Stage 6 PROMPT sheet 6/ Place value in numbers t 0millin The psitin f the digit gives its size Ten millins Millins Hundred thusands Ten thusands thusands hundreds tens units 4 5 6 7 8 Example The value f the digit is 0 000 000 The value f the digit is 000 000 The value f the digit is 00 000 The value f the digit 4 is 40 000 6/ Rund whle numbers Example Rund 4 679 t the nearest 0 000 Step Find the rund-ff digit - 4 Step Mve ne digit t the right - 4 r less? YES leave rund ff digit unchanged - Replace fllwing digits with zers ANSWER 40 000 Example Rund 45 679 t the nearest 0 000 Step Find the rund-ff digit - 4 Step Mve ne digit t the right - 5 5 r mre? YES add ne t rund ff digit - Replace fllwing digits with zers ANSWER 50 000 6/ Negative numbers l l l l l l l - - - 0 > - We say is bigger than - - < We say - is less than The difference between and - = 4 (see line) Remember the rules: When subtracting g dwn the number line When adding g up the number line 8 + - is the same as 8 = 6 8 - + is the same as 8 = 6 8 - - is the same as 8 + = 0 6/ Multiply numbers & estimate t check e.g. 5 x 4 COLUMN METHOD 5 4x 608 (x4) 4560 (x0) 568 6/ Use estimates t check calculatins 5 x 4 50 x 0 4500 is the symbl fr rughly equals 6/ Divide numbers & estimate t check With a remainder als expressed as a fractin e.g. 498 BUS SHELTER METHOD 0 8 0 8 r 5 4 5 4 4-0 - 0 ANSWER - 4 5 = 8 r =8 5
6/ cntinued With a remainder expressed as a decimal 0 8. 8 0 8. 8 5 4. 0 5 4 4. 0-0 - 0 ANSWER - 4 5 = 8. 8 6/ Use estimates t check calculatins 4 5 450 5 0 6/4 Factrs, multiples & primes e.g. + 4 x 6 5 = first ( + ) x = 9 first 6/6 Additin Line up the digits in the crrect clumns e.g. 48p +.84 + 9 0. 4 8. 8 4 9. 0 0+. 6/6 Subtractin Line up the digits in the crrect clumns FACTORS are what divides exactly int a number e.g. Factrs f are: Factrs f 8 are: 8 6 9 4 6 e.g. 645-47 6/7 Equivalent fractins H T U 6 4 5 4 7-8 The cmmn factrs f & 8 are:,,, 6, The Highest Cmmn Factr is: 6 PRIME NUMBERS have nly TWO factrs e.g. Factrs f 7 are: Factrs f are 7 S 7 and are bth prime numbers T simplify a fractin 7 Example: 6 First find the highest cmmn factr f the numeratr and denminatr which is 9, then divide 7 6 9 9 = 4 MULTIPLES are the times table answers e.g. Multiples f 5 are: Multiples f 4 are: 5 0 5 0 5... 4 8 6 0... The Lwest Cmmn Multiple f 5 and 4 is: 0 T change fractins t the same denminatr Example: 4 and 6/5 Order f peratins Bracket Indices Divide Multiply Add Subtract D these in the rder they appear D these in the rder they appear Find the highest cmmn multiple f the denminatrs which is, then multiply: 4 x x 9 x4 8 = and = x4
