Stage PROMPT sheet / Place value in numbers to million The position of the digit gives its size / Negative numbers A number line is very useful for negative numbers. The number line below shows: 7 - l l l l l l l l l - - - 0 Millions Hundred thousands Ten thousands thousands hundreds tens units The number line below shows: - + l l l l l l l l l - - - 0 7 Example The value of the digit is 000 000 The value of the digit is 00 000 The value of the digit is 0 000 The value of the digit is 000 / Round numbers to nearest 0, 00, 000, 0000, 00000 Example Round 79 to the nearest 0 000 o Step Find the round-off digit - o Step Look one digit to the right of - or more? NO leave round off digit unchanged - Replace following digits with zeros ANSWER 0 000 Example Round 79 to the nearest 00 000 o Step Find the round-off digit - o Step Look one digit to the right - or more? YES add one to round off digit - Replace following digits with zeros ANSWER 00 000 / Roman Numerals The seven main symbols I V X 0 L 0 C 00 D 00 M 000 / Written methods for addition Other useful ones include: IV IX 9 XL 0 XC 90 Line up the digits in the correct columns Start from RIGHT to LEFT e.g. + + 9 H T U 9 + / Written methods for subtraction Line up the digits in the correct columns Start from RIGHT to LEFT e.g. - 7 H T U 7 -
/ Mental methods for addition / Multiples & factors Start from LEFT to RIGHT Example think of: + as + 0 + But in your head say: 7 77 Example think of: + as + 00 + 0 + But in your head say: / Mental methods for subtraction Example think of: as 0 But in your head say: Example think of: - as - 00-0 - But in your head say: FACTORS are what divides exactly into a number e.g. Factors of are: Factors of are: 9 The common factors of & are:,,,, The Highest Common Factor is: MULTIPLES are the times table answers e.g. Multiples of are: Multiples of are: 0 0... 0... The Lowest Common Multiple of and is: 0 /9 Prime numbers Prime numbers have only TWO factors The factors of are: Factors of 7 are:,,,,,, 7 /7 Multi-step problems Based upon /. Words associated with addition: add sum altogether Words associated with subtraction: total is NOT prime 7 IS prime It is composite Prime numbers to 0 7 9 0 7 9 0 Subtract minus difference The number is NOT prime How many more? It has only ONE factor
/0 Multiplication using a formal method /0 Division using a formal method By a ONE-DIGIT number By a ONE-DIGIT number e.g. x 7 e.g. x 7 COLUMN METHOD 7x 97 GRID METHOD e.g. 9 )9 By a TWO-DIGIT number e.g. 9 SAME METHOD (Except write down some of your tables down first) 000 00 0 7 7 000 00 0 9 000 + 00 + 0 + 9 97 0 9 9 7 0 9 e.g. x e.g. x By a TWO-DIGIT number COLUMN METHOD x 0 (x) 0 (x0) GRID METHOD 00 0 0 000 00 0 00 00 e.g. 9 ALTERNATE METHOD Divide Multiply Subtract Bring down - Make a new number Divide... 0 9-7 - 0-0 0 0 9 x 00 + 700 +
/ Multiply & divide by 0, 00, 000 Cube numbers By moving the decimal point To multiply by 0 move the dp ONE place RIGHT e.g. X 0 0. x 0 To divide by 0 move the dp ONE place LEFT e.g. 0.. 0 0. By moving the digits To multiply by 0 move the digits ONE place LEFT e.g.. x 0. / Fractions To compare fractions the denominators must be the same and To multiply or divide by 00 move TWO places To multiply or divide by 000 move THREE places and / Square & Cube numbers Square numbers SO is bigger than To add and subtract fractions When the denominators are the same + Do not add the denominators - Do not subtract the denominators
/ To add subtract fractions (cont) When the denominators are different + + (x) (x) Multiply to make the denominators the same A mixed number can be changed back into an improper fraction ½ ¾ / Equivalent fractions These fractions are the same but can be drawn and written in different ways / Multiply fractions Multiply is the same as repeated addition + + + + (x) (x) x + + 9 Fractions can also be divided to make the fraction look simpler this is called CANCELLING or LOWEST FORM ( ) ( ) OR x 9 / Mixed & improper fractions An improper fraction is top heavy & can be changed into a mixed number can be shown in a diagram ½ ½ Improper fraction Mixed number /7 Round decimals
