Joe’s Jotter – Should I Persevere with Higher Level Maths in 2023?

 

More students over the last few years have taken on the task that is Leaving Cert Higher Maths. In June 2022, out of the 57,347 who sat a Leaving Certificate Mathematics Paper, 21,265 of them opted for higher level (37%). Even though the bonus points are very enticing, students need to be careful and be fully aware of what exactly they are embarking on. In my experience, there is a lingering doubt among many 5th and 6th years about being able to tackle higher Maths. Scoring low grades in class tests doesn’t really do much for confidence, but it doesn’t automatically mean you should change level. The question is: Should you remain battling higher level Maths or is it worth the time and effort at all?

This article should reassure those suitable for higher (those who fight the good fight day after day) that they can in fact achieve what they are aiming for. Each year, deciding Maths levels is a tricky issue for students and involves many considerations. It is made even more complex in this subject with the bonus points at play. For those of you who are unsure about higher Maths, it may be worth applying some logic to any inclination to switch. As well you know, us ‘Maths creatures’ are very logical beings lol.  I find that logic is more factual and definite in making decisions like this. It may be more sensible to apply a touch of it here, rather than just using pure emotion. Don’t get me wrong: your gut feeling is important too; but read on to understand what I mean…

I Can Take on this Challenge

Firstly, there is a misconception out there that if you fail Maths, you fail the full Leaving Cert. This isn’t true at all. The two worst things that can happen if you are unsuccessful in Maths is that you will have that low grade for Maths on your CV. Or, if a certain grade in Maths is a requirement for a specific third level course, you will not be offered that course no matter how many points you get; that’s as bad as it gets.

I think having a good Interest in Maths is a great starting point in taking on higher level. Enthusiasm for this subject will go a long way to achieving your desired goal in it.  Students, do you secretly enjoy the challenge of those long practical questions in double classes, or do you dread the thoughts of Maths homework each night? Do you like working with numbers or are you mis-understanding the majority of your teachers’ methods? These are some initial questions to ponder.

Personally, I feel that students know in their heart what level Maths they should be doing. If you feel in your gut that you are lost in class or if it is taking too much time away from other subjects; then reflect and talk it through now. If your anxiety about the subject is getting too high and your grades are dropping, it may be time to move. Definitely, if you have struggled to grasp much of the basic Algebra in fourth and fifth year, it may be a sign that the standard is too difficult for you. However, remember also that there are so many varied topics in Maths, and you may have a flair for some and no real interest in others. Very few of us are good at everything, even the best of the best.

Head Above Water

I always feel that students scoring above thirty percent (approximately) in Class, Christmas and Mock examinations should be able to raise their game to get over the line in the State exams. Students scoring consistently below thirty need to look into their heart and start conversations with their teachers, parents and indeed themselves about what to do. It is important not to remain in the class for the sole reason that your parents want you to do honours. Only you know the content of the Maths course you are studying and how it is going for you. Many students and even some Teachers place too much emphasis on the spring Mock result. I disagree with this premise and prefer to look at the bigger picture. From a percentage assessment point of view, I feel you need to look at a combination of exams sat (even fifth year ones) and indeed your Junior Cycle grade. Keep in mind that the upcoming mock examinations in springtime tests topics across the complete course at a time when you haven’t fully completed it yet.

Is there a Template for Staying or Going?

My intention in this article isn’t to outline a template for who should remain or drop down, as there are a lot of factors that need to be considered. I am simply encouraging you to reflect and balance the argument for yourselves. Over the years, I have taught a substantial number of students who I considered borderline higher level students. Many of them remained at higher and actually ended up outperforming those I perceived as rock solid higher level candidates. Maybe these students felt like they needed to work harder and hence prepared better consequently. There is a lesson in this. American Basketball player Kevin Durant once said, ‘Hard work always beats Talent when Talent doesn’t work hard enough’. The statistics also stack in your favour.  In June 2022, 98.4% of students who attempted higher level Maths got a H6 grade or above and therefore picked up the 25 bonus points. That is extremely high!

In general, your teacher won’t put you too far wrong when decision time arrives. By the middle of sixth year, they know your strengths, weaknesses, and the limits of your capabilities, assuming they have taught you since the start of fifth year. Timing is also an issue. If you do need to drop down to Ordinary level, I wouldn’t leave it any later than Easter. This gives you some time over the Easter holidays, and when you return for the final term, to get familiar with the Ordinary level standard and format of the exam paper. Changing levels on the day of the exam is totally unadvised and should not be considered.

Factors That Will Guide Level Choice

In summary, think about and discuss the below factors in detail with your parents and teachers before attempting to change levels in any subject. Along with mock performance, here are the other factors to consider when making decisions regarding level changes:

  • Your teacher’s opinion.
  • Your ‘potential’ points change.
  • Your Junior Cycle performance.
  • Your attendance in class thus far.
  • Your ‘working relationship’ with your teacher.
  • How much you enjoy studying the subject.
  • Results in previous Christmas and Summer tests.
  • How much of the course you have done thus far.
  • Your own gut feeling and attitude towards the subject.
  • Results in all your class tests since the beginning of fifth year.
  • The amount of effort you are putting into this subject balanced against others.
  • Minimum entry requirements for third level (e.g. a H6 in Maths maybe?).

