4 OPERATIONS operation sign word for the answer addition subtraction multiplication division + x ÷ sum difference product quotient INTEGER • a positive whole number, a negative whole number or zero • NOT a number part like a fraction or a decimal eg: -16, 3, 0, -1, 198, 35 POSITIVE NUMBER • A number located to the right of zero on the number line. NEGATIVE NUMBER • A number located to the left of zero on a number line. ADDING & SUBTRACTING NEGATIVE & POSITIVE NUMBERS • same signs add • different signs subtract eg. 5 + -2 = start at +5 (different signs subtract- so + -2 is subtract 2) subtract means move to the left on the number line 2 places ASCENDING ORDER • arranged from smallest to largest – it is going up • think of the “A” like a mountain you need to climb up • 25, 85, 109, 153, 286 DESCENDING ORDER • arranged from largest to smallest – it is going down • think of the “D” in descending and down • 600, 300, 200, 50, 10, PALINDROMIC NUMBERS Numbers that read the same backwards and forwards. The number "17371" is a Palindromic Number. "5" is also a Palindromic Number. But "1234" is NOT, because backwards it is "4321" (not the same) FACTOR A whole number that you can multiply with another number to make a third number. Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A number can have MANY factors! Factors get smaller! MULTIPLE A multiple is the product of a given whole number and another whole number. Multiples get bigger! Multiples are like skip counting! 5: 5, 10, 15, 20, 25, 30… PRIME NUMBER A number that has exactly 2 factors It can be divided evenly only by 1 and itself. The factors of a prime number are 1 and the number itself COMPOSITE NUMBER A number with more than 2 factors. FACTOR TREES Every composite number can be written as a product of its prime factors COMMON MULTIPLE A multiple that 2 or more numbers have in common. Multiples of 3: 3, 6, 9, 12, 18, Multiples of 6: 6, 12, 18, 24, 38 The first three Common Multiples of 3 & 6 are: 6, 12, 18 HIGHEST COMMON FACTOR The highest factor that 2 or more numbers have in common. Factors of 12: 1, 2, 3, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 The highest common factor of 12 & 18 is: INVERSE OPERATION opposite or reverse operation addition and subtraction are inverse operations if we start with 7, then add 3 we get 10, now subtract 3 and we get back to 7. multiplication and division are inverse operations if we start with 6, multiply by 2 we get 12, now divide by 2 and we get back to 6. ORDER OF OPERATIONS When there is more than one operation in a number problem, we complete the operations in a certain order. B I M D A S ORDER OF OPERATIONS When there is more than one operation in a number problem, we complete the operations in a certain order. Complete Apply Indices multiplication division from right Complete additionpossible andand subtraction fromleft lefttoto right Do any simplifying inside of brackets starting with innermost brackets and working out BIMDAS ROUNDING Find your number. Look right next door. 4 or less - just ignore. 5 or up, add 1 more. Are we done yet? No, not quite. Add zeroes to the right. SYMMETRY • Symmetry is when one shape becomes exactly like another if you flip, slide or turn it. • The "Line of Symmetry" (black dotted line) is the imaginary line where you could fold the image and have both halves match exactly. TRANSFORMATION • a change in position or size of a shape, including: • • • • • reflection - flip rotation - turn translation - slide enlargement - resize reduction - resize REFLECTIVE SYMMETRY • One half of a picture/shape is the reflection of the other half. • It is sometimes called “mirror” symmetry. SEQUENCE • • an ordered set of numbers, shapes or other objects arranged according to a rule the terms (the objects in the sequence) are separated by commas • • • • • • 2, 4, 6, 8, 10, __, __, __, __, __, C, D, E, F, G, __, __, __, __, __, 5, 10, 15, 20, 25, __, __, __, __, __, , , , , , , , , ___, ___, 10, 20, 30, __, __, __, __, __, 16, 15, 14, __, __, __, __, __, TIME Time is the ongoing sequence of events taking place. It can be the interval between events or the duration of an event. It is the past, present and future. We measure time using seconds, minutes, hours, days, weeks, months and years. Clocks and other measuring devices measure time. TIME TIME Thirty days has September, April, June and November; all the rest have thirty-one, except February with twenty eight Or in a Leap Year, that's the time when February's days are twenty-nine ANGLES • An angle is formed when two lines or two line segments meet at a point. • Angles are measured in degrees - this is the unit of measurement of an angle. For example, if an angle is 35 degrees, we write it like this: 35° the symbol for degrees. ACUTE ANGLE An acute angle is greater than 0° but less than 90°. acute angle OBTUSE ANGLE An obtuse angle is greater than 90° but less than 180°. obtuse angle RIGHT ANGLE A right angle measures exactly 90°. right angle REFLEX ANGLE Reflex angles are between 180° and 360°. reflex angle STRAIGHT ANGLE A straight angle is 180° • All of the angles on a straight line always add up to 180°. FULL ROTATION A full rotation is 360° • a half a rotation is 180° - a straight angle • a quarter of a