Ec-6 Generalist - Math

Front 1

Competency 013

Back 1

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

Front 2

NCTM

Back 2

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

Front 3

Jean Piaget- Stages of intellectual development

Back 3

Sensorimotor (birth-2 years)

Preoperational (years 2-7)

Concrete Operational (years 7-11)

Formal Operational (years 11-adult)

Front 4

Math Materials Grades k-1

Back 4

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

Front 5

Math Materials Grade 2

Back 5

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

Front 6

Math Materials Grade 3

Back 6

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

Front 7

Math Materials Grade 4

Back 7

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

Front 8

Math Materials Grade 5

Back 8

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

Front 9

Math Materials Grade 6

Back 9

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

Front 10

Competency 014: Number Concepts and Operations

Back 10

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

Front 11

Algorithm

Back 11

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

Front 12

Changing improper fractions

Back 12

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)

Front 13

adding and subtracting mixed numbers

Back 13

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.

Front 14

Changing mixed numbers to fractions

Back 14

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

Front 15

Competency 015: Patterns and Algebra

Back 15

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

Front 16

Performing operations with negative and positive numbers

Back 16

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

Front 17

Competency 016: Geometry and Measurement

Back 17

The teacher understand concepts and principles of geometry and measurement.

Front 18

Finding the perimeter

Back 18

Perimeter of a square P=4x

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

Front 19

Finding the perimeter cont...

Back 19

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.

Front 20

Finding the area

Back 20

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)

Front 21

Cube

Back 21

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

Front 22

Triangle, Rectangle, parallelogram, circle

Back 22

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

Front 23

Competency 017: Probability and Statistics

Back 23

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

Front 24

Range, Mean, Median, Mode

Back 24

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.

Front 25

Competency 018: Mathematical Processes

Back 25

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

Front 26

1950-1960

Back 26

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