In class we were doing some investigations about patterns and relationships between them, and at the end of the investigation, we would have to find an algebraic expression that would work every time for the pattern!

Patterns and Relations investigations answer sheet!

Stuck In My Teeth!!!

(**Note, we had the information about the first few figures but i will draw out all five.)

First We had to:

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

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

See ain't that pretty? Now for the next step!

Now that the B-E-A utiful chart is done, we now go on to the next step!

Isn't it weird that "x" is on the bottom?

3. Describe the patterns found in each row.

y= toothpicks Start with 3

Increase by 2 for each new figure

x=Figure # Start with 1

Increase by 1

b. Describe why the patterns increase the way that they do.

For every new figure , you get two new toothpicks!

Both of the Columns Increase

"x"=Figure # - Increase by one

"y"=Toothpicks - Increase by two

Isn't it weird that "x" is on the bottom?

3. Describe the patterns found in each row.

y= toothpicks Start with 3

Increase by 2 for each new figure

x=Figure # Start with 1

Increase by 1

b. Describe why the patterns increase the way that they do.

For every new figure , you get two new toothpicks!

that was easy right? Onto the next step:

4.Describe the relationship between the two columns.Both of the Columns Increase

"x"=Figure # - Increase by one

"y"=Toothpicks - Increase by two

I know its a weird pattern but its the first one i saw and its the simplest!

Onto the next Step

:

Onto the next Step

:

c. Write an algebraic equation to show this relationship.

(WARNING, an expression is the one without the answer. An EQUATION is the one with the answer. Remember that!)

(WARNING, an expression is the one without the answer. An EQUATION is the one with the answer. Remember that!)

2x + 1 = y

Let "x" equal - Figure number

Let "y" equal - Toothpicks

Let "x" equal - Figure number

Let "y" equal - Toothpicks

MAN that was easy! did you get it? i thought so!

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

2x+1=y

20th- 2(20)+1=41

2x+1=y

35th- 2(35)+1 = 71

2x+1=y

99th- 2(99)+1= 199

7.Make a graph for the first 6 terms and label the line according by its equation

Was that a little tricky? Not even!

Thanks for reading, please comment on any mistakes i have made or maybe you can compliment on my fabulous work!

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

2x+1=y

20th- 2(20)+1=41

2x+1=y

35th- 2(35)+1 = 71

2x+1=y

99th- 2(99)+1= 199

7.Make a graph for the first 6 terms and label the line according by its equation

Was that a little tricky? Not even!

Thanks for reading, please comment on any mistakes i have made or maybe you can compliment on my fabulous work!

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