Spring - Block 7

Reasoning and Problem SolvingSpring - Block 7Statistics

Year 6 Spring Term Week 12 – StatisticsOverviewSmall StepsNotes2020/21NCforObjectivesRead and interpret line graphsTime is limited at this stage inYear 6. Line graphs have beencovered extensively in Year 4 and5 so you may choose to skipthese steps or merge them intoone lesson. This will leave moretime for pie charts and the mean.Draw line graphsUse line graphs to solve problemsCirclesRead and interpret pie chartsPie charts with percentagesDraw pie chartsThe mean2

Year 6 Spring Term Week 12 – StatisticsRead and Interpret Line GraphsVaried FluencyNotes and GuidanceChildren will build on their experience of interpreting data incontext from Year 5, using their knowledge of scales to readinformation accurately. Examples of graphs are given but itwould be useful if real data from across the curriculum e.g.Science, was also used. Please note that line graphs representcontinuous data not discrete data. Children need to readinformation accurately, including where more than one set ofdata is on the same graph.What is the same and what is different about the two graphs?Mathematical TalkHere is a graph showing daily water consumption over two days.Where might you see a line graph used in real life?Why is the ‘Water Consumption’ graph more difficult tointerpret?How can you make sure that you read the informationaccurately?3At what times of the day was the same amount of water consumedon Monday and Tuesday?Was more water consumed at 2 p.m. on Monday or Tuesdaymorning? How much more?

Year 6 Spring Term Week 12 – StatisticsRead and Interpret Line GraphsReasoning and Problem SolvingEva has created a graph to track thegrowth of a plant in her house.a) On the 9th Julya more accuratemeasurementwould be 7.5 cm.Write a story and 3 questions for each ofthe 3 graphs below.b) Correct.Eva recorded the following facts aboutthe graph.a) On the 9th of July the plant was about9 cm tall.b) Between the 11th and 19th Julythe plant grew about 5 cm.c) At the end of the monththe plant was twice as tall asit had been on the 13th .Can you spot and correct Eva’smistakes?ac) On the 31st theplant wasapproximately 28cm tall, but on the13th it was only 10cm which is nothalf of 28 cm. Theplant was closerto 14 cm on the17th July.bc4Possible contextfor each story:a) A car speedingup, travelling at aconstant speed,then slowingdown.b) The heightabove sea level aperson is at duringa walk.c) Temperature inan oven when youare cookingsomething.

Year 6 Spring Term Week 12 – StatisticsDraw Line GraphsVaried FluencyNotes and GuidanceChildren will build on their experience of reading andinterpreting data in order to draw their own line graphs.This table shows theheight a rocket reachedbetween 0 and 60seconds.Although example contexts are given, it would be useful ifchildren can see real data from across the curriculum.Children will need to decide on the most appropriate scalesand intervals to use depending on the data they arerepresenting.Create a line graph torepresent the information.Mathematical TalkThe table below shows the population in the UK and Australia from1990 to 2015.What will the 𝑥-axis represent? What intervals will you use?What will the 𝑦-axis represent? What intervals will you use?How will you make it clear which line represents which set ofdata?Why is it useful to have both sets of data on one graph?5Create one line graph to represent the population in both countries.Create three questions to ask your friend about your completedgraph.

Year 6 Spring Term Week 12 – StatisticsDraw Line GraphsReasoning and Problem SolvingThis graph shows the distance a cartravelled.Rosie hascompleted thegraph correctly.The car has stilltravelled 15 milesin total, thenstopped for 15minutes beforecarrying on.This table shows the distance a lorrytravelled during the day.Rosie and Jack were asked to completethe graph to show the car had stopped.Here are their completed graphs.Create a line graph to represent theinformation, where the divisions along the𝑥-axis are every two hours.Create a second line graph where thedivisions along the 𝑥-axis are every hour.Compare your graphs. Which graph ismore accurate?Would a graph with divisions at each halfhour be even more accurate?Rosie:Jack:Who has completed the graph correctly?Explain how you know.6Children may findthat the secondline graph is easierto draw andinterpret as itmatches the datagiven directly.They may discussthat it would bedifficult to draw aline graphshowing half hourintervals, as wecannot be sure thedistance travelledat each half hour.

Year 6 Spring Term Week 12 – StatisticsLine Graphs ProblemsVaried FluencyNotes and GuidanceRon and Annie watched the same channel, but at different times.The graph shows the number of viewers at different times.Ron watched ‘Chums’ at 5 p.m. Annie watched ‘Countup’ at 8 p.m.What was the difference betweenthe number of viewers at the startof each programme? What was thedifference in the number of viewersbetween 6 p.m. and 8 p.m.? Whichtime had twice as many viewers as6 p.m.?Once children can read, interpret and draw lines graphs theyneed to be able to use line graphs to solve problems.Children need to use their knowledge of scales to readinformation accurately. They need to be exposed to graphsthat show more than one set of data.At this point, children should be secure with the terms 𝑥 and 𝑦axis, frequency and data.Mathematical TalkWhat do you notice about the scale on the vertical axis? Whymight it be misleading?What other scale could you use?How is the information organised? Is it clear?What else does this graph tell you? What does it not tell you?How can you calculate ?Why would this information be placed on a line graph and nota different type of graph?7Two families were travelling toBridlington for their holidays. Theyset off at the same time but arrivedat different times.What time did family A arrive?How many km had each familytravelled at 08:45?Which family stopped midwaythrough their journey?How much further had they left totravel?

