Teaching Historically Higher Tier Content To Foundation .
Teaching historically higher tier content to foundation tierstudentsChristian Seager, Trinity High SchoolList of resources1.Averages from grouped data – whodunit?Data sheet and worksheet – use the grouped data to work out who committed the crime.2.Vectors – whodunit?Data sheet and worksheet – use the vectors to work out who committed the crime.3.Expanding bracketsWorksheet – examples, practice questions, exam questions and checklist4.Scatter graphsWorksheet – examples, practice questions, exam questions and checklist5.RatioWorksheet – examples, practice questions, exam questions and checklist6.Stem and leaf diagramsWorksheet – examples, practice questions, exam questions and checklist7.Reverse percentages number gridWorksheet – find the answers to the questions in the number grid8.Standard form connect 4Worksheet – tackle the standard form questions to connect four answers on the grid9.Standard form follow meWorksheet – use standard and ordinary form to complete the sentence10. Trigonometry dominosWorksheet – solve the trig problems to play dominos11. Functional skills strategies and revision table matProblem-solving strategies for multi-step functional questions12. Revision table mat or posterTips for effective revisionChristian has taught at his current school, Trinity High School for nine years. He is Head ofMathematics after starting at Trinity as an NQT, and has helped Trinity rise from NationalChallenge in 2007 to the most improved school in England in the January 2013 league tables.Christian is supported by a fantastic team, including Melanie. Along with Melanie, Christianhas set up JustMaths, the fantastic support for fellow maths teachers, with loads of resourcesavailable on www.justmaths.co.uk.
Who, where and when?Who?One of the following four people has committed a crime.The criminal made 4 errors, the victim has made 0errors and two suspects have made 1, 2 or 3 errors.The ICT teacher saidThe music teachersaid:- The modal classof B is- The modal class160 h 170and median of Ais 20 t 30- The median of E is18000 S 20000- The modal class of F is150 h 160- The median of D is4 h 6- The median of E is14000 S 16000- The median of B is140 h 150- The modal class of B is150 h 160The English teachersaid:The Maths teachersaid:- The modal classand median of Dare the same- The modal classand median of Bare the same- The median of F is150 h 160- The median of F is140 h 150- The median of C is 37 to 39- The modal class and median ofC are NOT the same- The median of E is18000 S 20000-The modal class of E is50000 S 100000Now you need to work out where and when the crime was committed.www.justmaths.co.uk JustMaths 2012
Where?The murder was committed at one of the locations below, but which one?It happened where ALL the answers are true.The maths classroomThe dining hallThe gymThe playing fieldsThe total number of girls is 30.The total number of people in Table A is 40.The total number of trainers is 4.The total number of boys is 100.The total hours using a PS3 is 720.The total boys’ height is 14,900cm.The total time to get to work is 1130 hours.The total number of boys is 100.The total salaries are 1,565,000.The total girls’ height is 4430cm.The total in table C is 20.The total number of salaries is 7.When?Find the day where all the estimates of the means are correct:MondayIf table A is 28.25 and table C is 38 (to 1 significant figure)and table E is 17,388.89 (to 2 decimal places)TuesdayIf table B is 147.7 (to 1 decimal place) and table C is 40(to 1significant figure) and table D is 6.1 (to 1 significantfigure)WednesdayIf table A is 28.3 (to 1 decimal place) and table F is 200 (to1 significant figure) and table D is 6.1 (to 1 decimal place)ThursdayIf table C is 38.15, and table F is 100 (to 1 significantfigure) and table B is 147.7 (to 1 decimal place %Rainfall cmThe table shows the550.48distance from the city100.24centre and the rent of600.52850.8450.10two other apartmentsDistanceRentkm 22503.2180a) On the graph plotthese two points.(2)a)b) Describe the relationship between the distance from the centre andthe monthly rent.b)(1)(2)www.justmaths.co.ukDraw, by eye a line of best fit.(1)(2)c)Describe the relationship between the percentage of cloud cover andthe amount of rain.(1)d)Find an estimate for the percentage of cloud cover on a day with 0.6An apartment is 2.8km from the city centre.c) Find an estimate for the monthly rent for this apartment.On the graph, draw a scatter diagram of the results .cm of rainfall.(2) JustMaths 2013
Ready to be marked ?Exam QuestionChecklistThe scatter diagram shows the height, in cm, and the weight, in kg,for each of 20 members of a sports club.Answer checkeda)Write down the heightandweightheaviestofofthethe20members of the sportsclub.Points plottedLine of best fitKeywordsWeight .kgHeight .cm(2)Things to remember .b) Write down the type of correlation shown in the scatter diagram.(1)c) Draw, by eye, a line of best fit on the scatter diagram.(1)d) Estimate the weight of a person of height 155 cm.(2)e) Is it possible to estimate the weight of a person with a height of210 cm from the scatter diagram. You must give a reason (1)What went well .Teacher comment .
