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MATH TIPS for PARENTS NUMBER PROPERTIES THE OPERATION CALLED ADDITION Associative Property of Addition: • Changing the grouping of the terms (addends) will not change the sum (answer in addition) In Arithmetic: (5 + 3) + = (3 + 2) In Algebra: (a + b) + c = a + (b + c) Commutative Property of Addition • Changing the order of the numbers (addends) will not change the sum (answer in addition) In Arithmetic: + = + In Algebra: a+b=b+a Identity Property of Addition • Zero added to any given number (given addend), the sum will equal the given number (given addend) In Arithmetic: + = In Algebra: a+0=a Inverse Operation of Addition • Subtraction undoes the operation called addition In Arithmetic: If + = 11, then 11 - = and 11 - = In Algebra: a + b = c, then c - a = b and c - b = a THE OPERATION CALLED SUBTRACTION Inverse Operation of Subtraction • Addition undoes the operation called subtraction In Arithmetic: If 16 - = 7, then + = 16 and + = 16 In Algebra: c - b = a, then b + a = c and a + b = c THE OPERATION CALLED DIVISION Inverse Operation of Division • Multiplication undoes the operation called division In Arithmetic: If 48 / = 6, then x = 48 and x = 48 In Algebra: c / b = a, then b x a = c and a x b = c Line/Line Segment or Segment LINE A set of points Illustration: • The word “line” means straight line • Extends indefinitely in each of its two directions • A geometric line is the property these models of lines have in common; it has length but no thickness and no width; it is an idea • The edge of a ruler, a taut string or wire or an edge of this page is a model of a line LINE SEGMENT or SEGMENT: • A part of a straight line consisting of two points, called endpoints, and all the points that are between these points on the line • Has definite length Illustration: •P • Q Line of Symmetry/Midpoint of a Line LINE OF SYMMETRY: A line which divides a figure into two congruent parts When a figure is folded along a line symmetry, the parts fit exactly on one another Illustration: MIDPOINT ON A LINE: The point on a line segment which is the same distance from the endpoints; midway between the endpoints of a line segment Illustration: • •A Q• •B R• P Point Symmetry/Parallel Lines POINT SYMMETRY: Can be fitted onto itself by making 1/2 turn about a point Illustration: A point symmetry • B • D D C •O C B A PARALLEL LINES: Two lines in the same plane that not intersect Illustration: R S X W X Y Z Y A B C D Perpendicular/Parallel PERPENDICULAR BISECTOR: A line which bisects a segment and is perpendicular to it Illustration: R E C D G PARALLEL Travel the same direction apart of every point, so as never to meet, as lines, planes, etc Perimeter PERIMETER • The distance around a figure (polygon) • The perimeter of any polygon can be found by adding the measures of the sides of the polygon, if they are given in the same unit • When you find the perimeter of a figure, the length and the width must be in the same units If the dimensions of a figure are in inches, the perimeter will be in inches If the dimensions of a figure are in centimeters, the perimeter will be in centimeters If the dimensions of a figure are in feet, the perimeter will be in feet • Finding the perimeter of any polygon is based on addition of measures • The perimeter of some polygons can be expressed by a formula PERIMETER OF A RECTANGLE: Perimeter = x Length + x Width or P=2xL+2xW or P = x (L + W) PERIMETER OF A SQUARE: Perimeter = x length of one side or P=S+S+S+S or P = 4S PERIMETER OF A TRIANGLE: Perimeter = Side + Side + Side or P=S+S+S Plane/Plane Figure/Point PLANE Travel the same direction apart of every point, so as never to meet, as lines, planes, etc Illustration: PLANE FIGURE All the points of a figure lying on the same plane Illustration: a b c d e Z X Q R Y POINT An idea about an exact location; it has no dimensions whatsoever but is represented by a dot (•) There is an unlimited number of lines through a point Polygon (Regular Polygon/Figure/Plane