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.

## Saturday, April 14, 2007

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