RatioHow to . . .5 schools sent some students to a conference.One of the schools sent boys and girls.This school sent 16 boys.The ratio of the number of boys it sent to the number of girls itsent was 1:2The other 4 schools sent only girls.Each of the 5 schools sent the same number of students.Now have a go yourself . . .MUST - share the following in the ratio showna) 40 in the ratio 3:2b) 35 in the ratio 4:1c) 54 in the ratio 5:1d) 35 in the ratio 4:3e) 42 in the ratio 2:5f) 65 in the ratio 2:3SHOULD - share the following in the ratio showna) 30 in the ratio 2:2:1Work out the total number of students sent to the conference bythese 5 schools.b) 84 in the ratio 3:3:1c) 990 in the ratio 7:2:2 d) 64 in the ratio 5:2:1e) 240 in the ratio 5:3:2 f) 140 in the ratio 6:3:1COULDa)Mr A, Mr B and Mr C own 2, 3, and 6 parts of a business. They share the profit according to how manyparts of the business they own. If Mr C gets 132 howmuch profit did the business make?b)To make suet you need fat to flour in the ratio 1: 3.Jane has 180 g of flour. How much fat does she needto make the suet?c)The sides of a triangle are in the ratio 2 : 4 : 5. Themiddle sized side is 28 cm.(4)www.justmaths.co.uka). Find the length of the other two sides.b). Find the perimeter of the triangle. JustMaths 2013
Exam QuestionsQ1. Last year Kerry’s take home pay was 15 000 She spent40% of her take home pay on rent.She used the rest of her take home pay for living expenses,clothes and entertainment in the ratio 3 : 1 : 2How much did Kerry spend on entertainment last year?Ready to be marked ?ChecklistAnswer checkedWorking out shownKeywordsQ2. Talil is going to make some concrete mix. He needs tomix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.Talil wants to make 180 kg of concrete mix. He has:15 kg of cement85 kg of sand100 kg of gravelDoes Talil have enough cement, sand and gravel to make theconcrete mix?Things to remember .What went well .Teacher comment .
