Sy m met ry. Draw some patterns of your own, using centimetre squared paper and use the mirror to complete the reflected patterns.

Transcription

1 Sy m met ry Smile Worksheet 0251 You will need colour pencils, a mirror and centimetre squared paper. Put the mirror on the dotted line and look at the reflection. Remove the mirror and draw in the reflected pattern. The dotted line is called the line of symmetry. Draw some patterns of your own, using centimetre squared paper and use the mirror to complete the reflected patterns. RBKC SMILE 2001

2 Points and their Images You will need tracing paper and centimetre squared paper. Smile 0255 is the image of triangle ABC after a reflection. Copy this diagram. Join A to A1, B to B 1, and C to C 1. Mark the mid point of each of these lines. B B o Join up the three mid points. The line that joins the three mid points is called the line of symmetry. Copy this diagram. Draw the line of symmetry using the method above. Below are four shapes and their images. Trace the drawings below. By joining points to their images, draw in the line of symmetry.

3 Below are four shapes. o Copy the shapes on to squared paper. Using what you have learnt, draw the images in the given line of symmetry. For each shape, label the image of the marked points. R RBKC SMILE 2005

4 Squidge Smile 0257 You've heard of adding You heard of multiplying 3x Squidge is a bit of both 3*5 = 23 because = 23 (Read as 3 * 5 as 3 'squidge' 5.) Similarly = 7 and 4 x 3 = 12 4 * 3 = 19 because =19 Copy and complete the squidge table and fill in the answers. 3 i u. * Second number Look at the top row of your table Here are the next 3 numbers in this row 23, 25, 27. The numbers go up in 2's. Write down the next 3 numbers for every row. Describe the patterns in the table. RBKC SMILE 1994.

5 Squidge Smile 0257 Add = Squidge* Multiply x 3*5 = 23 Similarly: = 7 4x3 = 12 4*3 = 19 because 7+ 12= 19 Copy and complete the squidge table and fill in the answers..q D C. * Second number Look at the top row of your table Here are the next 3 numbers in this row; 23, 25, 27 The numbers go up in 2's. Write down the next 3 numbers for every row. Describe the patterns in the table. RBKC SMILE 2005

6 Smile 0258 Squidgeree 5 add 2 5 multiplied by 2 5+2=7-5x2 = 10 5 squidgeree = 70 because 7 x 10 = 70 (Read 5 2 as 5 squidgeree 2.) because 3 + 4=7 and 3x4 = 12 Copy the squidgeree table and fill in the answers. second number 7x12 = C Write down any patterns you can find. Squidgersquare Look at the example below of the squidgersquare operation. 6S2 = 4 because 6x2 = 12 '6 + 2 = 8 Make a squidgersquare table = 4 RBKC SMILE 1995.

7 Squidgeree Smile 0258 Add = Squidgeree Multiply x 5*2 = 70 Similarly: = 7 3x4=12 4 * 3 = 84 because 7 x 12 = 84 Copy and complete the squidge table and fill in the answers. * 1 Second number Write down any patterns you can find. Squidgersquare Look at the example below of the squidgersquare operation. = 4 because 6x2= = =4 Make a squidgersquare table. RBKC SMILE 2005

8 Smile Worksheet 0259 Shading Fractions 2 3 Shade in the fraction of the shape shown \ / / \ J5 11 RBKC SMILE 2001

9 Co-ordinates CENTRE POINT TREASURE SWAMBK DISTANCE EAST Find the ship on the map. Move 2 east, and then 1 north. You should be at the CAVE. The position of the CAVE is: Distance East (1) Copy and complete The cave is at (2, 1) The ROCK is at (4,1) The WRECK is at (, ) The TREASURE is at (, ) (2) a) What is at (2, 5)? b) What is at (2, 1)? c) What is at (1, 2)? d) What is at (4, 2)? (3) a) What is at (3, 2V2)? b) What is at (2y2, 4)? c) What is the position of the castle? (4) If you enjoy making up maps draw one of your own. Write down the positions of all the places you mark. (2,1) * ^Distance North Remember: Always start at the ship (0, 0) The first number is the Distance East The second number is the Distance North

10 AT3 Coo You will need cm squared paper Smile 0262 Co-ordinates 2 o 7 6 J V+\ ; t D (1) Copy this grid on cm squared paper and mark on all the letters carefully. 5 A) 1 4 * B A > c' X K 3 E «< G \ F (2) Find the point marked A. To get to A.... go across 1. then go up 3. (3) The co-ordinates of A are (1, 3). Is this the same as (3, 1)? Why not? (4) Write down the co-ordinates of all the points marked with letters. (5) Mark these letters on your grid:- L at (3, 7) P at (0, 6i) M at (8, 0) Qat (7f, 7i) N at (2, 5i) R at (2^, 1-J-) RBKC SMILE 1995.