Before making your final decision, take out a piece of paper and write down all the pros and cons of remaining at higher level or changing.  On the back of the sheet, write a few paragraphs on how you are actually feeling about it right now. Keeping the above list of factors in mind, the answer you are searching for should appear somewhere within these pages as your thoughts and feelings stream out. Use these thoughts to answer your own doubts and plough on from there. Contact me if I can advise you in any way. Joe

More details about Joe’s Maths Tuition Classes for 5th & 6th Year (Leaving Certificate Students) and his Award Winning ACE Maths Solution Books for all students can be found via the links:

ACE Maths Tuition Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

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Joe’s Jotter: Performing Well in Difficult Subjects (Case Study – Maths)

As you settle into the new year, teachers and parents totally understand that even though you are making great strides, you still have plenty of fears. From speaking with students over the years, I find it’s not the full set of exams that cause concern, it is usually only one or two subjects. Naturally everyone has their own talents and subjects they prefer. Personally, I was better at the Sciences than the languages, but I persevered and got the grades I wanted in the languages I chose.

Sometimes subjects you are not looking forward to are the ones that have you on guard and you end up doing better in; A paper on the day can go well in an exam you were dreading. I regularly hear welcome surprise coming from students on results day, with comments such as “I didn’t expect that result in xxxxx”. The moral of the story here is that too much concern about a subject could end in false worry and be draining you of energy; energy you need for revising all subjects and getting your head space right.

Preparing for one of your less favoured subjects is a blatant case of having to ‘get on with it’. Of course, it is easier to revise and work on subjects you enjoy and are good at, but you must not ignore the others. Studying and preparing the ‘frog subjects’ is probably the biggest challenge you will face in school. You must prioritise these subjects on your weekly ‘Lifestyle Study Timetable’. I will detail how to setup this timetable in a later blog feature. Author and reconstructive surgeon, Jack Penn, once said:

“One of the secrets in life is making steppingstones out of stumbling blocks”.

Building Confidence in Maths

Maths is one of those subjects that many students find difficult. To me Maths is about grafting to understand the basics, building your confidence, and not being prepared to give up easy. Always start by attempting the easier topic questions (usually the part a’s and b’s) and subsequently graduating to the part c’s and d’s. You should check your work as you go against a good quality solutions book and thus be constantly ‘learning by doing’. Here are some of my top tips to improve your performance in Maths (and its exam) at any level.

Joe’s Top Tips for Success in Maths

  1. Put formulas, explanation of words and keynotes into a little pocket notebook.
  2. Practice as many past exam questions as you can and check your answers against a fully developed and explained solutions book.
  3. Challenge yourself to try and come up with a second method of doing questions.
  4. Try to approach each question from different angles. Always write down something. Do not be afraid of making a mistake.
  5. Draw a diagram (if possible) and label it to simplify a question.
  6. Be familiar with what is and what is not in your log tables.
  7. When studying, exhaust all attempts to answer an exam question before referring to your solutions book. Do not give up easily.
  8. Read each question in Maths carefully underlining the key words and phrases.
  9. At all levels, if you feel overwhelmed by the length and difficulty of the course – start with basic Algebra
  10. Find yourself a study buddy to share questions and resources with. Discuss problems with each other and encourage.
  11. Use various Internet sites as a companion to improve your Maths skills.
  12. Consult your teacher about problems with topics or specific Maths questions during and after class.
  13. Start by attempting basic questions for each Maths topic, building up to a full exam question. Answer the exact question being asked.
  14. The word FAIL in Maths for me means First Attempt In Learning
  15. Do not be afraid to explain a solution to a question with words if you cannot do so with numbers and symbols.
  16. Spend five to ten minutes daily going over what you have learned in class that day.
  17. Every time you write down a formula, draw a box around it to help you remember it. Check if this formula is in your log tables. If not, you need to memorise it.
  18. Anything that you type into your calculator (related to a question) must be written on your answer book/copy also.
  19. Have all resources present when doing Maths questions i.e. Full Maths set, pencil, calculator, and log tables.
  20. 3rd and 6th Years, practice as many previous exam questions as you possibly can.
  21. Rewrite sample questions given in your textbook to get an understanding of the basics.
  22. It is ok to look at a solution to a question if you have tried your best to solve it alone. Use the answer to figure out the exact method for the question. Re-do it without help.
  23. Work with groups of friends on harder Maths questions. Bounce ideas off each other in order to understand and learn from their thinking.
  24. Always write out every single step of your answer. This will be easy to look back, revise and follow later.
  25. Talk positive about subjects you find difficult. Don’t throw away your shot at success by talking your way into failure.

In next week’s Joe’s Jotter, I will advise 2nd and 3rd year students on how to restart their revision routine. Don’t miss it. To view last week’s feature article on ‘How to Efficiently Review your Exam Scripts’, click here. Get in touch if I can help you in any way. Joe.

