Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 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 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 O 9 + / Written methods for subtraction Line up the digits in the correct columns Start from RIGHT to LEFT e.g. - 7 H T O 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: ad sum altogethe Words associated with subtraction: tot is NOT prime 7 IS prime It is composite Prime numbers to 0 7 9 0 7 9 0 Subtract minu differenc The number is NOT prime How many more? It has only ONE
/0 Multiplication using a formal method By a TWO-DIGIT number By a ONE-DIGIT number e.g. 9 SAME METHOD e.g. x 7 COLUMN METHOD 7x 97 (Except write down some of your tables down first) 0 9 9 7 0 9 e.g. x By a TWO-DIGIT number COLUMN METHOD x 0 (x) 0 (x0) / Multiply & divide by 0, 00, 000 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. /0 Division using a formal method By a ONE-DIGIT number e.g. 9 )9 By moving the digits To multiply by 0 move the digits ONE place LEFT e.g.. x 0. To multiply or divide by 00 move TWO places To multiply or divide by 000 move THREE places
/ Square & Cube numbers Square numbers 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) Cube numbers When the denominators are different + + (x) (x) Multiply to make the denominators the same / Equivalent fractions These fractions are the same but can be drawn and written in different ways / Fractions To compare fractions the denominators must be the same and and SO is bigger than Fractions can also be divided to make the fraction look simpler this is called CANCELLING or LOWEST FORM (x) (x) ( ) ( )
/ Mixed & improper fractions An improper fraction is top heavy & can be changed into a mixed number can be shown in a diagram ½ ½ /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 To the nearest whole number Improper fraction Mixed number A mixed number can be changed back into an improper fraction ½ 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 round off digit this digit is NOT or more ¾. rounded to nearest whole To one decimal place / Multiply fractions e.g. To round.7 to decimal place Multiply is the same as repeated addition 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.7 rounded to dp. x + + 9 OR x 9
hundreds tens ones tenths hundredths thousandths / Read & write decimals The value of each digit is shown in the table 7 00 0 0 00 00 7 000 7 000 7 000 /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 (x) (x) 0. % 00 / Order decimals /0 Convert metric measure Length Example To order 0., 0., 0. Write them under each other Fill gaps with zeros (place holders) Then order them 0. 0.0 0. 0.00 0. 0. smallest Order: 0. 0. 0. largest 000 Mass or weight kilograms (kg) x000 grams (g) Capacity or volume 000 litres (l) x000 millilitres (ml)
/0 Imperial measure / Area & Perimeter inch is about.cm Estimate area km. miles or miles km Number of whole squares( ) Number of ½ or more ( ) Estimated area squares kg is about.pounds 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 cm A litres of water s a pint and three quarters cm cm cm cm cm cm A gallon is about. litres cm cm cm Perimeter + + + + + cm cm cm A cm cm B cm cm Area of shape Area of A + B (x) + (x) + cm
/ Volume Volume is measured in cubes The cm cube cm / D representations of D shapes There are views: Plan view cm cm The volume of this cube is cm³ ( cubic centimetre) It holds ml of water Side elevation This cuboid contains cubes So the volume is cm³ Front elevation This D shape contains cubes So the volume is cm³ / Angles Types of angles Acute Obtuse (less than 90 0 ) (Between 90 0 & 0 0 ) / Units of time Time conversion year x days x Reflex (Between 0 0 & 0 0 ) hours x0 x0 0 min Measure and draw angles 0 sec Time intervals Always go to the next whole hour first Example: 00 to 0min + h min h min 00 0900 To be sure, count the number of degrees between the two arms of the angle
/ Angles / Reflection Reflection in a vertical line Angles on a straight line add up to 0 0 or right angles ( x 90 0 ) Reflection in a horizontal line 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 / Translation right & down Opposite sides are parallel Diagonals are equal Diagonals bisect each other (cut in half) 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 A square is a special rectangle
Days absent /9 Line graphs Find the difference Hull 00 Leeds 7 Manchester 0 0 Sheffield 0 9 York /0 Interpret information in tables Distance table Example: Find the distance between Leeds and York Answer: 0miles Example : What was the difference in temperature between 00 and 0? Answer:. 0 C 0 0 C. 0 C Timetable Example: How long is the film? Answer:.0. h min min.0am Educational programme 7.00 Cartoons 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 Find the sum of the data Example: What was the total number of days absent over the years? Answer: + + 7 + 7 + 9 + days Table of results of goals scored Example: Did boys or girls score the most goals? Answer: Boys: +++ Girls: 7+ Boys scored the most goals 0 0 Year Year Year Year Year Year