Lessons Learnt Level 1 and 2 Maths 2020-21
Hello and welcome to ÃÛÌÒapp’s Functional Skills blog for November 2021. This month we will be looking at Functional SkillsÌýmathsÌýat Levels 1 and 2 andÌýtaking a lookÌýback at what we have learnt in 2020-21.Ìý
In 2020-21 the pass rates for Functional SkillsÌýmathsÌýat Level 1 and 2 were not at their highest andÌýwere not where we would have wantedÌýthem to be. For a fuller analysisÌýtake a lookÌýat ourÌýpreviousÌýblogÌýon pass rates.ÌýTo help support with this moving forward, theÌýmathsÌýteamÌýtook a lookÌýat the trends over theÌýyearÌýand this is their findings.Ìý
Working OutÌý
Learners are not showing enoughÌýworkingÌýand as a result lose marks for inaccurate answers.Ìý Process marks can be awarded for working even if the answer is inaccurate. Learners should be encouraged to show their working out whereverÌýpossibleÌýand it would be beneficial for them if this was laid out logically and clearly too. Let’sÌýtake a lookÌýat a question from one of our Level 1 practice papers.Ìý
- Here are 4 numbers.Ìý
29.4Ìý Ìý -Ìý Ìý 50.8Ìý Ìý-Ìý Ìý24.7Ìý Ìý-Ìý Ìý19.9
Work out the mean of these numbers. (3)Ìý
We can see there are three marks for this question. Looking at what's on the mark scheme we canÌýclearly see how those marks are awarded:
- Begins to calculate mean (1 mark) - Mark Grid A
- 29.4 + 50.8 + 24.7 + 19.9 = 124.8
- Full process to calculate mean (1 mark) - Mark Grid AB
- "124.8" divided by 4 = 31.2
- Accurate figure (1 mark) - Mark Grid ABC
- 31.2 (NB Accept any suitable mathematical layout for calculation.
The learner will get all three marks for clearly stating the answer, in this case 31.2. However, if they were to get that wrong, they would getÌýone mark for knowing they need to add the numbers up (showing theirÌýworking) and two marks for doing this and then dividing by four. Even if they added the numbers up incorrectly, they would still get marks. There is no harm in walking the learners through how the questions are marked if it means they may get some process marks.Ìý
Carrying Out ChecksÌý
This oldÌýfavouriteÌýis in there again.Ìý
Checks are not being carried out by a significant number of learners.Ìý
- If a reverse calculation check is requested a calculation AND answer is expected.ÌýIf no original working is shown how can aÌýlearner,Ìýthen show a reverse calculation?ÌýÌýÌýAnother reason whyÌýthe need forÌýworkingÌýisÌýagain key.ÌýÌý
- If estimation is requested, then learners should estimate key figures and show a simplified calculation which they should be able to carry out ‘in their heads’.Ìý
- If the learner is asked to simply show a check, then they are allowed to choose which check to show.Ìý
Carrying out checks are so important and should really be a natural part of what a learner does in the classroom, in the assessment and, in reality, inÌýeveryday life. Carrying out a check not only helps them answer the check questions, but it also helps ensure their answers are correct more of the time.Ìý
Using CalculatorsÌý
The use of calculators should also be practiced, it is not enough to assume that learners can effectively use a calculator.ÌýTypical things seen are:Ìý
- Some learners do not use all the figures on their screens when continuing a calculation and so lose accuracy marks. For example,Ìýif money is being used just working pounds is notÌýfunctional,Ìýwe expect the learner to work in pounds and pence throughout the question.ÌýÌý
- Some learners continue to use pen and paper methodsÌýwhenÌýworking on the calculator section of the paper. ThisÌýis not good practice.ÌýThe timing of the paper does expect the use of a calculator and the figures used are also intended to be processed by a calculator.ÌýAppropriate use of equipment is a requirement.Ìý
- Learners do need to be able to use the equals and clear buttons appropriately.ÌýErrorsÌýare occurringÌýwhenÌýpreviousÌýnumbers are not clearedÌýproperlyÌýand they carry over into a new calculation.Ìý
