options: Gain familiarity with factors and multiples.

Interpret the structure of expressions.

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

Rewrite rational expressions.

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

Solve systems of equations.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

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

Work with radicals and integer exponents.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving addition and subtraction.

Multiply and divide within 100.

Represent and solve equations and inequalities graphically.

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

Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

Work with addition and subtraction equations.

Add and subtract within 20.

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

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

Generate and analyze patterns.

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

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Perform arithmetic operations on polynomials.

Use the four operations with whole numbers to solve problems.

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.
problem_activity: Activity
In this activity, students work to solve linear equations and recognize the solution in graphs. This skill will help students when they examine quadratic equations and their solutions in the associated Algebra 1 lesson.
Student Facing
A person is hiking from the top of a mountain into a valley. The function
\(2,\!000 - 32t\)
represents their elevation in feet above sea level,
\(t\)
minutes after they started their hike.
What does a solution to the equation
\(2000-32t=0\)
mean?
Use technology to create a graph of
\(y=2,\!000-32t\)
. Where do you see the solution to that equation on the graph?
A new electronic device originally costs
$
1,000 but loses
$
175 worth of value every year.
Write a function that represents the worth of the device after
\(s\)
years.
How many years until the device is worth
$
0?
Use technology to graph the function. Where can you see the solution to your equation on the graph?
Student Response
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Activity Synthesis
The purpose of the discussion is to notice the connection between solutions of equations and the graph of both sides of the equation. Select students to share their solutions. Ask students:
“Why are both solutions to these questions related to the horizontal intercept?” (Since both questions asked about when the value is 0, it makes sense to look at the points where
\(y = 0\)
which is along the horizontal axis.)
“How could you find the worth of the electronic device after 4.5 years?” (Substitute 4.5 for
\(s\)
in the equation and solve for the value.)
“How could you find the number of minutes it takes to reach an elevation of 100 feet above sea level?” (Substitute 100 in the equation for
\(y\)
and solve for
\(t\)
.)


correct_option_index: 1

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