Draw a Picture. The three towns of Garden City, Scott City, and Oakley are located along a straight highway. The distance between Garden City and Oakley.

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Presentation transcript:

Draw a Picture

The three towns of Garden City, Scott City, and Oakley are located along a straight highway. The distance between Garden City and Oakley is 81 mi. Scott City is located between Garden City and Oakley and is 36 mi. from Garden City. How far is it from Scott City to Oakley? Example 1

Think: What is the relationship of these towns to each other? Use a picture to show the relationship. Garden City Scott City Oakley 36 81

Think: What is being asked? What mathematical operator does the relationship suggest? Represent the unknown with a variable: d = the distance from Scott City to Oakley. Use the picture to select the operation of addition: d + 36 = 81.

Think: How is the equation solved? Subtract 36 from both sides of the equation: d + 36 – 36 = 81 – 36. The distance from Scott City to Oakley is 45 mi.

Think: As you look back at the diagram, does 45 mi. seem reasonable considering the facts given in the problem? Yes, the answer is correct, since = 81.

There are eight friends at a party. If everyone at the party shakes hands with everyone else at the party, how many handshakes occur during the party? Example 2

Think: Use a diagram to help you visualize the handshakes at this party. A A B B C C D D E E F F G G H H If person A shakes hands with everyone in the room, 7 handshakes will occur.

Think: What happens when B starts to shake hands? B B C C D D E E F F G G H H There are 6 additional handshakes. Person C will have 5 additional handshakes, and so on down to person G.

Think: How can the total of all handshakes be determined? There are a total of = 28 handshakes at this party.

Think: To check this answer, think back through the problem using the diagrams to make sure the answer is reasonable.

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