‘Sail on the Seas of ambition and land on the shore of success.’

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Tuition Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

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Photo:@ZhangChaosheng

Joe’s Jotter: Useful Insights for Parents on…Secondary School Maths

 

I think it may be interesting for both students and parents to consider the following observations I have become aware of in Maths over the last number of years. Maths is a very emotive subject, and everyone has their own way of understanding and practicing it. This presents its own set of difficulties. The below insights and observations should help you as a parent to reach out and help your child with Maths in a more positive way. Read on…

The Second Year Maths Dip

Firstly, in general, I have noticed that some of my students (and those of my colleagues) experience a slight dip in performance in Maths during their second year in secondary school. This is partly due to workload and the fact that the first-year common course is quite basic. This dip for girls is not as pronounced as for boys. There is also a drop off in fifth year, but it isn’t as extreme as the second year one. If your child is heading into second year, you need to be aware that this could be the case for them. I believe that working diligently on their algebra, fractions, and general numeracy (external to the calculator) are the key elements to overcoming barriers. These topics are the three main pillars of Junior Cycle Maths and underpin and are linked to every other topic on the course.

We all need to keep in mind that online learning has not suited some students and that they have missed out on that key face-to-face contact with teachers, especially in Maths. As a parent, it is important that you encourage positivity around this subject and remind them that every student in the country is in the same boat. From a personal point of view, I noticed that last year’s Junior Cycle class did struggle (more than usual) with a variety of topics, but it did eventually come together for them in the end. I expect that the incoming third year cohort will take a while to settle back (through no fault of their own) this year. In fairness, it may take many of them until after Christmas before they settle down into a pattern of revision and work across all subjects. It is understandable that they may not hit the ground running this year and we all need to be cognisant of this.

Girls – Go for it!

From the students I have taught since the Project Maths syllabus was introduced in 2008, I have noticed another trend in my classes. I have spotted that female students are less likely to take risks when attempting past exam questions. The new phrasing of questions on Maths papers suit boys better, as they are less conscious of what they are writing down and are less afraid of being wrong. In my opinion, it is important for girls to express their opinions freely and openly and we, as teachers, need to help them develop this skill. I think it is important for all students not to get unduly perturbed if they cannot get a certain part of a question out perfectly. In Maths now, it is more important to go onto another question (within the allotted time), instead of looking to complete every single question part absolutely perfect.  I feel that Churchill’s (not the dog) quote is quite apt for our modern day Maths syllabus.

“Perfection is the enemy of Progress”.

Winston Churchill (Former Prime Minister of the UK)

One does not really have time for 100% perfection on a Maths paper as they tend to be ‘question packed’, and unlike other subjects, there isn’t time for admiring your work. Students should apply this principle across the board to all their Maths tests in 2022/23.

The New Practical Style Questions

Thirdly, girls especially need to practice more exam questions involving engineering and mechanical parts. My reasoning for this is that, in general, most of the student cohort studying Engineering, Construction studies and Design/Communication Graphics (DCG) at Leaving Certificate are boys, and girls are not being exposed to this specific type of learning. With more everyday life practical questions being the order of the day in Maths, it is inevitable that more technical and mechanical questions will appear in years to come, and girls and parents of girls need to be aware of this. This trend will slowly become more pronounced if the Governments’ promotion and focus on the Science, Technology, Engineering and Maths (STEM) subjects continues and I expect it will.

Always Follow Your Passion

Lastly, in a survey conducted a few years ago, twenty-nine percent of Irish parents surveyed thought that technology subjects weren’t suitable for girls and fifty-three percent of girls in secondary school dropped STEM subjects due to pressure from their parents. These statistics may be contributing to the lack of representation of females working in STEM. Students and parents need to be aware of the excellent third level courses and future career opportunities available in these areas for both genders. Students need to be encouraged to explore all avenues of interest and follow their passions. Pursuing a spinoff of the subjects that a student enjoys each day in school wont set them too far wrong. Joe

**You can achieve more than you actually expect.**

 

To view last weeks feature article on ‘Transitioning into 1st Year or back to school’, click here.

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2023) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Tuition Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

 

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Joe’s Jotter: What Maths You Should Know for Higher Level Paper 2 2022

 

Leaving Higher Maths Paper 2 usually contains Probability and Stats, Trig, Geometry, Inferential Statistics and Co-ordinate Geometry, Area and Volume.

  • Your Paper 2 is on the Monday so you will have some time to look over. Again watch out for topics appearing here that should appear on Paper 2.
  • Paper 2 is more about the formula’s so use them if you are stuck
  • Label your diagrams and Label co-ordinates (x1, y1)
  • Do not get caught up in one or two topics – cover all your topics
  • Note that Financial Maths came up on P2 2018 – Be careful..
  • Proofs can be mixed between the two papers

What do you need to learn off for Paper 2?