Year 6 Spring Term Week 12 – StatisticsLine Graphs ProblemsReasoning and Problem SolvingWhat could this graph be showing?Possible response:This graph showsthe height of twodrones and thetime they were inthe air.For example:The graph below shows some of MrWoolley’s journeys.Label the horizontal and vertical axes toshow this.What is the same and what is differentabout each of these journeys?Is there more than one way to label theaxes?What might have happened during thegreen journey?8Possibleresponses:All the journeyswere nearly thesame length oftime.The journeys wereall differentdistances.The red and bluejourney weretravelling atconstant speedsbut red wastravelling quickerthan blue.During the greenjourney, MrWoolley mighthave been stuck intraffic or havestopped for a rest.

Year 6 Spring Term Week 12 – StatisticsCirclesVaried FluencyNotes and GuidanceUsing the labels complete the diagram:Children will illustrate and name parts of circles, using thewords radius, diameter, centre and circumference confidently.RadiusThey will also explore the relationship between the radius andthe diameter and recognise the diameter is twice the length ofthe radius.DiameterCentreCircumferenceFind the radius or the diameter foreach object below:Mathematical TalkWhy is the centre important?The radius is .What is the relationship between the diameter and the radius?If you know one of these, how can you calculate the other?The diameter is . I know this because .Complete the table:Can you use the vocabulary of a circle to describe andcompare objects in the classroom?9

Year 6 Spring Term Week 12 – StatisticsCirclesReasoning and Problem SolvingAlex says:The bigger the radiusof a circle, the biggerthe diameter.I agree with Alexbecause thediameter isalways twice thelength of theradius.Here are 2 circles. Circle A is blue; Circle B3is orange. The diameter of Circle A is the4diameter of Circle B.A bar model maysupport children inworking these oute.g.Do you agree? Explain your reasoning.Spot the mistake!Tommy has measured and labelled thediameter of the circle below.He thinks that the radius of this circle willbe 3.5 cm.a) 9 cmb) 16 cmc) 4.5 cmd) 8 cmTommy hasmeasured thediameterinaccuratelybecause thediameter alwaysgoes through thecentre of the circlefrom one point onthe circumferenceto another.If the diameter of Circle B is 12 cm, what isthe diameter of Circle A?If the diameter of Circle A is 12 cm, what isthe radius of Circle B?If the diameter of Circle B is 6 cm, what isthe diameter of Circle A?If the diameter of Circle A is 6 cm, what isthe radius of Circle B?Is Tommy right? Explain why.10

Year 6 Spring Term Week 12 – StatisticsRead and Interpret Pie ChartsVaried FluencyNotes and GuidanceChildren will build on their understanding of circles to startinterpreting pie charts. They will understand how to calculatefractions of amounts to interpret simple pie charts.There are 600 pupils at Copingham Primary school.Work out how many pupilstravel to school by:Children should understand what the whole of the pie chartrepresents and use this when solving problems.a)b)c)d)Mathematical TalkTrainCarCyclingWalkingClasses in Year 2 and Year 5 were asked what their favourite drinkwas. Here are the results:What does the whole pie chart represent? What does eachcolour represent?Do you recognise any of the fractions? How can you use this tohelp you?What fraction of pupils in Year 5 chose Fizzeraid?How many children in Year 2 chose Rolla Cola?How many more children chose Vomto than Rolla Cola in Year 2?What other questions could you ask?What’s the same and what’s different about the favouritedrinks pie charts?What other questions could you ask about the pie chart?11

Year 6 Spring Term Week 12 – StatisticsRead and Interpret Pie ChartsReasoning and Problem SolvingIn a survey people were asked what theirfavourite season of the year was. Theresults are shown in the pie chart below.If 48 people voted summer, how manypeople took part in the survey?Summer is aquarter of thewhole pie chartand there are 4quarters in awhole, so48 4 184people in total.96 people took part in this survey.121418of 96 48of 96 24of 96 1212 people votedcats.How many people voted for cats?3of the people who voted for dogs weremale. How many females voted for dogs?8Explain your method.What other information can you gatherfrom the pie chart?Write some questions about the pie chartfor your partner to solve.1248 people voteddogs.1of 48 686 3 18.18 females votedfor dogs.

Year 6 Spring Term Week 12 – StatisticsPie Charts With PercentagesVaried FluencyNotes and GuidanceChildren will apply their understanding of calculatingpercentages of amounts to interpret pie charts.150 children voted for their favourite ice cream flavours. Here aretheir results:Children know that the whole of the pie chart totals 100 %.How many peoplevoted for Vanilla?Encourage children to recognise fractions in order to read thepie chart more efficiently.How many morepeople voted forChocolate thanMint Chocolate Chip?Mathematical TalkHow many peoplechose Chocolate,Banana and Vanilla altogether?How did you calculate the percentage? What fractionknowledge did you use?There are 200 pupils in KeyStage 2 who chose theirfavourite hobbies.How else could you find the difference between Chocolate andMint Chocolate?If you know 5 % of a number, how can you work out the wholenumber?If you know what 5 % is, what else do you know?How many pupils choseeach hobby?13