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Algebra I - EC: A1.1.1.5.2

Algebra I - EC: A1.1.1.5.2

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. Factor the following expression. 9x – 3.
  1. Factor the following expression. x2 – 4x.
  1. Factor the following expression. x2 – 36.
  1. Factor the following expression. x2 + 7x + 12.
  1. Factor the following expression. x2 – 11x – 12.
  1. Factor the following expression. -2x2 + 10x + 28.
  1. Factor the following expression. 5x3 + 5x2 – 60x.
  1. Factor the following expression. -x2 + 13x + 30.
  1. Factor the following polynomial expression. 30x6 – 42x4 + 72x2 – 18x + 120.
  1. Factor the following polynomial expression. 63ab – 81a2b + 36ab3 + 210a4b5.
  1. A square has an area of x2 + 18x + 81 in2, what is the side length, in terms of x, of the square.
  1. A rectangular swimming pool has an area of x2 + x – 30 feet squared, what is the perimeter, in terms of x, of the pool.
  1. A circle has an area of cm2, what is the length of the radius, in terms of x.
  1. Write 3 equivalent expressions that are all factored forms of 2x2 – 6x – 80.
  1. What is the factored form of the following expression?
    (3m2n3 – 2mn + 13m4n5) – (5mn + 2m2n3 – m4n5)
  1. A physicist must factor several trinomials that are all of the form: x2 + mx – n. Give one example of a factored trinomial where m and n are both positive and one factored example where m and n are both negative.
  1. Create 3 quadratic expressions that can be factored. Make one expression a trinomial. Make the second expression a difference of two squares expression. Make the third expression one that includes a greatest common factor.
  1. What is the factored form of the following expression when x = -4?
    xp2 + 4xp – 12

Answer Key/Rubric

  1. 3(3x – 1)
  2. x(x – 4)
  3. (x + 6)(x – 6)
  4. (x + 4)(x + 3)
  5. (x – 12)(x + 1)
  6. -2(x – 7)(x + 2)
  7. 5x(x + 4)(x – 3)
  8. (-x – 2)(x – 15) or (x + 2)(-x + 15) or -1(x – 15)(x + 2)
  9. 6(5x6 – 7x4 + 12x2 – 3x + 20)
  10. 3ab(70a3b4 + 12b2 – 27a + 21)
  11. x + 9 inches
  12. 4x + 2 feet
  13. x + 6 cm
  14. 2(x – 8)(x + 5) = (2x – 16)(x + 5) = (x – 8)(2x + 10)
  15. mn(14m3n4 + mn2 – 7)
  16. Various Answers - could be x2 + 5x – 6 = (x + 6)(x – 1) and x2 – 11x – (-10) = (x – 10)(x – 1)
  17. Various Answers - could be 1. x2 + 2x + 1 = (x + 1)(x + 1), 2. x2 – 25 = (x + 5)(x – 5) and 3. 3x2 – 33x + 90 = 3(x – 5)(x – 6)
  18. -4(p + 3)(p + 1)
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