options: Interpret the structure of expressions.

Use polynomial identities to solve problems.

Solve systems of equations.

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

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

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

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

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

Create equations that describe numbers or relationships

Work with addition and subtraction equations.

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

Multiply and divide within 100.

Write and interpret numerical expressions.

Analyze patterns and relationships.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving addition and subtraction.

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

Add and subtract within 20.

Solve equations and inequalities in one variable.

Perform arithmetic operations on polynomials.

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

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

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Represent and analyze quantitative relationships between dependent and independent variables.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Gain familiarity with factors and multiples.
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: 0

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