  • Constructions Numbered 1-22
  • JCH Theorems 4, 6, 9, 14 and 19
  • LCH Theorems 11-13
  • Eight Trigonometric Identities 1-7 and 9
  • Some Statistics Terms (explain the words….‘population’, ‘sample’ etc)
  • Some Geometry Terms (explain the words…‘axiom’, ‘theorem’ etc )

See your textbook for all of these

Geometry

  • Geometry and Trigonometry often come up together
  • This idea of Similar Triangles is quite popular lately
  • There’s a bit of learning here:
  • Students need to Learn Constructions and Learn Theorems off by heart
  • Practice these and know all the steps
  • The best way to learn your proofs and constructions is to keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.
  • This could well be mixed with Trigonometry or Area and Volume
  • This is usually one short question on the paper (Section A)
  • In order to learn your proofs and constructions, keep writing them out. Pin the ones you find difficult to remember up onto your wall. Repeat this process.

Trigonometry

  • 3d Shapes are popular. The advice here is to break the shape into 2/3 triangles and solve using SOH/CAH/TOA, Pythagoras, Sin or Cosine Rule.

[Sin and Cosine Rule is in the Log Tables]

  • Be able to read the period and the range from a Periodic graph or a Periodic function
  • Be able to solve Trig Equations (this also may appear on P1 also)
  • You need to be able to prove 8 trig identities – these are listed in your textbook
  • The advice here is go over the questions from 2014-2019 as practice
  • This can be mixed with an Area and Volume Diagram or Co-ordinate Geometry
  • Triangles and Circles linked
  • Understand Trigonometric graphs including Periodic functions (period. Range etc)
  • Go over the past exam questions from 2014-2019 as practice here

Area and Volume

  • Started to get popular from 2017 onwards
  • We sometimes see combined shapes here so it’s a good idea to redraw diagrams
  • Have a look at Q7 2018 and Q7 2017 as practice
  • Can appear on Paper 1

Co-ordinate Geometry of the Line and the Circle

  • They can come up together or on their own
  • They tend to be more in Section A and could be two short questions
  • All the Important formula for these topics is on Page 18 and 19 of the log tables
  • I feel the ‘Big 3 formulas’ are Important (always have a great chance of appearing)
  1. Perpendicular distance between a point and a line
  2. Dividing a line in a given ratio
  3. Finding the angle between two lines using the Tan Formula

[ALL THREE OF THESE ARE IN THE LT]

  • Know the idea of slopes well. Slope formula (LT), m = -x/y & rise/run
  • Know the method for finding the equation of a tangent to the circle. This will involve the slope and maybe the radius of a circle
  • Be able to find the centre and radius of any circle given its equation..

Note that the equation can appear in different formats….

  • This tends to be more in Section A of Paper 2
  • Mixed with Geometry

Probability

100% chance of probability appearing…

  • Know the following three formula’s off by heart (Not in LT)…………… There is a great chance one of these will appear…..
    1. Formula for Conditional Probability – Probability of an event A occurring given that event B occurs.
    2. Formula to show that two events are independent
    3. Formula to show that two events are mutually exclusive
  • One of the following topics usually comes up every year:
    1. Bernoulli Trials (Know how to spot this & apply formula)

or

  1. Expected value of an event
    • e.g. Expected profit from A GAA club lottery
  • It doesn’t tend to be a long question (Section B) except in 2015 when it was mixed with patterns. It could be too short questions on Section A however
  • There isn’t really any help from Log Tables here so learn the above

Statistics

  • Be able to understand z scores for the normal curve
  • The Empirical rule can also appear. Symmetry is the secret to solving. Learn and practice this:
  1. 98% of the population falls within one standard deviation of the mean
  2. 95% of the population is within two standard deviations of the mean
  3. 68% of the population is within three standard deviations of the mean
  • Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
  1. Know Confidence Intervals for a Sample Proportion
  2. And Know Hypothesis Testing

Both could well appear on Section A but more likely on Section B. Try and understand these as opposed to just learning off the methods like a robot

  • Know how to analyse data by measuring its middle – Mean, Median and Mode. Know about data spread – range, inter-quartile range and standard deviation.
  • Know how to analyse data by measuring its middle – Mean, Median and Mode, as well as its spread – range, inter-quartile range and standard deviation.
  • Correlation and correlation co-efficient does pop up the odd time
  • The Empirical rule does also appear every so often. See the diagram in the Log tables on Page 36. Symmetry is the secret here. Learn and practice this:
  1. 98% of the population falls within one standard deviation of the mean
  2. 95% of the population is within two standard deviations of the mean
  3. 68% of the population is within three standard deviations of the mean
  • Inferential Statistics. This is where we use the data from a small sample to assume something is true or not for the full population
  1. This is a mix of Probability and Stats
  2. This has a good chance of appearing
  3. Confidence Intervals/Hypothesis Testing or both could well appear
  4. It could appear on Section A but more likely on Section B
  • Try and understand confidence interval and hypothesis testing as best you can as opposed to just learning off the methods like a robot.

To view my recent feature article on ‘Best Practice for LC Higher Maths Paper 1’, click here.