Rules for rounding. Find the round off digit. Move one digit to its right. Is this digit or more Yes add one to the round off digit No don t change the round off digit The value of each digit is shown in the table hundreds tens units tenths hundredths thousandths 7 To the nearest whole number e.g. To round. to the nearest whole round off digit this digit is or more. rounded to nearest whole e.g. To round. to the nearest whole 00 0 0 00 00 7 000 7 000 7 000 round off digit this digit is NOT or more. rounded to nearest whole To one decimal place e.g. To round.7 to decimal place round off digit this digit is or more.7 rounded to dp. e.g. To round. to the nearest whole round off digit this digit is NOT or more / Order decimals Example To order 0., 0., 0. Write them under each other Fill gaps with zeros Then order them 0. 0.0 0. 0.00 0. 0. smallest Order: 0. 0. 0. largest.7 rounded to dp. / Read & write decimals /9 Decimal & Percentage equivalents
Learn Fraction Decimal Percentage 0. 0% 0. % 0. 0% 0 0. 0% 00 0.0 % Some fractions have to be changed to be out of 00 inch is about.cm km. miles or miles km (x) (x) 0. % 00 kg is about.pounds /0 Convert metric measure Length A litres of water s a pint and three quarters Mass or weight A gallon is about. litres 000 kilograms (kg) x000 grams (g) Capacity or volume 000 litres (l) x000 millilitres (ml) /0 Imperial measure / Area & Perimeter
Estimate area Volume is measured in cubes The cm cube cm cm cm The volume of this cube is cm³ ( cubic centimetre) It holds ml of water Number of whole squares( ) Number of ½ or more ( ) Estimated area squares This cuboid contains cubes So the volume is cm³ Shapes composed of rectangles Put on all missing lengths first For perimeter ADD all lengths round outside For area - split into rectangles & add them together This D shape contains cubes So the volume is cm³ cm cm cm cm / Units of time Time conversion x cm year x cm cm cm cm days hours x0 x0 cm min Perimeter + + + + + cm 0 cm 0 sec cm A cm cm Area of shape Area of A + B (x) + (x) + cm B cm cm Time intervals Always go to the next whole hour first Example: 00 to 0min + h min 00 0900 h min / Volume / D representations of D shapes
There are views: Plan view Side elevation Angles on a straight line add up to 0 0 or right angles ( x 90 0 ) Front elevation / Angles Types of angles Acute Obtuse (less than 90 0 ) (Between 90 0 & 0 0 ) Reflex (Between 0 0 & 0 0 ) Angles about a point add up to 0 0 or right angles ( x 90 0 ) /7 Properties of the rectangle A rectangle is a quadrilateral ( sided shape) All angles are 90 0 Opposite sides are equal Measure and draw angles Opposite sides are parallel Diagonals are equal To be sure, count the number of degrees between the two arms of the angle Diagonals bisect each other (cut in half) / Angles A square is a special rectangle / Reflection
Reflection in a vertical line Find the difference Example : What was the difference in temperature between 00 and 0? Answer:. 0 C 0 0 C. 0 C Reflection in a horizontal line Find the sum of the data Example: What was the total number of days absent over the years? Answer: + + 7 + 7 + 9 + days 0 / Translation right & down Days absent 0 Year Year Year Year Year Year In reflection and translation the shapes remain the same size and shape CONGRUENT In reflection the shape is flipped over In translation the shape stays the same way up /9 Line graphs /0 Interpret information in tables
Distance table Example: Find the distance between Leeds and York Answer: 0miles Hull 00 Leeds 7 Manchester 0 0 Sheffield 0 9 York Timetable Example: How long is the film? Answer:.0. h min min.0am 7.00 Cartoons Educational programme 7. News and weather.00 Wildlife programme 9.00 Children's programme.0 Music programme.0pm Sports programme.00 News and weather.0 -.pm Film Table of results of goals scored Example: Did boys or girls score the most goals? Answer: Boys: +++ Girls: 7+ Boys scored the most goals