Maths Grade 2 Knowledge Organiser

Transcription

1 Maths Grade Knowledge Organiser.Multiply & divide by 10, 100, Equivalence of fractions and decimals Fractions They must have the same denominator 5 7 e.g. 6 By moving the decimal point To multiply by 10 move the decimal point ONE place RIGHT e.g.. x 10 = To divide by 10 move the dp ONE place LEFT e.g.. x 10 = 0. By moving the digits To multiply by 10 move the dp ONE place RIGHT e.g..5 x 10 = 5..1 Rounding decimals Now the fractions can be ordered Decimals Give them all the same number of digits e.g. 0., 0.0, 0., Now the decimals can be ordered Convert between fractions & decimals Decimals to fractions Look at the digit required Look at the first digit NOT required. 7 5 e.g. To round 5. 7 to 1dp Answer 5.5 digit NOT required increase this by 1 Is this 5 or more? YES e.g. To round 5. to 1dp Fractions to decimals - by changing e.g. 5 = 10 = 0. e.g. 9 = = 0.75 Answer 5. leave this alone digit NOT required Is this 5 or more? NO - delete Fractions to decimals - by dividing e.g. = = 0.75

2 . Order of operations Bracket Indices Divide Multiply Add Subtract Do these in the order they appear Do these in the order they appear.5 Simplify Ratio How it is written Yellow : Red = : 6 How it can be simplified e.g. + x 6 5 = first Yellow : Red = 1 :. Powers and roots we say squared or the square of - It means x = 16 we say cubed or the cube of - It means xx = - we say to the power of - It means xxx = 1 The inverse operation for power is root 16 = = 1 = There are keys on the calculator to all of these Simplify by cancelling Examples : 6 = 1 : 10 5 : 15 5 = :.6 Fractions Add & subtract with same denominator e.g. 1 + = = 1 Multiply is just repeated addition e.g. x = + = = Simplify fraction See what number divides exactly into both the numerator and denominator e.g. 15 e.g Fraction of quantity with calculator means 5 x 5 e.g. To find of x = 0 E7 Percentage of quantity NO calculator Use 50% 10% 1%

3 .7 Percentage of quantity-with calculator Change the percentage to a decimal e.g. % of 0 ½ % of 0kg = 0.0 x 0 = 0.5 x 0 = 19.0 = 10kg 0% of 5 litres = 0. x 5 = 1.6 litres. Decimals Add & subtract- Line up the decimal points Multiply take out decimal point Multiply Put decimal point back in e.g.. x 0. x (remove decimal points) (multiply) 1. (put decimal point back in- decimal places) Divide make divisor into a whole number Multiply both numbers e.g.. 0. (multiply both numbers by 10) Number patterns Look to see how numbers are connected Multiples Multiples of 6 are: 6,, 1,, 0... Factors Factors of 6 are: 1, 6,, Prime numbers Prime numbers have only TWO factors,, 5, 7, 11, 1, 17, 9, 1, 7... Sequences 1,, 9, 16, 5, 6... are all square numbers 1,, 7, 6, 5... are all cube numbers 1,, 7, 10, 1, increase b each time.11 Manipulate expressions Only like terms can be added & subtracted e.g. a + b cannot be added a - a cannot be subtracted a + a = a 5a a = a Terms can be simplified when multiplying e.g. a x b = ab a x a = 6a.9 Order negative numbers l l l l l l l > - We say is bigger than - -1 < We say -1 is less than E9 Add & Subtract Negative numbers Remember the rules: When subtracting go down the number line When adding go up the number line E. Solve equations by balancing e.g. x = 7 (add to each side) x = 10 (divide both sides by ) x = 5 e.g. x +1 = 5 (subtract 1 from each side) x = (multiply both sides by ) x = + - is the same as = is the same as = is the same as + = 10

4 . 1 Symmetries.15 Transform Shapes Order of Line Symmetry this is the number of times a shape can be folded so that one side falls exactly onto the other side Reflection A shape flipped over a line This shape has line symmetry ORDER Order of Rotational Symmetry this is the number of times a shape falls into its outline in one complete turn Rotation A shape turned round a point A parallelogram has rotational symmetry order Translation A shape moved along a line.1 Angles Types of angles Acute Right Obtuse (less than 90 0 ) (Exactly 90 0 ) (Between 90 0 & 10 0 ) Tessellation Shapes are joined without gaps or overlapping e.g. Straight Reflex Complete line turn (10 0 ) (Between 10 0 & 60 0 ) (60 0 ).16 D drawings of D shapes Angles of a triangle- add up to 10 0 Isometric drawing Angles of a quadrilateral add up to 60 0 = x 10 0 = 60 0 Never join the dots horizontally Nets

5 .17 Read & interpret conversion graphs.19 Area and perimeter of rectangle e.g. To convert kg and pounds 0 Area is the amount of space inside the outline of a shape Perimeter is the length of the outline of a shape 1 16 Area of rectangle = length x width 1 Pounds 10 cm cm Kilograms Draw lines on to take readings Area of rectangle = l x w = x = cm Perimeter of the rectangle Read the scale carefully e.g. Read & interpret timetables Station Time of leaving Peterborough 0 Huntingdon St Neots 09 0 Sandy Biggleswade Arlesey 09 e.g.time taken to travel from Peterbrough to Sandy min + 15min = 1min.1 Units of measure Metric units Length Weight Capacity 10mm =1cm 1000g=1kg 1000ml=1 litre 100cm =1m 10ml=1centilitre 1000m=1km Imperial units Length Weight Capacity 1 inch=.5cm. pounds 1kg 1gallon.5litres 1 foot=0cm 1 mile 1.6km Perimeter = OR x + x cm.0 Probability Calculate probability P(event) = No. of outcomes which give the event Total number of outcomes Probability of an event NOT happening If p(event) = p P(event NOT happening) = 1 - p e.g. If p(rain ) = 0. p(no rain = 1 0. = 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

6 Spinner. Find all possible outcomes Outcomes can be presented: In a list In a table or sample space Example of a sample space To show all possible outcomes from spinning a spinner and rolling a dice. Construct a pie chart Transport Frequency Angle Car 1 x Bus x Walk 15 x Cycle x 9 7 Total frequency = = 9 0 per person Dice Interpret pie charts over 59 Greece Ireland over 59 under 15 under million people.5 million people Here we are not told how many people are in the survey 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