Student Self Check

Student Self Check

Critique

Opening

Critique

Revise your work on the Self Check problem from the last lesson, based on the following questions.

  • Did you identify the quantities in the situation, both known and unknown, and then use a tool to represent how the quantities are related?
  • Did you make a conjecture about the amount the waiter gave the busboy? Is this amount less than or greater than $45?
  • How can you demonstrate that your answer is correct?

INTERACTIVE: Double Number Line Tool

INTERACTIVE: Ratio Table Tool

Math Mission

Opening

Revise your work, correct other students’ solutions, and solve a similar problem.

Chen’s Work

Work Time

Chen's Work

The problem:

A waiter at a restaurant shares his tips with the busboy in a ratio of 5:2. If the waiter had $45 after sharing his tips, how much did he give the busboy?

Chen says:

“My tape diagram shows that 2 units are equal to the waiter’s $45, because the ratio is 5:2. So each unit represents half of $45, or $22.50. The busboy is represented by 5 units. And $22.50 × 5 is $112.50. So the waiter gave the busboy $112.50.”

  • What mistake did Chen make?
  • Is there a way he could have used a tape diagram to solve the problem correctly? Explain.

Carlos’s Work

Work Time

Carlos's Work

The problem:

A waiter at a restaurant shares his tips with the busboy in a ratio of 5:2. If the waiter had $45 after sharing his tips, how much did he give the busboy?

Carlos says:

“I used a double number line. First I made a number line for the waiter that went from 0 to 65, counting by 5s. Then I made a number line for the busboy. I lined up $5 for the waiter with $1 for the busboy. Then I could see what lined up with $45 for the waiter. Since $9 lines up with $45 for the waiter, the waiter gave the busboy $9.”

  • What mistake did Carlos make?
  • Is there a way he could have used a double number line to solve the problem correctly? Explain.

Jan’s Work

Work Time

Jan's Work

The problem:

A waiter at a restaurant shares his tips with the busboy in a ratio of 5:2. If the waiter had $45 after sharing his tips, how much did he give the busboy?

Jan says:

“I set up a ratio table. I knew when the waiter got $5, the busboy got $2, because the ratio was 5 to 2. So I put that in the table. Then I wanted to see what would happen when the waiter got $45, so I added $40 to $5 and put it in the table for the waiter. I wanted to do the same thing for the busboy, so I added $40 to $2 and got $42 to match up with the $45 for the waiter. So when the waiter gets $45, the busboy gets $42.”

  • What mistake did Jan make?
  • Is there a way she could have used a ratio table to solve the problem correctly? Explain.

Revise Your Work

Work Time

Revise Your Work

Working with a partner, use what you learned from correcting student work to solve this problem.

  • A waiter shares his tips with the busboy in a ratio of 9:2. If the waiter had $36 after sharing his tips, how much did he give the busboy?

INTERACTIVE: Double Number Line Tool

INTERACTIVE: Ratio Table Tool

Prepare a Presentation

Work Time

Prepare a Presentation

Explain how you revised your work. Support your explanation using both your work on the Self Check and your new work.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates' suggestions for correcting the student work and their approaches to solving the new waiter problem.

As your classmates present, ask questions such as:

  • Did correcting the student work help you solve the new waiter problem? How?
  • How does your tool show the ratio between the amount the waiter keeps and the amount he gives to the busboy?
  • Can you identify a unit in a tape diagram, on a double number line, and in a ratio table?

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 of the most important things I learned in this unit is …