Help with Opening PDF Files

Chapter 21

Part 1: For the problem in the Teacher's Edition, page 578

Provide the students with a copy of the Problem Worksheet (PDF file).

Talk with the students about how they would set up a graph by asking questions such as:

• What is the highest number you need to show on the graph? (32)
• The scale has to be greater than 1. What would be a good choice for a scale?
• How would you label the graph?

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on regrouping twice.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the first page of the Description of Investigation and Student Report (PDF file), by having one of your students read aloud the assignment, or by having the students read the assignment individually.

Put the students in groups of two to four to work on the investigation.

Doing the Investigation

Have the students share their answers and discuss how they solved the problems, by asking questions such as:

• For Question 1, how do you know that 432 x 5 will give you the greatest answer? (Since 5 is the greatest number, you'll get the greatest number if you multiply every digit by 5. The best number to multiply by is 432 because the next-greatest number, 4, is in the hundreds place and the least number, 2, is in the ones place.)
• For Question 2, how do you know that 359 x 2 will give you the least answer? (Since 2 is the least number you'll get the least number if you multiply every digit by 2. The best number to multiply by is 359 because 3 is the least of the three numbers left and it is in the hundreds place, and 9 is the greatest of the three numbers left and it is in the ones place.)
• For Question 3, how do you know that 439 x 1 will give you an answer between 400 and 450? (I used the identity property of multiplication to get an answer between 400 and 450.)