## Different Methods to Solve Problems

## Opening

# Methods to Solve Problems

Watch the video.

Take notes about the methods that Jack, Lucy, and Karen use to solve the problem.

VIDEO: Pencils

Watch the video.

Take notes about the methods that Jack, Lucy, and Karen use to solve the problem.

VIDEO: Pencils

Use three different methods to solve a problem involving proportional relationships.

A collection of 20 marbles weighs 30 ounces. Each marble in the collection weighs the same amount.

How much does a collection of 36 marbles weigh? (Assume that each marble in the new collection weighs the same as each marble in the 20-marble collection.)

Solve the problem three different ways: Karen’s method, Jack’s method, and Lucy’s method.

- How can you set up the problem as a proportion?
- How can you find the weight of one marble? What would you call that weight?
- The formula for a proportional relationship is of the form

*y*=*kx*, where*k*is the constant of proportionality. How can you find*k*? - What are the two variables in this problem?

- Describe each method you used to solve the marble problem.
- Think about the words—particularly the mathematical vocabulary—you used to describe each method. What do the words mean? Are there any words that you used to describe one method but not the other two?
- Be prepared to share your description of each method with the class.

Graph the formula that you wrote when you used Karen's method to solve the marble problem.

Take notes about your classmates' explanations of how they used the three methods to solve the marble problem.

As your classmates present, ask questions such as:

- What is the unit rate in the marble problem?
- What is the constant of proportionality in the problem?
- Why would you write a formula to help you solve a proportion problem?
- When would you set up a proportion and solve for a single value?
- Describe the form of the formula for a proportion problem.
- Which of the three methods do you like best? Which do you think is easiest? Which do you think is most difficult?

Write a summary about the different ways to solve proportion problems.

Check your summary.

- Do you describe three different methods for solving problems involving proportional relationships?
- Do you describe the form of the formula for a proportional relationship? Do you explain what each part of the formula represents?
- Do you show how the unit rate and the constant of proportionality are connected?
- Do you explain why using a formula with a constant of proportionality might be more efficient than setting up and solving proportions when solving a group of problems with the same underlying proportional relationship.

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

**My favorite method for solving a proportion problem is ___ because …**