Find four squares. Find four squares. Smile Worksheet Smile Worksheet The dots are the corners of four squares. Find and draw the squares.

Transcription

1 Smile Worksheet 1812 Smile Worksheet 1812 Find four squares Find four squares The dots are the corners of four squares. Find and draw the squares. The dots are the corners of four squares. Find and draw the squares. RBKC SMILE 2001 RBKC SMILE 2001

2 Crossword n n Smile Worksheet A c r o s s 1. Three times three 3. One pair 7. Take away seventeen from twenty 8. Four times five Twelve fives Sixteen divided by two One less than two Eight times five The number of days in a week One dozen Twenty minus seven D o w n 13. Double Half of ten A 15. D 18. Centimetres in a metre (two words) 16. Four plus two mm (two words) RBKC SMILE 2001

3 You will need several copies of the worksheet 1818A and colours. Smile 1818

4 A helicopter spots three cars travelling due North along a narrow country lane and takes a photograph of the scene. Parked 1. If the iane is only wide enough for two cars to pass each other safely, and the cars continue at the same, steady speeds, what do you think will happen in the next few seconds? 100m 20 m/s 100m Note: Speed is sometimes measured in metres per second (mis) instead of miles per hour (mph). A rough equivalence is W.m/s to 20 mph. 30 m/s j in

5 Imagine that you are sitting in the helicopter. Every second you take a photograph of the scene below. Your first three photographs will look like this: I D D $iv /';* psk D *ffi$xg&* ^I-r-S,->»:> D sh BE D D 2. On a sheet of blanks, complete a series of photographs taken at 1 second intervals. Colours will be useful. 3. Write about what happens. 4. Suppose that the black car had been travelling slowly at 10 metres/second. What would happen and when? Turn over if«pi5 «S';r

6 More traffic situations As you fly northwards you photograph other traffic situations. Some of these are shown below. The speeds (in m/s) are written on the car roofs. 50m m Parked 7. 60m 60m 180m Parked 60m 70m Parked Draw each of these situations in turn, on a separate "snapshot blank". Be careful to give each car its correct speed and starting position. Write about what happens. 9. The diagram opposite shows a traffic situation involving five cars. Arrange these cars in order of speed. Can you find a quick way to tell which car is going fastest? <D OC 0 X A o X A. o X A o X A o 0 A X 0 O Time L\ X tt _ O 0 X. O > c <» ) X O This activity is taken, with kind permission, from The Language of Graphs, a collection of teaching materials by Malcolm Swan (ISBN ).

7 Smile Worksheet 1818a Snapshot blank ) 180_ D) c JO CO 0) o c CO 160_ 140_ 120_ * * * 100_ 80_ 60_ 40 _. 20_ 0_ Time in seconds RBKC SMILE 2001

8 Smile 1821 Dvertaking Pillar box 100m Telephone box Tree 10m The black car is travelling at 10 metres per second and the white car is travelling in the opposite direction at 20 metres per second. 1. How long will it take the black car to reach the pillar box? 2. How long will it take the white car to reach the telephone box? 3. When will these two cars meet each other? 4. How far will they be from the tree at that time? Note: Speed is sometimes measured in metres per second (m/s) instead of miles per hour (mph). A rough equivalence is 10 m/s to 20 mph.

9 One method for solving this problem involves drawing a graph. Here a graph has been drawn which shows the distance of each car from the tree at the beginning (0 seconds) and after 1 second. O Represents the white car Represents the black car Distance from tree in metres. 110 ( ) ( <» ^ "" Time in seconds 5. Copy the above diagram onto graph paper and complete the graph for each car at 1-second intervals. 6. When and where will the two cars meet? Is your answer the same as before?

10 They grey and the white cars are travelling in the same direction. 110m Draw a graph showing distance from the tree (0-200 metres) against time (0-10 seconds) to answer the questions below. 7. When will the grey car overtake the white car? 8. How far will they be from the tree at that time?

11 Diagram A shows three cars travelling at a constant speed. Diagram B is a view of the same piece of road 10 seconds later. B 80m 20m T ff 200m 80m 20m 9. Draw a graph to show what happened during these 10 seconds. 10. Write an account of what happened. This activity is taken, with kind permission, from The Language of Graphs, a collection of teaching materials by Malcolm Swan (ISBN )

12 Smile 1822 Product of primes It will be useful to work with someone else. 1. Find two whole numbers bigger than 1 that multiply together to make... (a) 39 (b) 95 (c)187 (d) 247 And the big challenge... (e) Find a number bigger than that is the product of two primes.

