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

Generate and analyze patterns.

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

Analyze patterns and relationships.

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

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

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

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Create equations that describe numbers or relationships

Use the four operations with whole numbers to solve problems.

Interpret the structure of expressions.

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

Use polynomial identities to solve problems.

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

Represent and solve equations and inequalities graphically.

Perform arithmetic operations on polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

Solve systems of equations.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

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

Work with addition and subtraction equations.

Use properties of operations to generate equivalent expressions.

Rewrite rational expressions.

Represent and solve problems involving multiplication and division.

Multiply and divide within 100.
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: 2