Stem and LeafHow to . . .Sixteen babies are born in a hospital.Now have a go yourself . . .Q1. Here are the times, in minutes, taken to solve a puzzle.510151287203524152033152410810201610In the space below, draw a stem and leaf diagram to show these times.Here are the weights of the babies in kilograms.2.4 2.7 3.5 4.4 4.5 4.1 4.4 2.84.1 3.8 3.8 4.2 3.3 3.0 3.7 3.3Show this information in an ordered stem and leaf diagram.Find the median time to solve this puzzle.Q2. Jim did a survey on the lengths of caterpillars.Information about the lengths is given in the stem and leaf diagram.Key:13 5 7 720 6 8 8 8 931 5 5 5 5 6 8 941 552a) Work out the median.(3)www.justmaths.co.ukKey: 5 2 means 5.2cm. cmb) Work out the range. cmc) Work out the mode. cmd) Work out the inter-quartile range. cm JustMaths 2013
Exam Questions.Thenumbers below list the ages of the members of a tennis 523382631271716255236Ready to be marked ?ChecklistOrder correctKey includeda) Construct a stem and leaf diagram with these ages.KeywordsThings to remember .b) Use it to find the following:How many members the club has.The modal age of the members.What went well .Their median age.The range of their ages.Teacher comment .The fraction of members who are over 40.(8)
esreveR segatnecreP (!)093172221850574709530007132602219320358749Work out the answers to the questions then search for the answers in the grid(Ignore any decimal points e.g. 42.7 becomes 427)1.In a sale, all prices are reduced by 30%. The sale price of a jacket is 33.60Work out the original price of the jacket.2.The price of a new washing machine is 376 which includes Value Added Tax(VAT) at 17.5% Work out the cost of the washing machine before VAT wasadded.3.Employees at a firm get a pay increase of 4% After the pay increase, Mel earns 24,960 How much did Mel earn before the pay increase?4.Top Shop is having a 20% off sale and I have treated myself to a new handbag– it cost 40, how much was it before the sale?www.justmaths.co.uk JustMaths 2014
5.A limited edition version of perfume contains 10% more than the normal bottle.The special bottle contains 88 ml. How much does the normal bottle contain?6.The recent advert for Jaffa cakes makes the claim that the boxes are 24%bigger. The new boxes contain 31 biscuits, how many did it have before?7.I want to sell vegetable boxes at a farmers market - the vegetables will cost me 7.60. How much would I need to sell them for to get 15% profit?8.Christian invests some money in a bank account. Interest is paid at a rate of8% per annum. After 1 year, there is 291.60 in the bank account. How muchdid Christian invest?9.A new car drops in value by 30% in its first year. After a year, it is worth 8,400 what was the cost of the car?10. Christian has bought some shares. The value of the shares fell by 4% since hepurchased them and they are now worth 5200. What was their original value?11. Fize has just reduced his personal best for the 100 m by 25% to 12.9 seconds.What was his previous personal best?THINK YOU’VE NAILED IT? .How can you check your answers?1. In a class there are 9 people out on a school trip to the Museum of Maths. Thisis 20% of the class.o How many are there in the class when no one is off ill?o How many are in the class today?2. If 35% of an amount is 70 what is 100%?3. On the 1st May the Museum of Maths increased it prices by 25% to 9 andvisitors in May dropped by 8% to 55,476o What was the price in April?o How many visitors were there in April?o Their costs haven’t changed but the museum made 30% profit in May.How much profit did they make in May?o How much profit did they make in April?o Was it a good idea to raise the prices?www.justmaths.co.uk JustMaths 2014
