options: Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

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

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

Solve systems of equations.

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

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

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

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

Multiply and divide within 100.

Work with radicals and integer exponents.

Represent and solve problems involving addition and subtraction.

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

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships

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

Use properties of operations to generate equivalent expressions.

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

Analyze patterns and relationships.

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

Rewrite rational expressions.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.
problem_activity: Activity
Students interpret inequalities that represent constraints or conditions in a real-world problem. They find solutions to an inequality and reason about the context’s limitations on solutions (MP2).
Launch
Allow students 10 minutes quiet work time to complete all questions followed by whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Provide students with access to blank number lines. Encourage students to attempt more than one strategy for at least one of the problems.
Supports accessibility for: Visual-spatial processing; Organization
Student Facing
Noah scored
\(n\)
points in a basketball game.
What does
\(15 < n\)
mean in the context of the basketball game?
What does
\(n < 25\)
mean in the context of the basketball game?
Draw two number lines to represent the solutions to the two inequalities.
Name a possible value for
\(n\)
that is a solution to both inequalities.
Name a possible value for
\(n\)
that is a solution to
\(15 < n\)
, but not a solution to
\(n < 25\)
.
Can -8 be a solution to
\(n\)
in this context? Explain your reasoning.
Student Response
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Anticipated Misconceptions
Students might have trouble interpreting
\(15 < n\)
because of the placement of the variable on the right side of the inequality. Encourage students to reason about the possible values of
\(n\)
that would make this inequality true.
Activity Synthesis
Invite selected students to justify their answers. Extend the discussion of the basketball game to consider how scoring works and whether any number could represent the points scored by a player. For example, could a player have scored 1 point?
\(2\frac12\)
points? 0 points? -3 points? Is it reasonable for a player to score 200 points in a game?
Reading, Speaking, Representing: MLR3 Clarify, Critique, Correct.
To support students in their ability to read inequalities and their number line representations as well as to critique the reasoning of others, present an incorrect response to the prompt “Draw two number lines that represent the two inequalities.” For example, use the first number line representing
\(15 < n\)
to contain an error by shading the line and arrow to the left instead of the right. Then correctly display the second number line. Tell students the response is not drawn correctly even though the numbers and open circles are correct. Ask students to identify the error, explain how they know that the response is incorrect, and revise the incorrect number line. This helps prompt student reflection with an incorrect written mathematical statement, and for students to improve upon the written work by correcting errors and clarifying meaning.
Design Principle(s): Optimize output (for explanation)


correct_option_index: 2