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

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

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

Work with addition and subtraction equations.

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

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Represent and analyze quantitative relationships between dependent and independent variables.

Generate and analyze patterns.

Analyze patterns and relationships.

Multiply and divide within 100.

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

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve systems of equations.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Gain familiarity with factors and multiples.

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

Rewrite rational expressions.

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

Interpret the structure of expressions.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Perform arithmetic operations on polynomials.

Use polynomial identities to solve problems.

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

Understand and apply properties of operations and the relationship between addition and subtraction.
problem_activity: Warm-up
The purpose of this warm-up is for students to revisit ideas they learned in the previous lesson about balanced hangers:
You can add or subtract the same thing on each side and the hanger stays in balance.
You can divide each side by the same number and the hanger stays in balance.
Launch
Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Facing
Figures A, B, C, and D show the result of simplifying the hanger in Figure A by removing equal weights from each side.
[IMG]
Here are some equations. Each equation represents one of the hanger diagrams.
\(2(x + 3y) = 4x + 2y\)
\(2y = x\)
\(2(x + 3y) + 2z = 2z + 4x + 2y\)
\(x + 3y = 2x + y\)
Write the equation that goes with each figure:
A:
B:
C:
D:
Each variable (
\(x\)
,
\(y\)
, and
\(z\)
) represents the weight of one shape. Which goes with which?
Explain what was done to each equation to create the next equation. If you get stuck, think about how the hangers changed.
Student Response
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Anticipated Misconceptions
Some students may think a variable stands for more than one object. Tell these students that a variable only stands for one object, as it also only represents one number.
Activity Synthesis
Ask students to explain how they decided on the matching equation. As students discuss the final questions, highlight responses that emphasize the same objects being removed from each side creates the next figure in line. The exception to this is the move from Hanger B to Hanger C, where the number of objects on each side is halved. Ask students to explain why this is an okay move, even though different objects are being removed from each side (1 square and 3 triangles on the left, 2 squares and 1 triangle on the right). Refer to MLR 2 (Collect and Display).


correct_option_index: 1