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

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Joe’s Jotter: Shorthand Best Practice for LC Maths Paper 1

 

General Guidance for Leaving Cert Higher Maths Paper 1

  • Leaving Cert Paper 1 in Maths is on Friday 10th June so you may have two/three papers done already (Eng/Engin/Home Ec).. i.e. The bulk of the prep for Maths Paper 1 needs to be done from the week before as a result of this.
  • Paper 2 material can come up on Paper 1 and vice versa – i.e. 2015/2017 Trig Functions appeared. Financial Maths appeared on P2 in 2018 even though it’s more of a P1 topic. A&V can appear on both
  • There is no specific layout to the paper year to year – Any topic can appear anywhere.
  • Topics tend to mix together into one question. So….I wouldn’t leave any topics out
    • Example Prob/Stats and Geom/Trig
  • I wouldn’t do extra questions on the paper as you will run out of time
  • Night before exam – Check…Maths set, pencils, two alarms, your usual calculator etc
  • Only answer the question that’s being asked. Read it three times.
  • Often the answer can be hidden somewhere inside the Information given in question
  • Do not scribble or tippex out any writing and make it unreadable. Draw an X through it and make sure it is readable – this could be worth marks and will be corrected.
  • Always give your answer in the form requested in the question e.g. surd form
  • Always use the correct units.. e.g. m2 for the area of a rectangular field etc
  • Only round off your answer at the very end of the sum. Retain as much of the decimal as you can through the question to ensure accuracy and full marks.
  • If you don’t give your answer in the correct form, round off decimal places or leave out the units, you will more than likely lose one marks
  • Exams are scanned in and are then corrected by a person (examiner)
  • When revising, break the course into sections and break each section into sub-topics in order to make it more manageable to tackle. Practice loads of past exam questions.

Sample Marking Scheme Scale for LC Maths

This is an example of how the paper is marked and shows the opportunities to pick up marks depending on how many marks is allocated to each question.

LC Maths Exam Paper Layout [Red Text – 2022 only] – Paper 1 and 2

The layout is normally 6 short questions (150 marks) and 3 or 4 long questions (150 marks). This is not the layout in 2022.

  • In 2022, we have Section A: 6 short questions of thirty marks (Do 4 of these).
  • Section B: These are the more practical real life scenario Questions..4 long questions on the paper (Do 2 of these) (fifty marks each). [Both Higher and Ordinary level]
  • Even though there is a choice on both papers, I would NOT attempt an extra question in either Section A or Section B
  • My proposed Timing for 2022: (Apply the 20:30 rule for Exams 2022)
    • 10 mins to read paper and carefully choose questions at the start
    • Short Question (4) (30 marks) – Max of 20 minutes each
    • Long Questions (2) (50 marks) – Max of 30 minutes each
  • Set out a time budget plan before your exam and stick to it.

How do attempt marks (Low Partial Credit) work in Maths?

You can pick up 2/5 and 4 or 5 out of 10 for just getting one step in the right direction. This is called Low Partial Credit

  • This could just be writing down line one

OR

Writing down the correct formula and subbing a relevant value into it [‘Relevant substitution’]

OR

Bringing down the last answer and doing something sensible with it

  • Write down everything – a formula from your Log tables, a step, a piece of English, a diagram, a table anything at all. If you type something into your Calculator, write it down. The examiner will be desperate to give you 2/5 or 3/10 or 6/20 or whatever Low partial credit is for each part. They will take no pleasure at all in giving you zero.
  • You may use a different way to solve a question (with success) that’s not written on the examiners marking scheme – this is full marks.
  • If you make more than one attempt on a question, make sure to leave both visible on the paper.. Never scribble out anything. Never write a ‘?’ on your paper.
  • Draw a single line through a method you feel is incorrect, it will be checked and may be allocated marks

What if I need an answer from the previous part to answer the next part?

There are two possible scenarios’ here. If you got an answer you think may be wrong and need to use it further down the question, carry it down anyway. If you didn’t get an answer at all and need one further down, explain in a note to the examiner that you are going to guess the answer needed and use it. You might word it something like:

“I didn’t get a value for x in part a so I’m going to assume that x=10 here.”

Do this and continue on…You can still get high marks for this question

What do you do if you mind goes blank?

  1. Fill in something you have done in class related to the question being asked.
  2. Use all the Information given in the question in some way.
  3. Use a formula you think that may be relevant to the question.
  4. Any correct element to a question will give you low partial credit.

What are the core skills I cannot live without for LC Higher Maths?

  • Solving a linear and quadratic equation
  • Solve a simultaneous equation (Basic JC Method or by substitution)
  • Subbing into a formula
  • Being familiar with Log Table Formulas (See below)

Why are Log Tables so important..?

Each student will have a set of log tables on their desk when they go into the exam hall. You will not be allowed to bring in your own set of log tables. Know whats in your log tables but more importantly whats not in your log tables. Be familiar with roughly where each formula is in the tables, so you are not in a mild tizzy trying to find one. Learn off the formula’s not in your Log tables. Enter these into a hardback notebook now and start memorising them. Guidance and advice for Maths Paper 2 will follow very soon. Stay tuned to Joe’s Jotter Blog for updates. Joe

To view last week’s feature article on ‘The ACE Exam Day Quick Ref Guide’, click here.

