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Level 5 prompt
- 1. Level 5 5/2 Order negative numbers PROMPT sheet l l l l l l l -3 -2 -1 0 1 2 3 5/1 Multiply & divide by 10, 100, 1000 By moving the decimal point 2 > -2 We say 2 is bigger than -2 To multiply by 10 move the dp ONE place RIGHT -1 < 3 We say -1 is less than 3 e.g. 3.4 x 10 = 34 5/3 Number patterns To divide by 10 move the dp ONE place LEFT Look to see how numbers are connected e.g. 3.4 x 10 = 0.34 Multiples By moving the digits Multiples of 6 are: 6, 12, 18, 24, 30... To multiply by 10 move the dp ONE place RIGHT Factors Factors of 6 are: 1, 6, 3, 2 e.g. 3.52 x 10 Prime numbers Prime numbers have only TWO factors =35.2 2, 3, 5, 7, 11, 13, 17, 29, 31, 37 ...... Sequences 1, 4, 9, 16, 25, 36 ... are all square numbers 5/2 Rounding decimals 1, 8, 27, 64, 125 ... are all cube numbers 1, 4, 7, 10, 13, 16 ... increase b 3 each time Look at the last number required Look at the first number NOT required e.g. To round 5 . 47 to 1dp 5/4 Order fractions and decimals last number required 1st number NOT required Fractions They must have the same denominator 5 7 2 3 increase this by 1 Is this 5 or more? YES - delete e.g. 6 12 3 4 10 7 9 8 12 12 12 12 e.g. To round 5 . 43 to 1dp Now the fractions can be ordered last number required 1st number NOT required Decimals Give them all the same number of digits leave this alone Is this 5 or more? NO - delete e.g. 0.3, 0.304, 0.32, 0.33 0.300 0.304 0.320 0.330 Now the decimals can be ordered
- 2. 5/5 Cancel a fraction to its lowest terms 5/8 Multiply by a two digit number See what number divides exactly into both the Try different methods to find which suits you numerator and denominator ÷4 e.g. 152 x 34 COLUMN METHOD e.g. 8 2 152 12 ÷4 3 34x 608 (x4) ÷5 4560 (x30) 15 3 e.g. 5168 40 8 ÷5 e.g. 152 x 34 GRID METHOD 100 50 2 5/6 Order of operations 30 3000 1500 60 4 400 200 8 Bracket Indices Divide 152 x 34 = 3400 + 1700 + 68 = 5168 Do these in the order they appear Multiply Add e.g. 152 x 34 CHINESE METHOD Do these in the order they appear Subtract 0 1 0 1 3 e.g. 3 + 4 x 6 – 5 = 22 3 5 6 5 0 2 0 first 2 4 4 0 8 5/7 Fraction of quantity with calculator 5 1 6 8 = 5168 4 means ÷ 5 x 4 e.g. 152 x 34 RUSSIAN METHOD 5 e.g. To find 4 of £40 Half Double 5 £40 ÷ 5 x 4 = £40 152 x 34 76 68 5/7 Percentage of quantity with calculator 38 136 Cross out 19 272 left hand Change the percentage to a decimal 9 544 side even e.g. 8% of £240 12 ½ % of 80kg 4 1088 numbers = 0.08 x 240 = 0.125 x 80 2 2176 = £19.20 = 10kg 1 4352 80% of 52 litres Add what is left = 0.8 x 52 272 + 544 + 4352 = 5168 = 41.6 litres
- 3. 5/8 Divide by a two digit number 5/9 Negative numbers Try different methods to find which suits you Remember the rules: When subtracting go down the number line e.g. 4928 ÷ 32 BUS SHELTER METHOD When adding go up the number line Divide Multiply 8 + - 2 is the same as 8 – 2 = 6 Subtract 8 - + 2 is the same as 8 – 2 = 6 Bring down - Make a new number 8 - - 2 is the same as 8 + 2 = 10 Divide ... 0 154 32 4 9 2 8 5/10 Ratio -3 2 How it is written 172 -1 6 0 128 Yellow : Red -1 2 8 = 2 : 6 000 4928 ÷ 32 = 154 How it can be simplified e.g. 4928 ÷ 32 CHUNKING METHOD 4928 Yellow : Red 3200 100 X 32 = 1 : 3 1728 1600 50 X 32 Simplify by cancelling 128 Examples 128 4 X 32 2÷2: 6÷2 = 1 : 3 4928 ÷ 32 = 154 10÷5 : 15÷5 = 2 : 3 e.g. 4928 ÷ 32 SHORT DIVISION METHOD 5/10 Direct proportion (Except write down some of your tables down first) e.g.1 5 miles is approximately 8km. 32 How many miles are equal to 24km? 64 0 1 5 4 24km ÷ 8km = 3 96 32 449172 128 5 miles x 3 = 15 miles 128 160 e.g.2 It takes 90 Lego bricks to 4928 ÷ 32 = 154 build 3 planes How many bricks would be needed for 11? 1 plane uses 90 ÷ 3 = 30 bricks 11 planes will use 11 x 30 = 330 bricks
