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K`NEX for hands-on Maths

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1. This is the full version of the Guide K NEX for hands on Maths including 101 hands on maths activities with the K NEX construction kit ee D k a 4 K Le 1 D E f B a i E Dh 4 pay ame S pm SP o 8 ER K www knexusergroup org uk Contents Introduction K NEX for hands on Maths Delivering K NEX activities 4 101 KNEX maths activities Appendices A Answers to questions B Number sheets C K NEX order form Index SS 1 Introduction The K NEX construction kit has been used successfully in schools and in other forms of education since 1995 Initially KNEX was seen just as an innovative and exciting way of helping children understand the Design and Technology curriculum but increasingly KNEX has been put to many different uses including e Design and Technology curriculum e Maths curriculum e Adult numeracy e Science curriculum e Early Years e Children s clubs e Childcare schemes e Family learning e Home education All K NEX sets include instructions for building a range of models but very few of the sets include any instructions or guidance for using K NEX in maths activities despite its many strengths in this area The purpose of this guide is to rectify this omission by providing lots of ideas for using K NEX in e Maths curriculum at Key Stages 1 2 3 and 4 e Out of school maths education eg maths clubs e Adult numeracy curriculum Note that the Guide
2. e 4 red connectors Q2 Can you show your age in K NEX numerals 1 whit t Q3 Can you use the numerals to write down today s j d date in the format dd mm yy where the symbol is a and use them to make the shape below grey rod Q4 Can you use the numerals to write down the time in digital clock format in the format hh mm where the symbol is two tan connectors 33 Number square Extra equipment Numerals from Appendix B Make the four by four number square shown below lat ad am Se Q1 Can you make one of the models in the instruction book that came with your K NEX set by counting out the pieces and then using them to build the model 31 Counting shapes Count out e 12 white rods e 12 green rods f e 8 green connectors w 12 EN B e 5 white connectors ZR and use them to make the shape below y 1 3 14 4 5 1 e 4m mr s Copyright 2005 K NEX User Group www knexusergroup org uk 13 Q1 Can you use the number square to find 4x2 4x3 and 4x4 Q2 Can you make a number square which is 5x5 Q3 Can you make a number square which is 10x10 34 Number line Extra equipment Numerals from Appendix B Make the number line shown below Q1 Can you use the number line to work out 1 3 3 4 8 2 and 7 5 Now make a number line with zero and with negative numbers as shown below Q2 Can you use this number line to work out 3
3. 50 Draughts For 2 players Build an 8 by 8 draught board using the small square design shown below b en EN Ask each player to make three paper planes from a sheet of A5 paper with a design which ensures that when thrown each dart will lodge in the dartboard Also draw a line on the floor which the players will need to stand behind when throwing their darts You Copyright 2005 K NEX User Group www knexusergroup org uk 18 Then play a game of draughts using 16 white connectors and 16 blue connectors as pieces will need to experiment to find the best distance between the board and the line perhaps 1 to 3 metres Players then take turns to throw their three darts at the dart board You should adopt a scoring method that is best suited to the number skills of the players For instance each player starts with 301 and the score each turn is subtracted from the total The first player to reach zero or below wins the game For players with less skill you might number the dart board with numerals 1 to 8 and score upwards from zero to say 101 You can also search for variations on the game of darts on the internet There are many of them all of which require number skills to a greater or lesser degree 52 Ten pin skittles For 2 4 players Build the tabletop skittles model and the ten pins shown below Copyright 2005 K NEX User Group www knexusergroup org uk 19 To play stan
4. 3 4 6 and 2 4 35 Money line Extra equipment Numerals from Appendix B Make the money line shown below MIL Itty E Sp fe ge ege lt a E S Q1 By placing orange connectors onto the number line can you make a total of 37p and then 1 61 36 Simple scales Make the scales shown below Q1 If you put three white connectors on one side of the scales how may white connectors will you need to put on the other side to make the scales balance Q2 If you put two white connectors on one side of the scales how many grey connectors will you need to put on the other side to make the scales balance Copyright 2005 K NEX User Group 37 Scales with multiple positions 4 Q1 If you put three white connectors on the innermost position on one side of the scales how many grey connectors do you need to balance them and where should they be placed Make the scales shown below FL Q2 If you put three white connectors on the central position on one side of the scales how many grey connectors do you need to balance them and where should they be placed 38 Costing with K NEX Make the K NEX bird table shown below Q1 If each rod costs 5p and each connector costs 10p what is the total cost of the bird table Q2 Can you design and build a bird table that is only half the cost of the one shown www knexusergroup org uk 14 39 Maths investigation gear rati
5. NEX maths activities covering mainly shape and space The set includes e 920 pieces to complete 28 different activities from instructions e 2 strong plastic compartmentalized storage cases e Comprehensive full colour instruction manual Suggested age range 5 Number that one set can support 6 students working in groups of 3 Copyright 2005 K NEX User Group K NEX Discovery building set A general purpose set that provides a good introduction to K NEX and its capabilities The set includes e 259 pieces to build 20 different models from building instructions e Strong plastic compartmentalized storage cases e Comprehensive full colour instruction manual Suggested age range 5 Number that one set can support 2 students K NEX Simple machines deluxe set An enormous K NEX set that is ideal as a general purpose K NEX resource 5 A for schools d Up clubs childcare 3 EX schemes and family learning The set includes e 3 400 pieces of K NEX e amains powered 12v motor ML INE SE Te 2 WW VA H 3 4 Leg FS Seng A e 5 teacher s guides Levers Pulleys Gears Wheel amp Axles Inclined Planes e 5 lesson plans for key stages 1 amp 2 e instructions to build a science fair model the 4 tall Big Ball Factory Suggested age range 5 to 95 Number that one set can support Supports 20 30 students working in teams of 2 3 www knexusergroup org uk 38 K NEX
6. and measure 4 1 1 2D activities from instructions The activities below use only 2 dimensional 2D KNEX shapes 1 K NEX rods K NEX sets come with a limited number of the longer rods but you can always join two shorter rods together if you run out of the longer ones le Ze TT M A lt lt D ven es Join two green rods two white rods two blue rods and two yellow rods together as shown below to prove it for yourself 2 KNEX connectors All K NEX connectors can be connected to at least one K NEX rod and the largest can be connected to eight rods To help gain familiarity with K NEX connectors make the model shown below AA HA NS The angle between any two adjacent rods connected to a connector is 45 This makes K NEX very good for making shapes that have angles of 45 90 and 135 such as squares rectangles right angled triangles and octagons as you will see in the next few Activities If you need to make an angle other than 45 90 or 135 in KNEX you can often do this with a KNEX hinge connector shown above Copyright 2005 K NEX User Group 3 Five sizes of K NEX triangle The length of the K NEX rods have been carefully chosen so that whichever rod you use to make the longest side of a right angled triangle the other two sides will require the next smallest rod Try this for yourself and make the five triangles shown below 4 Learni
7. does not attempt to explain how to teach maths in these settings but rather provides a wealth of resources to assist those working in this field This Guide is available as both a printed Guide and a PDF version on CDROM Adobe Acrobat is required to view the Guide on CDROM Version 1 2 27 5 05 Author Andy Shercliff of the K NEX UK User Group a not for profit division of 4children2enjoy Ltd Email info knexusergroup org uk 1 1 Who is this guide for This Guide has been written for everyone who has an interest in Maths education including e Headteachers e Teachers e Adult tutors e Family learning practitioners e Children s club leaders and helpers e Childcare scheme leaders and helpers e Home educators 1 2 What is K NEX K NEX is one of the most successful construction kits in the world second in popularity only to Lego It is based around a series of rods which can be joined together by connectors such as the one shown in our logo Once they have mastered using these simple components children and adults alike can use their imagination to make potentially millions of different models It is ease of use and versatility that make K NEX such a good investment for educational purposes whether in schools home education children s clubs childcare schemes family learning or post 16 education You will find that there is no age limit for enjoying K NEX it is suitable for all ages from 5 to 95 The
8. multiple positions as an equation in which Weight on left x distance from pivot Weight on right x distance from pivot 4 2 2 Activities that are games The activities below are all games that will help develop number skills 46 Pick a rod For 2 to 4 players Put 10 red rods and 10 yellow rods into a box and then turn the box upside down to create a pile of rods on the tabletop The first player tries to take a rod from the pile If he she manages to do so without any of the other rods moving the player keeps the rod and the player tries to take another rod As soon as the player causes a rod to move other than the one being taken he she must let go of the rod being taken Play then passes on to the next player and so on until all rods have been taken Players then count up their rods to see who has won You should determine your own scoring system according to the numeracy skill level of the players For instance score 9 points for a red rod and 6 for a yellow rod After playing the game a few times you might ask your students to come up with a variation on the rules for instance by including different numbers and Copyright 2005 K NEX User Group lengths of rod or introducing K NEX connectors into the game 47 Colour game For 2 to 6 players Give each player a white connector with eight blue rods attached to it The object of the game is to add eight different connectors to the ends of
