Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Lesson Plans: Introduction Lesson Plan 1: The X Factor - Trinomials and Algebra Tiles Lesson Plan 2: Curses and Re-Curses! It's Happening Again.

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

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
C. Multiplicative identity property
• 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