BASIC GEOMETRY

Point: A point is a location in space. It is represented by a dot. Point are usually named with a upper case letter. For example, we refer to the following as "point A"

Line: A line is a collection of points that extend forever. The following is a line. The two arrows are used to show that it extends forever.

We put two points in order to name the line as line AF. However, there are an infinite amount of points. You can also name it line FA

Line segment: A line segment is part of a line. The following is a segment. A segment has two endpoints. The endpoints in the following segments are A and F. Notice also that the line above has no endpoints.

Ray: A ray is a collection of points that begin at one point (an endpoint) and extend forever on one direction. The following is a ray.

Angle: Two rays with the same endpoint is an angle. The following is an angle.

Plane: A plane is a flat surface like a piece of paper. It extends in all directions. We can use arrows to show that it extends in all directions forever. The following is a plane

Parallel lines When two lines never meet in space or on a plane no matter how long we extend them, we say that they are parallel lines The following lines are parallel.

Intersecting lines: When lines meet in space or on a plane, we say that they are intersecting lines The following are intersecting lines.

Vertex: The point where two rays meet is called a vertex. In the angle above, point A is a vertex.


REFERENCE: http://www.basic-mathematics.com/basic-geometry.html

MULTIPLYING BY POWERS OF TEN

Follow the following shortcut when multiplying by powers of ten

Whole numbers multiplied by powers of 10

When multiplying a whole number by a power of ten, just count how many zero you have and attached that to the whole number

Examples:

1) 56 × 10

There is only one zero, so 56 × 10 = 560

2) 45 × 10,000

There are 4 zeros, so 45 × 10000 = 450000

3) 18 × 10,000,000

There are 7 zeros, so 18 × 10,000,000 = 180,000,000

Decimals multiplied by powers of 10

When multipying a decimal by a positive power of ten (positive exponent), move the decimal point one place to the right for each zero you see after the 1

Examples:

1) 0.56 × 10

There is only one zero, so move the decimal point one place to the right.

0.56 × 10 = 5.6

2) 0.56 × 100

There are 2 zeros, so move the decimal point two places to the right

0.56 × 100 = 56

3) 0.056 × 1000

There are three zeros, so move the decimal point 3 places to the right.

0.056 × 1000 = 56

4) 0.056 × 100,000

0.056 × 100,000 = 0.056 × 1000 × 100 = 56 × 100 = 5600

When multipying a decimal by a negative power of ten (negative exponent), move the decimal point one place to the left for each zero you see before the 1

Note that 0.1 = 10^-1, 0.01 = 10^-2, 0.001 = 10^-3, and so forth....

We call 10^-1, 10^-2, and 10^-3 negative powers of 10 because the exponents are negative

Examples:

1) 56 × 0.1

There is only one zero, so move the decimal point one place to the left.

56 × 0.1 = 5.6

2) 560 × 0.01

There are 2 zeros, so move the decimal point two places to the left

560 × 0.01 = 5.6

2) 560 × 0.001

There are 3 zeros, so move the decimal point two places to the left

560 × 0.001 = 0.560

3) 0.56 × 0.1

There is only one zero, so move the decimal point one place to the left.

0.56 × 0.1 = 0.056

4) 0.56 × 0.01

There are 2 zeros, so move the decimal point two places to the left

0.56 × 0.01 = 0.0056



REFERENCE: http://www.basic-mathematics.com

EFFECTS OF DISCALCULIA

DISCALCULIA AND CAUSES

 DYSCALCULIA:

Dyscalculia is a brain-based condition that makes it hard to make sense of numbers and math concepts. Some kids with dyscalculia can’t grasp basic number concepts. They work hard to learn and memorize basic number facts. They may know what to do in math class but don’t understand why they’re doing it. In other words, they miss the logic behind it.

Other kids understand the logic behind the math but aren’t sure how and when to apply their knowledge to solving problems.

Dyscalculia goes by many names. Some public schools refer to it as a “mathematics learning disability.” Doctors sometimes call it a “mathematics disorder.” Many kids and parents call it “math dyslexia.”

