Problem Solving Strategy ~ Guess and Check ~

Content

 Process Problem 1 Process Problem 2 Process Problem 3 Problem Worksheet

Process Problem 1

Marty did 2 of these activities. He paid for them with a \$10.00 bill. His change was \$3.75. What 2 activities did Marty do? (Hint: Make a guess. Then check your guess.)

 Activity Cost Movies \$3.50 Putt-Putt Golf \$3.00 Skating \$2.00 Go-Kart Rides \$2.75

Understanding the Problem

· How many activities did he do? (2)
· How much money did he have? (\$10.00)
· What was his change? (\$3.75)

Planning a Solution

· How much money did he have? (\$10.00) What was the change? (\$3.75)
· How much did he spend? (\$6.25)
· If he saw the movies and golfed, how much money would he have spent? (\$6.50) Did he do these 2 activities? (No, they cost too much.)

Finding the Answer

Guess and Check

· Try movies and skating—\$3.50 + \$2.00 = \$5.50. (too little)
· Try movies and go-karts—\$3.50 + \$2.75 -- \$6.25. (correct)

The activities that Marty did are the movies and the go-kart rides.

Problem Extension

Marty's friend Joe went also, but he was not limited to 2 activities. He took \$10.00 and brought back\$2.25. What activities did he do? (golf, skating, go-kart rides)

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Process Problem 2

I wrote 5 different numbers on 5 cards. The sum of the numbers is 15. What numbers did I put on the cards? (Hint: Make a guess. Then check your guess.)

Understanding the Problem

· How many numbers did I write? (5)
· What is the sum of the numbers? (15)
· How many numbers on each card? (1)
· Are any 2 numbers the same? (No, they are all different.)

Planning a Solution

· Could 1 of the numbers be 15? (No, because the rest would be 0 and we said that all the numbers were different.)
· Select 5 numbers and check to see if their sum is 15.

Finding the Answer

Guess and Check

· Try 0,1,2,3,4—0 + 1 + 2 + 3 + 4 = 10 (too little)
· Try 1,2,3,4,5—1 + 2 + 3 + 4 + 5 - 15 (correct)

The numbers are 1, 2, 3, 4, and 5.

Problem Extension

If the numbers are even and different and their sum is 30, what are the numbers? (2,4,6,8,10)

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Process Problem 3

David's age this year is a multiple of 5. Next year, David's age will be a multiple of 7. How old is David now?

Understanding the Problem

· What do we know about David's age this year? (multiple of 5)
· What do we know about David's age next year? (multiple of 7)

Planning a Solution

· List some multiples of 5. (5, 10, 15, . . .) Multiples of 7. (7, 14, 21, . . .)
· Guess what David's age might be this year and add 1 to it to see if that number is a multiple of 7. (See solution.)

Finding the Answer

Guess and Check

· Try 10 and 11. (No, 11 is not a multiple of 7.)and so on

Make an Organized List

 Multiples of 5 5 10 15 20 Multiples of 7 7 14 21 28

David is 20 years old now.

Problem Extension

In how many more years will David's age be a multiple of both 5 and 7? (In 15 years, when he is 35)

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Process Worksheet: Guess and Check

1. Mary has 6 coins, which have a total value of 67 cents. What combinations of coins could she have? Use denominations of 1¢, 5¢, 10¢ and 25¢.

2. Navigate your spaceship to the "Black Hole". The product of the numbers along your path must be 2592.

 Start 6 2 10 3 4 9 2 7 1 8 2 4 5 Black Hole

3. The sums of numbers on each side of the magic triangle are all the same. Find two solutions for the magic triangle using a different number in each box.

 10

/

\

 24

/

\

 16
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4. a) How many shots at this target are needed to make a score of 300?

b) Find four different combinations where the value of the shots on the target totals 300.

5. If r is less than 10, what value of r makes r3749r0 divisible by 60? (there are two possibilities.)

6. Find a set of 3 consecutive even numbers whose sum is 294.

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