Math Content Test

Rational Number

A number that can be written as a fraction

A= 3.14r^2 (Pi r squared)

Area of a circle

A=1/2bh

Area of a triangle

Base 60 number system

Babylonians greatest accomplishment

Commutative Property

Changing the order of the numbers and still get the same answer in addition or multiplication Ex. 2x4= 8, and 4x2=8

Aztec

Civilization flourished around 1325 BCE. They were skilled builders and engineers accomplish astronomers and mathematicians.

Attribute Blocks

Colored blocks that come is different colors, shapes, and sizes Helps with sorting, classifying, investigating, sequencing, patterns, symmetry, congruency, similarity, thinking skills, geometry, and organization of data

angles that add up to 90 degrees

Complimentary angles

Equity

Excellence in mathematics education requires. It is high expectations and strong support for all students

Associative Property

Group any numbers together with addition or multiplication Ex: 3 (4 x 5) = 60 and 5 (3 x 4)= 60

Base 10 blocks

Helps with place value, operations on whole numbers, decimals, comparing, ordering, classification, sorting, number concepts, area, periemter

-1

If a negative number is raised to the 0th power, the number is

1

If a number is raised to the 0th power, the number is

combination

If the order does not matter, its a _______________

permutation

If the order matters, it is a ______________

1st grade

In the Texas curriculum, the teaching of place value is required in which of the following?

Mayans

Invented the concept of 0

Babylonians

Numbers with base 60

PEMDAS

Order of Operations

Irrational Number

Real number that cannot be expressed as a ratio of integers (they continue forever) Ex. 3.14

Multicative Inverse

Reciprocals of each other Ex: 0.5=1/2 and the reciprocal of 1/2 is 2

More than 180 degree, but less than 360 degrees

Reflex angle

angles that add up to 180 degrees

Supplementary angles

Upper elementary

The use of digital cameras, balanced metric weight sets, and virtual manipulatives available on the Internet is most appropriate for children in which of the following grade levels?

Scalene Triangle

Triangle with no congruent sides

Equilateral Triangle

Triangle with three equal sides and three equal angles

Isosceles Triangle

Triangle with two equal sides and two equal angles

(10^3x2^3)

What does (10x2)^3 simplify to?

Distributive Property

When an expression involving addition is then multiplied by something. This property tells us that that we can add first and then multiply OR multiply each term inside the ( ) by the multiplier first and then add Ex: 5 (4+7)

Egyptians and Babylonians

Which of the following were the first mathematicians to impact the development of modern-day mathematics?

Minuend

a quantity of number from which another is to be subtracted

supplementary angles

are two angles that add up to 180

complementary angles

are two angles that add up to 90

Pie charts

are used to help visualize relationships based on percentages of a possible 100%. Requires and understanding of percentages which makes it inappropriate for children in early grades

Formal operational stage

begins around eleven years of age and continues into adulthood. Focus on the ability to use symbols and think abstractly

Greeks

built on accomplishments of the Egyptians and Babylonians and further developed math. They discovered rational numbers. Could not accurately express all mathematical values, and then developed irrational numbers

function

can be used to understand how one quantity varies in relation to changes in second quantity. Ex: relationship between price per pound

Mayan

civilization around 700 BCE, developed an elaborate calendar and independently from Arbs, the mathematical concept of zero.

real numbers

describes any number that is positive, negative, or zero and can be used to measure continuous quantities

Hindus

developed system o math that allowed for astronomical calculations. They developed a technique of compilation that later influenced the development of modern day algebra.

prooperational stage

development includes the processes of symbolic functioning, contraption, intuitive thought, egocentric and inability to conserve.

Six principles that should guide mathematics instruction

equity, curriculum, teaching, learning, assessment, and technology

concrete operational stage

exhibit the developmental processes of decentering, reversibility, conservation, serialization, classification, and elimination of egocentrism

planes

flat surface without edges and are two-dimensional, meaning they make infinite length and width but no depth

Can hieles level formal deduction

focus is on higher levels of geometry, using various theorems to teach how tow triangles are congruent

Pictorial, bar, line, pie

four graphs used in grades pre-k-6th?

the van heel theory

has been recognized for its role in describing the levels of thinking associated with learning or geometry, it also had been developed as a general theory of math education.

