Today we did a Patterns and Relations Investigation Answer Sheet. The title of our investigation was “ Trapezoids are cool “. We had to draw out patterns, and describe what’s happening to the pattern found in each row. We also had to describe why the patterns increase the way that they do. After that, we wrote the relationship between the figure numbers and the numbers of trapezoids. Then we had to write the algebraic equation to show the relationship. To make it easier to predict what the 20th, 35th, and 99th diagram would look like. After that, we predicted which diagram would use 30, 50, and 125 blocks.**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.** starts at 1 and goes up by 1

**Y. **increasing by 2, even numbers, starts at 2

**3B.** *Describe why the patterns increase the way that they do.*

You start with 2 trapezoids and add 2 more to make a new pattern.

**4.** **Describe the relationship betwee****n the two columns.**

Figure number PLUS itself

Figure number TIMES 2

**4C.** **Write an algebraic equation to show this relationship.**

N + N or 2N

N = figure number < *REMEMBER TO PUT THIS, OR YOU'LL LOSE HALF A MARK.*

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

**20th -** 2n = 2(20) = 40

**35th -** 2n = 2(35) = 70

**99th -** 2n = 2(99) = 198

**6.** **Predict which diagram will use 30, 50, and 125 blocks.Make a graph for the first 6 terms and label the line according by it’s equation.**

**30 blocks -** 2n = 30 = 2(15) = 30

30 = 30 ( verification)

**50 blocks -** 2n = 30 = 2(25) = 50

50 = 50

**125 blocks -** 2n = 126 = 2(63) = 126

126 = 126

*** You change 125 to 126 to make it easier, but if you want to solve it using 125 then ..**

**125 blocks -** 2n = 2(62.5) = 125

125 = 125