options: Reason about and solve one-variable equations and inequalities.

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.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Multiply and divide within 100.

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

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

Interpret the structure of expressions.

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

Analyze patterns and relationships.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Write and interpret numerical expressions.

Perform arithmetic operations on polynomials.

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

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

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Add and subtract within 20.

Solve equations and inequalities in one variable.

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Activity
In this practice activity, students prepare for the associated Algebra 1 lesson by practicing applying some of the properties they will need to use.
Student Facing
Evaluate:
\(\dfrac{3^5}{3^4}\)
\(\dfrac{3^1}{3^0}\)
\(\dfrac{3^{\text-1}}{3^{\text-2}}\)
\(\dfrac{3^{100}}{3^{99}}\)
\(\dfrac{3^{x+1}}{3^x}\)
Solve for
\(m\)
:
\(\dfrac{2^m}{2^7}=2\)
\(\dfrac{2^{100}}{2^m}=2\)
\(\dfrac{2^m}{2^x}=2\)
Write an equivalent expression using as few terms as possible:
\(3(x+1) + 4 - (3x + 4)\)
\(2(x+1) + 5 - (2x + 5)\)
\(2(x+2) + 5 - (2(x+1) + 5)\)
\(\text-5(x+1) + 3 - (\text-5x + 3)\)
\(\dfrac{5^{x+1}}{5^x}\)
\(\dfrac{7^{x+4}}{7^x}\)
Student Response
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Activity Synthesis
Either display the correct solutions or invite students check with another student to see if their answers are the same.  If there are any differences between solutions, invite students to ask questions or discuss whole group.


correct_option_index: 24