Babylonians

have a number system of base 10

Similar

if they have the exact same shapes, even if they do not have the same sizes

Congruent

if they have the same shape and size

Inductive reasoning

involves examining particular instances to come to some general assumptions. This type of reasoning is informal and intuitive.

scientific notation

is a form of writing a number as the product of a power of 10 and decimal numbers greater than or equal to 1 and less then 10.

tessellation

is a pattern formed bythe repetition of a single unit of shape that, when repeated, fills the plane with no gaps and no overlaps

Natural number

is a postive integer or a nonnegative interger. Are all the whole numbers. They do not include negative numbers, fractions, or decimals

point

is a specific location, taking up no space, having no area, and frequently represented by a dot. Considered to have no dimensions

intergers

is a whole number that includes all positive and negative numbers including zero; do not include decimals or fractions

algorithm

is an established and well defined step-by-step problem-solving method a=used to achieve a desired mathematical result

Rational

is any number that can be expressed as the quotient or fraction of two integers

Line segment;endpoint

is any portion of a line between two points on that line. It has definite start and a definite end called_____.

Chord

is any segment that goes from one point on the edge of a circle to any other point on the edge

logical reasoning

is closely related to childrens language development. Instruction should help students learn to organize ideas, understand what they are studying, and explain their thinking as they solve problems

Technology

is essential in teaching and learning mathematics; it influences the teaching of mathematics while enhancing and facilitating students learning

Ray

is like a line segment, except it extends forever in on direction

linera function

is one whose graph is a straight line. Equation- y=mx+b

absolute value

is the distance of a number from zero on the number line

thematic instruction

is the organization of curriculum content based on themes or topics

Statistics

is the science of study of data. It is used to describe, analyze, evaluate, and interpret information. The information is then used for predicting, drawing inferences, and making decisions

estimation

is used to make an approximation that is still close enough to be useful

van hiele level of analysis

learners begin to talk and notice the properties of the shapes. Teachers can focus on the various components of the geometric shape

Van Hiele levels visualization

learners developed a mental picture of each shape; therefore, teachers need to provide a of good physical examples and non examples for exploration

Deductive approach

learning step by step

inductive teaching

learning through examples

Rounding

may be used to estimate a sound, difference, or product and to make mental approximation

Jean Piaget

observed and recorded the intellectual abilities of infants, children, and adolescents. Stages were related to brain growth and led him to conned that the thinking and reasoning of children were dominated by preoperatonal thought

The concept of zero

originated in India around 500ce. Came from the hindu tradition

line graphs

present information in a fashion similar to bar graph, but they use points and lines.

Matrix

rectangular array of numbers, symbols, or expressions, arranged in rows and columns; used to solve linear techniques

deductive reasoning

requires moving from an assumption to a conclusion. It is resigning from the general to the specific, and it is supported by deductive logic

van hiele level informal deduction

students stop relying on visualization and now use relationships to make a conclusion. Focus is o the first two level for students in K-8.

addends

terms being added

Classification

the child can name and identify sets of objects according to appearance, size, or other characteristics; the child can arrange objects based on characteristics

Decentering

the child can take into account multiple aspects of a problem to solve it; the child can form a conclusion based on reason rather perception.

Serialization

the child is able to arrange objects in an order according to size, shape, or any other attribute, the child can arrange geometric forms by shape, size, color, and thickness of them

Elimination of egocentrism

the child is able to view things from one another perspective; the child can retell a story from another child perspective

Reversibility

the child understand that the objects can be changed and then returned to their original state; the child can determine that 4+4=8 and 8-4=4, the original quantity

Compositions of functions

the domain (the x-values) of the next function

Product

the result of multiplying

Analysis

the systematic reflection which teacher engage

Pictorial graph

they represent a transition from the real objects graphs to symbolic graphs. Used to introduce children to graphing in pre-k through 1st

Prism

three-dimensional solid consisting of a collection of polygon with two congruent parallel faces that are polygons are lateral faces that are parallelograms

Conservation

understanding that quantity, length, or number of items is unrelated to the arrangement of appearance of the jets or items. Ex: child may think penny worth more then dime cause size

the number system

used in modern days is described as hindu-arabic numeration system. It uses # 0-9

Bar graphs

used to represent two elements of a single subject

front-end estimation

uses the leading or left-most digit to make an estimate quickly and easily

arab contributions

were the first civilization to solve sophisticated algebraic equations to solve sophisticate algebraic equations such as those currently used in science and engineering. They also developed and perfected geometric algebra. They founded non-Euclidian geometry.

Egyptians

wrote number using hieroglyphs