More details about Joe’s Maths Tuition Classes for Junior Cycle and Leaving Certificate (2022) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

*****

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Joe’s Jotter: ACE’ing your Christmas Exams 2021

First, Second and Fifth years; you will be commencing your Christmas exams soon. In the case of Second and Fifth years, it is another step towards your State exams and of course you want to put on a good show for work done over the last few months. Consequently, your preparation needs to start now for these exams. If you have very little revision done up to now, it’s not too late to salvage a decent percentage in order to set you up for the second term. It is never too late to start revising. Here are ‘Six of the best’ tips to ready yourself for the upcoming challenges:

  1. Set up a ‘Lifestyle Study Timetable’.

You need to put some kind of a plan in place for the next few weeks and I believe the ‘Lifestyle Study Timetable’ fits that bill. In summary, draw out a weekly timetable containing thirty minute study blocks each tagged with a five minute break after each one. Each block will contain a topic from one of your subjects. Prior to entering topics required to be revised; enter your school times and all the leisure activities or events you will be involved in and need to commit to that week. Keep some catch-up blocks free each weekend in case plans change during the week. It is better to have a plan in place that needs tweaking than no plan at all. Be ambitious but realistic with your plan ensuring it is short term. This will allow you to improve and adjust the next renewal of it. Full details of how to construct the ‘Lifestyle timetable’ is contained in my two hundred page ACE Study Guide textbook.

  1. Consolidate.

I would advise you, at this point, to consolidate the main topics you have studied with your teachers since September. Prepare no new material while also being realistic what you can get covered in a couple of weeks. Your teacher should be able to give you a broad outline of the main topics for consideration for this exam.

  1. Summarise.

Start writing out summaries of the core topics in your own words, whether this is using notes from your teacher or Information from your textbook. Mind maps, bullet points, pocket hardbacks, posits and flash cards are all useful for this. I am a firm believer in students having their own set of notes that can be read and understood easily. As with any exam, you do not want to be trawling through pages of notes as deadline day looms. Start putting these good habits in place now and you can build on them in January.

  1. Tend to all Subjects.

It is important not to neglect the subjects that aren’t your favourite or that you may not excel in. The first piece of homework you tackle every evening should be from these subjects and they should also get more time (blocks) on your ‘Lifestyle Study Timetable’. You are better off to have the majority of percentage scores for subjects around the class average, as opposed to having very high and very low percentages across a mix of subjects. Give each subject the respect it deserves, and balance time spent on them as best you can. Focus on your weaknesses, as it is likely your talents in the other subjects will balance overall grades out. This also applies within subjects. Getting very low scores in certain subjects can really drain confidence and leave you wondering “Where do I go from here”?

  1. Listing and Ticking.

List out the set of topics (subject by subject) you plan to cover for these exams onto an A3/A4 sheet. Put an ‘S’ beside a given topic when summarised and then tick it off when you feel confident you could answer a potential exam question on it. Having these lists on your wall will provide an added incentive to get more done. Ticking off each list and watching the workload shrink will help you feel so much better about how your revision is progressing. ‘To do’ lists are another variation of this. I use these in my business every day and find them excellent. Ticking off tasks done at the end of each day gives me great satisfaction. Try it and see yourself!

  1. Build Yourself Up.

Eating well is important as your body is more inclined to break down with colds, flu’s, and bugs at this time of year. It will be really difficult to do any constructive preparation if you develop that niggling cold or sore throat. In my opinion the best foods to enhance your system at this time of year are porridge, lemon/orange juice, hot soups, curries, stews, hot roast dinners, mugs of hot drinks and of course loads of water, to name but a few. Sugary cereals or Energy/Fizzy drinks will never improve your health or help illness resistance. Get your parents on board here by making sure they have stocked up the nutritional and warm homely winter foods to get you through to the last Christmas exam.

Finally, put a good solid effort into your revision over the next few weeks and you can relax then and enjoy Christmas with your family and friends. Your endeavours will be worth it when you see your grades being posted out in January. Take pride in your work at school, just as your parents take so much pride in everything you do. Good luck. Joe

More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022) and his Award Winning ACE Maths Solution Books can be found via the links below.

ACE Maths Classes: acesolutionbooks.com/ace-maths-tuition

ACE Maths Solution Books: acesolutionbooks.com/buy-my-books

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Joe’s Jotter: Exam Time is Feeding Time

Food provides all the essential nutrients that we require for healthy living and to fuel our daily activity. A car can work well, but if it doesn’t have any fuel it can’t go anywhere. Unfortunately for us, no single food provides all the nutrients required, so a mixture and range of different foods must be consumed in our diet. Research has shown that the healthier we eat, the better we feel and the more we can focus on tasks at hand.