STANDARD FORM (1) - Connect 4Working in pairs – each person takes it in turns to choose a question from the question grid to answer. The correct solution will be found in the answer grid (if your solution is notin the grid, you need to reconsider your answer), and you can colour that box on the answer grid. To win, you need to connect four answers in a line (horizontally, vertically ordiagonally) on the answer grid.Question GridAnswer GridWrite 47,500,000 in Write 4.56 x 104 as Write 8.43 x 10-4 asstandard form.an ordinary number an ordinary number0.0008034.56 x 1041.6 x 10Write 5.6 x 10 as anordinary numberWrite 16 x 106 instandard formWrite 45,600 instandard form.0.00204745,600Write 0.0047 instandard formWrite 50,000,000 instandard form.-4Write 5 x 107 as anordinary numberWrite 160 x 106 in Write 2.047 x 10-3 asan ordinary numberstandard formWrite 4.56 x 10 asan ordinary numberWrite 4.56 x 10 asan ordinary numberWrite 0.0023 instandard formWrite0.0016x10-1 instandard formWrite0.016x10-3 instandard formWrite 0.987 instandard formWrite 456,000 instandard form.Write 4.75 x 10 asan ordinary number5www.justmaths.co.uk-571.6 x 10-450,000,000-32.3 x 10-59.87 x 100.00004561.6 x 10-14.75 x 1070.00056847,500,000-4-34.7 x 1054.56 x 100.00084378.03 x 101.6 x 107456,0005 x 10 JustMaths 2013
. ever wondered why?START1.44 x 1049.9 x 10-16.4 x 10-220.46400099017.6320203.6TIRSNHYIUH6.4 X 1041.24 x 103.2 X 1009.9 x1023.56 x 1013.2 X 1033.2 X 10-26.4 x 1033240.0363.6 x 10-21441.44 x 10-217603.63.6 x 10117614.40.01242.036 x10-2TDKSAUSRNA6.4 x 1023.60 x 1000.03240.00361.76 x 10-10.991.76 X 10-20.1440.0640.01240.02036641.79 x 1033.24 x 1021.76 x 101.24 x10-20.1763.6 x 10-33.24 x 10-23200RBNTOIRYEE6.4 x 1013.2 X 1021.76 X 1031.44 x 1026.4 x 10-22.036 x10-20.014417.61.24 x10-21.76 X 1020.01766400.0321.44 x 10-164003.20.06435.63.6 x 10212.4UEOHGSULKN2.04 x 1011790360.020362.036 x1023601.44 x 1011.76 x 101(1.2 x 102)2FINISHwww.justmaths.co.uk JustMaths 2012
8.763.72In triangle ABCBAC 90oAB 11 cmAC 13 cmFind angle ACB40.2422o47.46cm19 m14 mx19633o22.65y49.06yFINISH1118 cm28o13.8 cm70.41x31o28o17 cm7xxSTART31.0141o J3201thsaMustFind the areaFind angle BCAAm15Bm17o16 cm21cx6.24C40.3729.397 m ladder leansagainst a house making an angle of 63owith the floor. Howfar up the house doesthe ladder reach?
Underline the key bitsRead the questionPick the maths to useWork must be organisedExtract the key informationLink your workingOne sentence at the endDecide what the question isProblem-solvingstrategies forMULTI—STEPfunctionalquestionsSounds obvious I know!!The question willprobably includeaspects of severaldifferent mathstopicsThink of a rough estimateIs your answer sensible?Check your answerKorrect units used?Try to get the spellingright! . Oops!Always look at diagramsAllow for different maths skills Re-read the questionKalculations must be shownNow do the work.NOTE: the maths involved isnot always difficult. The problem is working out what is being asked, deciding whatmaths you need to use and remembering toexplain your answer.
ularTake regbreaksWork throughpast papersakeMa bleetatimWatch thetutorials orrevision clipsyour SINGMATHSadle owethe forwomulayouneremem ed tober & whatis in thepaperKnow whattopics tofocus on Make a list andupdate itregularlyGoogle it!tge dodke rTarkBUmaem a mhetis ng emhuscStudy with afriend teachthem a topic &vice versaouyeur SE aske d U edaMan endeevha omm guidrec isionIts norevninggood just owIT!ESU.ediua gUse or mareviskeion cpopp ards, alet orapreziforkAsifplhereusunFollowaths@ReviseJustMTo revise maths you need to DO maths!/
ularTake regbreaksWork throughpast papersakeMa bleetatimWatch thetutorials orrevision clipsyour SINGMATHSadle owethe forwomulayouneremem ed tober & whatis in thepaperKnow whattopics tofocus on Make a list andupdate itregularlyGoogle it!tge dodke rTarkBUmaem a mhetis ng emhuscStudy with afriend teachthem a topic &vice versaouyeur SE aske d U edaMan endeevha omm guidrec isionIts norevninggood just owIT!ESU.ediua gUse or mareviskeion cpopp ards, alet orapreziforkAsifplhereusunFollowaths@ReviseJustMTo revise maths you need to DO maths!/
The total number of trainers is 4. The dining hall The total number of boys is 100. The total hours using a PS3 is 720. The total boys’ height is 14,900cm. The gym The total time to get to work is 1130 hours. The total number of boys is 100. The total salaries are 1,565,000.
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Paper 5: Physics 1 Higher tier Paper 6: Physics 2 Foundation tier Paper 6: Physics 2 Higher tier have been amended to include the correct equations for combined science and for the correct tier. 132, 161, 299, 332 The title for Paper 6: Physics 2 Higher tier has been corrected, as it previously was titled paper 2. 309
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