## Saturday, April 14, 2007

### Scriber Diving - Patterns and Relations 1

1. Draw out the next two patterns in the space below.

2. Make a table to show the results of your investigation.

3. Describe the patterns found in each row.
x = Gets larger by 1
= Numerical order
= Consecutive numbers
= Starts with one

y = Gets larger by 2
= All odd numbers
= Starts with 2

3.B. Describe why the patterns increase the way that they do.
-The pattern starts at 3 because it takes three tooth picks to create a triangle.
-It then goes up by 2 because there is already 1 triangle and you're just sharing a tooth pick.
-They are all odd numbers because...

4. Describe the relationship between the two columns.
= y is larger
= We have to + or x
= figure + figure + 1
= 2 times figure + 1
= 2n + 1
= n = figure #

4.C. Write an algebraic equation to show this relationship.
= n = figure #

2n + 1 =
2(30) + 1 =
60 + 1 =
61

5. Predict the 20th, 35th, and 99th diagram will look like.

n = figure #

20th -

2n + 1 =
2(20) + 1 =
40 + 1 =
41

35th -

2n + 1 =
2(25) + 1 =
50 + 1 =
51

99th -

2n + 1 =
2(99) + 1 =
198 + 1 =
199

6. Predict which diagram will use 31, 51, and 125 tooth picks.
2n + 1 = tooth picks

31 tooth picks -

2n + 1 = 31
2(15) + 1 = 31
30 + 1 = 31
31

51 tooth picks -

2n + 1 = 51
2(25) + 1 = 51
50 + 1 = 51
51

125 tooth picks -

2n + 1 = 125
2(62) + 1 = 125
124 + 1 = 125
125

-Jake M.