## Project Maths Advice from an Official Examiner

Seminar advice from a Chief Examiner for Project Maths

• Units Matter – If they are present in your question, they are required in your answer
• Do not put anything into the calculator that you have not already written on your paper.
• You could get almost full marks (High Partial Credit) for just one slip/mistake in your question. This could even be 7/10 – See marking scheme for Q5 JCH 2011.
• You need to be able to deal with real life statistics
• Past exam statistics questions are great practice for future exams
• Algebra (Strand 4) is currently the worst answered section
• Measuring and estimating the heights of objects outside is now a more important part of Geometry and Trigonometry
• Trigonometry is the second worst answered question
• The hand symbol is now gone. You now must show your work for all questions
• You need to practice the steps to solving the unseen problem
• The Slope of a line is important especially its context in the question. e.g positive correlation–as one increases so does the other
• Attempt everything on the paper – you could receive some marks (low partial credit (LPC)) for very little work. If you make two or three attempts, they will all be corrected. Your best step in the right direction could get LPC.
• Marks will be allocated for all work on a diagram printed on your paper.
• Never rub/tippex out any work even if you think it isn’t neat (Girls – take note). Draw a line through it and it will be corrected.

## Project Maths Advice from an Official Examiner

Project Maths Advice from an Official Examiner
Project Maths Advice from an Official Examiner
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.

## Information on the Assessment of Project Maths

Assessment with ‘Project Maths’

Project Maths is quite different to the old syllabus, but for some people that can be an advantage. The old syllabus focused more on ensuring that you get the right answer, and they preferred to write the equation or question in full mathematical terms on the papers.

With Project Maths, the focus is shifted towards trying to make you understand concepts and ideas rather than worrying about the correct answer in every question. The questions have much more reading components, almost like small comprehensions which require you to find the relevant numbers and figures to solve the problem. The marking schemes have changed also (they aren’t very reliable right now, because they change them so frequently). You can get a lot of the marks for a question by showing every step of your work, writing down relevant formulae etc. In most questions, only 3-4 marks are going for the actual answer because they are trying to emphasise the importance of understanding the method of your work rather than racing to find the answer.

To put it simply, the equations and problems are basically similar to the old course, but they are presented to you in a much more complicated, English-based manner.

## Information on the Assessment of Project Maths

Information on the Assessment of Project Maths
Information on the Assessment of Project Maths
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.

## Advice on Answering Project Maths Exam Questions

Project Maths

Specifically, students should follow these steps in preparation for Project Maths type questions:

1. Know the theory and equations. If you dealing with a trigonometry problem and you know how to apply the three basic trigonometric ratios – Pythagoras theorem, the sine rule and the cosine rule – then you have all you need to solve a right angled or a non-right angled triangle problem. (It is a good idea to practice the use of these relationships with the old format exam papers)
2. Look through the wording of the question and pick out the maths related information. Bring a highlighter and highlight the relevant pieces of the question. Watch out for numbers written as words, for example thirty instead of 30
3. If no diagram is drawn for you, try to draw one yourself. Mark in the numerical information you are given. This can be very helpful to visualise what you are being asked
4. Relate the information you have to the theory and equations. Have you got a right angled triangle or a non-right angled triangle? Have you got two right-angled triangles that need to be solved separately? This will point you to the appropriate equations to be considered
5. Do not leave any blanks. Attempt every question.If you leave a blank the examiner will have no choice but to give you zero marks for that question. If you attempt the question you will probably get some marks and perhaps more than you think
6. When asked for your opinion, always try to relate your opinion to the mathematical concepts

Most importantly, remember there are tens of thousands of other students in the same position. You are not alone and as long as you are familiar with the theory and equations, you should have everything you need to solve the problems.

## Advice on Answering Project Maths Exam Questions

Advice on Answering Project Maths Exam Questions
Advice on Answering Project Maths Exam Questions
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.