13 Smile Worksheet 1824 Silver Earrings A large part of the cost of making jewellery is the metal itself. If this square of sheet silver costs 1 how much would these cost? to You may like to invent some more......give the cost of each one. RBKC SMILE 2001

14 OIMIIt? IMM A game for 2 players The winner is the player who is the first to reach exactly 10. Start with 0. to add on 5, 1 or 0.5. Try different target numbers.

15 Smile Worksheet 1828 Find the Shape Can you find and colour in these shapes? Rectangle Triangle with all sides equal (equilateral triangle) Triangle with 2 sides equal (isosceles triangle) Triangle with no sides equal (scalene triangle) Right-angled triangle Hexagon Kite Rhombus (diamond) Parallelogram Pentagon Octagon Did you find any other shapes? RBKC SMILE 2001

16 SMILE 1830 o The 'smoothing out' An activity for two people. A bus is travelling at 10 metres per second towards a bus stop 50 metres away. What do you think the distance-time graph will look like for the bus?

17 Your graph may have looked like one of the following: A 'One second photograph' graph. DU Bus Stop Distance along road in metres I I 10-1 I Time in seconds. A'Cine film'graph. 60 Bus Stop Distance along road in metres Time in seconds. During the first 5 seconds, the bus is travelling at a constant speed of 10 m/s. Then, on arrival at the bus stop, it suddenly slops dead in it's tracks! This is shown by the way in which the graph makes a sudden turn. What would happen if a real bus behaved in this manner?

18 In the real world, a bus begins to slow down before it reaches the stop, and gradually comes to a halt. The following graphs show this. 'One-second photographs' of a real bus. Distance (metres) 60 w _ Bus Stop t * * I B 1 * 1 \ 1-1 ' I , Time (seconds) 'Cine film' graph of a real bus. Distance (metres) 60 Bus Stop Time (seconds) 1) a. When does the driver begin to brake? b. When does the bus actually stop? c. For how long is the bus decelerating? (slowing down) Notice that the above graphs are smooth curves. This is because the bus changes speed gradually.

19 For each of the situations drawn below, sketch a distance-time graph which will describe the events of the next few seconds mn GARAGE T-- -ti**.* *_-.. " O--^.^ &^& r POd n This activity is taken, with kind permission, from Th< Li;)i;<;.ii :^ot (7-,j;)/is, a collection of teaching materials by Malcolm Swan ISBN

20 Smile 1832 MINIMUM INFORMATION / KoA/e dreuvrv a ijb dfa\*j Meena Can Meena really draw a triangle identical to Geeta's? Investigate different sets of questions that Meena could ask. What is the smallest number of questions she needs to ask?

21 You will need a pack of cards with one missing. Which card is missing? Explain how you worked it out.

22 (-. > : :> ^ o< ) -^ ^ ^-// V0? (^] (^\ (~^\ f-v {*!) V * V V *) \*4. ""-^- ^X ^-.^_^*s ^ ^

23 Smile 1843 O A hexagon has 6 sides, It can have... h 1 right angle... or 2 right angles... J L ~i or 3 right angles or 4 right angles... j TJ A hexagon cannot have 6 right angles Why? n or 5 right angles

24 r i J)=3 loj [9 (T- Cr- C^J f=3o ^> t=3 f 1 P 1 u u <s C=0o I0l5) ^>

25 Polygons and Right Angles A hexagon has 6 sides. It can have... Smile right angle or 2 right angles... j L or 3 right angles., A hexagon cannot have 6 right angles. or 4 right angles or 5 right angles Investigate How many right angles other polygons can have. Why? RBKC SMILE Mathematics 2005 Polygons and Right Angles A hexagon has 6 sides. It can have... Smile right angle or 2 right angles or 3 right angles... A hexagon cannot have 6 right angles.... or 4 right angles or 5 right angles... Investigate } How many right angles other polygons can have. Why? RBKC SMILE Mathematics 2005

26 Smile Worksheet How many straight lines can you find with exactly 3 points? Straight Lines 1. Find 3 points in a straight lina.-jhey must be exactly in line. 3. Make a similar puzzle for a friend. RBKC SMILE 2001

27 Smile 1845, of this strip has been shaded How many different ways can you shade? 5 What about other fractions?

28 Symmetrical Triangles Smile Worksheet 1847 Four small triangles are shaded... line of symmetry... to give a symmetrical shape. line of symmetry line of symmetry Create symmetrical triangles by shading four smaller triangles. Draw in the line of symmetry each time. \ / RBKC SMILE 2001

29 Three by Three Smile 1848 This is a game for two players. One player has 3 blue counters and the other has 3 red counters. Put the counters on the board one at a time in turn. Try to get your 3 in a line. Take turns to move your counter along a line to the next space until somebody gets 3 in a line. RBKC SMILE 2001

