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Algebra I - EC: A1.1.1.5.3

Algebra I - EC: A1.1.1.5.3

Continuum of Activities

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

  • Instructional activities designed to be integrated into planned lessons
  • Questions/activities that grow in complexity
  • Opportunities for differentiation for each student’s level of performance

Activities

  1. Simplify , x≠-7, 3.
  1. Simplify , x≠-8, 11.
  1. Simplify , x≠-3, 0.
  1. Simplify , x≠-5, 0.
  1. Simplify , x≠ -2, -1.
  1. Simplify   , x≠-7, -3.
  1. Simplify , x≠0, 5.
  1. Simplify , x≠-6, 2.
  1. Simplify , x≠-8, 7.
  1. Simplify , x≠ -25, 2.
  1. Simplify , x≠-3, 4.
  1. Simplify , x≠ -7, 0, 9.
  1. Simplify , x≠-2.
  1. Simplify , x≠-1, 6.
  1. Simplify , x≠ -91, 0.
  1. When a = x2 – 24x + 144 and b = 3x2 – 36x, what is the simplified form of ?
  1. Explain why the values x = 4 and x = -5 are excluded when simplifying the following rational expression:  .
  1. Simplify the following rational expression:   x ≠-2, 3, 4.
  1. Create a rational expression that simplifies to the expression .
  1. Simplify the following rational expression: 
  1. One rectangle has an area of x2 – 9 inches. A square’s area is x2 – 6x + 9, what is the simplified ratio of the square’s area to the rectangle’s area.
  1. Simplify the following rational expression: 
  1. Why can’t   be simplified for most values of a and b, while can always be simplified?
  1. Explain why it would help you to look at the excluded values for x when simplifying a rational expression.
  1. Determine values for a and b so that can be simplified to the form where a, b, c, and d are all integers.

Answer Key/Rubric

  1. 1
  1. If, x were to equal either 4 or -5, then the denominator of this expression would be zero, so it would be an undefined expression.
  1. Various answers including: 
  1. 1 – x
  1. When you add or subtract different numbers to a value (x) the prime factorization of the numbers completely changes meaning that any common factors in the individual numbers are not necessarily present in their sum. On the other hand, when you are multiplying a value (like x) by other numbers the factors of x are always found in the product and since those factors are common to both the numerator and denominator, they can always be canceled out of the rational expression.
  1. Since the excluded value for a rational function are the zeros of the denominator, you could always use those zeros to create factors for the denominator. For example, in the expression       ?      the excluded values are x≠-2, -4. This means that the factors for the denominator are (x+2)(x+4).

  2. Various answers including a= 6 and b=10

 

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