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.)

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

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.

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. 

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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