9. 05 K NEX User Group www knexusergroup org uk 22 Q1 Can you use the callipers to measure the length of some small objects and the diameter of a ball 65 Measuring wheel Extra equipment Sheet of thin white card 2 large gear wheels 2 small gear wheels Make the K NEX measuring wheel opposite Affix a sheet of card beneath the pointer and align the pointer so that it points vertically when the wheel is on the ground Mark this position as Om Now run the measuring wheel along a 10m tape measure and mark off the position of 1m 2m 3m etc Q1 Can you use your measuring wheel to measure the length and width of the room you are now in Q2 Can you use your measuring wheel to make a plan of the building you are in and its grounds see also Activity 76 Copyright 2005 K NEX User Group www knexusergroup org uk 23 66 Water tank Extra equipment supermarket carrier bag Make the K NEX water tank below Q1 Find the heaviest object that your crane can lift without it falling over Now modify your crane by adding white connectors to the grey counterweight arm Q2 Again find the heaviest object that your crane can lift without it falling over Q3 Why does increasing the distance between the counterweight and crane enable the crane to lift B heavier weights Q1 Calculate the volume of the tank in mm and convert the volume into millilitres Q4 Can you adapt your crane to
10. 1 Moon base Use K NEX to make six buildings you would need on a moon base and lay these out with streets Then build a moon buggy to travel along the street Q1 How far would the moon buggy have to travel to visit every building Q2 Can you give the moon buggy driver directions to visit every building 4 4 Handling data All the activities in this subsection relate to handling data The questions shown against each Activity are only examples you may wish to think up your own questions for each activity that best suit the ability and experience of your students 4 4 1 Activities from instructions The activities below can be completed from the instructions provided 82 Organisation chart Extra equipment Numerals from Appendix B write on back K NEX is good for making all sorts of diagrams in which interconnections are shown Try the one below which is the organisation chart for a company www knexusergroup org uk 28 Q1 Find out the number of students in your group that have blond brown or black or other colour hair and enter the numbers into a K NEX data table Q2 Throw a dice 20 times and make a K NEX data table to record the number of times that the dice falls on 1 2 3 4 5 or 6 Q3 Make a K NEX data table that contains a railway timetable or bus timetable for a local train or bus service Y j v gt N MrC K MrsE b Ms G 85 Bar chart DM Lam LE sf Mo Extra equipment Numera
11. 4 which have a definitive answer A 1 Shape and Space Activity 4 Q1 The triangle in this activity is an equilateral triangle The triangles in Activity 3 are all isosceles triangles Q2 The angles in the equilateral triangle are all 60 Activity 5 Q1 One way to achieve this is to make one square with sides of blue rods and the other with sides of green rods Q2 No Q3 Yes Q4 Yes Activity 7 Q1 45 and 135 Activity 8 Q1 45 and 135 Activity 9 Q1 135 Activity 10 Q1 All the right angled triangles in Activity 3 other than the smallest can be filled in with two triangles All the squares in Activity 5 can be filled in with two or more triangles Q2 The rectangle in Activity 6 can be filled in with a combination of triangles and squares as can the octagon in Activity 9 Activity 11 Q1 45 90 and 135 Activity 12 Q1 Yes Q2 Examples 7 can be rotated to become the letter L and 9 can be rotated to become 6 Activity 13 Q1 The shape is symmetrical about a vertical line through its centre and also a horizontal line through its centre Q2 Yes Q3 Activity 3 each has 1 line of symmetry Activity 4 3 lines Activity 5 4 lines Activity 6 and 7 2 lines Activity 8 1 line Activity 9 8 lines Activity 10 4 lines Activity 11 8 lines Activity 14 Q1 A rectangle Q2 3 1 and 1 3 Activity 15 Q1 M Forward 190 Righ
12. Order form To use this order form please print it out and fill in every field marked with an asterisk Then fax to 0208 196 2248 or mail to K NEX User Group 87A Newton Road Mumbles Swansea SA3 4BN f you have any queries on completing this form please email us via info knexusergroup org uk Date ordered Your Purch order ref Organisation Address Telephone Name Position Signature Order not valid unless signed Part no Description Price Quantity Value 78720 K NEX Elementary Maths set 79028 K NEX Intermediate Maths set J K S T RE 78650 NEX Discovery building set 79520 K NEX Simple machines deluxe set Nett value of goods All orders are subject to our Terms and conditions which may be found at http www knexusergroup org uk acatalog tandc html 721 B ANR RNA AEN R EN MI ER PRE ER 3 6 7 8 9 12 28 ER CES 3 6 11 12 22 28 32 ADACUS NEE 6 16 ere Teo WEE 3 adult COMIC AON EEN 4 adult numeracy ee 2 4 age tange aieea a e a E een 38 EE 2 3 5 AID DEAE NS Rta rs re ne eU S EE 3 6 16 AIDHADOLE SANS nes Pr rs 6 12 andie eran iv E 3 7 8 12 21 27 28 a ao de de 2 4 6 15 21 22 28 34 Do CALE getest 4 5 6 27 29 31 32 Can 61 Ai ae ree nen net a were dd es 4 CAS as 5 23 25 27 28 29 31 32 39 CID eee 5 24 CDROM EE an ohne es 2 5 10 23 COM AR ne een T TT 30 challenge 3 4 5 6 12 20 28 32 CHA
13. Q1 Can you make two other sizes of K NEX squares one below Shapes are said to be similar if they are the same shape but a different size All the squares above are similar Q2 Do similar shapes have the same length sides Q3 Do similar shapes have the same angles Q4 Are the triangles in Activity 3 similar 6 Rectangle Q1 The eight angles in the above octagon are all the A rectangle has right angles like a square but two of same What angle are they the sides are longer than the other two sides Build the 2 C build an K NEX oct in which not all K NEX rectangle shown below S RA n del wig LS sides and angles are the same 10 Filling in 2D K NEX shapes Most 2D K NEX shapes can be filled in with triangles squares etc Build the K NEX square below and fill it in with triangles as shown Q1 Can you build three other sizes of rectangle 7 Rhombus In squares and rectangles the sides are said to be parallel because they run in the same direction The easiest way to test if two lines are parallel is to extend Q1 Which of the other shapes in Activities 3 to 9 can them in both directions If they lines eventually meet be filled in just with triangles then they are not parallel you can extend parallel Q2 Which shapes can be filled in with a combination lines for ever and they will still not meet of triangles and squares A four sided shape with two sets of parallel sides of equal length
14. SA beoe E 4 CHING ES seine a a aa a 2 4 children SCD soit eit Ra ins 2 chiaren s CID RS Rene dun nn 4 CAS O RS Ale D una uis 4 CIOCK EE 6 13 25 26 28 CO le 32 COMPARE a De ta nedae a 30 Communication skills essere 3 COMPUTER A eee diae ai aire 4 CONCITIPM ES SM HE 3 8 12 gay poer 2 COOKGIN ALCS sce CE ots v esten s D a Ar rM DEZ 3 6 9 COSUMG esL D UL LEE 6 14 20 21 COUMUNO Met ue 3 6 13 EE RU UE E el ele DEE 5 CUD ESS an ere 3 6 11 12 15 16 21 33 34 elle el 6 11 12 21 33 a DEREN ARR E NP PERROS 4 6 28 29 31 32 34 data ele Ee e TEE 5 Design and Technology 2 dagrar t 4 aller e 4 8 12 28 SI Let DEE E CVS OF EEN 18 drawing Le 6 12 EaNy cic TR M 2 Gase OF EE 2 educationel Value iota cube ore Ra cte vA iocum Sor does 2 QUATION and ORO 3 17 EELER 7 21 33 un du BEE 3 6 16 ee UE rie EE 5 familteriSdtiQll esee Unica tn Unis Dota ics Dio Cu ten 4 famiy learning ais decisa eoi depen EEE 2 4 FE COIG S EE 4 ele 2 TO GW RE 17 30 TRAC OB nd a OR eee 3 6 15 game ssena Gea 6 17 18 19 20 21 32 gear EE 6 15 33 gear wheel eeeeeeeseeeeeee 5 15 23 33 EEN M URN 3 grap PE 4 6 27 29 Ranay uin EN 4 Nard TEAC ME 2 home Ze Ile re TEE 2 4 Index instruction book 4 13 Idee EE 4 HAWES CCMA ee ee SE Me 2 Dieter 7 21 33 K NEX education set 4 5 le n EE 2 PAY OUI A euet pec TS ei tie 4 learning diff
15. UM 5 DYLANI ecc 6 11 12 33 FANGS in nina Reet 2 4 5 6 21 31 38 Kier llel Bees ue TT NOS 6 7 8 11 13 Kee REESEN 3 6 9 OMS EENEG 6 8 room layouten a a a 4 5 FOLA UON Ada ri Ni 3 6 9 91 PR ERRORES 30 32 ies MM RR T MK Tx 3 Ge En ee nie 4 6 14 17 24 28 SCHOOIS ee ne eee e ait 2 RD LOI LE MIS Kee ee ee eege 2 secondary school a SL tree 4 shape and epace 3 6 7 33 38 simple machines 0 ccecceeceeeeeeeeeneeeneeeaeeeneeeneeeseeeees 2 SOINS Dmm 4 6 13 EE Mp 4 6 25 27 spreadsheet annannnnannannnnannnnnnnnnnnnnnnnnnne 4 6 29 30 square 3 6 7 8 10 11 12 13 14 15 16 18 21 33 E PA DR isth ene erase 6 8 gie 2 SUD WACOM eege 3 SUPV GS VINNG nn dirt ele nue 28 SV IMM CUE e EE 3 6 9 12 33 table 4 5 6 9 14 18 20 21 27 28 29 31 32 TEGAN WOEK ING T ss 5 Mess 4 11 13 20 24 25 26 27 28 30 le NER TTE de A 5 TOW EEN 6 16 17 20 28 34 iine ER a 4 ANS ATOME outre tc e aote vu tue peut Docs A 3 6 9 MEDER 6 8 triangle 3 6 7 8 9 10 12 13 15 16 21 22 33 34 NOT OS TREES 2 Uie successerat E onse TON 4 Big 4 User Kee 4 39 WIS TT RC M e 4 VerSalillby iit ou bore iE oie oca tte 2 rell rt 4 6 21 22 24 34 NEDSH Sas dd ecrans 4 5 del EE 20 21 24 28 3 WNO EE 4 AS Un ee 9 VE LEE 9 ZETO LS EN ege 13 14 19 22