rotation is 90° - a right angle ANGLES IN A TRIANGLE • All of the angles in a triangle always add up to 180°. ANGLES IN A QUADRILATERAL • All of the angles in a quadrilateral always add up to 360°. ADJACENT ANGLES • Two angles are Adjacent if they have a common side and a common vertex (corner point), and don't overlap. VERTICALLY OPPOSITE ANGLES • Vertically opposite angles are the angles opposite each other when two lines cross. • They are always equal in size. In this example, a° and b° are vertically opposite angles and are equal in size. POLYGONS POLYGONS A closed (all the sides join up) twodimensional shape All sides are straight. A polygon does not have any curved sides – so a circle is not a polygon because it has a curved side. TYPES OF TRIANGLES A triangle is a polygon with 3 angles and 3 sides There are two ways to name triangles • On the basis of angles • On the basis of sides ACUTE ANGLED TRIANGLE • A triangle whose all the angles are acute is called an ACUTE ANGLED TRIANGLE . RIGHT ANGLED TRIANGLE • A triangle in which one of the angle is right angle is called RIGHT ANGLED TRIANGLE. OBTUSE ANGLED TRIANGLE • A triangle in which one of the angle is obtuse angle is called OBTUSED ANGLED TRIANGLE . EQUILATERAL TRIANGLE • A triangle whose all the sides are of equal length is called equilateral triangle. ISOSCELES TRIANGLE • A triangle whose any two sides are of equal measure is called scalene triangle. SCALENE TRIANGLE • A triangle whose no two sides are of equal measure is called scalene triangle. QUADRILATERALS • A quadrilateral is a closed 2D shape with four sides and four angles. • Quadrilaterals are named based on their sides and angles. SQUARE • A quadrilateral with all sides equal, all angles are right and opposite sides are parallel RECTANGLE • A rectangle is a quadrilateral with opposite sides parallel and all angles are right PARALLELOGRAM • A quadrilateral with opposite sides parallel and opposite sides equal RHOMBUS • A quadrilateral with all sides equal, opposite sides parallel and opposite angles equal TRAPEZIUM • A quadrilateral with one pair of opposite sides parallel Parallel lines FRACTIONS • When an object is divided into a number of equal parts then each part is called a fraction 2 3 numerator: tells us how many parts in the fraction we are looking at denominator: tells us how many equal parts in the whole object PROPER AND IMPROPER FRACTIONS • An improper fraction has a numerator larger than the denominator. • A proper fraction has a numerator smaller than the denominator. FRACTIONS - MIXED NUMBERS A mixed number has a whole number and a fraction part. • A mixed number can be written as an improper fraction and visa versa. • 2 17 3 5 5 ADDING FRACTIONS • if the denominators are the same, just add the numerators and keep the denominators the same. 1 2 4 4 SUBTRACTING FRACTIONS • if the denominators are the same, just subtract the numerators and keep the denominators the same. 5 2 8 8 MULTIPLYING FRACTIONS • multiply the numerators, multiply the denominators 4 2 X x 5 3 DIVIDING FRACTIONS • KEEP – CHANGE – FLIP • keep the first fraction the same, change the division sign to multiplication, flip the second fraction 3 1 ÷ 4 2 PERIMETER • Perimeter is the measurement around the outside (the fence) of a shape Length + + Width Width + Length + AREA • Area is the measurement of the inside of a shape Length x Width GRAPHING COORDINATES cartesian plane quadrants origin x axis y axis coordinates 2D shapes D stands for DIMENSIONS The 2 dimensions are : i. length ii. width/height Shapes with these 2 dimensions are called 2D SHAPES. 2D shape L L L W W W L – The length of the shape W – The width of the shape The faces of a 2D shape are FLAT. Parts of a 2D shapes Face Side Corner Angle square 4 sides 4 corners rectangle 4 sides 4 corners triangle 3 sides 3 corners circle 1 curved side 0 corners rhombus 4 sides 4 corners trapezium 4 sides 4 corners pentagon 5 sides 5 corners hexagon 6 sides 6 corners heptagon 7 sides 7 corners octagon 8 sides 8 corners nonagon 9 sides 9 corners decagon 10 sides 10 corners Reading & Saying Really Big Numbers • start from the left • read the numbers before the space as if you were reading in the one’s column • say the place value group you are in when you get to the space (except for the one’s period) • continue until all number have been read 813 634 907 521 429 503 492 110 54 661 038 992 005 417 310 839 042 168 496 400 90 6 2 734 2 000 700 30 4 What is the value of the underlined digit? What is the value of the underlined digit? 386 What is the value of the underlined digit? 682 EXPONENT (POWER) • A number that indicates how many times a factor is repeated: • Given 23 the exponent is three. BASE • The number that is a repeated factor when written with an exponent: • Given 23 the base is two. VARIABLE • A variable is a symbol used to represent an unknown number: • In the term 3x the variable is x, it means 3 multiplies by x. TYPES OF LINES OBLIQUE LINES Oblique lines are like diagonal, but don’t run from corner to corner. How many oblique lines? On a scale of 1 – 5, how was your “performance” today? Be truthful with yourself – did you participate fully? Were you listening? Did you do what you were asked? Did you improve in any way?
