EC-6 Generalist - Math

Competency 013

The teacher understands how students learn mathematical skills and uses that knowledge to plan, organize, and implement instruction and assess learning.

NCTM

National Council of Teachers of Mathematics: Principles and Standards for School Mathematics.

Jean Piaget- Stages of intellectual development

Sensorimotor (birth-2 years)

Preoperational (years 2-7)

Concrete Operational (years 7-11)

Formal Operational (years 11-adult)

Math Materials Grades k-1

beads, strong, sewing cards, snap cubes, straws, color tiles, two-color counters, macaroni, beans, cereal, cancy, raisings crackers, buttons, sticks, stones, shells, paper clips, toothpicks, legos, egg cartons, teddy bear counters, board games, pictographs

Math Materials Grade 2

blocks, cubes, chips, measuring cups, attribute shapes, money models, number lines, dominoes, unifix cubes, clock faces, ruler, yard stick, metric stick, balance scales, linear graphs

Math Materials Grade 3

base ten blocks, tangrams, pattern blocks, playing cards, scales: customary and metric, magnetic numbers, chalk boards, spinners, dice, calendar, fractional shapes, games, measuring tape, 0-99 charts, bar graphs

Math Materials Grade 4

geomatric solids, geoboards, calculators, protractors, tangrams, pentominoes, graphing paper, fraction kit, platform scale, customary weight set, metric weight set, graphing boards, scatter plot graphs

Math Materials Grade 5

cuisenaire rods, virtual minipulatives, calculators, graduated cylinders, timers, metric beaker set for volume, metric trundle wheel, fraction tower cubes, connecting cubes, board games, fraction tiles, geoboards, pie charts and graphs

Math Materials Grade 6

cuisenaire rods, virtual manipulative, calculators, attribute logic block, algebra tiles, video games, math software games, ipods, balance metric weight set, computer/internet, smart boards, digital cameras, camcorders, computer templates

Competency 014: Number Concepts and Operations

The teacher understands concepts related to numbers, operations and algorithms, and the properties of numbers.

Algorithm

well-defined step by step problem solving method used to achieve a desired mathematical result.

Changing improper fractions

to change an improper fraction like 5/2, to a mixed number, divide the numberator by the denominator and represent the remainder as a fraction, for example: 2 1/2 (5/2=4+1/2=2x2+1/2=2 1/2)

adding and subtracting mixed numbers

add or subtract the fractions, then add or subtract the whole numbers. "Borrow" from the whole numbers if necessary to complete to complete the operation as needed.

Changing mixed numbers to fractions

to change a mixed number, multiply the denominator by the whole number, then add the result to the numberator to obtain the new numerator. ex. 2 3/4= 2x4+3/4=8+3/4= 11/4

Competency 015: Patterns and Algebra

The teacher understands concepts related to patterns, relations, functions, and algebraic reasoning.

Performing operations with negative and positive numbers

negative x positive = positive (-6 x -5 =30) positive x positive = positive (6 x 5 = 30) positive x negative = negative (6 x -5= -30)

Competency 016: Geometry and Measurement

The teacher understand concepts and principles of geometry and measurement.

Finding the perimeter

Perimeter of a square P=4x

Perimeter of a Rectangle P=2l+2w or P=2(l + w)

Finding the perimeter cont...

Perimeter of a square (multiply four times the measure of a side of the square ex. p=4s

Perimeter of a rectangle add twice the length of the rectangle to twice the width of the rectangle

Perimeter of a triangle add the measures of the three sides of the triangle.

Finding the area

multiply the measure of the length of the rectangle by the measure of the width of the triangel. A= L X W

Area of a square by squaring the measure of the side of the square. a=s(squared)

Cube

a three-demensional solid figure f(faces) v(vertices) e(edges) f + v = e + 2

Triangle, Rectangle, parallelogram, circle

(triangle)a = b x h/2
(rectangle)a = l x w
(parallelogram)a = l x h
(circle)a = 3.14r(squared)

Competency 017: Probability and Statistics

The teacher understands concepts related to probability and statistics and their applications

Range, Mean, Median, Mode

Range - set of data is the difference between the greatest and the least numbers in the data set.
Mean- set of data is the average of the data values.
Median- st of data is the middle value of all the numbers.
Mode- the value or values that appear in a set of data more frequently than any other value.

Competency 018: Mathematical Processes

The teacher understands mathematical processes and knows how to reason mathematically, solve mathematical problems, and make mathematical connections within and outside of mathematics.

1950-1960

significant changes in content of elem math programs, new content added, standard content taught at earlier grade levels