16. ach other Activity 1 2 therods and connectors can be used to make five different sizes of right angled triangle Activity 3 and six different sizes of KNEX square Activity 5 3 KNEX squares can always be subdivided into four K NEX triangles Activity 10 4 KNEX can be used to build cubes and other 3D shapes Activities 18 to 22 In getting students started with K NEX we would recommend starting with some of the simpler KNEX shape and space activities as shown in Section 4 1 These will give an understanding of the geometry and use of K NEX and the confidence to progress to more advanced activities The activities in Section 4 1 will help students to understand e 2D shapes e 3D shapes e Similarity e Angles e Patterns and relationships e Translation rotation and reflection e Symmetry e Coordinates e Scale e Logo Copyright 2005 K NEX User Group 2 2 Number Students who are using K NEX to build models carry out the activities in this Guide or to complete K NEX challenges are applying their maths skills and knowledge constantly As an example the completion of any one of the models in the instruction booklet that arrives with a KNEX set may involve 1 Interpreting a 2D representation of a 3D model 2 Selecting components by size shape and colour 3 Counting the number of each component needed Deciding which component to add next Aligning each component so that it will fit into the pa
17. ape 4 1 3 K NEX challenges All the Activities below are KNEX challenges for which no instructions are required It is recommended that students complete some of the 2D and 3D Activities earlier in this section before attempting any of these challenges Copyright 2005 K NEX User Group 24 K NEX picture Q1 Can you make a K NEX picture in a frame to hang on the wall It can either be a picture of a real life object or simply a pattern made up from triangles squares and other shapes 25 KNEX maze Q1 Can you use K NEX to build a maze with e One entry point e One finishing point at the centre e Only one way to get from the starting point to the finishing point e Lots of ways to get lost Q2 Can you use Logo to write down directions for completing the maze see Activity 15 26 K NEX alphabet Q1 Can you use K NEX to make an alphabet and then use the letters to spell your name 27 K NEX drawing aids Extra equipment K NEX wheel without a tyre Q1 Can you make K NEX drawing aids that will enable you to draw on a piece of paper e A Straight line e A second line at an angle of 90 to the first line e A third line at an angle of 45 to the first line e A circle Q2 Can you use the drawing aids to draw a design for a simple wheeled vehicle such as a shopping trolley or baby buggy 28 KNEX ferris wheel Build a Ferris Wheel out of KNEX When you have finished Q1 Iden
18. ation purposes Once you purchased your set we recommend that a you build some of the models in the accompanying instruction book b youlook at pages on the User Group website www knexusergroup org uk such as Handy Hints Instructions and Challenges c You complete some of the simpler maths activities in Section 4 You might also like to consider attending one of the User Group s training courses as shown on the Training page of the website 3 2 Venues and room layout Many venues are suitable for KNEX maths activities including e Primary schools e Secondary schools e Out of school clubs e FE colleges e Universities e Adult education centres e Family learning centres e Local companies e Community centres K NEX maths activities can easily be carried out in a classroom or similar sized room or if the numbers participating are too large in a bigger room such as a school hall The relatively small amount of equipment needed for most K NEX maths activities means that they can be delivered on a whole class basis The most common room layout is students seated in fours at tables with each table sharing a box of K NEX and students working in pairs to complete their K NEX activity Activities can also be provided to students on an individual basis for instance if you are using the activities to test their current level of skills and knowledge However working in pairs is to be preferred in most instances bec
19. ause of the opportunity it provides to develop the use of www knexusergroup org uk 4 mathematical language and teamworking skills Two alternative approaches to working at tables in pairs are e Working on the floor in groups of 3 or 4 to complete larger K NEX activities such as the map of New York City Activity 80 e Providing K NEX activities outdoors in dry warm weather such as making a plan of the school grounds using the K NEX measuring wheel and theodolite Activity 76 3 3 Selecting K NEX maths activities Section 4 contains 101 K NEX maths activities suitable for a wide range of ages and abilities Some of the factors you may like to consider in selecting maths activities for your own group of students are a What are your educational objectives b What level of skills and knowledge do the students already have c Which activities will best complement the other maths activities you have planned d Will the challenges be completed on the table top on the floor or outside e Whatis the timeslot available for the activity f Canthe activity be completed with only a standard tray of KNEX components or does it require special KNEX components such as gear wheels g Will the activity require preparation such as photocopying one of the number sheets in Appendix B see section 3 5 h How will you present the activity to the students The main alternatives in presenting the activity to the
20. by placing a rectangular mirror upright along the yellow line The yellow line is called a line of symmetry Copyright 2005 K NEX User Group www knexusergroup org uk 9 16 Pantograph m Extra equipment pointer short pencil Activities 3 and 5 showed how K NEX triangles and i Pe squares can be built in different sizes A pantograph a is a simple device for copying drawings to make them lt 9 8 bigger or smaller Build the K NEX pantograph below Ha E S 1 Oa ____ 3 e T Lb d b 4 b X4 Ss 1 3 4 itg t d 0 Earl E Ai b EIN Q1 What shape would yet you get if you build a K NEX model with its corners at 3 1 3 4 1 1 and 1 4 Q2 Make a triangle with two yellow rods and a red rod Place it on the grid with the right angled corner on coordinate 1 0 Then write down the coordinate of the other two corners of the triangle 15 Logo The coordinates in Activity 14 provide one way of specifying instructions to build a KNEX model Another way of providing instructions is via the language Logo B The Logo commands for the letter P shown below starting at point A are a Forward 190 ie 190mm one grey rod b Right 90 ie 90 degrees c Forward 85 ie 85mm one yellow rod d Right 90 e Forward 85 f Right 90 g Forward 85 Q1 What Logo commands are required to make the i letters M and N E The pointer shown in th
21. class are e Explaining the activity verbally to the class e Photocopying the relevant page of Section 4 e Printing the page in colour from the CDROM that accompanies this Guide e Displaying the CDROM page to the class ona data projector and screen 3 4 Buying the K NEX needed Once you have become familiar with K NEX decided on the venue and room layout for your maths activities and chosen the activities to offer you will be in a position to buy the K NEX needed The basic requirement will usually be a sturdy plastic compartmented tray containing a good selection of all the basic K NEX rods and connectors for each group of 4 students All the sets listed in Appendix C will provide this although the larger sets contain a higher number of K NEX components in each tray Depending on the K NEX maths activities you have chosen you may also need Copyright 2005 K NEX User Group e Number sheets photocopied from Appendix B e Any extra materials needed to complete the activity such as white card or a plastic carrier bag e Special KNEX components such as gear wheels see photo below All the sets can be purchased either by 1 Faxing or mailing us a written purchase order using the form in Appendix C or your organisation s usual purchase order form or 2 Buying the K NEX sets by credit card or invoice via the on line shop in our website www knexusergroup org uk If you are buying K NEX to be us
22. ctive K NEX desk tidy for them and cost it using the following table Rehd e rem me Now put a red rod across the diagonal of the yellow square above This demonstrates that the area of a right angle isosceles triangle is half the area of the square in which it is contained Purple and yellow connector Other connectors Q1 How much do you think they ought to sell your desk tidy for Now build the equilateral triangle below 58 Shopping trolley game Q1 Can you design and build a shopping trolley with K NEX and then invent a game for young children in which they must throw a dice and then fill up their shopping trolley with items priced from 1 to 6 according to the number thrown Q3 Use a ruler to measure the length of the one of 59 Ludo like game the sides of the triangle in mm Now calculate the Q1 Can you make a board out of K NEX which is perimeter of the triangle the length of all three sides similar to a Ludo or Monopoly board and then invent a EES game to play on it Q4 Also measure the height of the triangle and then calculate the area of the triangle half the base x 4 3 Measure height All the activities in this subsection relate to measure The questions shown against each Activity are only examples you may wish to think up your own Build the K NEX cube below questions for each activity that best suit the ability and experience of your students 4 3 1 Activities from in
23. d for any incidental direct indirect or consequential injury or Website www knexusergroup org uk Copyright 2005 K NEX User Group damages from your use or reliance on the Guide K NEX is the registered trademark of K NEX industries Inc Copyright 2005 K NEX User Group www knexusergroup org uk 2 2 K NEX for hands on maths This section gives an overview of the maths skills and knowledge that can be developed with the help of K NEX activities The four subsections relate to the main subdivisions of the maths curriculum in schools and in adult education Section 4 then contains K NEX activities corresponding to each subsection Note that the Guide does not attempt to relate the K NEX activities to different ages key stages or levels in the curriculum Rather a multitude of KNEX activities is provided from which the teacher or tutor can select to suit the needs and abilities of their students Note also that in addition to helping students to gain maths skills and knowledge K NEX can also help to deliver the common requirements of the National Curriculum including e Problem solving skills e Creative skills e Communication skills 2 1 Shape and Space One of the major strengths of K NEX is that it is a rod and connector construction kit based on a consistent and easy to understand geometry The main rods and connectors are shown opposite and Section 4 shows how 1 the different lengths of rod relate to e
