options: Generate and analyze patterns.

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

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

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Work with radicals and integer exponents.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

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

Solve systems of equations.

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

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

Reason about and solve one-variable equations and inequalities.

Perform arithmetic operations on polynomials.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Multiply and divide within 100.

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

Understand the relationship between zeros and factors of polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

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

Gain familiarity with factors and multiples.

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

Analyze and solve linear equations and pairs of simultaneous linear equations.
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: 5