A comprehensive instructional lesson on evaluating linear and quadratic functions across multiple representations including algebraic equations, tables, coordinate graphs, and mapping diagrams, featuring dedicated multi-tiered scaffolding and specialized ENL dual-language resources.
Tables & Mapping Diagrams / Tablas y Diagramas de Mapeo
3. Table for \( k(x) \) / Tabla de Valores
\( x \) (Input)
-3
0
2
5
\( k(x) \) (Output)
-7
2
8
17
\( k(2) = \) ________
\( k(-3) = \) ________
\( k(0) = \) ________
If \( k(x) = 17 \), \( x = \) _____
4. Mapping for \( m(x) \) / Diagrama
Input (x) -2 1 4 Output m(x) 0 5 11
\( m(1) = \) ___
\( m(-2) = \) ___
\( m(4) = \) ___
PART 3 / PARTE 3
Coordinate Graphs (Blue Line \( f(x) \), Green Parabola \( g(x) \))
x y 2 4 -2 2 4 -2 -4 f(x) g(x)
a) \( f(2) = \) ________
Read y at \( x = 2 \)
b) \( f(-1) = \) ________
Read y at \( x = -1 \)
c) \( g(0) = \) ________
Vértice / Vertex
d) \( g(3) = \) ________
Read y at \( x = 3 \)
Reverse Input / Entrada Inversa:
Find \( x \) if \( f(x) = 2 \): \( x = \) ____
Find \( x \) if \( g(x) = 0 \): \( x = \) ____ & ____
Part 4: Drone Model & Explanation / Modelo de Dron y Explicación \( H(t) = 12t + 30 \)
Evaluate \( H(5) \):
\( H(5) = 12(5) + 30 = \) _______ ft
Meaning: After 5 sec, altitude is ______ ft.
English: "To evaluate \( f(4) \), replace \( x \) with , multiply, and subtract 5 to get ."
Español: "Para evaluar \( f(4) \), reemplazo \( x \) con , multiplico, y resto 5 para obtener ."
EXIT TICKET / BOLETO DE SALIDA Mastery Check • Entregar al Final
Turn In / Entregar • 7 Pts
1. Evaluate \( f(4) \) for \( f(x) = 5x - 7 \):
\( f(4) = 5(\quad\quad) - 7 \)
\( \quad\quad = \quad\quad - 7 = \) ____________
2. Evaluate \( g(-4) \) for \( g(x) = x^2 + 5 \):
\( g(-4) = (\quad\quad)^2 + 5 \)
\( \quad\quad = \quad\quad + 5 = \) ____________
Math Regents Prep • ENL Dual-Language Worksheet Page 2 of 2
Practice 1 Sentence Stems:
• Linear: "When input is 4, the output is 7." / "Cuando la entrada es 4, la salida es 7."
• Quadratic: "The value of \( g(5) \) is 32." / "El valor de \( g(5) \) es igual a 32."
Part 4 Explanation Frames:
• English: "To evaluate \( f(4) \), replace \( x \) with 4, multiply by 3, and subtract 5 to get 7."
• Español: "Para evaluar \( f(4) \), reemplazo \( x \) con 4, multiplico por 3, y resto 5 para obtener 7."
Common Student Misconceptions & Coaching
1. Squaring Negatives without Parentheses:
Students typing -3^2 in calculators get -9. Insist that input replacement MUST use parentheses: (-3)^2 = 9.
2. Confusing \( f(x) = k \) vs. \( f(k) \):
When given \( f(x) = 2 \), students often substitute 2 for \( x \). Emphasize that \( f(x) \) is the output (\( y \)-value), so look for \( y = 2 \) to find \( x = 0 \).
Lesson Facilitation & Turn-In Protocol:
Warm-Up (0-5 min): Students complete Do Now directly on the top of Page 1. Quick 1-minute partner check.
Lab Practice (6-35 min): Circulate with targeted support for Part 3 graph reading. Provide ENL sheets for bilingual students.
Exit Ticket (36-45 min): Students complete bottom of Page 2 independently. Collect entire 2-page handout for daily grading.
Math Regents Prep • Teacher Solutions Guide Page 2 of 2
