options: Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Work with addition and subtraction equations.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Use the four operations with whole numbers to solve problems.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

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

Analyze patterns and relationships.

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

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

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

Gain familiarity with factors and multiples.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.

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

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

Solve systems of equations.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

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

Create equations that describe numbers or relationships

Use polynomial identities to solve problems.

Generate and analyze patterns.

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

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

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

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Activity
The activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable, and choosing parameters of an equation that will result in its graph looking a certain way.
Launch
Arrange students in groups of 2. Give students two minutes of quiet work time on the first question, and ask them to check their answers with their partner before starting the second question. Call attention to the scale on the axes. Identify students who use the scale to select the parameters for their linear equation.
Student Facing
Evaluate each expression when
\(x\)
is -3.
\(x^2\)
\(\text-x^2\)
\(x^2+20\)
\(\text-x^2+20\)
For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.
[IMG]
Student Response
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Activity Synthesis
Invite students to share various equations that each graph could represent. Use different but equally correct equations to help students generalize. For example, either
\(y=x+15\)
or
\(y=x+12\)
makes sense for graph C, because it looks like
\(y=x\)
, and is shifted up by some number between 10 and 20. So we know that the equation this graph represents is in the form
\(y=x+b\)
, where
\(b\)
is positive, even though we can’t tell its exact value from the given information.


correct_option_index: 17