When studying for exams, some students tend to stay up late and forget to eat and drink properly or maybe worse, they eat too much of the bad stuff. The following are five short exam nutrition recommendations (in depth discussions about added sugar have been omitted here, with it being the obvious heralded evil):

  1. Eat a breakfast

Parents: if your child skips breakfast before school, they are more likely to be tired throughout the day and will have reduced concentration levels. If breakfast is a busy time of day in your house, then feeding your children what they need quickly might be a daunting experience, but it doesn’t have to be. By stocking up on all the ingredients you need beforehand, you can deliver quick healthy breakfasts that they will enjoy.

Alternatively, if your kids aren’t hungry or everyone is in a rush out the door, make sure there are plenty of easy-to-grab pieces of fruit, yoghurt, smoothies, and muesli bars (sugar free) that can be eaten quickly on the go. In an ideal world, everyone should sit down at the same time and share food together, although I do realise that this isn’t always possible. I feel strongly that sugary cereals are a ‘no no’. Some of these cereals can contain up to one-third added sugar. I would advise all parents to check the ingredients on cereal boxes before bringing them to the checkout and ultimately the breakfast table.  

  1. Increase ‘brain food’ intake

Proteins from lean meat, fish, eggs, fruit, nuts, and whole grains are foods that help keep the brain mentally alert. Snacking on nuts and dried fruit will help prevent concentration levels dipping. Keep in mind that fruit like bananas, blueberries, and oranges all have natural sugars that will give a lift when feeling tired. Brain food is the fuel that helps us think clearly, make good decisions, and maintain concentration when fatigue develops during critical periods, for example, during the last half an hour of an exam.

  1. Snack healthy

When your head is in the books and time is ticking by, you might be tempted to skip a meal to keep up momentum. Your brain needs food and water to keep working and mental fatigue can cloud your brain, especially if an exam is close by. I would recommend the following healthy snacks to get you through study bumps: Whole wheat toast with peanut butter, fruit smoothies, berries, honey, dried fruit and nuts, hard boiled eggs, low fat chocolate milk, vegetables with dip or a low sugar granola bar. Graze away on the Guilt Free Good Stuff (GFGS) as you revise and move towards exam time.

  1. Minimise caffeine

Caffeine is a stimulant that is present in coffee and many energy drinks. Energy drinks are a total disaster in my opinion, as they provide a false high followed by a sugar crash. Sleep can also be affected by caffeine and I know a good few adults who abstain from caffeine after four p.m. as it disturbs their sleep. I would recommend water, peppermint tea or even a small glass of milk to aid sleep and as a healthy replacement for caffeine.

  1. Consume good fats

Fats are an important component of the diet and have received an enormous amount of bad publicity over the last twenty-five years. As a rough guide, saturated (bad) fats are generally solid at room temperature and tend to be animal fats (such as the fats found in butter or margarine). Unsaturated (good) fats are liquid at room temperature and are usually vegetable fats (such as olive oil, rapeseed oil, oily fish (sardines, tuna, mackerel, or salmon)). Unsaturated fats or good fats are an important nutrient for you to intake as a student. The following are other sources of Unsaturated fats: cheese, dark chocolate, eggs, nuts, coconut and coconut oil, peanut butter, pistachios, and walnuts.

Eating well and drinking plenty of water in the lead up to any exam is as important as the quality of the notes you prepare prior to sitting it. Joe

To view last weeks feature article on ‘Guiding Your Child Through the Exams’, click here.

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More details about Joe’s ACE Tuition (Maths and English) Classes for Junior Cycle (2022) and Leaving Certificate (2021) Students, ACE Maths Assessments, and his Award winning ACE Maths Solution Books can be found via the links below. Be sure to pick up your copy today!

W: acesolutionbooks.com

FB: facebook.com/JoeMcCormackEducationalExpert/

#:   #JoesJotter

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Project maths-the silver bullet or a step in the right direction?

Project Maths –the silver bullet or a step in the right direction?

