Creating Equations from Number Patterns (Functions) Today’s Lesson Creating Equations from Number Patterns (Functions)

Warm-Up Activity We will warm up today by working on our number sense skills.

What are some other ways to write this number? 175% 1.75

What are some other ways to write this number? 162.5% 1.625

What are some other representations of this number? 10,023,756 What are some other representations of this number? ten million, twenty-three thousand, seven hundred fifty-six 10,023,756.0

Whole-Class Skills Lesson Today, you will formulate equations of functions based on patterns in manipulatives and tables.

What pattern do you see with the perimeter of these squares? 1 1 1 Number of Squares Perimeter 1 4 2 8 3 5 nth What pattern do you see with the perimeter of these squares?

What does the next set of squares look like in the pattern? 1 1 1 What does the next set of squares look like in the pattern? 1 1 1

12 What is the total perimeter for the three squares? 1 4 2 8 3 5 nth Number of Squares Perimeter 1 4 2 8 3 5 nth What is the total perimeter for the three squares? 12

What does the next set of squares look like in the pattern? 1 1 1 1 1 1 What does the next set of squares look like in the pattern? 1 1 1 1

16 What is the total perimeter for the four squares? 1 4 2 8 3 12 5 Number of Squares Perimeter 1 4 2 8 3 12 5 nth What is the total perimeter for the four squares? 16

What does the next set of squares look like in the pattern? 1 1 1 1 1 1 1 1 1 1 What does the next set of squares look like in the pattern? 1 1 1 1 1

20 What is the total perimeter for the five squares? 1 4 2 8 3 12 16 5 Number of Squares Perimeter 1 4 2 8 3 12 16 5 nth What is the total perimeter for the five squares? 20

What expression will allow you to find the nth term? Number of Squares Perimeter 1 4 2 8 3 12 16 5 20 nth 4n

The number of squares, n is the independent variable. Perimeter 1 4 2 8 3 12 16 5 20 nth 4n The perimeter is the dependent variable. Perimeter = 4n This is a function.

y = 3x + 1 x y We can evaluate this function by using substitution 4 2 7 3x + 1 Choose any value for x. This is the independent variable. 2 7 The function tells you what to do with the value chosen for x. 13 Once you substitute your value for x, the function returns the value for the dependent variable, y. 22

1 1 1 Number of Triangles Perimeter 1 3 2 6 4 nth What pattern do you see with the perimeter of these equilateral triangles? 9 12

What does the next set of triangles look like in the pattern? 1 1 1 What does the next set of triangles look like in the pattern? 1 1 1

9 What is the total perimeter for the three equilateral triangles? 1 3 Number of Triangles Perimeter 1 3 2 6 4 nth What is the total perimeter for the three equilateral triangles? 9

What does the next set of triangles look like in the pattern? 1 1 1 1 1 1 What does the next set of triangles look like in the pattern? 1 1 1 1

What is the total perimeter for the four triangles? 1 1 1 1 Number of Triangles Perimeter 1 3 2 6 9 4 nth What is the total perimeter for the four triangles? 12

What equation will allow you to find the nth term? Number of Squares Perimeter 1 3 2 6 9 4 12 nth 3n

What would the perimeter of 100 triangles be? Number of Triangles Perimeter 1 3 2 6 9 4 12 nth 3n = 3(100) = 300 The perimeter of 100 triangles is 300. 3n