Sequences and Equations

Common Core State Standards MACC.7.EE.1.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. MACC.7.EE.1.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Highlights Mathematical Practice #8 Look for and make use of repeated reasoning.

Sequences and Equations These dot diagrams show the beginning of a sequence of patterns: What would the fifth pattern in the sequence look like?

Sequences and Equations These dot diagrams show the beginning of a sequence of patterns: Something look like this?

Sequences and Equations If we were to continue the pattern, how many dots of each color will there be in the 10 th pattern?

Sequences and Equations How can we write an algebraic expression for the number of white dots? term12345n white dots13579???

Sequences and Equations How can we write an algebraic expression for the number of white dots? term12345n white dots n – 1

Sequences and Equations How can we write an algebraic expression for the number of black dots? term12345n black dots23456???

Sequences and Equations How can we write an algebraic expression for the number of black dots? term12345n black dots23456n + 1

Sequences and Equations How can we write an algebraic expression to find the total number of dots? One way to do this is by looking at the patterns again.

Sequences and Equations How can we write an algebraic expression to find the total number of dots? term12345n total dots ???

Sequences and Equations How can we write an algebraic expression to find the total number of dots? term12345n total dots n3n

Sequences and Equations How can we write an algebraic expression to find the total number of dots? Another way to do this is by looking at the algebraic expressions we found.

Sequences and Equations Number of white dots + Number of black dots = Total number of dots 2n – 1n + 13n3n

Sequences and Equations These dot diagrams show the beginning of a sequence of patterns: What would the fifth pattern in the sequence look like?

Let’s look at another pattern: Write an algebraic expression to find the number of white dots. term1234n white dots2345???

Let’s look at another pattern: Write an algebraic expression to find the number of white dots. term1234n white dots2345n + 1

Let’s look at another pattern: Write an algebraic expression to find the number of black dots.

Let’s look at another pattern: Write an algebraic expression to find the number of black dots. term1234n black dots3456n + 2

Let’s look at another pattern: Write an algebraic expression to find the total number of dots.

Algebraically, term1234n total dots579112n + 3 Using a table,