Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman).

Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically.

Discuss the importance of the preservation of equality when solving equations.

Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution.

Generalize and apply symbolic strategies for solving linear equations.

Identify, explain, and correct errors in a given solution of a linear equation.

Demonstrate the application of the distributive property in the solving of linear equations. E.g. $2(x + 3); 2x + 6 = 5$

Explain why some linear relations. E.g. $x/a = b, a ≠ 0$ and $x/a + b = c, a ≠ 0$ have a given restriction and provide an example of a situation in which such a restriction would be necessary.

Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem.

Explain the algebra behind a particular algebra puzzle such as this puzzle written for 2008:

• Pick the number of times a week that you would like to go out to eat (more than once but less than 10).
• Multiply this number by 2 (just to be bold).
• Add 5.
• Multiply it by 50.
• If you have already had your birthday this year add 1758. If you have not, add 1757.
• Now subtract the four digit year that you were born.
• You should have a three digit number. The first digit of this was your original number. The next two numbers are your age.