11 You will need cm squared paper. Smile 0263 c Co-ordinates 3 Here is a picture of Sammy the sausage dog. Draw a grid on cm squared paper and copy Sammy exactly on to it ) What are the co-ordinates of:- (a) Sammy's nose (c) his eye (b) the end of his tail (d) the bottom of his ear? 2) Draw a new grid and number the lines across and up from 0 to 10. In each question below plot the points and join them as you go. (a) (1, 1) (3,1) (2,3) and back to (1,1) (b) (5, 1) (6,2) (5,3) (4,2) and back to (5,1) (c) (7, 1) (9,1) (7,3) and back to (7, 1) (d) (1, 4) (3,4) (3,6) (1, 6) and back to (1, 4) (e) (4, 6) (7,6) (8,8) and back to (4, 6) Write down the names of the shapes you have drawn.

12 Cartoon Coordinates Joining the coordinates listed on the left hand side will give the drawing of a bear. Joining the coordinates on the right hand side will give the drawing of a landscape. Bear Draw a grid which goes across to 20 and up to Landscape Draw a grid which goes across to 32 and up to Smile Worksheet Plot the points and join them with a ruler as you go. Stop at the end of each section. 32 (3, 17) (3,5) (19,5) (19,17) (3,11) (2, 13) (2, 19) (3,21) (5, 26) (6, 28) (10,30) (12,30) (16,28) (17,26) (19,21) (20,19) (20,13) (19,11) Two small (3, 12) (5, 12) (5,7) (3,7) (19,12) (17,12) (17,7) (19,7) (7, 20) (7,21) (6,21) (6, 19) (7, 19) (7, 20) (15,20) (15,21) (16,21) (16,19) (15,19) (15,20) (7, 15) (7, 16) (6, 16) (6, 14) (7, 14) (7,15) (15, 15) (15, 16) (16,16) (16,14) (15, 14) (15, 15) (7, 10) (7,11) (6,11) (6,9) (7,9) (7, 10) (15,10) (15,11) (16,11) (16,9) (15,9) (15,10) circles centred at (9, 25) (10,25) (12,25) (11,24) (10,25) (3,21) (6, 24) (10,26) (12,26) (16,24) (19,21) (11,5) (11.1) (6, 24) (8, 23) (11,22.5) (15,5) (14,23) (15,3) (16,24) (7,5) (4, 29) (7, 3) (12,31) (10,31) (18,29) and (13, 25) (11.2) (1,8) (8,3) (6,3) (5,2) (5,1) (17, 1) (17,2) (16,3) (14,3) (11.2) (13,8) (13, 10) (14,10) (14,8). (22, 8) (2, 10) (10,19) (18,10) (25,19) (27,21) (29, 19) (13,16) (18,20) (29, 10) (23, 17) (28, 19) (32,16) (20, 18) (23,21) (26, 18) (6, 30) (4, 28) (4, 26) (6, 24) (8, 24) (10,26) (10,28) (8, 30) (6, 30) (12,26) (10,26) (6, 32) (6, 30) (12,28) (10,28) (2, 28) (4, 28) /Q OO\ \O, Of.) (6, 22) (6, 24) (2, 26) (4, 26) (8, 22) (8, 24) (27, 4) (27, 3) (28, 4) (27, 4) (26, 3) (24, 5) (23, 5) (22, 5) (21,6) (20, 6) (19,5) (18,5) (17,7) (16,7) (15, 6) (14,6) (14, 5) (15,5) (16,3) (17,2) (17,0) (18,0) (18,2) (22, 2) (22, 0) (23, 0) (23, 2) (24, 2) (24, 3) (23, 5) You may like to design a cartoon coordinate of your own. RBKC SMILE 2001