- Efficient use of calculators should be encouraged.ÌýFor example,Ìýwhen addingÌýfourÌýnumbers they should be added as a string and not just two at a time.Ìý
New AreasÌýOfÌýTheÌýCurriculumÌý
All new topics should be taught prior to taking an assessment. While we understand that scheduling assessments through the year means learners may have not completed all their guided learning hours,Ìýassessing prior to the completion of learning is setting up many learners to fail and would not happen in other subjects. You would not expect a history learner to complete theirÌýGCSEÌýwithout having studiedÌýall the subjects, nor would you expect an apprentice to complete theirÌýEPAÌýif they had not covered all the content.Ìý
Many learners are not able to group data in equal groups, find simple interest (new topics at level 1) nor are they able to find compound interestÌýor estimate the meanÌý(new topics at level 2). TheseÌýskills have improved over theÌýyear,Ìýbut further improvement is still possible.ÌýTo support this, ÃÛÌÒapp has produced someÌýadditionalÌýassessment style questions on some areas ofÌýnew contentÌýto give tutors and learners more opportunities to practice. These areÌýavailable under resources onÌýourÌýwebsite -
Old AreasÌýOfÌýTheÌýCurriculum
In addition to theÌýnew content, there are some older topics that could still be improved.Ìý
DivisionÌý
Learners need to have a better grasp of long division, especially for the non-calculator paper.ÌýThe evidence from the assessmentsÌýshowsÌýthis is still a struggle for many learners and that teaching time should be set aside for this skill.ÌýThe question on mean aboveÌýrequires the learners to be able to divide. Not being able to do so will cost them a minimum of a mark in that question.Ìý
Area, Perimeter and VolumeÌý
There is an ongoing issue with some learners confusing area,ÌýperimeterÌýand volume. Tutors are encouraged to discuss the differences and look at words which may be in questions to help learners differentiate the required skill,Ìýe.g.Ìýedge andÌýperimeter;Ìýcover and area.Ìý
It might help to look at the practical sideÌýwithÌýthis andÌýtryingÌýto relate it to something they know. Working with professional footballers fromÌýSouthendÌýUnited, I used to describe perimeter as the line around the edge of the pitch and area as the space inside the penalty box. Once they had grasped this understanding, they were able to apply this to different contexts in their assessments.Ìý
Top Ten AreasÌýOfÌýWeaknessÌýForÌýLearnersÌý
These are the top ten areas of weaknessÌýdemonstratedÌýby learners in their assessments. We would really recommend spending some time thinking about these topics andÌýlooking atÌýourÌýexemplification documentÌýfor some ideas on what the learners need to know and how we might approach the questions:Ìý
Level 1Ìý
- Simple InterestÌý
- Grouped Frequency TablesÌý
- BearingsÌý
- ScalesÌý
- Pie ChartsÌý
- ChecksÌý
- Area/Perimeter/VolumeÌý
- ConversionÌý
- Mean/RangeÌý
- Negative Numbers/BidmasÌý
Level 2Ìý
- CalculatingÌýWithÌýFractionsÌý
- CompoundÌýInterestÌý
- PercentageÌýFindingÌýTheÌýOriginalÌýValue/PercentageÌýProfitÌý
- EstimatingÌýTheÌýMeanÌý
- InverseÌýProportionÌý
- CircleÌýFormulaeÌý
- Area/Perimeter/SurfaceÌýArea/VolumeÌý
- InterpretingÌýTheÌýRangeÌý
- RatioÌýPart toÌýWholeÌý
- CompoundÌýMeasuresÌýInÌýProblemsÌý
ResultsPlusÌý
The final piece of advice would be to ensure you keep usingÌýResultsPlusÌýto see the areas of weakness that your learners have after their assessments, even if they pass. This not only allows youÌýsupportÌýthem in theirÌýresitsÌýor progression, but you may also be able to see trends across your learners that might help you evolve your teaching and improve results.
Chris Briggs -ÌýSector Manager Post 16 English and Maths