24. d the ten pins upright at equal spacing around the tower and throw the weight so that it spins around the tower on the end of the string You will need to adjust the length of the string so that a typical throw knocks over some but not all of the pins The simplest game is to score one point for each pin knocked over with play then moving on to the next player A better approach if the number skill of the players are good enough is to score the game as in ten pin bowling with each player having two throws before play moves on to the next player In this way a player can get a strike all 10 pins on first throw or a spare all ten pins in two throws and this causes the score on the next throw s by that player to be doubled For 2 4 players Extra equipment 5 small K NEX wheels Numerals from Appendix B sloping table Build the scoring box shown below and attach the numerals 1 to 5 to five K NEX wheels Put the scoring box at the end of a small table and raise one end of the table by putting books under the legs at that end Players score by letting go of a wheel at the high end of the table so that it rolls down towards the scoring box If the wheel enters one of the numbered compartments in the box the player scores the multiple of the number on the wheel times the number of the compartment For example rolling a wheel with a 3 numeral into the compartment numbered 4 scores 12 If the wheel misses t
25. d use it to help students get a feel for probabilities between 096 and 10096 TN KA SR mese WI hs ut EA S REN ai sii tn Bleu ere esu dis Watt DE eph Cut S 1 How probable is it that the L the next General Election ROT Lo dl ha Aa H bit a x dst POTS het SE ah D pt abour Party will win Q2 How probable is it that it will snow on Christmas Day You should operate the pointer on a completely flat 94 Learning about mean median mode and range surface and check that it not biased towards stopping Q1 Spin the number pointer from Activity 91 100 in any one particular place before use i times and write down the results in a table Q2 Use the data table to create a K NEX bar chart Q1 Predict how often the pointer will stop on 15 if you spin it 80 times Now actually spin it 80 times If your prediction is wrong can you explain why Q3 Calculate the mode median mean and range of 92 Horse racing pointer your results Extra equipment White card Modify the spinner from Activity 91 to make a horse racing pointer as shown below Copyright 2005 K NEX User Group www knexusergroup org uk 31 95 Coding machine Extra equipment White card The Enigma machine was used in the second world war as a coding machine to keep messages secret You can make a simple coding machine out of K NEX as shown below The top section slides backwards and forwar
26. ds to allow you to change the code as often as you want Q1 Can you use your coding machine to send secret messages to a friend 4 4 2 Activities that are games The activities below are games that will help develop data handling skills 96 Predictions 2 to 4 players Extra equipment Four sided spinner from Activity 90 Build the K NEX stand below with a row of eight upright rods for each player only 3 rows shown Copyright 2005 K NEX User Group The object of the game is for a player to put a yellow connector on all eight upright rods in his her row The players take turns to spin the spinner and before spinning it predict the number 1 to 4 that the number will stop on If they are right they add a yellow connector onto one of their eight upright rods The game can be made more sophisticated by using a spinner or pointer in which there is not an equal chance of the same number coming up Eg a pointer with numbers placed in different sized sectors similar to the horse names in different sized sectors in Activity 92 97 Horse racing game 2 to 4 players Note that this is a betting game but one that nevertheless will help students to understand probability Use the horse racing spinner from Activity 92 One player acts as Bookie and sets odds for each horse name eg 3 1 Tinker 2 1 Tailor Before each spin the other players place bets on a horse of their choice using counters for mo
27. e photo can be made by sharpening a blue K NEX rod with a pencil sharpener until it has a blunt point Pointer Copyright 2005 K NEX User Group www knexusergroup org uk 10 Next find a sheet of A3 paper or make one by joining together two sheets of A4 paper Draw a square on the paper with sides 4cm long as shown Attach the fixed leg of the pantograph to the bottom left hand corner of the paper Then trace over the square with the pointer with one hand whilst at the same time pressing down on the pencil with your other hand You will see a square appear but larger than the original Q1 What length of side does the new square have The new square is a different size because the pantograph has yellow rods between the fixed leg and pointer but red rods between the pointer and pencil Q2 What will happen if you replace the four red rods with yellow rods and copy the square again Q3 What will happen if you replace the four red rods with blue rods and copy the square again Q4 Can you use you pantograph to copy a simple line drawing out of a book eg Winnie the Pooh 4 1 2 3D activities from instructions The activities below use 3 dimensional 3D K NEX shapes 17 Building 3D shapes with K NEX K NEX is also very good for building 3D K NEX shapes The blue and the purple connectors are specially designed to be joined together when building 3D shapes Follow the instructions below to see how to join the
28. e rods and orange connectors so that the hour hand turns at the right speed in relation to the minute hand You may prefer to provide a clock face which has the numerals 1 to 12 written on a circular sheet of white card beneath the hour and minute hand rather than just using the numerals 3 6 9 and 12 as shown above Copyright 2005 K NEX User Group Q1 How many times does the big hand go around when the little hand goes around once Q2 Can you use the clock to find the time difference between quarter to 2 and twenty past 3 www knexusergroup org uk 25 72 Digital clock Extra equipment Numerals from Appendix B Make the K NEX digital clock below Note that the minute wheel only shows the time in 5 minute intervals Q1 Use the clock to show the time your lesson started and the time your lesson will finish Q2 Can you use the clock to find the time difference between 7 45 and 10 20 Q3 How would the clock need to be changed to become a 24 hour digital clock Copyright 2005 K NEX User Group www knexusergroup org uk 26 73 Sundial 60 Use a spreadsheet to create a line graph or bar Extra equipment Sheet of thin white card CNAN Hom ns table Make the K NEX sundial below Q3 How far does your car go before it stops altogether Can you calculate the average speed between the starting point and stopping point Q4 During which part of the journey is your car going fastest Could yo
29. each activity The CDROM version contains larger images and extra photos for some of the activities The Appendix contents are as follows 4 1 Shape and Space 2D activities from instructions K NEX rods K NEX connectors Five sizes of K NEX triangle Learning about triangles Six sizes of K NEX square Rectangle Rhombus Trapezoid Octagon Filing in 2D K NEX shapes Eight pointed star Translation rotation and reflection 13 2D symmetry 14 Coordinates 15 Logo 16 Pantograph 3D activities from instructions 17 Building 3D shapes with Oe et E er Dr oe O N K NEX 18 Cube 19 Cuboid 20 Pyramid 21 Prism 22 Nets 23 3D symmetry Activities that are K NEX challenges 24 K NEX picture 25 KNEX maze 26 KNEX alphabet 27 KNEX drawing aids 28 K NEX ferris wheel 4 2 Number Activities from instructions 29 Sorting by shape size and colour 30 Counting rods and connectors 31 Counting shapes 32 KNEX numerals 33 Number square 34 Number line 35 Money line 36 Simple scales 3 Scales with multiple positions 38 Costing with KNEX 39 Maths investigation gear ratios 40 Learning about fractions 41 Learning about squares cubes and roots 42 Abacus 43 Learning about number sequences 44 Estimating with K NEX 45 Algebra with K NEX Activities that are games 46 Pick a rod 47 Colour game 48 Dominoes 49 3s and 5s spider s web 50 D
30. ed as a central resource in your school or educational establishment rather than just as a maths resource or if you want to buy sets that include special components such as gears you may also find it useful to look at the full range of KNEX education sets in the on line shop 3 5 Number sheets Some of the K NEX maths activities in this Guide require that numbers are affixed to K NEX connectors For example to label the axes in a bar chart Appendix B includes Number sheets for the most commonly used numbers and styles These sheets should be printed out on thin card laminated if possible and attached to the relevant KNEX connector with Bluetac or similar 3 6 And finally Once you have used a number of the K NEX maths activities in Section 4 you may like to develop your own activities KNEX is very versatile and there is the potential to develop 1001 K NEX maths activities not just the 101 listed in this Guide Good luck And please email us e If you have any queries or suggestions on the K NEX maths activities in Section 4 e If you need any help choosing the most appropriate K NEX education sets e If you have any ideas for improvements to this Guide www knexusergroup org uk 5 Section 4 101 K NEX Maths activities This Section contains 101 K NEX maths activities The subsections correspond to the subsections in section 2 The printed version of the Guide contains only one or two small photos for