CAUSES OF DISCALCULIA:

Here are some of the possible causes of dyscalculia:

• Genes and heredity: Studies of dyscalculia show it’s more common in some families. Researchers have found that a child with dyscalculia often has a parent or sibling with similar math issues. So dyscalculia may be genetic.
• Brain development: Researchers are using modern brain imaging tools to study the brains of people with and without math issues. What we learn from this research will help us understand how to help kids with dyscalculia. The study also found differences in the surface area, thickness and volume of parts of the brain. Those areas are linked to learning and memory, setting up and monitoring tasks and remembering math facts.]
• Environment: Dyscalculia has been linked to exposure to alcohol in the womb. Prematurity and low birth weight may also play a role in dyscalculia.
• Brain injury: Studies show that injury to certain parts of the brain can result in what researchers call “acquired dyscalculia.”

IMPORTANCE OF MATH IN EARLY CHILDHOOD

Math skills taught in early childhood education are designed to provide the foundation children need to succeed in elementary school and beyond. Educators should focus lessons in early childhood around the basic skills that build up to advanced mathematics in high school and college. From preschool to the end of elementary school, children are setting the foundation for future life skills.

Basic math skills for preschoolers

Early childhood education should introduce simple mathematical concepts. By introducing children to basic terminology early in childhood, teachers are making the elementary education a little easier, and introducing math concepts should start when children are around three years old.

By setting the foundation to understand terminology and concepts early, children are prepared to apply the information in a classroom setting. The concepts are already understood, so elementary teachers are able to focus on the application of ideas.

While preschool children might not yet be ready to learn the practice of the math skills, they can gain a basic idea of the practice through language and practice.

Number sense

Number sense, or the basics of learning about numbers, is the first vital math skill a child must develop before reaching kindergarten. Children must learn to count forwards and backwards early in childhood to learn the relationship between numbers in the future. Number sense is a vital skill that early childhood educators should focus on teaching before children reach kindergarten.

While kindergarten classes review the basics of counting forward and backward, early childhood educators can set a stronger foundation by focusing on learning to count before reaching elementary school. By focusing on number sense, teachers are providing math skills that are necessary for future concepts and advanced calculations.

Learning numbers through representation or pictures

Children are naturally visual and can build relationships between numbers and a represented item. According to the National Center for Infants, Toddlers and Families, using representation or pictures to clarify a relationship is making the use of mathematics real to a child’s mind.

Early childhood education should focus on representing numbers with items, pictures or even family members. For example, learning the basics of counting can use pictures of apples or favorite fruits to help children recognize that the number represents the items depicted.

Teaching through representation or pictures will allow children to make connections between the real world and the math skills that are vital for academic success. Without making a connection between life and math, children can become confused about the information provided in a classroom.

Adding and subtracting

While early childhood education should introduce the concepts before the skills, teachers can begin the basics of adding and subtracting before children move into elementary school. The basic skills are used in normal childhood interactions, such as sharing cookies by subtracting from the original number to ensure the children have the same number of treats.

By focusing on the basics of adding and subtracting, teachers can provide a stronger foundation in math skills for the future. Depending on the age of children, the basics of adding and subtracting might limit the skills to sharing food items or adding items to play activities that encourage children to count the extra items.

According to the National Association for the Education of Young Children, teachers can make use of examples that arise during play activities to teach the ideas of adding or subtracting items. It is an opportunity to teach the skills without actively creating lesson plans that are too advanced for childhood literacy and knowledge.

Preschool math provides academic building blocks

The basic math skills teachers provide in early childhood education set the building blocks for the entire academic career. Without learning simple skills like number sense, math concepts and simple application of ideas like adding, children are not prepared to move into elementary education. Fortunately, young children are able to learn at a remarkable rate and teachers can apply concepts or math skills to normal childhood activities.

reference: http://education.cu-portland.edu

ROMAN NUMERALS:

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols:^[1]

Symbol	I	V	X	L	C	D	M
Value	1	5	10	50	100	500	1,000

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Hindu-Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

MATHEMATICAL SYMBOLS:


Symbols save time and space when writing. Here are the most common mathematical symbols:

ANGLE:
an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.