Mathematics Enhancement Programme TEACHING SUPPORT: Year 5

Transcription

1 Mathematics Enhancement Programme TEACHING SUPPORT: Year 5 Multiplication tales Up to 0 0 Units 0 mm = cm 000 mm = m 00 cm = m 000 m = km ml = cl 000 ml = litre 00 cl = litre g = kg 000 kg = tonne seconds = minute 60 minutes = hour hours = day 7 days = week 5 weeks = year months = year Numers h = 00 t = 0 T = 0 H = 0 T = 00 Th = 0 H = 00 T = 000 Negative Numers negative numers zero positive numers CIMT, University of Plymouth

2 Compass Points NNW NORTH NNE North West North East WNW ENE West East WSW ESE South West South East SSW South SSE Roman Numerals I 5 V 0 X 50 L 00 C 500 D 000 M Even / Odd Whole numers ending in 0,,, 6, 8 are EVEN (and divisile y with no remainder). Whole numers ending in, 3, 5, 7, 9 are ODD (and have remainder when divided y ). Equivalent Fractions 0 = = 8 =... = = 00 =... Adding/Sutracting Fractions a c + = a + c (a, and c are natural numers, that is, numers used for counting) a c = a c CIMT, University of Plymouth

3 Decimals 0.a 0.a a = ( a = 0,,..., 9) 0 a = + ( a, = 0,,,..., 9) 0 00 Fraction, Decimal, Percentage Equivalents 00% % % 50% 3 75% Similarly, 0 = 0. 0%, 0 = %, etc. Shapes : D Triangle (3 straight sides) Quadrilateral ( straight sides) Rectangle (opposite sides equal and parallel,and four right angles) Square (all sides equal and four right angles) (Note that all squares are rectangles and all rectangles are quadrilaterals.) Polygon (any closed D shape with sides (edges) all straight lines) Pentagon (any 5-sided polygon: a regular pentagon has all internal angles of 08 and all sides the same length) CIMT, University of Plymouth 3

4 Hexagon (any 6-sided polygon; a regular hexagon has internal angles of 0 and all sides of equal length) Octagon (any 8-sided polygon; a regular octagon has internal angles of 35 ) Trapezium (a quadrilateral with at least one pair of sides parallel) Rhomus (a quadrilateral with equal sides; opposite sides are parallel) Parallelogram ( pairs of equal and parallel sides) Shapes : 3D Cue (all sides equal so each face is a square) Cuoid (all opposite sides equal so each face is a rectangle) Sphere Square-ased pyramid Triangle-ased prism Triangle-ased pyramid CIMT, University of Plymouth

5 Nets A net is a -D figure which can e folded to make a 3-D shape Convex and Concave Shapes Concave: a straight line cannot always e drawn etween any two points on the shape that is always inside the shape. In each of the examples elow, the two points are inside the shape ut the straight line drawn etween them passes outside the shape. Convex: a straight line drawn etween any two points on the shape will always lie inside the shape, as can e seen from the example elow. Symmetry image mirror image The whole shape has one line of symmetry. mirror line CIMT, University of Plymouth 5

6 Four lines of symmetry are shown here. Similarity (a) These shapes are similar. () These shapes are similar. (The sides are in the same ratio, that is, : in (a) and : (i.e, : and 3 : 6) in (). Congruence Congruent shapes are identical in shape and size ut can e rotated or reflected; the shapes shown are congruent. Parallel and Perpendicular Lines right angle (a quarter of a circle) right angles Lines are perpendicular Lines are parallel CIMT, University of Plymouth 6

7 Transformations and Enlargements Transformations are ways of moving a shape; for example, reflection, rotation and translation. A reflection is otained y drawing the image of a shape in a mirror line. An example is shown opposite. Original shape Mirror line Reflection A rotation is otained when a shape is rotated aout a point, the centre of rotation, through a specified angle. An example is shown opposite. Centre of rotation Rotation 80 y Rotation 90 anti-clockwise Original shape x Rotation 90 clockwise y A translation moves a shape so that it is in a different position ut retains the same size, area, angles and line lengths. The diagram opposite shows the translation in x - direction 3 in y - direction 3 x Enlargements are similar to transformations ut they alter (enlarge or reduce) the size of the shape. the shape on the left elow has een enlarged y a scale factor of to give the image on the right. y Scale factor x CIMT, University of Plymouth 7

8 Divisor or Factor and Multiple Any whole numer that divides exactly into a whole numer with no remainder is called a divisor or factor of the numer.,, 3,, 6 and are all divisors (or factors) of. Any whole numer that can e divided y a whole numer with no remainder is called a multiple of the numer. 5, 0, 5, 0,... are all multiples of 5. Perimeter, Area and Volume The perimeter is the total distance around the outside of a D shape. cm The area is the quantity inside a D shape. cm perimeter = = cm cm cm area = 8 square cm The volume is the numer of cuic units that will exactly fill a 3D shape. 3 cm cm volume = 3 = cuic cm Illustrating Data You can illustrate data with a: Tally Chart The tally chart represents 8 items of data Bar Chart No. of cars The ar chart represents 8 items of data (3 Red, 6 Blue, Green, Black and Silver cars) 0 Red Blue Green Black Silver Colours of cars CIMT, University of Plymouth 8

9 Pictogram Pie Chart Red Blue Green Black Black Key cars The pictogram represents the 8 cars aove. A pictogram must always have a key. Silver Black Green Red Blue The pie chart represents the 8 cars. As there are 8 items of data, the angle representing each item is 360 = 0. 8 So the angle for Red = 3 0 = 60, Blue = 0, etc. Median of a set of numers is the middle value when they are arranged in order., 5, 3,,, 9, 8,, 3,, 5, 8, 9 Mean of a set of numers is the average value calculated y adding all the numers in the set and then dividing y the total numer of numers in the set., 5, 3,,, 9, 8 mean = = 8 7 = Mode of a set of numers (or ojects) is the numer (or oject) that has the highest frequency, that is, occurs most often. for the set of numers, 7, 3,, 7,, 3, 5,, 7 we have Frequency I I 3 I I I I 5 I I I I 3 highest frequency So the mode is 7 as it occurs most frequently. CIMT, University of Plymouth 9