13 Smile 0265 Odd and Even You will need: counters. There are 9 socks on the washing line... 4 pairs of socks... and 1 single sock 9 is an odd number. 6 shoes make 3 pairs of shoes. 6 is an even number. a) Take 4 counters. How many pairs can you make? Is 4 an odd number or an even number? b) Take 7 counters. How many pairs can you make? Is 7 an odd number or an even number? Are these numbers odd or even? (c) 11 (d) 23 (e) 10 (05 (h) 18 (i) 25 (j) 14 (k) 3 (g) 17 (I) 1 RBKC SMILE 2001

14 Angles of a Polygon A polygon is a closed shape with 3 or more straight sides. Smile 0267 Draw a quadrilateral. Choose a vertex and draw a diagonal from it. The quadrilateral is split into 2 triangles. The sum of the angles of each triangle is 180. What is the sum of the angles of a quadrilateral? Draw a pentagon. Choose a vertex and draw diagonals from it. How many triangles are there? What is the sum of the angles of a pentagon? 3. Draw these polygons. How many triangles are there in each polygon? What is the sum of the angles in each polygon? Copy and complete this table. Polygon Number Number of Angle of sides I triangles Sum Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Decagon Explain how to find the angle sum of any polygon fl- RBKC SMILE 1996.

15 Smile 0268 Exterior Angles of Polygons You will need square gummed paper and scissors. A polygon is a closed shape with three or more straight sides. A pentagon is a polygon with 5 sides. It has 5 exterior angles. Draw a pentagon on gummed paper and label the exterior angles a, b, c, d and e. Cut out the 5 exterior angles and fit them together. Stick them in your book. The angles shold fit together to make 1 complete turn or Do this with 5 more polygons (not just pentagons). Perhaps you can explain your results. You may like to find out more about polygons by looking in Smile 2163 Geometry Facts. RBKC SMILE Mathematics 2005

16 Smile 0268 Exterior Angles of Polygons A polygon is a closed shape with three or more straight sides. A pentagon is a polygon with 5 sides. It has 5 exterior angles. Draw a pentagon on gummed paper and label the exterior angles a, b, c, d and e. Cut out the 5 exterior angles and it them together. Stick them down. The angles should fit together to make 1 complete turn or 360 Do this with 5 more polygons (not just pentagons). Perhaps you can explain your results. You may like to find out more about polygons by looking in SMILE 2163 Geometry Facts. RBKC SMILE 1994.

17 Smile 0269 Finding Exterior Angles This is a quadrilateral The sides have been extended in an anti-clockwise direction to create the exterior angles. Exterior angle a = 105 b = 84 c = 83 d = 88 The sum of the exterior angles is = 360 C Draw 5 large polygons, not just quadrilaterals. For each polygon: extend the sides in either an anticlockwise or a clockwise direction to create the exterior anglles of the polygon. measure and record the exterior angles calculate the sum of the exterior angles

18 You probably found that the sum of exterior angles for each polygon was very close to 360. Your answers are unlikely to be exactly 360 because it isi impossible to measure exactly. If it was possible to measure exactly, you would find that the sum of the exterior angles of any polygon is 360. In the questions below: a) sketch the polygon and mark the angles given. b) calculate the angles marked with letters. RBKC SMILE Mathematics 2005

19 Smile Worksheet 0272 Vehicle Survey You are going to carry out a 20 minute traffic survey. Go to where you can see a main road. Take this worksheet with you. Street... Traffic Direction... Time started... Finished... Use this chart to keep count of the vehicles. Cars Bicycles Buses Coaches Motor Bikes Mopeds Scooters Vans Heavy Lorries Fire Engines Police Cars Ambulances Comment on your results. Draw a bar chart to show your results. RBKC SMILE 2001

20 How much longer? r Smile a A A B C D F G H This example answers the questions which is longer, 'BE or GJ, and how much longer? BE = 4.5cm GJ = 5.0cm So GJ is 0.5cm longer than BE GJ is 5mm longer than BE Copy and complete this question to find which is longer, DG or CE (1) DG = 4cm CE = 3.5cm is 0.5cm longer than is 5mm longer than For each question find which is longer and write how much longer in cm and in mm (2) EF, FG (5) BF, CF (8) AB, GH (3) CF, FH (6) BG, GE (9) DH, BE (4) AE, EH (7) FB,CE (10) FH, CA (11) Draw a line which is 6cm long. Label it XY. (12) Draw a line which is 0.5cm longer than XY. (13) Draw a line which is 5mm shorter than XY.

