Select one of the equations from the card sort and solve the equation.

Justify each step of your solution. One equation has been done for you as an example.

Prepare a presentation that shows and justifies each step of your solution and explains how each step relates to the situation.

Challenge Problem

An isosceles triangle has a perimeter of 12$\frac{1}{2}$ inches.

The length of the shortest side is 4 inches less than the length of one of the two equal sides.

What are the lengths of the three sides of the triangle?

Solve the problem by writing and solving an equation.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about the steps and justifications your classmates used to solve the equation they chose.

Hint:

As your classmates present, ask questions such as:

How does each step of the equation represent each part of the situation?

How did you figure out which quantity in the situation x represents?

Does the solution to the equation make sense in terms of the problem?

Solve Equations

Formative Assessment

Summary of the Math: Solve Equations

Read and Discuss

Follow the steps and justifications below.

Identify variables in the starting equation:

y − 2x − 7 = x + 3

Add 2x + 7 to both sides by the addition property of equality:

(y −2x − 7) + (2x + 7) = (x + 3) + (2x + 7)

Rearrange terms using properties of operations:

y + (2x − 2x) + (7 − 7) = (x + 2x) + (3 + 7)

Combine like terms using the distributive property:

y + x(2 − 2) + 0 = x(1 + 2) + 10

Simplify both sides to get a new equation:

y = 3x + 10

In this example, 2x + 7 is added to both sides of the equation. But any number could have been added, and the resulting equation would still have been true, as long as the same number was added to both sides. Notice how parentheses are used to keep terms organized, and how the associative property and commutative property of addition are used to rearrange the terms.

Hint:

Can you explain how to use properties of operations to solve equations?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.