31. er in this section before attempting any of these challenges 56 Costed bridge You are an architect who has been invited to enter a competition to design a new bridge to cross the Thames in London At this stage the competition organisers want to see a K NEX model of your bridge which must be strong enough to span a gap of 1m between two tables The winning design will be the bridge that spans this gap at the lowest cost To cost your bridge design use the following table Grey rod www knexusergroup org uk 20 Other rods White and blue connector Purple and yellow connector Other connectors Yellow rod L In the event of two bridge designs being submitted with the same cost the winning design will be the Q1 Use a ruler to measure the length of the one of bridge that can support the most weight at its centre the sides of the square in mm Now calculate the perimeter of the square the length of all four sides 57 Costed desk tidy together and the area of the square length x width A famous chain of office supplies stores wants to add Q2 Make a rectangle out of red and yellow rods and a new desk tidy to their product range The desk tidy calculate its perimeter and area will be built out of K NEX so that it can be sold ready for assembly and it must be capable of holding five pencils a ruler 10 paper clips and an eraser The desk tidy must be low cost or customers will not buy it Can you build an attra
32. er to this question is no as the lower the starting point the slower the pendulum will travel However friction in the K NEX pendulum may result in there being some variation A 4 Handling data Activity 82 Q1 Mrs A Q2 Mrs E Mr F and Ms G Copyright 2005 K NEX User Group Activity 89 Q1 The probability is that the dice will show a three ten times in 60 throws Throwing a perfect dice will only result in a three on average 1 out of every six throws so there is no guarantee that 10 throws out of 60 will be a three Also the K NEX dice is not perfect and may be biased towards certain sides because of irregularities or because of the throwing style Q2 Seven can be achieved as 1 6 6 1 2 5 5 2 3 4A or 4 3 Probability of getting a seven is therefore 6 in 36 possibilities ie 1 6 Activity 90 Q1 The probability is that the spinner will show a two five times in 20 spins Spinning a perfect spinner will only result in a two on average 1 out of every four throws so there is no guarantee that 5 spins out of 20 will be a two Also the K NEX spinner is not perfect and may be biased towards certain sides because of irregularities or because of the spinning style Q2 Five can be achieved by1 4 4 1 2 30r 3 2 Probability of getting a five is therefore 4 out of 16 possibilities ie 74 Activity 91 Q1 The probability is that the spinner will show a 15 ten times in 80 spins Spinning a perfect spinner will onl
33. erals from Appendix B The spinner is used by spinning it and then waiting until it stops on one edge Note that we use the word dice in this Guide to refer to a single dice rather than the less common and therefore possibly confusing word die as the singular of the plural word dice Make the K NEX dice below Q1 Predict how often the spinner will show a 2 if you spin it 20 times Now actually spin it 20 times If your prediction is wrong can you explain why Q2 Make a second four sided spinner How many different ways can you achieve a total of 5 with two spinners What is the probability of you getting 5 if you spin both spinners at once Q3 Can you use your two spinners to play one of the games in Section 4 2 2 Copyright 2005 K NEX User Group www knexusergroup org uk 30 91 Number pointer Extra equipment Numerals from Appendix B An alternative to a spinner is a pointer which spins around in a static frame and points to a number colour or word when it stops Make the K NEX pointer below You can set the size and number of the sectors of the circle to whatever value you like When the pointer spins the narrower the sector the lower the probability of that horse winning when the pointer is spun Q1 Can you work out the probability of the pointer stopping on each of the horse s names 93 Probability line Extra equipment Numerals from Appendix B Make the probability line below an
34. ernative a clock can be used to count the seconds out loud Copyright 2005 K NEX User Group 4 3 3 Activities that are K NEX challenges All the Activities below are K NEX challenges for which no instructions are required It is recommended that students complete some of the Activities earlier in this section before attempting any of these challenges 79 Rubber band scales Extra equipment 4 rubber bands weights from 100g to 1Kg white card Make a K NEX cage to hold one or more weights and hang it from a K NEX frame Affix a strip of white card vertically alongside the cage Now use the weights in different combinations to calibrate the scales by marking off the position of the cage when it is supporting 100g 200g 300g etc Q1 Can you use your scales to weight small objects 80 Map of New York City Find a street map of New York City on the internet and identify the position of well known buildings such as the Empire State Building Use K NEX rods and connectors to make a street plan of an area of New York and add in small models of the well known buildings Mark the direction North on the plan Q1 Can you write down directions from the Empire State Building to another well known landmark a Byusing turn first right turn third left etc b Byusing compass directions and distance go North West for 20m turn South for 10m etc c Byusing the Logo language forward 20 right 90 etc 8
35. from data stored in a table The K NEX based data handling activities in Section 4 4 are designed to complement computer based work by giving students hands on experience in e Sorting and classifying e Collecting data e Tables e Diagrams e Graphs e Charts e Mode median mean and range e Probability e Maths investigations 3 Delivering K NEX activities The purpose of this section of the Guide is to provide some general guidance in planning and delivering the K NEX activities listed in Section 4 Note that the section does not include guidance for specific educational settings Such guidance may be found in our other K NEX Guides which are e Guide to using K NEX in Family Learning e Guide to using K NEX in Children s clubs and Childcare schemes e Guide to using K NEX in Primary Schools e Guide to using K NEX in Secondary schools e Guide to using K NEX in Post 16 education e Guide to using K NEX in Home Education e Guide to using Kid K NEX with 3 7 year olds Copyright 2005 K NEX User Group 3 1 Becoming familiar with K NEX If you do not have any K NEX at present it is a good idea to start by purchasing a small KNEX education set You can then familiarise yourself with K NEX before going on to decide which K NEX activities to offer Appendix C provides an overview of the K NEX education sets that are most suited to maths activities and you may like to choose one of the lower cost sets for familiaris
36. he box altogether there is no score For players without the necessary multiplication skills you may prefer to omit the numerals on the wheels and just score using the compartment number After the students have played the game a few times you may like to suggest that they invent their own rules for this game 54 Number box For 2 4 players Extra equipment Numerals from Appendix B Build the number box shown below Copyright 2005 K NEX User Group Place the box in the middle of a small table and give each player five white connectors Players take turns to place their five connectors overhanging the edge of the table and then flip each one into the box Scoring can simply be to add up the numbers on the compartments into which the five connectors are flipped or you can invent a scoring method such as one based on Darts or Wheel roll above 55 Tower of Hanoi For 1 player Build the K NEX model shown below The object of the game is to move all of the connectors to the rightmost rod so that they end up in the same sequence You may only move one connector at a time and you must never allow a connector to rest on a smaller connector Search Tower of Hanoi on the internet for further details 4 2 3 Activities that are K NEX challenges All the Activities below are KNEX challenges for which no instructions are required It is recommended that students complete some of the Activities earli
37. iculties eeeeseeeeseeeeee 2 LENCO LT E 4 7 8 11 20 21 22 23 HO Osea ae Heer HR MH pH HER 3 6 10 12 28 AR el HMM Hp HIP 4 RSS ee Le 4 mathematical language 5 MaS un eme nues 2 3 4 5 6 15 38 39 HAS ID aues a a a 2 maths CUM IC UNUM 22220 maman dede e 3 IESSE en ee 6 12 BRIT UTEM 4 6 31 Ineas ul Gui han Le in 4 6 21 27 28 34 measuring instruments 4 Meda ES ee D ne Mu de iid tussis 4 6 31 jor suite TT 4 BETEN eege 3 6 14 ANE le Io a esu 6 14 17 18 20 PCIE DUC AU OVW Occ cS 3 National Curriculum eese 3 4 negative numbers 14 dis ae DRM PROCERES ERIT NOR 6 11 ite siew NING ari odes ce d rea re 3 6 14 number sequence 1essesseseee nennen 3 6 16 number Shell sur re 2 5 34 number square ssh EE 3 numeral 6 9 13 17 18 19 20 25 34 ODICCIINOS tt 2 OCTAGON PE m 6 7 8 leet eg EEN 38 39 OUAOOIS ak vc cases esa A A CR ia 5 OU Ob sehool Club scoop en eres P CREER wet edes 4 pantograp NEE 6 10 eic 8 Suel piores ian 6 24 27 28 34 Dertfieler eyin an E 4 6 21 34 Siet 2 DrediC UOM M ER Seinen caused 6 30 31 32 ail Eege Le E 4 DIS ANSE ne Ra A unis 6 11 12 22 33 Drobabllity send 4 6 30 31 32 34 ProblemissolviTiQ BEE 3 DUFCNAS ere M TR
38. ilding you are in or a local park or field 77 Level or Sextant Extra equipment Sheet of thin white card 360 protractor You can also use the K NEX theodolite from Activity 76 as a level or sextant to measure the angle between two distant objects in the vertical plane The measuring wheel and theodolite allow you to make simple 2D maps but they take no account of the height of different objects on the map The Level can be used when surveying to determine the height of distant objects by measuring the vertical angle of a line between the Level and the distant object Search the internet to find how to create a 3D map from horizontal angles theodolite vertical angles Level and distances Q1 Can you use your Level to add contour lines to the map you made in Activity 76 Q2 Sextants used to be used to help ships to find their position at sea Use the internet to find out how your Level could be used as a sextant 4 3 2 Activities that are games The activities below are games that will help develop measuring skills 78 Timed challenge 2 to 4 players Measure how many times the Pendulum in Activity 69 will swing in 30 seconds Place a box of K NEX on the table in front of the players Each player takes it in turn to try and build as tall a K NEX tower as they can in successive turns of 30 seconds Everyone else counts out loud the number of swings of the pendulum until the finish time is reached As an alt
