Solve real-world and mathematical problems by writing and solving one-step equations of the form \(

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Cluster

Reason about and solve one-variable equations and inequalities.

Abe earns $30.00 for raking his neighbor’s leaves. He bought lunch and has $22.75 left. The equation x+22.75=30.00 can be used to determine x, the amount of money, in dollars, Abe spent for lunch.

Which value of x represents the amount of money, in dollars, Abe spent on lunch?

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Evidence of Learning Statements

Students with a level 1 understanding of this standard will most likely be able to:

Students with a level 2 understanding of this standard will most likely be able to:

Students with a level 3 understanding of this standard will most likely be able to:

Students with a level 4 understanding of this standard will most likely be able to:

Solve an equation in the form x + p = q when p, q, and x are all whole numbers.

Identify the variable quantity in a real-world or mathematical situation.

Choose an appropriate equation to model a given situation or real-world problem.

Solve equations of the form px = q when p, q, and x are all whole numbers.

Solve real-world or mathematical problems by writing and solving equations of the form x + p = q or

px = q when p, q, and x are all non-negative rational numbers.

Explain the relationship between the context and the written equation in both verbal and written form.

 

 

Instructional Focus Statements

Level 3: 

Students should develop a conceptual understanding of solving one-step equations involving positive rational numbers (including zero), fractions, and decimals.  Instruction should be focused on real-world problems with students generating equations based on the given situations. Students should illustrate the equation in problem situations with visual representations, such as bar models, and use reasoning and prior knowledge to solidify their understanding.

Level 4:

As students deepen their understanding of solving one-step equations resulting from real-world situations, they should not only create an equation from a real-world or mathematical situation but also identify and interpret dependent and independent variables with respect to the context. Solving equations is a process of reasoning to find the number(s) which make an equation true, which can include checking if a given number is a solution. Although the process of reasoning will eventually lead to standard methods for solving equations, students should be flexible working with different examples where looking for structure will produce more efficient solution paths. This allows them to explain their reasoning for selecting the specific solution path.