Math Investigations

Help with Opening PDF Files

Chapter 19

Part 1: For the problem in the Teacher's Edition, page 484

The students can practice their research skills by finding out how each chess piece moves, or you can provide them with the data sheet that shows how each chess piece moves found in the Problem Worksheet (PDF file).

Ask, How does the rook move? (Can move only in a straight line, but can be vertical or horizontal. Can move forward and backward. Can move only on horizontal or vertical VACANT squares.)

Ask the students to discuss how they can keep track of all the possible moves for a rook on square D2. One way to keep track is to number all the ending positions of each of the moves, starting with the number 1. The number of the last move counted will tell you the number of different moves possible.

The paragraph about the chess moves should contain the information given on the data sheet for page 484.

14 moves
The ending position of each move is given in the diagram of the chessboard below.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 2 on theoretical probability.

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

Doing the Investigation

Discuss the recommendations for Ms. Bradshaw that the students came up with. In the discussion, bring out the fact that even though you get three tickets with Raffle A and only one ticket with Raffle B, Raffle B is still a better choice. This is because fewer tickets are sold for Raffle B than for Raffle A. So in general, the raffle where you can get more tickets for the same amount of money is not necessarily the best choice.


If you spend $5 for Raffle A, you get three raffle tickets, and 1,800 raffle tickets will be sold altogether. Your chances of winning are 3/1800 or 1/600.

If you spend $5 for Raffle B, you get one raffle ticket, and 500 raffle tickets will be sold altogether. Your chances of winning are 1/500.

So you have a better chance of winning Raffle B than Raffle A.

Student Report

The letter back to Ms. Bradshaw gives the students an opportunity to tell Ms. Bradshaw which raffle she should enter and why, thus communicating about mathematics.

Houghton Mifflin Math Grade 6