30 Smile Worksheet III Search Example ;90= =100 Find groups of numbers that add up to 100. If you enjoyed this, make up a search of your own. RBKC SMILE 2001

31 Smile Worksheet 1856 What Shapes? * What shapes can you make? 1 (Z, r\ f~ f>\ > (2. "f~ W Z3 H /7 \f> IcPC'C/dC't? IxiliariylC' ; 1 I : *!' \!? w \ i i f: 0!:!: I t> * 1, 4 ; i. i : : ;;?i St? } : Use a mathematical dictionary to identify and label each shape. RBKC SMILE 2001

32 Smile 1857 These two pieces will fit together to form a 3x3x3 cube.

33 Draw pieces which will fit with each of these shapes to form a 3 x 3 x 3 cube. In each case show the inside view.

34 ' 6. 8.

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36 TICKS SMILE 1861 Match the dipsticks and tanks.

37 in co CM CO CM CO CM CD in co CM T- O (0 in CO CM CD CO

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40 Smile Worksheet 1862 Even Animal Join the even numbers »b/ 57 e H Start , qfi 26 «.36 ' '28 * 3 30* ' RBKC SMILE 2001

41 SMILE 1867 o Four Cubes Each of these solids is made of 4 cubes. Make 2 of each Use your 8 solids to make 4 larger cubes. What do you notice?

42 Symmetry Match Smile Worksheet 1868 Cut out and match the pieces. continued on next sheet

43 Symmetry Match (page 2) RBKC SMILE 2001

44 BACK TO BACK Smile 1872 activity for two people. You will need multi-link cubes. \tj${ Sit back to back. One person make a solid from some of the cubes. Describe it to your partner so that she can build one exactly the same.

45 Smile 1873 Polygon Symmetries You can draw a quadrilateral with... no lines of symmetry... or 1 line of symmetry. Can you draw a quadrilateral with 2 lines of symmetry?... 3 lines..?... 4 lines..? What happens with other polygons?

46 Smile 1874 OOT HOW loo DO HOT A '' >N

47 Smile 1875 These are multiple patterns in Urdu number script. Can you work out the numerals in your own number script? What other number patterns can you make in Urdu?

48 Smile 1881 HINDI ADDITIONS These additions are in Hindi number script. Can you work out what each numeral is in your own number script?

49 Smile 1885 OPTIMISING This pack contains 4 problems about maximum and minimum. You. NvujHt fmd <Jb Kfllpful to

50 Smile 1885 a 15 of the open box that be made Paper

51 CONES Smile 1885d Volume of a cone = Vb n r2 h A sector is removed from a 10 cm radius circle and the remaining paper is formed into a cone. What is the maximum volume the cone can have?

52 Smile 1885c Books

53 A publisher has the problem of pricing a new book. If too much is charged, the profit per book will be high but not many will be sold. If too little is charged the sales will be high but the profit per book will be low. The price needs to be set so that the total profit is maximised.

54 The marketing department estimates the following sales at different prices. Price Forecast Sales The production costs are 1.75 per book. What is the optimum price? Give your answer to the nearest 5p. What other factors might complicate this problem in real life?

55 Baked Beans Smile 1885b The manufacturers of baked beans would like to maximise their profits. They sell baked beans in tins of 500ml. IBAKEM IBEANSI What is the minimum surface area of metal needed? Do beans come in tins of this shape?

56

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61 Smile 1897

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63 of ^rflats. 2 Amandep lives in the flat with the red door. \ \"xx - a tape recorder: 4 Tea is drunk in the flat with the green door 5 The girl studying accountancyotv The flat with the green door is immediately below the top flat which has a white door 7 BronwenfidrinKs CoKe. 8 Physics is studied in the flat with the yellow door.

64 SCofTeefs^runik inthemidclfeflal:. 30 Carol lives in the bottom flat. M 12 Esther studies engineering. 137he chemistry student drinks Shandy. 14 Theremote-ControlTV is in the fiat next to the flat in which physics is studied, 15 Carol lives in the flat next to the flat with the blue door WHO DRINKS LEMONADE? WHO HAS THE MICRO-COMPUTER? There are five sets to look for: GIRLS'NAMES COLOURS OF DOORS ELECTRONIC EQUIPMENT DRINKS SUBJECTS OF STUDY

65 o o O)

66 Smile 1899 Number words Start with a number. How many letters We there? Writedown the number. THREE How many letters are there? 5... and so on... FIVE FOUR Start chains with different numbers. What do you notice? Try making chains in other languages.