options: Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

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

Understand the relationship between zeros and factors of polynomials.

Use polynomial identities to solve problems.

Add and subtract within 20.

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

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Create equations that describe numbers or relationships

Work with radicals and integer exponents.

Rewrite rational expressions.

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

Reason about and solve one-variable equations and inequalities.

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

Multiply and divide within 100.

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

Solve systems of equations.

Write and interpret numerical expressions.

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

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

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

Perform arithmetic operations on polynomials.

Use properties of operations to generate equivalent expressions.

Work with addition and subtraction equations.

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

Represent and analyze quantitative relationships between dependent and independent variables.
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: 22