21 Angles: the compass Smile 0281 BStartfacmq^^^^^^^^^^^^^^l Turn ^^^^^^^^^^^^ EndfacmqB ^^^B^^^^^^E^^^^^HwHchwav * 1 how muci^^^^^^k^^^b^^^^i i North left Jtum West w 1 E /t w ^ i E < *\ \ < N B ^tart facing ^^^^^^^^^^^^^^^B ' urn ^^^^^^^^^^^^^B tnci facing ^ N which way how much N i East right 1 turn East W FA E < % W h ^ r V^J i 3 Copy and complete this table. I I BMlfl North East Turn End Diagram which way I how much facing left right i turn 1 turn West East 4- -$- a North left i turn b South left i turn c West right T turn d North right turn e East left 2 turns f g h i 1 k North West North East West South right right left left right right 1J turns mm South West West West East 1 West right South RBKC SMILE 1995.

22 Angles from tessellations Smile 0284 Here is part of a tessellation of squares. 1. How many angles are there at A? 2. What fraction of a complete turn is each angle? 3. A complete turn is 360, so what is the angle at each corner of a square? Here is part of a tessellation of equilateral triangles. 4. How many angles are there at B? 5. What is the angle at each corner of an equilateral triangle? Here is part of a tessellation of regular hexagons. 6. What is the angle at each corner of a regular hexagon? \ Here is part of a tessellation of squares and regular octagons. 7. Work out the angle at each corner of a regular octagon. RBKC SMILE 1997.

23 Smile 0286 Right-angles You will need: compasses Clockwise rotation Turning in the same direction as the hands of a clock. Anti-clockwise rotation Turning in the opposite direction as the hands of a clock. faqi A quarter turn is called a right-angle. Draw a circle. Mark on North, South, East and West. One right-angle has been marked with a square. Mark the other right-angles in the same way. How many right-angles are there? Copy and complete this table. Start facing Which direction End facing Number of right-angles a South Anti-clockwise East 1 Start facing North. b East Anti-clockwise South Rotate clockwise to face South. c South Clockwise West d North Clockwise East How many right-angles did you turn through? e West Anti-clockwise North f South Anti-clockwise North g 12 Clockwise 6 Start facing 3. Rotate clockwise to face 6. h i 3 6 Clockwise Clockwise 12 9 How many right-angles did you turn through? j k 9 12 Clockwise Anti-clockwise 3 9 I 12 Anti-clockwise 3 RBKC SMILE 1996.

24 Rolling the dice You will need two dice. «L\J j 1Q * i \y Barchart Smile Worksheet 0288 "I Q i In some games you have to roll 2 dice and add the scores. The highest possible score is The lowest possible score is If you are playing a game like Monopoly it might be useful to know which totals most often occur. Do the following experiment to find out: 1) Roll the dice. 2) Add the scores. 3) Shade one square in the correct column on the barchart. 4) Repeat until one column is full. After you have completed the experiment answer these questions. Which column is full? Which column has least squares shaded? You should have more 7's then 12's. Can you give reasons why? 17 1 C >. 0 -M c 11 V 10 it n I 9 1 7J o i 4f q 1 2l <& Total on dice RBKC SMILE 2001

25 Experiments Smile 0290 You will need a dice. 1) You are going to throw a dice 60 times. About how many 4s are you likely to get? Try it. Record each result in a tally chart as you go along. Is the result what you expected? Turn over

26 2) How many heads would you expect to get if you tossed a coin 50 times? Can you explain why? 3) How many times would you expect to get 2 if you spun this 50 times? Can you explain why?