39. is called a rhombus Build the one shown 11 Eight pointed star below You can make many other two dimensional shapes zo out of K NEX Build the eight pointed star below Se 4 NNI AT CT e e CH ss EN as JH PR p d ava ave 4 AX bea res Tata Ta Ue ta mf dn AW DT PR 4 ae A avi A eu bot D 4 he 2a P E e at Y 4 Tat A 2 Q1 What are the angles in the above rhombus Q2 Can you use four hinges to make a rhombus m which has different angles Q1 What different angles can you find in the above star Copyright 2005 K NEX User Group www knexusergroup org uk 8 12 Translation rotation and reflection Now build the K NEX shape below Make the K NEX letter E shown below and place it on the table or desk in front of you Now experiment by moving it around You will find there are three ways of moving it Translation where you slide the shape across the table still in the upright letter E position Rotation where you turn or rotate the letter E mih Two of the lines of mn in this shape are highlighted with yellow rods Q1 Can you find more than two lines of symmetry in the picture above Q2 Are the shapes in Activities 3 to 11 symmetrical Q3 How many lines of symmetry does each shape Reflection where you pick up the letter turn it over possess and put it down again This is called reflection because what yo
40. ke the connectors up in a box and For 2 4 players then deal them out face down so that each player has y the same number of pieces Also put a box of KNEX Extra equipment Numerals from Appendix B on the table containing an assortment of rods and a white connector on the table as a starting point for the spider s web Build the dart board shown below and hang it on the wall so that the centre of the dart boards is at eye height for the players The players take it in turn to add a rod and a yellow connector to the spider s web attached either to the x white connector or to any other yellow connector already added to the spider s web m 9 After attaching their yellow connector and rod the player adds up the total on all the yellow connectors that have only one rod attached to them If the total adds up to a multiple of 3 or 5 the player scores the divisor of that total For instance score 3 if the total is 9 3 x 3 or score 4 if the total is 20 5 x 4 If the total is a multiple of both 3 and 5 score the sum of both divisors eg 15 scores 3 5 as it is both 3 x 5 and 5 x 3 Sounds complicated but it is actually very simple For students for whom determining multiples of 3 and 5 would be too difficult introduce different rules eg score a point after each turn if the total is an even number After the students have played the game a few times suggest that they invent their own rules for the game
41. lift even heavier weights Q2 Fill the tank with water to test whether your d calculation is correct Why might there be a small difference between the calculated value and the 69 Pendulum measured value Extra equipment string Make the K NEX pendulum below 67 Weighing scales Extra equipment Small weights Make the K NEX weighing scales below Q1 Use the scales to measure the weight of a number Grandfather clocks use a pendulum to measure time MU er Q1 How many times will your pendulum swing You may need to adapt the ends of the arms so that backwards and forwards in one minute MEY CAN SODOMIE Ne EE Q2 Does it make a difference how high the pendulum chosen Bam Extra equipment string selection of objects to lift Make the K NEX crane below starts to swing from Copyright 2005 K NEX User Group www knexusergroup org uk 24 70 Clock face Extra equipment Numerals from Appendix B Make the K NEX clock face below You may prefer to provide a clock face beneath the hour and minute hand which has the numerals 1 to 12 written on a circular sheet of white card rather than just using the numerals 3 6 9 and 12 as shown above Q1 Can you set the clock to 6 o clock quarter past 5 and twenty to 10 71 Analogue clock Extra equipment Numerals from Appendix B 2 rubber bands Make the K NEX clock below You will need to adjust the diameter of the two pulleys made from blu
42. ls from Appendix B White card Q1 Who is the boss of Mr D The process of converting computer based Q2 Who works for Mr D spreadsheets into bar charts is very simple so simple that students may not fully understand the 83 Flowchart steps that have been carried out Making bar charts rrr out of K NEX gives students a deeper understanding SE of their production gained by hands on experience K NEX is also good for flowcharts Build the one ET barbae below shown below 4 Bowl y Hit 4S8 wicket P 2 i 3 Q1 Can you make a flowchart for a subject of your choice using yellow white and green connectors as above 84 Data table Extra equipment White card CE 4 q I 4 HN Brown uu Blue i Green Data tables are normally drawn on paper or entered directly onto a computer However building the frame of a data table out of KNEX provides a hands on alternative that is particularly effective for displaying the data to others Build the data table below Q1 Can you make bar charts to show the results in the data tables you created in Activity 84 86 Line graph Extra equipment Numerals from Appendix B Attractive line graphs can also be built with KNEX Build the line graph below rr d r ap v R oy IK 4 Black 12 i aX A P EM S J ja res un Je Brown 16 I ER Q1 Can you make line graphs to show the results in the data
43. m together LS A mm dc aft Ls be a ius p A K A A 18 Cube A cube is a 3D shape in which all 12 faces are of equal length Build the cube below Q1 How many faces does a cube have Q2 What shape is each face Q3 Can you build a cube using only blue rods Copyright 2005 K NEX User Group 19 Cuboid A cuboid is a shape in which the faces are two squares and four rectangles Build the cuboid shown below Q1 Can you build a cuboid using only blue rods and yellow rods 20 Pyramid Build the pyramid shown below Q1 What shape is the base of the pyramid Q2 What shape are the other faces of the pyramid Build the prism shown below Q1 What shape are the ends of the prism Q2 What shape are the other faces of the prism Simple 3D shapes can be built by folding up a net which includes every side of the 3D shape Make a net for a cube as shown below and fold it up into a cube www knexusergroup org uk 11 Q1 Can you make a net for a cuboid a pyramid and a prism 23 3D symmetry Activity 13 explained how to identify lines of symmetry in 2D K NEX models Build the model below to demonstrate how 3D models can also have lines of symmetry Q1 How many lines of symmetry have the cube cuboid pyramid and prism in Activities 18 to 21 Q2 Can you add yellow K NEX rods to indicate the lines of symmetry for each sh
44. ney The Bookie then spins the pointer Winning players receive a payout calculated from the odds on the winning horse All other players lose their bets You may wish to allow the Bookie to set odds that give him or her a statistical probability of winning more than he she pays out as in real life 4 4 3 Activities that are K NEX challenges All the Activities below are K NEX challenges for which no instructions are required It is recommended that students complete some of the Activities earlier in this section before attempting any of these challenges 98 Premiership table Q1 Can you make a K NEX data table which contains the names of all the football teams in the Premiership and then keep it up to date after every match is played Students may like to show for each team wins draws losses points goals for and goals against 99 School dinners Q1 Can you make a K NEX bar chart showing what students chose to eat for lunch 100 Dice with more than six sides Q1 A dice is simply a 3D object with six equal sized faces that falls on one face when thrown Can you make a 3D object with more than six equal sized faces and invent a game to play with it 101 Spinner with more than four sides Q1 Can you make an eight sided spinner from K NEX and invent a game to play with it www knexusergroup org uk 32 Appendix A Answers to questions This Appendix contains answers only to those questions in Section
45. ng about triangles The triangles above are called right angled triangles because they all include one right angle A right angle is 90 Both the other angles in each K NEX triangle above are 45 As you can see the three angles 90 45 and 45 add up to 180 and indeed the three angles of any triangle always add up to 180 As well as making right angled triangles using the standard K NEX connectors you can also use hinges to make triangles Try the one below Some triangles have special names An equilateral triangle has three sides of equal length An isosceles triangle has only two sides of equal length Q1 Which of the triangles you made in this Activity and in Activity 3 are equilateral triangles and which are isosceles triangles Q2 Can you calculate the size of the three equal angles in the equilateral triangle www knexusergroup org uk T 5 Six sizes of K NEX square 8 Trapezoid A square has four sides of equal length and all the It is also possible to make a four sided shape which angles are right angles Can you make the four has two sides that are parallel and two sides that are different sized K NEX squares below not parallel Any four sided shape with only 2 parallel sides is called a Trapezoid Build the one below Dm d r Q1 What are the four angles in the above trapezoid 9 Octagon An eight sided shape is called an Octagon Build the
46. os 41 Learning about squares cubes and roots Extra equipment Small and medium sized gear wheel Make the K NEX square shown below Make the K NEX fan shown below Q1 How many smaller squares are contained in the large square You can find the answer either by Q1 Count how many times the fan turns for a 360 e counting the small squares or turn of the handle This is called the gear ratio Itiplying th ber of ide by th Q2 Can you work out how the two gear wheels ee Eege squares wide by the provide this gear ratio The above shape is 4 squares wide and 4 squares high so the total number of squares is 4 x 4 16 E Another way of writing this is 4 squared 16 or 4 Make the shape shown below which is a square 16 containing two triangles 40 Learning about fractions Q2 Build a shape that is six squares wide and six squares high and use it to find 6 Q3 If you made a large square out of K NEX that contained 49 small squares how many squares wide would it be Another way of expressing this question is What is the square root of 497 Now make the K NEX cube below Q1 Is each triangle 75 74 or 4 of the area of the square Now make the shape below which is a square containing four triangles Q2 Is each triangle 75 74 or 4 of the area of the square Q3 Can you build a shape which contains a triangle that is 1 8 of the total area Q4 Can you build a sha
