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Sequences and Equations

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.

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Sequences and Equations

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  1. Sequences and Equations

  2. 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.

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

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

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

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

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

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

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

  10. 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.

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

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

  13. 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.

  14. Sequences and Equations

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

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

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

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

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

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

  21. Algebraically, Using a table,

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