Pictures, Diagrams and Patterns
 Lesson
 Topic Index | Grade 6 Math | Intermediate Test Prep | StudyZone

  
 

Some math problems require us to draw pictures, diagrams, or use patterns in order to reach a solution. When you need to solve a problem you can use the steps below to help:
  1. Read the problem carefully.
  2. Think about ways in which you might be able to use a pictures, diagram, or patterns in working through the problem.
  3. Draw out the parts of the problem that can be represented graphically.
  4. Solve the problem.

Use the samples below as a guide to help you in using pictures, diagrams, and/or patterns to solve problems.

 

 Example one: Using Pictures
Audrey, Bobby, Charles, Diane, and Emily sit in the same row of desks in math class.  The two boys sit one after the other.  Diane, the tallest, is in the last seat.  Charles sits right in front of his twin sister.  Audrey sits in between the other two girls.  In which order are they sitting?

Step 1: Read the Problem carefully

Step 2:  Think about how you can use pictures or diagrams to help you solve the problem

Knowing that Diane sits in the last seat we can draw a box representing her desk at the end of the row. 

Step 3: Draw out your problem.

Step 4: Solve the problem.



We also know that Audrey sits in between the other two girls.  Since Diane is in the last row we must put Audrey in front of Diane and Emily in front of Audrey.
Next, Charles sits in front of his sister.  The only available desk in front of a girl is the desk before Emily.
Finally, the two boys sit one after the other.  Therefore Bobby must sit in front of Charles.
The correct order is: Bobby, Charles, Emily, Audrey, Diane.

 

 Example two: Using Diagrams
 
Problem: Rachel had two pairs of socks, four pairs of pants, and three shirts to choose from one morning to make an outfit for school.  How many different outfit combinations can Rachel make?

Solution:

One possible approach to answering this problem is to draw a diagram to help us find the solution.

There are 24 outfit combinations for Rachel to choose from.

 

 Example three: Using Patterns

Problem:
A wealthy uncle gave his nephew John this choice as he graduated from high school: he could either have $500,000 or he could, over the course of 30 days, have one penny on the first day and double it every day after that taking the total amount on the 30th day.  Which should he choose?

Solution:

Let’s find out first what the total would be after the 30 days…
Day 1:  $0.01            Day 16:  $327.68
Day 2:  $0.02                      Day 17:  $655.36
Day 3:  $0.04                      Day 18:  $1310.72
Day 4:  $0.08                      Day 19:  $2621.44
Day 5:  $0.16                      Day 20:  $5242.88
Day 6:  $0.32                      Day 21:  $10,485.76
Day 7:  $0.64                      Day 22:  $20,971.52
Day 8:  $1.28                      Day 23:  $41,943.04
Day 9:  $2.56                      Day 24:  $83,886.08
Day 10:  $5.12                    Day 25:  $167,772.16
Day 11:  $10.24                  Day 26:  $335,544.32
Day 12:  $20.48                  Day 27:  $671,088.64
Day 13:  $40.96                  Day 28:  $1,342,177.20
Day 14:  $81.92                  Day 29:  $2,684,354.40
Day 15:  $163.84                Day 30:  $5,368,708.80
 
As you can see, by following the pattern of doubling the dollar amount every day, by the 27th day, the total amount has already passed the $500,000 mark.  In conclusion, John should then choose the “doubling option” because on the 30th day he would have $5,368,708.80.

 

 Remember:

When you solve problems you can use three things to help you with the process.

1. Pictures

  2. Diagrams

             3. Patterns

 

  
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