Identifying Errors In Reasoning

Identifying Errors In Reasoning

Maya Buys Two Shirts

Opening

Maya Buys Two Shirts

Watch the video about a sales situation.

The salesperson made a mistake. Maya critiqued the reasoning of the salesperson.

  • As you complete today’s Work Time problems, think about how you could finish Maya’s statement.
  • How could you show the salesperson that his reasoning is incorrect?

VIDEO: Shirt Sale

Math Mission

Opening

Identify and explain mistakes in reasoning about percents.

Bags of Apples

Work Time

Bags of Apples

Mr. Stevens bought two bags of apples. Each bag had a label saying “25% off.” Mr. Stevens figured out that altogether he saved 50%.

  • What mistake in reasoning about percents did Mr. Stevens make?
  • Using examples, explain why Mr. Stevens’s reasoning is incorrect.

 

Hint:

How did Mr. Stevens come up with the number 50%?

Pay Raises

Work Time

Pay Raises

Lucy’s sister got a 15% pay raise. Her brother got a 10% pay raise. Lucy determined that her sister’s pay raise is 5% greater than her brother’s pay raise.

  • What mistake in reasoning about percents did Lucy make?
  • Using examples, explain why Lucy’s reasoning is incorrect.

Hint:

How did Lucy come up with the number 5%?

Cows

Work Time

Cows

A farmer’s herd of cows is 20% smaller than it was the previous year. The farmer figured out that if each cow can increase milk production by 20%, then milk production will be the same as it was last year.

  • What mistake in reasoning about percents did the farmer make?
  • Using examples, explain why the farmer’s reasoning is incorrect.

Hint:

  • What amount would you take 20% of the first time you see the 20% in the problem?
  • What amount would you take 20% of the second time you see the 20%?

Birds

Work Time

Birds

Karen read that the population of birds on an island increases by 20% each year. She figured out that the population would therefore double after five years.

  • What mistake in reasoning about percents did Karen make?
  • Using examples, explain why Karen’s reasoning is incorrect.

 

Hint:

What does it mean for a population to “double” in terms of percent? How do you think Karen came up with this percent based on what she read?

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that shows your work for one of the problems. Create an alternate “conclusion” to replace the mistaken conclusion, and explain why your conclusion is correct.

Challenge Problem

Jack said that the percent change from $20 to $25 is 25% and the percent change from $25 to $30 is 20%. Lucy said that Jack cannot be right: because both the differences are $5, the percent change must be 25% for both sets of numbers.

Who is right? Explain why.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ explanations of the mistakes in reasoning about percents that people make.

Hint:

As your classmates present, ask questions such as:

  • How did you decide what numbers to use in your example?
  • Can you try another example to see if you get the same result?
  • Can you think of another situation in which a person might make this type of mistake?
  • Do you think your explanation is convincing? How could you make it better?

Mistakes With Percents

Formative Assessment

Summary of the Math: Mistakes With Percents

Write a summary about the common mistakes in reasoning with percents that people make.

Hint:

Check your summary.

  • Do you give examples of mistakes?
  • Do you explain why the reasoning behind these mistakes is incorrect?

Salary

Formative Assessment

Salary

Complete this Self Check by yourself.

Marcus’s dad earns $40.85 per hour. He has just learned that his company is giving him a 6% pay raise. What will his new salary be?

  1. Write an equation.
  2. Write the solution as a complete sentence.

A Dress on Sale

Formative Assessment

A Dress on Sale

Karen’s sister finds a dress that she wants to buy. The regular price of the dress is $56.99, but it is on sale for 45% off. What is the sale price of the dress?

  1. Write an equation.
  2. Write the solution as a complete sentence.

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.

An example of a mistake that people often make with percents is …