6/8 Add & subtract fractins Make the denminatrs the same T multiply by 0, mve each digit ne place t the left e.g. 5.6 x 0 = 56 e.g. 7 + 5 0 7 = + 0 0 = 9 0 e.g. 4-5 0 = - 5 5 = 5 D nt add denminatrs Hundreds Tens Units tenths 5 6 5 6 T divide by 0, mve each digit ne place t the right 6/9 Multiply fractins Write 5 as 5 Multiply numeratrs & denminatrs 4 e.g. 5 x e.g. x 5 5 8 = x = 5 0 = = 6/9 Divide fractins e.g. Write 5 as 5 Invert the fractin after sign Multiply numeratrs & denminatrs 5 4 e.g. 5 = x 5 4 = x 5 = 0 = = = 0 0 5 6/0 Multiply/divide decimals by 0, 00 thusands hundreds tens units. tenths hundredths thusandths 4 5. 6 7 e.g. 5.6 0 = 56=.56 Tens Units tenths hundredths 5 6 5 6 T multiply by 00, mve each digit places t the left T divide by 00, mve each digit places t the right AN ALTERNATE METHOD Instead f mving the digits Mve the decimal pint the ppsite way 6/ Multiply decimals Step remve the decimal pint Step multiply the tw numbers Step Put the decimal back in Example: 0.06 x 8 => 6 x 8 => 48 => 0.48 6/ Divide decimals Use the bus shelter methd Keep the decimal pint in the same place Add zers fr remainders Example: 6.8 5. 5 6 5 ) 6. 8 0
6/ Fractin, decimal, percentage equivalents LEARN THESE: = 0.5 = 5% 4 = 0.5 = 50% = 0.75 = 75% 4 = 0. = 0% 0 Percentage t decimal t fractin 7 7% = 0.7 = 00 7 7% = 0.07 = 00 70 70% = 0.7 = 00 = 0 7 Decimal t percentage t fractin 0. = 0% = 0 0.0 = % = 00 9 0.9 = 9% = 00 Fractin t decimal t percentage 4 80 = = 80% = 0.8 5 00 Change t 00 0. 7 5 = 8 = 8). 0 6 0 4 0 = 0.75 = 7.5% 8 9 = = 0.75 = 75% 4 Cancel by 6/ Fractin f quantity 4 means 5 x 4 5 e.g. T find 4 f 40 5 40 5 x 4 = 40 6/ Percentage f quantity Use nly 50% - 0% - 0 % - 00 Example : T find 5% f 400 0% = 40 0% = 80 5% = 0 5% = 40 6/4 Similar shapes When a shape is enlarged by a scale factr the tw shapes are called SIMILAR shapes m 5cm b 6m a Scale factr = 6 = Length a = 5 x = 0cm Length b = 8 = 4cm 6/4 Unequal sharing x 8cm Example- unequal sharing f sweets A gets B gets shares 4 shares => sweets 4 sweets x4 => sweets 6 sweets x4 6/5 Express missing numbers
Examples a 4 = 8 algebraically An unknwn number is given a letter b 0 8cm a = s a = 6 0cm b + = 80 s b = 48 0 c 8 + c = 0 s c = If the nth term is 5n + st term (n=) = 5x + = 6 nd term (n=) = 5x + = rd term (n=) = 5x + = 6 6/7 Pssible slutins f a number sentence Example: x and y are numbers Rule: x + y = 5 Pssible slutins: x = 0 and y = 5 x = and y = 4 x = and y = x = and y = x = 4 and y = x = 5 and y = 0 d d d d = 60 0 s d = 0 0 6/8 Cnvert units f measure METRIC When cnverting measurements fllw these rules: 6/5 Use a wrd frmula Example: -Time t ck a turkey Ck fr 45min per kg weight Then a further 45min Fr a 6kg turkey, fllw the frmula: 45min x 6 + 45min =70min + 45min =5min = 5h 5min 6/6 Number sequences Understand psitin and term Psitin 4 Term 7 5 +4 Term t term rule = +4 Psitin t term rule is x 4 - (because psitin x 4 = ) nth term = n x 4 - = 4n - Generate terms f a sequence When cnverting frm a larger unit t a smaller unit we multiply (x) When cnverting frm a smaller unit t a larger unit we divide ( ) UNITS f LENGTH 0mm = cm 00cm = m 000m = km UNITS f MASS 000g = kg 000kg = tnne UNITS f VOLUME 000ml = litre 00cl = litre 6/9 Cnvert units f measure METRIC/IMPERIAL LEARN: 5 miles = 8km UNITS f TIME 60sec = min 60min = hur 4h = day 65days = year Miles 5 x8 kilmetres Miles x 5 8 kilmetres 6/0 Perimeter and area f shapes
