Solve equations and inequalities in one variable.

Use properties of operations to generate equivalent expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.
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: 29