Problem Solving Strategy ~ Make an Organised List ~

Content

 Process Problem 1 Process Problem 2 Process Problem 3 Problem Worksheet

Process Problem 1

Doug has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shirt, a grey shirt, and a striped shirt. How many different outfits can he put together? (Hint: Cornplete the organised list.)

Pants     Shirts

Black—White
Black—Red
Black—
Black—

Pants      Shirts

Green—
Green—
Green—
Green—

Understanding the Problem

· How many pairs of pants does Doug have? (2)
· How many shirts does Doug have? (4)

Planning a Solution

· Suppose Doug wears his black pants. What color shirt can he wear? (white, red, grey, or striped)
· If Doug wears his striped shirt, how many different outfits can he wear? (2: striped—black and striped—green)
· If Doug wears the green pants, can he wear all 4 shirts? (yes)

Make an Organized List

Black—White
Black—Red
Black—Gray
Black—Striped

Green—White
Green—Red
Green—Gray
Green—Striped

Doug can make 8 different outfits.

Problem Extension

Suppose Doug bought a third pair of pants that were tan. How many different outfits can he put together now? (12)

Process Problem 2

Ryan numbered his miniature race car collection according to the following rules:

1. It has to be a 3-digit number.

2. The digit in the hundreds place is less than 3.

3. The digit in the tens place is greater than 7.

4. The digit in the ones place is odd.

If Ryan used every possibility and each car had a different number, how many cars did Ryan have in his collection? (Hint: Make an organised list.)

Understanding the Problem

· How many digits are there in the numbers? (3)
· What digits could be in the hundreds place? (1 or 2) Fens place? (8 or 9) Ones place? (1, 3, 5, 7, or 9)

Planning a Solution

· If 1 is in the hundreds place, what digits could be in the tens place? (8 or 9) Ones place? (1, 3, 5, 7, or 9)
· What are the possible numbers having a 1 in the hundreds place and an 8 in the lens place? (181, 183, 185, 187, and 189)
· Are there are any other numbers you can use in the hundreds place if you leave the 8 in the tens place and the odd numbers in the ones place? (yes, a 2) What are the numbers? (281, 283, 285, 287, and 289)
· What other digit can be used in the tens place? (9)

Make an Organized List

181    281    191    291
183    283    193    293
185    285    195    295
187    287    197    297
189    289    199    299

Ryan had 20 cars in his collection.

Problem Extension

Ryan added some cars to his collection but changed only one rule. The digit in the hundreds place has to be less than 4. If Ryan used every possible number and each car was numbered differently, how many new cars did he add to his collection? (10)

Process Problem 3

There will be 7 teams playing in the Maple Island Little League tournament. Each team is scheduled to play every other team once. How many games are scheduled for the tournament?

Understanding the Problem

· How many teams have entered the tournament? (7)
· If team A plays team B. will they play each other again? (no)

Planning a Solution

· How many games will team A play? (6) How many more games will team B play? (5)
· If there were only 2 teams in the tournament, how many games would be played? (1 ) 3 teams? (3) 4 teams? (6)
· Write the names of 7 teams and show which teams each one will play. (See solution.)

Make an Organized List Make a Table/Look for a Pattern
Team: A B C D E F G
 No. of Teams No. of Games 2 1 3 3 4 6 5 10 6 15 7 21
Plays: B C D E F G |
C D E F G | |
D E F G | | |
E F G | | | |
F G | | | | |
G v v v v v v
6 + 5 + 4 + 3 + 2 + 1 = 21

Pattern: The number of games played increases by the number of teams playing less 1.

There are 21 games scheduled for the tournament.

Problem Extension

There were 15 people signed up for Lincoln School's chess tournament. Of the 15, 12 were students and 3 were teachers. If each teacher played each student 1 time, how many games were played? (3 x 12 = 36)

Process Worksheet: Make an Organised List

1. Doug has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shirt, a grey shirt and a striped shirt. How many different outfits can he put together?

2. Ryan numbered his miniature race car collection according to the following rules:

a. It has to be a 3-digit number.

b. The digit in the hundreds place is less than 3.

c. The digit in the tens place is greater than 7.

d. The digit in the ones place is odd.

If Ryan used every possibility and each car had different number, how many cars did Ryan have in his collection?

3. There will be 7 teams playing in the Maple Island Little League tournament. Each team is scheduled to play every other team once. How many games are scheduled for the tournament?

4. Marvin counted the marbles he had collected. He counted more than 40 but less than 70. When he put the marbles in groups of 5, he had 1 left over. When he put them in groups of 4, he had 1 left over. When he put them in groups of 3, he had 1 left over. How many marbles did Marvin collect?

5. The number 475 is a three-digit number that uses only the three digits 4, 5, 7. How many three-digit numbers can be formed using these three digits, if repeated digits are allowed?

6. I am a counting number. All three of my digits are odd but different. The sum of my digits is 13. The product of my digits is greater than 30. The sum of my tens’ and hundreds’ digits is less than my units’ digit. Which two numbers could I be?