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Competency 015

Competency 015. Patterns and Algebra. The teacher understands concepts related to patterns, relations, functions, and algebraic reasoning. Competency 015. Patterns and Algebra. Competency 015. Numbers and their Properties.

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Competency 015

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  1. Competency 015 Patterns and Algebra The teacher understands concepts related to patterns, relations, functions, and algebraic reasoning.

  2. Competency 015 Patterns and Algebra

  3. Competency 015 Numbers and their Properties Commutative property= El orden de los factores no altera la suma o el producto. Ejemplo: a + b = b + a 2 + 3 = 3 + 2 Suma 2 x 3 = 3 x 2 Multiplicación Associative Property= El orden de asociar las sumandos o los factores no altera el resultado. Ejemplo: (a + b) + c = a + (b +c) (2 + 3) + 3 = 8 ó 2 + (3 + 3) = 8 (2 x 2) x 3 = 12 ó 2 x (2 x 3) = 12

  4. Competency 015 Numbers and their Properties Property of Zero= La suma de cero a un numero es el mismo numero y la multiplicación por cero siempre es cero. Suma = 2 + 0 = 2 Multiplicación = 2 x 0 = 0 Distributive Property= Se puede sumar y después multiplicar o multiplicar y después sumar: a ( b + c) = (a x b) + (a x c) 2 ( 2 + 3) = (2 x 2) + (2 x 3) = 10

  5. Competency 015 Linear and Nonlinear Functional Relationship Linear function= Vamos a encontrar los valores de los pares ordenados o las coordenadas de una función. f(x) = 3x² -4x + 1 by “0” f(0) = 3(0)² -4(0) + 1 = 1 f(x) = 3x² -4x + 1 by “1” f(1) = 3(1)² -4(1) + 1 = 0 f(x) = 3x² -4x + 1 by “2” f(2) = 3(2)² -4(2) + 1 = 5 f(x) = 3x² -4x + 1 by “3” f(3) = 3(3)² -4(3) + 1 = 15

  6. Competency 015 Algebraic Pattern Algebraic Pattern= It is a set of numbers and variables in a specific order that form a pattern. You need to apply a math operation in order to solve a algebraic pattern problem. For example:

  7. Competency 015 Patterns Patterns: Los patrones son usados para enseñar la relación lógica y el razonamiento matemático. Los patrones ayudan a predecir el siguiente numero u objeto en el orden de las cosas. 4, 6, 10, 12, 16, 18, 22, 80, 40, 20, ____, ____, _____

  8. Competency 015 Operations with Algebraic Expressions Addition and subtraction: Para sumar o restar expresiones algebraicas, tienen que existir expresiones algebraicas similares. 2X³ + 7X³ = 9X³ 20X² - 5X² = 15X² Multiplication and division: 4F² . 3F ³ = 12F 20X = 4X ³ 5X² 5 5 Multiplication of Binomials: (x – 4) (2X – 3) = 2X ² -3X – 8X + 12 = 0 2X ² - 11X + 12 = 0

  9. Competency 015 Operations with Algebraic Expressions Performing Operations with Negative and Positive Numbers: Negativo x (negativo) = Positivo -4 x -3 = 12 Positivo x (Positivo ) = Positivo 3 x 5 = 15 Negativo x positivo = negativo -5 x 2 = -10 Positivo x negativo = negativo 6 x -3 = -18

  10. Competency 015 Graphs and Symbolic Representation Tables: Es una representación ordenada de datos. Graphs: Es una representación pictórica de los datos.

  11. Competency 015 Graphic Representation Los candidatos a maestros requerirán que estudien gráficos, tablas, y cuadros. De PK a 4to grado hay 4 tipos de gráficos: Pictórico, de barras, lineal y de torta o pastel.

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