Matching Equations To Problems

Matching Equations To Problems

Pencil, Pen, and Notebook

Opening

Pencil, Pen, and Notebook

A pencil costs 50 cents less than a notebook.

A pen costs 3 times as much as a pencil.

A pen costs 90 cents.

  • Let x = the cost of the notebook. What does the notebook cost?
  • Review each equation in the table. Does it represent the situation described above? Select "Yes" or "No" for each.

HANDOUT: Determine the Cost of the Notebook

Math Mission

Opening

Represent situations using equations, and construct each step of the solution process.

Situations and Equations

Work Time

Situations and Equations

Match the situations to the equations.

INTERACTIVE: Matching Situations and Equations

Hint:

You may need to write equivalent expressions in order to find some of the matching equations.

Prepare a Presentation

Work Time

Prepare a Presentation

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 1212 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.

One thing that still confuses me is …