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Insights Into Algebra 1 - Teaching For Learning
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Topic Overview Lesson Plans Student Work Teaching Strategies Resources
Workshop 5 Properties Lesson Plans
Lesson Plans:

Introduction

Lesson Plan 1: The X Factor - Trinomials and Algebra Tiles

Lesson Plan 2: Curses and Re-Curses! It's Happening Again.
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NCTM Standards


Lesson Plan 1: The X Factor - Trinomials and Algebra Tiles

Overview Procedures For Teachers Related Standardized Test Questions Materials

The questions below dealing with factoring polynomials have been selected from various state and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.

  • Taken from the New York Regents High School Examination, Mathematics (August 2002):
    A rectangular park is three blocks longer than it is wide. The area of the park is 40 square blocks. If w represents the width, write an equation in terms of w for the area of the park. Find the length and the width of the park.

    Solution: w(w + 3) = 40, w2 + 3w - 40 = 0, (w + 8)(w - 5) = 0, w + 8 = 0 or w - 5 = 0, w = -8 or w = 5. The width must be positive, so w = 5 and l = 8. The width of the park is five blocks and the length of the park is 8 blocks.
  • Taken from the New York Regents High School Examination (January 2003):
    What are the factors of x2 - 10x - 24?

    A. (x - 4)(x + 6)
    B. (x - 4)(x - 6)
    C. (x - 12)(x + 2) (correct answer)
    D. (x + 12)(x - 2)
  • Taken from the Virginia Standards of Learning Assessment (Spring 2002):
    Which property justifies the following statement?

    If 3a + 3b = 12, then 3(a + b) = 12

    A. Commutative property of multiplication
    B. Distributive property for multiplication over addition (correct answer)
    C. Multiplicative identity property
    D. Associative property of addition
  • Taken from the Virginia Standards of Learning Assessment, Algebra I (Spring 2002):
    Which is the complete factorization of 2x2 + 5x + 3?

    A. (2x + 1)(x + 2)
    B. (2x + 1)(x + 3)
    C. (2x + 2)(x + 1)
    D. (2x + 3)(x + 1) (correct answer)
  • Taken from the Virginia Standards of Learning Assessment, Algebra I (Spring 2002):


  • Taken from the Virginia Standards of Learning Assessment, Algebra II (Spring 2001):
    Which is a zero of the function f(x) = x2 + 6x + 8?

    A. -8
    B. -4 (correct answer)
    C. 2
    D. 4
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