options: Use polynomial identities to solve problems.

Understand the relationship between zeros and factors of polynomials.

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

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

Multiply and divide within 100.

Analyze patterns and relationships.

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

Represent and solve problems involving multiplication and division.

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

Work with radicals and integer exponents.

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

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Use properties of operations to generate equivalent expressions.

Solve systems of equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Solve equations and inequalities in one variable.

Add and subtract within 20.

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

Represent and solve equations and inequalities graphically.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

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

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Generate and analyze patterns.
problem_activity: Warm-up
Students reflect on equivalent expressions that represent the area of a shaded rectangle which is part of a larger rectangle of unknown width.
Launch
Allow students 2 minutes of quiet work time, followed by a whole-class discussion.
Student Facing
A rectangle with dimensions 6 cm and
\(w\)
cm is partitioned into two smaller rectangles.
Explain why each of these expressions represents the area, in cm
2
, of the shaded region.
\(6w-24\)
\(6(w-4)\)
[IMG]
Student Response
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Activity Synthesis
Ask students to share their reasoning.
\(6w-24\)
should be straighforward: the area of the entire rectangle is
\(6w\)
, and the area of the unshaded portion is
\(6 \boldcdot 4\)
or 24, so the area of the shaded portion is
\(6w-24\)
.
Students may have more trouble with
\(6(w-4)\)
. The key is to understand that the longer side of the shaded portion can be represented by
\(w-4\)
.
[IMG]


correct_option_index: 15