Maths teacher and ASTI member Joe McCormack looks at the impact and challenges of Project Maths The new Project Maths course is well and truly upon us now at this stage. This new way of teaching and learning maths will be given a fair shot to see if it can raise maths competency and increase the cohort of students who take higher level maths. Last June, Strands One and Two of the Project Maths syllabus were examined in the Leaving Cert with students studying the new course on Probability/Statistics and Geometry/Trigonometry, alongside other topics from the ‘old’ maths syllabus. This cohort only began to study the new syllabus in Fifth Year and so the students were in the precarious position of having to try to understand the “Project Maths way” in just two years. While, in general, the “old” course saw the above topics examined as separate questions with little linkage between them, June’s exam paper, in some places, linked topics together. I welcome this new association since we now live in an integrated world where problems, both academic and real life, need to be solved using a mutli-pronged approach. The Leaving Cert class of 2013 will need to need to be even more competent in dealing with the new concepts as they take on Strands Three and Four of Project Maths. Like the 2012 students, this year’s class will have studied the old syllabus at Junior Cycle, which means they have to work hard to adjust to the new course. Most teachers would agree that it would have been more beneficial for Project Maths to be introduced to only First Year students initially, with these students working their way up through the system, building on the concepts from the foundation up. Leaving Cert 2012 The results are now out for the class of 2012, so what are their implications and what kind of reaction have they got thus far? Firstly, an increase in the numbers opting for the Higher Level maths paper was anticipated, but the surge of 35 percent on last year’s numbers exceeded expectations. In actual terms, the uptake on this paper increased from 16pc to 22pc. This year 11,100 candidates sat the higher level paper, up from 8,235 in 2011. Almost all of them (98pc) were eligible for the additional 25 bonus CAO points because they achieved a D3 or higher in the subject. This should give great encouragement and reassurance to students in two minds whether to take this level. The bonus points inevitably contributed to higher CAO cut-off points in areas such as science and technology. Points for such courses were expected to rise anyway, driven by the increase in demand from students heeding the advice of Government and employers in relation to jobs. However, this initiative does not seem to have distorted the points system as much as was expected with only approximately 3,000 students using maths as one of their six CAO subjects and thereby benefiting from the bonus points. This would indicate that different or additional measures may be needed. Employers have welcomed the results but warned there was no room for complacency. Student feedback Students’ experiences and feedback on Projects Maths, in general, are mixed. From my experience, the First Years are enjoying the common introductory course. For example, the new Probability section allows them to get involved in more practical maths in the classroom, enhancing their learning on the primary school topic ‘chance’. I believe the more practical questions will increase students’ interest in the subject because they relate more to student’s everyday experiences. The teacher will have more opportunities for open discussions on topics in class and allowing students to back up their answers with relevant information should also allow them to express themselves more, leading to them developing a deeper knowledge of topics. In parallel with this, if a student can argue their case properly in the context of what they are being asked, they could be in line for very high marks. I see this as a positive development as it will foster creativity and promote independent thinking. However, in my opinion, there needs to be a more balanced paper set at all levels. Some elements of the papers were marked too easy while topics in other areas were too difficult. I would be more in favour of questions that are fair with a more rigorous marking scheme applied, if necessary. It would be nice if students finished their Post Primary Maths experience satisfied that they did their best and that the rewards reflect their efforts. They shouldn’t feel traumatised to a point that preparation for other exams might be compromised. This year, most students got the result they deserved anyway so why should we put our students through this? We, as teachers, want to see our students given a genuine opportunity to show what they have learned. I feel that they cannot do this with complicated over wordy questioning aligned with some abstract university type problems. Surely every student deserves simple language and somewhat relevant questions on their paper? Social media has allowed students to feedback openly on the new course. The idea of being able to write on the paper is clearly one they welcome. However, practical issues must also be considered: will the length of a student’s answer be influenced by the amount of space allocated for each sub question? Unfortunately, I think a weaker student could be drawn into the idea that a small amount of space for a question might mean a very short solution is required. Also, students must be given enough room to write their answers to a particular part of a question on the same or next page. Teaching challenges There is no doubt that teachers will need to adjust to this new practical way of teaching their subject. They will need to choose their books carefully and use a wider range of resources outside these books. They will need to think outside the box and try to bring some of these new topics to life using practical examples and real life demonstrations. They will need to be more ICT proficient; I believe the Department may need to look at some more Continuous Professional Development in maths specific ICT. One of the biggest challenges for the classroom maths teacher is time. At the moment, it is hard to gauge how much time to spend on each topic and sub topic. Teachers will learn, as each year passes, to structure the course better, including the topic order and timeline. They will learn to choose the best paths through each topic while keeping a closer eye on the syllabus than ever before. However, I believe the Leaving Certificate courses at both Higher and Ordinary Level in their current format may now be too long. Looking through the available exam papers, the length of some of the questions has increased significantly. Those schools that haven’t done so already may need to introduce a double maths class on their senior cycle timetable. In parallel, I envisage a situation where schools may start investing Transition Year maths time to teach some of the Project Maths syllabus and concepts. The marking scheme will be interesting too with the new credit system seeing students being marked from zero up. At present there are a number of graded versions inside the marking scheme. After seeing how this year’s papers were marked, many teachers I spoke to felt the Department hasn’t yet hit the target with the weighting of marks. Students and teachers need to be given more concrete information on how the exam is being assessed. I welcome the Department’s Initiative to create a “Professional Diploma in Mathematics” course. This is a free two year course to upskill maths teachers and to support the implementation of Project Maths. There is an incentive there for many maths teachers to improve their skills and the Department has, in fairness, improved the resources available to teachers via the Project Maths team. In general, we as maths teachers are still a little sceptical about Project Maths. There is also a concern about some topics that have been removed from the syllabus that may be necessary for some mathematically related university courses. In a survey of 253 members of the Irish Maths Teachers Association (IMTA), over 77 percent thought students would benefit if maths teaching in schools was combined with industrial visits to view real-life application of maths. The Government has little money to spend; industry must be encouraged to support the work of maths teachers as much as possible to bolster the effectiveness of Project Maths.

Project maths-the silver bullet or a step in the right direction?

Project maths-the silver bullet or a step in the right direction?
Project maths-the silver bullet or a step in the right direction?More details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022), ACE Maths Assessments and Solution Books via the links below.