- 4. 5/12&13 Properties of 2D & 3D shapes 5/14 Angles Types of angles Symmetries Acute Right Obtuse Order of Line Symmetry (less than 900) (Exactly 900) (Between 900 & 1800) this is the number of times a shape can be folded so that one side falls exactly onto the other side Straight Reflex Complete line turn (1800) (Between 1800 & 3600) (3600) This shape has line symmetry ORDER 4 Order of Rotational Symmetry this is the number of times a shape falls into its outline in one complete turn Angles of a triangle A parallelogram has rotational symmetry order 2 Names of shapes – Quadrilaterals Angles of a triangle add up to 1800 Square rectangle parallelogram 5/15 Transform Shapes Reflection A shape flipped over a line Rhombus trapezium kite Names of shapes - Triangles Rotation A shape turned round a point Right angled Isosceles Equilateral 3D shape Translation A shape moved along a line face edge vertex
- 5. 5/16 Measure and draw angles 5/19 Area and perimeter of rectangle Area is the amount of space inside the outline of a shape Perimeter is the length of the outline of a shape Area of rectangle = length x width 3cm To be sure, count the number of degrees between 8cm the two arms of the angle Area of rectangle = l x w =8x3 5/17 Scales = 24cm2 16 Perimeter of the rectangle 4 00 Perimeter = 3 + 8 + 3 + 8 OR 2x3 + 2x8 22cm 12 3 00 5/20 Probability 8 2 00 Probability scale 4 Unlikely likely 1 00 0 1 l l l 0 0 l l l gram s o un c e s Impossible Evens Certain Work out the value of each small division before taking any readings Calculate probability 5/18 Units of measure P(event) = No. of outcomes which give the event Total number of outcomes Metric units Length Weight Capacity Probability of an event NOT 10mm =1cm 1000g=1kg 1000ml=1 litre 100cm =1m 10ml=1centilitre happening 1000m=1km Imperial units If p(event) = p Length Weight Capacity P(event NOT happening) = 1 - p 1 inch=2.5cm 2.2 pounds≈1kg 1gallon≈4.5litres 1 foot=30cm e.g. If p(rain ) = 0.3 1 mile≈1.6km p( NOT rain) = 1 – 0.3= 0.7
- 6. 5/21 Averages and Range Mode – most frequent measure Median – middle measure (put them in order) Mean – total of measures ÷ no. of measures Range – highest minus lowest measure Range measures how spread out the measures are Mode, median & mean gives an average The range and one of the averages is used to compare distributions 5/22 Probability – repeating an experiment LEARN Different outcomes are possible from repeating an experiment The larger the number of trials, the more valid the result 5/23 Interpret graphs & diagrams G re e c e Ire la n d o ve r 5 9 o ve r 5 9 under 15 under 15 40 – 59 40 – 59 15 – 39 15 – 39 1 0 m illio n p e o p le 3 .5 m illio n p e o p le Here we are not told how many people in any of the sectors We can therefore only comment on proportion by comparing the sizes of sectors in each pie chart e.g. there is a larger proportion of the population under 15 in Ireland than Greece It does not mean there are more people