47. our estimates by building the models and counting the rods and connectors you have used 45 Algebra with K NEX Build the one level tower and then the two level tower shown below Now search for some instructions for using your K NEX abacus on the internet 43 Learning about number sequences Make the shape shown below a L mr 4 ne og a 10 If you look at each row in this shape you will find e 1 triangle in the first row e 3 triangles in the second row e 5 triangles in the third row Copyright 2005 K NEX User Group www knexusergroup org uk 16 The one level tower requires 12 yellow rods and 8 double purple connectors The two level tower requires 20 yellow rods and 12 double purple connectors Adding a third level to the tower would require a further 8 yellow rods and 4 double purple connectors Another way to write this down is as a formula One level tower 12Y 8P Two level tower 20Y 12P Three level tower 28Y 16P where Y Number of yellow rods and P Number of double purple connectors Q1 Can you write down the formula for a four level and a five level tower Q2 If L is the number of levels in a tower can you write down the formula which is true for a tower with any number of levels K NEX can also be used to help students understand the concept of equations For example Q3 Can you express the answer to Q2 in Activity 37 Scales with
48. pe which contains a triangle that is 3 8 of the total area Copyright 2005 K NEX User Group www knexusergroup org uk 15 The larger cube contains 8 small cubes and is 2 Q1 Add a fourth row of triangles below the shape cubes high 2 cubes long and 2 cubes wide This can How many triangles does it contain t 5 t 3 5 be expressed as 2 cubed 8 or 2 8 Another way of asking this question is Q4 How many small cubes would a large cube contain if it was 3 cubes high 3 cubes long and 3 cubes wide le what is 3 Q5 If a large cube contained 64 small cubes how 44 Estimating with K NEX l hao Li MONO Build the two level tower shown below Q2 What is the next number in the sequence E e Ee Another way of expressing this question is What is the cube root of 64 42 Abacus The abacus has been used for thousand of years as a device for carrying out numerical calculations very quickly Build the abacus shown below Q1 How many yellow rods and double purple connectors would you need to add a third level to the tower Now build the tower to check whether you were right The process of thinking how many extra rods and connectors are needed is called estimating Q2 Estimate how many blue rods and white connectors you would need to build a large K NEX square which contains 9 smaller squares Q3 Estimate how many of each rod and connector you would need to build a roundabout Check y
49. raughts 51 Darts 52 Ten pin skittles 53 Wheel roll 54 Number box 55 Tower of Hanoi Activities that are K NEX challenges 56 Costed bridge 57 Costed desk tidy 58 Shopping trolley game 59 Ludo like game 4 3 Measure Activities from instructions 60 Learning about area and perimeter 61 Learning about volume 62 Ruler 63 Pair of compasses 64 Calipers 65 Measuring wheel 66 Water tank 67 Weighing scales 68 Crane 69 Pendulum 70 Clock face 1 Analogue clock 72 Digital clock 73 Sundial 74 Speed investigation ramp 75 Speed investigation pendulum 76 Theodolite 7 Level or sextant Activities that are games 78 Timed challenge Activities that are KNEX challenges 79 Rubber band scales 80 Map of New York City 81 Moon base 4 4 Handling data Activities from instructions 82 Organisation chart 83 Flow chart 84 Data table 85 Bar chart 86 Line graph 87 Spreadsheet 88 Pick a connector 89 Dice 90 Four sided Spinner 91 Number pointer 92 Horse racing pointer 93 Probability line 94 Learning about mean median mode range 95 Coding machine Activities that are games 96 Predictions 97 Horse racing game Activities that are KNEX challenges 98 Premiership table 99 School dinners 100 Dice with more than six sides 101 Spinner with more than four sides 4 1 Shape and Space All the activities in this subsection relate to shape
50. re is also a version of K NEX with bigger components for 3 5 year olds called Kid K NEX as shown in the photo Building K NEX models helps children and adults to understand subjects such as structures forces simple machines and maths in the way that Meccano educated an earlier generation However Meccano was aimed and advertised exclusively at boys whereas both girls and boys find K NEX easy and enjoyable to use K NEX can also be used effectively with adults once they have mastered the basic techniques for joining rods and connectors together It is also worth remembering that even though educational organisations use K NEX because of its high educational value children and adults enjoy using K NEX simply because it is fun This makes K NEX a good vehicle for engaging hard to reach learners such as those from deprived areas those with learning difficulties and those with behavioural and emotional problems Any organisation purchasing this Guide may print pages to assist them to provide K NEX activities to their own students Apart from this restricted permission to print the Guide must not be printed photocopied or otherwise reproduced without our prior agreement in writing We have endeavoured to make sure that the information in this Guide is current and correct We cannot guarantee that there will be no errors or omissions and we do not either expressly or implicitly warrant the use thereof No liability is assume
51. re the exact distance between the top of the ramp and the finishing line To race a car place it at the top of the ramp and then let it go Use a stop watch to record the start time and the finish time when the back of the car crosses the finishing line Q1 Can you calculate the average speed of your car between the start line and finish line Can you improve your car so that it will go faster Q2 Does the angle of the ramp make a difference to the average speed Create a table that shows the speed of the car for different angles between 10 and Copyright 2005 K NEX User Group www knexusergroup org uk 27 A theodolite is used to measure angles between buildings and other distant objects in the landscape when making maps To do this you must look down the line of sight at the first distant object and record the angle shown on the protractor Then rotate the line of sight so you can look down it to see the second distant object and again record the angle Finally subtract one angle from the other to find the angle between them You can also use the measuring wheel from Activity 65 to measure distances for your map The process of measuring angles and distances for a map is known as surveying Search for surveying on the internet to find out how to create a map from angles and distances Q1 Can you use your theodolite together with the measuring wheel in Activity 65 to make a map of the grounds of the bu
52. rt completed model Once students have become familiar with K NEX by building models from instruction books and completing some of the simpler Shape and Space activities they can then progress onto Number activities selected from Section 4 2 These activities are designed to help students to understand e Counting e Addition e Subtraction e Multiplication e Division e Number lines e Number squares e Simple fractions e Money e Number sequences e Squares and cubes e Square and cube roots e Estimating e Algebra e Equations Note that the activities in Sections 4 1 4 3 and 4 4 will also help to develop the above number skills www knexusergroup org uk 3 2 3 Measure Maths in the National Curriculum and the Adult Numeracy Curriculum both require students to gain a good understanding of Measure The K NEX activities in Section 4 3 will help provide this via the following topics e Length e Mass e Capacity e Time e Speed e Units e Measuring instruments e Reading scales e Perimeter e Area e Volume e Maps layouts and directions 2 4 Handling data Students make regular use of computers in developing maths skills and knowledge for instance by using spreadsheets to develop a knowledge of data handling However there is a danger that an over reliance on computer based methods can result on students not understanding the basic principles involved For instance how a bar chart may be built
53. structions The activities below can be completed from the instructions provided 60 Learning about area and perimeter Build the square shown below Q1 Use a ruler to measure the length of the one of the sides of the cube in mm Now calculate the volume of the cube length x width x height Q2 Make a cuboid out of 8 red and 4 yellow rods and calculate its volume Copyright 2005 K NEX User Group www knexusergroup org uk 21 Build the K NEX prism below Q3 Calculate the volume of the prism which is the area of the triangle at one end times the length Q4 Build some other 3D shapes out of K NEX and calculate their volume Make the K NEX ruler below Q1 Use the ruler to measure the length of some everyday objects around the room 63 Pair of compasses Make the pair of K NEX compasses below Pointer The pointer shown in the photo can be made by sharpening a blue K NEX rod with a pencil sharpener until it has a blunt point Q1 Use the compasses to draw circles with five different diameters 64 Calipers Extra equipment Ruler Make the K NEX callipers shown below Fix a ruler onto the callipers so that the inside edge of the left hand jaw is aligned exactly to zero on the ruler The other jaw is designed to slide so that it can be moved to touch the outer edge of the object being measured You can then read off the object s length on the ruler a Be I III Copyright 20