Figures/Simple Closed Figure) POLYGON A simple closed figure that consists only of line segments REGULAR POLYGON: A polygon with congruent sides and congruent angles FIGURE: In Geometry, any sets of points PLANE FIGURES: Rectangle, square and circle are the most common SIMPLE CLOSED FIGURE: A Simple Closed Figure is one that does not intersect (cross) itself If it is made up of line segments it is called a polygon Illustration: Polygon (Parallelogram/Pentagon/Octagon/Quadrilateral/Rectangle) PARALLELOGRAM: A quadrilateral in which opposite sides are parallel PENTAGON: A polygon with five sides OCTAGON: An eight-sided polygon QUADRILATERAL: A polygon (simple closed figure) formed by four line segments RECTANGLE: A quadrilateral (polygon) with two pairs of parallel sides and four right angles (4 sides and square corners) Illustration: P O M N Polygon (Square/Trapezoid) SQUARE: A quadrilateral (polygon) with congruent sides the same length and four right angles Also, the product when a number is multiplied by itself Example: x = 9, The square of or 3 Illustration: Z Y W X TRAPEZOID: A quadrilateral (polygon) with only one pair of parallel sides Illustration: 12" 8" 22" Polygon (Triangle) TRIANGLE: A figure (polygon) with three sides KINDS: EQUILATERAL TRIANGLE: A triangle all of whose sides are congruent ISOSCELES TRIANGLE: A triangle with at least two sides congruent RIGHT TRIANGLE: A triangle with one right angle SCALENE TRIANGLE: A triangle with no congruent sides • LEGS (of a right triangle): The two sides in a right triangle that are also sides of the right angles leg H Hypotenuse c Illustration: B K G b a leg SCALENE A ISOSCELES C EQUILATERAL RIGHT • HYPOTENUSE: The side opposite the right angle in a right triangle Protractor/Prism/Ray PROTRACTOR An instrument for measuring angles just as a ruler is an instrument for measuring line segments PRISM A closed space figure The bases are congruent polygons in parallel planes RAY • A point on a line and all the points in one direction from the point • Has infinite length and only one endpoint (vertex) • The sides of the angle Illustration: R S NOTE: FIGURE 1: Q FIGURE 1: RS and SQ are used to form the Acute Angle RSQ D FIGURE 2: E G FIGURE 2: DE and EG are used to form the Obtuse Angle DEG Region/Size/Space Figure/Straight Edge/Vertex REGION A closed curve and all the points inside it SIZE Refers to the amount of opening between the side (rays) of the angle SPACE FIGURE A figure encloses a part of space STRAIGHT EDGE Has no marks on it with which measurements can be made; by tracing along its edge one can construct a line segment VERTEX A common endpoint of two rays, two segments, or three or more edges of a space figure C S Illustration: FIGURE 1: B R A NOTE: FIGURE 1: Point B is the Vertex of angle CBA T Q FIGURE 2: Point R is the Vertex of Angles QRS, SRT and TRQ FIGURE 2: UNITS OF MEASURE Length/Liquid/Weight LENGTH ENGLISH 12 inches (in.) feet (ft.) 36 inches 5280 feet METRIC = = = = foot (ft.) yard (yd.) yard (yd.) mile (MI.) 1000 milliliters (mm) 100 centiliters (cm) 10 deciliters (dm) 1000 liters = = = = meter meter meter kilometer LIQUID ENGLISH cups (c.) pints quarts METRIC = pint (pt.) = quart (qt.) = gallon (gal.) 1000 milliliters (ml) 100 centiliters (cl) 10 deciliters (dl) 1000 liters (l) = liter (l) = liter (l) = liter (l) = kiloliter (kl) WEIGHT ENGLISH METRIC 16 ounces (oz.) = pound (lb.) 2000 pounds = ton (T.) 1000 milligrams (mg) 100 centigrams (cg) 10 decigrams (dg) 1000 grams = gram (g) = gram = gram = kilogram Equivalent Units/Time EQUIVALENT UNITS LENGTH LIQUID WEIGHT 2.5 centimeters is about inch .9 meter is about yard 1.6 kilometers is about mile .95 liter is about quart 3.79 liters is about gallon 28.35 grams is about ounce .45 kilogram is about pound TIME 60 seconds (sec.) 60 minutes (min.) 24 hours (hr.) days 365 days 366 days 10 years 20 years 100 years = = = = = = = = = minute hour day week (wk.) year (yr.) leap year decade score century
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