27 Which set? Smile 0291 The numbers 1-13 are placed in this diagram. 1. List the numbers inside triangle A. This set is 'multiples of 3'. 2. List the numbers inside square B. Which set is this? 3. List the numbers inside circle C. Which set is this? 4. Which number is inside set A, but is not inside set B or set C? Which sets is the number '3' inside? 6. Which numbers are not inside set A? 7. Which sets is the number '1 2' inside? 8. In which two sets can you find both '3' and '6'? 9. Which number is inside all three sets? 10. Which number is in set A and set B but not in set C? 11. '11 'and '13' are not in any set. Can you see why? Look carefully at your answers to questions 1, 2 and 3. RBKC SMILE 1995.

28 ' Doubling Patterns Smile Worksheet 0292 Example: '"'"' X2 6- X * - ''"' 'JL f\ X t,:-: M;12 J jt^mcujuiliamm.^it'' **± WWWNMMWWM ^ : I 1 Jt _ '-_'-_ """" atmaw^ :..:". ^T^j[l - ; mwniumtrmwm^r. ^1 >< ; muu i> \J r^ x2 x This sequence is made from the last digit of each number above: 8 Fill in the missing numbers in these sequences: v O v O 1) 7 Jii x2.* * v '? MMmwtta X 2 X 2 X2 pqo Xk! ^X_2 X2 : ""W' '"P".-.---j^ Ov/O jur~t~~if»- """" "p 1 ' i ---up) j^ «MIMMMMt -^ U / / \ ^r V 4 \ / 01.4 x 2 ^ x 2 ^1 1 > 4 _x2 <i MB 1MB t x 2 QQ x_2 x2 x2 occ Jjjj-K _x2 4 ^ MMnaiM» -^ ^ ^ u 1 / 2 \ ^r ^ «, & \ / turn over

29 3) 9 x2 x2 x2 x x2 x2 Q -,-.,., O 4) 5 x2 x2 x2 x2 640 x2 x2 x2 5 > 0 0 5) All these patterns can be shown on two diagrams. Can you fill in the missing numbers? 2 8 f RBKC SMILE 2001

30 You will need a ruler Measuring Lengths Smile t The length of this line is 6.7cm t f 1) How long is this line? 2) Measure these five lines. Write down their lengths. B 3) Put the lengths of AB, CD, EF, GH, JK in order of size with the shortest first. Turn over

31 The lengths of the sides of this triangle are 7.4 cm, 5.0 cm and 6.6 cm , cm So the perimeter of the triangle is 19.0 cm. Find the perimeters of these shapes: 5) 7)

32 Smile 0295 Nets of a Cube You will need: cm squared paper, scissors. This is a cube. It has 6 square faces. lis diagram has 6 squares. Copy it on to squared paper. Cut it out. Fold along the lines. Make a cube from it. This diagram is a net of a cube. Draw it in your book.

33 Copy these diagrams and try to make cubes from them. Are they nets of a cube? Draw a different diagram with 6 squares. Can you fold it into a cube? If it is a net of a cube, draw it in your book. There are many nets of a cube. Try to find them. Draw each one in your book. RBKC SMILE 1995.

34 Smile 0297 You will need a pegboard and pegs. This rectangle shows that 15 = 3x5 1. Draw 10 more rectangles and label them like this: example: 6 = 2x3 a) How many different rectangles can you find for 18? Draw and label each one. b) How many different rectangles can you find for 12? Draw and label each one. c) How many different rectangles can you find for 20? Draw and label each one. 3. Can you find any numbers that have 3 or more different rectangles? Draw and label them. RBKC SMILE 1997.

35 You will need a pegboard and pegs Smile = 3x4 20 = 4x5 16 = 4x4 1) What special shape is the last rectangle? 2) Make square patterns using (a) 4 pegs (b) 9 pegs (c) 25 pegs. iquare patterns can be drawn for 4, 9, 16, 25. rhey are called square numbers. 3) Find at least 5 more square numbers. Draw and label the square pattern for each. 4) Which of these are square numbers? 28, 49, 62, 64, 78

36 Smile 0299 Three squared 3x3 can be written as 32 and read as 'three squared 1 3 x 3 = 32 = 9 So three squared is nine. Copy and complete a) 42 = d) 12 2 = b) 52 = e) 100 = c) 72 = f) 81 = Turn over

37 Continue this pattern I 2 = -1x1 =1 22 = 2x2 = 4 32 = 3x3 = 42 = 4x4 = 122 = How many square numbers are there between 1 and 100? Challenge : How many between 1 and ?