54. t 135 Forward 85 Left 90 Forward 85 Right 135 Forward 190 N Forward 130 a red rod Right 135 Forward 190 Left 135 Forward 130 Activity 16 Q1 Answer by measurement Copyright 2005 K NEX User Group Q2 The copied square will be the same size Q3 The copied square will be smaller Activity 18 Q1 6 Q2 A square Activity 20 Q1 A square Q2 Triangles Activity 21 Q1 A triangle Q2 Rectangles Activity 23 Q1 Cube 6 lines of symmetry Cuboid 3 lines Pyramid 1 line Prism no lines A 2 Number Activity 31 Q1 8 Q2 1 Q3 4 Activity 33 Q1 8 12 and 16 Activity 34 Q1 4 7 6 2 Q2 0 2 2 Activity 36 Q1 3 Q2 Answer by experiment Activity 37 Q1 Answer by experiment Q2 Answer by experiment Activity 38 Q1 49 rods at 5p and 23 connectors at 10p 4 75 This answer assumes that a double purple connector counts as one connector Activity 39 Q1 The fan turns about 2 75 times for every turn of the handle Q2 The number of teeth on the two gear wheels determines the gear ratio The small wheel has 14 teeth and the larger wheel has 34 teeth giving a gear ratio of 34 14 Activity 40 Q1 72 Q2 14 Activity 41 Q1 16 Q2 36 Q3 7 Q4 27 Q5 4 Activity 43 Q1 7 Q2 7 www knexusergroup org uk 33 Activity 44 Q1 8 yellow rods and 4 double purple connectors Q2 24 blue rods and 16 white connectors Activity 45 Q1 Four le
55. tables you created in Activity 84 Copyright 2005 K NEX User Group www knexusergroup org uk 29 87 Spreadsheet Extra equipment Numerals from Appendix B Building a KNEX spreadsheet can help students to better understand concepts such as rows columns cells and formulae Build the K NEX spreadsheet below gts e Q1 Predict how often the dice will show a 3 if you throw the dice 60 times Now actually throw the dice 60 times If your prediction is wrong can you explain why Q2 If you were to make a second dice how many different ways could you throw a total of 7 What is the probability of you getting a 7 he di l f th Q1 Can you enter the results from the first question in es Bus A ror BEER Activity 84 into a K NEX spreadsheet DUM Q2 Can you add an extra cell to calculate the total 90 Four sided spinner number of students and an extra column that contains a calculation of the percentage of students with EE EE different colour hair Make the four sided K NEX spinner below 88 Pick a connector K NEX rods and connectors can be used in many different ways to demonstrate probability One of the simplest is to put a selection of different connectors into a bag and ask students to select them one at a time Q1 Can you predict the probability of choosing a red connector Q2 Can you predict the probability of choosing a red connector followed by a yellow connector Extra equipment Num
56. the rods as shown below The first player to achieve this wins the game P Put into a bag one of each of the above eight connectors for every player eg if 4 players put in 4 of each of the eight connectors Players then take turns to take a connector out of the bag If they don t already have the connector taken out of the bag they add it onto the end of a rod If they do already have it they put the connector back in the bag Note that this is designed as very easy game for younger children because after a bit of practice they will be able to find the connector they want inside the bag by the feel of its shape For 2 to 4 players Extra equipment Numerals from Appendix B Make a set of dominoes to the design shown below and then add printed numerals to create the dominoes 1 1 1 2 1 3 1 4 1 5 1 6 2 2 2 3 2 4 2 5 2 6 3 3 3 4 3 5 3 6 4 4 4 5 4 6 5 5 5 6 6 6 Use the dominoes to play a game of dominoes in which players add a domino with matching numeral to either end of the line until the first player uses up their last domino You can also search for variations on the game of dominoes on the internet There are many of them all of which require number skills to a greater or lesser degree 49 3s and 5s spider s web For 2 to 4 players Extra equipment Numerals from Appendix B www knexusergroup org uk 17 Affix the numerals from 1 to 5 to a series of yellow 51 Darts connectors Sha
57. tify and count the 2D shapes used in your Ferris Wheel triangles squares etc Q2 Identify any congruent shapes used Q3 Identify and count the 3D shapes used in your Ferris Wheel cubes etc Q4 Identify and count the angles used in your Ferris Wheel Q5 Work out how many lines of symmetry the wheel in your Ferris Wheel has 4 2 Number All the activities in this subsection relate to number The questions shown against each Activity are only examples you may wish to think up your own questions for each activity that best suit the ability and experience of your students www knexusergroup org uk 12 Note that most of the activities in subsections 4 1 4 3 and 4 4 will also help students to develop number Skills 4 2 1 Activities from instructions The activities below can be completed from the instructions provided 29 Sorting by shape size and colour Find one each of the K NEX connectors shown in the photo below Q1 How many triangles can you find in this shape Q2 How many squares can you find in this shape Q3 How many rectangles can you find in this shape 32 KNEX numerals Make the K NEX numerals in the photo below vy 4 l Lu Q1 Connect as many rods as you can to each connector Write down the number of rods that each connector can connect to 30 Counting rods and connectors Count out e 4 yellow rods Q1 Can you make the numerals 4 5 6 7 8 9 and zero e 4 blue rods
58. u end up with is the same as a Q4 Can you show each line of symmetry by adding reflection of the shape in a mirror yellow rods 14 Coordinates Extra equipment Numerals from Appendix B Build the K NEX grid shown below and attach the numerals with Bluetac or similar E 4 HS lelek Many computer based drawing packages allow you to apply translation rotation and reflection to a shape though reflection is often referred to as flip Q1 Can you make a numeral 2 and flip it to become the numeral 5 Q2 Which other letters or numerals turn into a different letter or numeral when they are rotated or flipped 13 2D symmetry Extra equipment Mirror Build the KNEX shape below The numerals up the left hand side are known as the w X axis and number the horizontal lines The numerals across the bottom are known as the y axis and number the vertical lines At every intersection of a horizontal line and a vertical line there is a white connector and a green rod Each white connector has a coordinate x y which is the number of the horizontal line followed by the number of the vertical line Now build a K NEX triangle with its corners at 1 1 This shape is symmetrical because the part of the 2 2 and 1 3 as shown shape above the horizontal yellow line is a mirror image of the part of the shape below the horizontal yellow line You can confirm this
59. u measure its speed at this point 75 Speed investigation pendulum Extra equipment String stop watch Make the K NEX pendulum from Activity 69 Using a stop watch calculate how many times it takes for the pendulum to swing ten times from a given starting point Measure the distance of the pendulum s swing and then calculate the average speed of the pendulum Repeat the investigation from different starting points and produce a table and line graph of the results Now place a sheet of thin white card over the base of the sundial and put it outside in the sunshine At each Q1 Does the time taken to swing ten times vary with hour and half hour mark off the position of the shadow the different starting points you have chosen onto the card 76 Theodolite As an alternative you can use a torch to create the shadow in a darkened room and simulate the sun Extra equipment Sheet of thin white card 360 moving protractor Make the K NEX theodolite below and affix the 360 74 Speed investigation ramp protractor as shown Extra equipment ramp stop watch Make the K NEX racing car shown below 0 j A D Mo SAS A 2 keeft 5 air Ree EEN eR Use a board to build a ramp that is about 1 5m long and set it at an angle of 30 to the floor with a clear bare floor in front of it for the cars to run on Mark a finishing line across the floor approximately 3m in front of the bottom of the ramp Measu
60. vel 36Y 20P Five level 44Y 24P Q2 4Y AP L 8Y 4P A 3 Measure Activity 60 Q1 Perimeter is 4 x 115 460mm Area is 115 x 115 13 225mm Q2 Perimeter is 2 x 115 2 x 160 550mm Area is 115 x 160 18 400mm Q3 Perimeter is 3 x 115 345mm Q4 Area is 100 x 115 2 5 750mm Activity 61 Q1 Volume is 115 x 115 x 115 1 520 875mm Q2 Volume is 115 x 160 x 160 2 944 000mm Q3 Area of triangle 115 x 85 9 775mm Volume is 9775 x 160 1 564 000mm Activity 66 Q1 Volume of cube is 115 x 115 x 115 1 520 875mm which is 1521ml Q2 The differences will arise because a the rods and connectors take up some of the volume and b the bag bulges outwards when filled with water Activity 68 Q3 Balance is achieved when Weight x Distance of weight from centre of tower is the same on both sides A heavier weight on one side can therefore be balanced by increasing the distance of the weight on the other side from the centre Activity 69 Q1 In a perfect pendulum the answer to this question is no as the lower the starting point the slower the pendulum will travel However friction in the K NEX pendulum may result in there being some variation Activity 71 Q1 12 Q2 95 minutes Activity 72 Q2 155 minutes Q3 One way to achieve this would be to build an hour wheel with 24 different hour numerals from 00 to 23 Activity 75 Q1 In a perfect pendulum the answ
61. y result in a 15 on average 1 out of every eight throws so there is no guarantee that 10 spins out of 80 will be a 15 Also the K NEX spinner is not perfect and may be biased towards certain sides because of irregularities or because of the spinning style Activity 92 Q1 Tinker 2595 Tailor 12 596 Sailor 37 596 Soldier 2596 Appendix B Number sheets The number sheets in the following three pages are designed to be photocopied cut out and attached to K NEX white or yellow connectors If you want any blank labels we suggest you print out one of the number sheets cut out labels of the desired size and then write on the back in thick felt pen www knexusergroup org uk 34 DAD 9X9 X9 O00 3 3 3 111273 4 4 4 14 15 16 5515171819 6 6 6 2025 30 TT T 854045 50 55 60 Copyright 2005 K NEX User Grou ae Cte 0 0 007 200000 Se S 99 2 7272 OOOO 20p 200 200 4 D 8 mem ne 6 RT ere Xe TEE OUS Appendix C K NEX Order Form K NEX Elementary Maths set N A starter set that provides a good introduction to the use of K NEX to learn about shape and space The set includes e 143 pieces to complete 11 different activities from instructions e Strong plastic compartmentalized storage cases e Comprehensive full colour instruction manual Suggested age range 5 Number that one set can support 2 students K NEX Intermediate Maths set A medium sized maths set that provides a good range of K

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