options: Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

Generate and analyze patterns.

Create equations that describe numbers or relationships

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

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

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

Multiply and divide within 100.

Write and interpret numerical expressions.

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

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

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

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

Work with addition and subtraction equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Rewrite rational expressions.

Perform arithmetic operations on polynomials.

Represent and solve problems involving addition and subtraction.

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

Use the four operations with whole numbers to solve problems.

Use properties of operations to generate equivalent expressions.

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

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

Solve systems of equations.

Add and subtract within 20.
problem_activity: Warm-up
The purpose of this warm-up is for students to practice solving an equation for an unknown value while thinking about a coordinate pair,
\((x,y)\)
, that makes the equation true. While the steps to solve the equation are the same regardless of which value of
\(x\)
students choose, there are strategic choices that make solving the resulting equation simpler. This should be highlighted in the discussion.
Launch
Encourage students to not pick 0 for
\(x\)
each time.
Student Facing
For each equation choose a value for
\(x\)
and then solve to find the corresponding
\(y\)
value that makes that equation true.
\(6x=7y\)
\(5x+3y=9\)
\(y+5-\frac13 x=7\)
Student Response
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Activity Synthesis
Collect the pairs of
\(x\)
’s and
\(y\)
’s students calculated and graph them on a set of axes. For each equation, they form a different line. Have students share how they picked their
\(x\)
values. For example:
For the first problem, choosing
\(x\)
to be a multiple of 7 makes
\(y\)
an integer.
For the last problem, picking
\(x\)
to be a multiple of 3 makes
\(y\)
an integer.


correct_option_index: 19