Shapes can have the SAME area but different perimeters The area f each shape is 9 squares A B Example : Triangle with side and angles given Draw line AB = 7cm Draw angle 4 0 at pint A frm line AB Draw angle 47 0 at pint B frm line AB Extend t intersect the lines at C C C A 4 0 47 0 7cm B Perimeter f each shape is different A ; B 4; C -6 6/ Area f parallelgram & triangle 6/ Cnstruct D shapes CUBE & its net Area f parallelgram Area f parallelgram = b x h 5cm = 8 x 5 = 40cm 8cm Area f triangle (½ a parallelgram) Area f triangle = b x h = 8 x 5 5cm 0cm 8cm CUBOID & its net 6/ Vlume Vlume f cubid Vlume = l x w x h = 5 x x = 0cm cm Vlume f cube Vlume = l x w x h = x x = 7m m m 5cm m cm TRIANGULAR PRISM & its net 6/ Cnstruct D shapes 6/4 Prperties f shapes
TRIANGLES sum f angles = 80 0 ISOSCELES triangle equal sides & equal angles 08 0 7 0 EQUILATERAL triangle equal sides & ALL angles 60 0 SCALENE triangle All sides & angles different interir & exterir angle add up t 80 0 the interir angles add up t: Triangle = x 80 0 = 80 0 Quadrilateral = x 80 0 = 60 0 Pentagn = x 80 0 = 540 0 Hexagn =4 x 80 0 = 70 0 etc QUADRILATERALS sum f angles = 60 0 Square rectangle parallelgram 6/5 Parts f a circle The circumference is the distance all the way arund a circle. The diameter is the distance right acrss the middle f the circle, passing thrugh the centre. The radius is the distance halfway acrss the circle. The radius is always half the length f the diameter. (d = x r) r (r = ½ x d) Rhmbus trapezium kite REGULAR POLGONS all sides the same Plygns have straight sides Plygns are named by the number sides sides triangle 4 sides quadrilateral 5 sides pentagn 6 sides hexagn 7 sides heptagn 8 sides ctagn 9 sides nnagn 0 sides decagn Sum f exterir angles is always 60 0 6/6 Angles and straight lines
Angles n a straight line add up t 80 0 Translatin -A shape mved alng a line 48 0 0 48 0 + 0 = 80 0 Angles abut a pint add up t 60 0 Example Mve shape A right & 4 dwn Can als be written as a vectr Right -4 Dwn 46 0 4 0 A 46 0 + 90 0 + 4 0 = 60 0 Vertically ppsite angles are equal 46 0 4 0 4 0 46 0 B Ntice: The new shape stays the same way up The new shape is the same size Reflect a shape in x-axis 6/7 Psitin n a c-rdinate grid Reflect a shape in y-axis 6/8 Transfrmatins 6/9 Graphs
Pie chart Transprt Frequency Angle The mean is usually knwn as the average. The mean is nt a value frm the riginal list. It is a typical value f a set f data Mean = ttal f measures n. f measures Car x 9=7 0 Bus 4 4 x 9=6 0 Walk 5 5 x 9=5 Cycle 8 8 x 9=7 Ttal frequency = 40 60 0 40 = 9 0 per persn car bus walk cycle e.g.- Find mean speed f 6 cars travelling n a rad Car 66mph Car 57mph Car 7mph Car 4 54mph Car 5 69mph Car 6 58mph Mean = 66+57+7+54+69+58 6 = 75 6 = 6.5mph Mean average speed was 6.5mph Line graph Line graphs shw changes in a single variable in this graph changes in temperature can be bserved. 6/0 The mean