## Project Maths Geometry Keywords

AXIOM

COROLLARY

THEOREM

SIMILAR ?’s

CONGRUENT ?’s

RIGHT ANGLE (900)

ARC OF CIRCLE

SECTOR OF CIRCLE

SEMICIRCLE

ISOCELES ?

EQUILATERAL ?

SCALENE ?

EXTERIOR <

INTERIOR <

TRANSVERSAL

VERTICALLY OPPOSITE

ALTERNATE

PERPENDICULAR

PARALLEL

COLLINEAR POINTS

STRAIGHT EDGE

CONSTRUCT

VERTEX OF A ?

VERTICES OF A ?

RAY

STRAIGHT LINE <

1800

CONVERSE

IMPLIES

PROOF

POLYGON

PARALLELOGRAM

RHOMBUS

BISECT

BISECTOR

INCENTRE OF A CIRCLE

INCIRCLE

SSS

SSA

ASA

HYPOTENUSE

OPPOSITE

TANGENT

CIRCUMCIRCLE

CIRCUMCENTRE OF A CIRCLE

CENTROID OF A CIRCLE

ORTHOCENTRE OF A CIRCLE

PERPENDICIULAR BISECTOR

MIDPOINT OF A LINE

CHORD

DIAMETER

LONGEST SIDE

SHORTEST SIDE

AREA OF TRIANGLE (?)

AREA OF PARALLELOGRAM

DIAMETER

## Project Maths Geometry Keywords

Project Maths Geometry Keywords
Project Maths Geometry Keywords
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.

## Project Maths Statistics Keywords

PRIMARY DATA

SECONDARY DATA

CATEGORICAL DATA

NUMERICAL DATA

POPULATION

SAMPLE

STEM AND LEAF PLOT

CORRELATION

HISTOGRAM

SCATTERPLOT

OUTLIER

LINE OF BEST FIT

ORDINAL DATA

NOMINAL DATA

PIE CHARTS

BAR CHARTS

LINE PLOT

DISCRETE DATA

CONTINIOUS DATA

CENSUS

SIMPLE RANDOM SAMPLING

STRATIFIED SAMPLING

CLUSTER SAMPLING

CONVENIENT SAMPLING

ETHICAL ISSUES

CLINICAL TRIALS

DATA HANDLING CYCLE

QUESTIONNAIRE

SYMMETRIC DISTRIBUTION

NEGATIVELY SKEWED

POSITIVELY SKEWED

CORRELATION COEFFICIENT

CAUSAL RELATIONSHIP

MEAN

MEDIAN

RANGE

INTERQUARTILE RANGE

DATA

UPPER QUARTILE

LOWER QUARTILE

CENTRAL TENDENCY

BIAS

## Project Maths Statistics Keywords

Project Maths Statistics Keywords
Project Maths Statistics Keywords
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.

## Information on the Inception of Project Maths

Information Leaflet on Project Maths Inception 2010
Project Maths is an NCCA led project which signifies the most fundamental change to maths teaching and learning at second level since the 1960s. Project Maths is being phased in over a number of years. The project will be rolled out nationwide in September 2010, at both first and fifth year in every school.

Why?

Project Maths began as a result of concerns about:
the level of performance of Irish students in the international context (PISA);
the relatively small number of students taking the exam at higher level Leaving Cert;
evidence that students were not able to apply mathematical knowledge and skills, except in the most practised way and in familiar contexts;
the difficulties students had in coping with mathematics at third level;
employers contending that Irish students have good knowledge but poor understanding and lack problem solving skills;
the need to supply qualified people in the area of maths and science for the knowledge economy.
When?

The maths teachers in all schools have received their first two rounds of training a year in advance of introduction. The training for all maths teachers will continue for a further three years. The Department of Education and Skills (DES) is fully committed to providing this support for teacher professional development throughout the implementation phase. The project is fully funded by the DES.

In September 2010, the introduction of Strand 1 (statistics and probability) and strand 2 (geometry and trigonometry) will form the first stage in a phased introduction of revised syllabuses in maths over a three year period. All five strands have been completed by the NCCA’s mathematics committees.

Assessment

There is a change in the type of exam questions asked, with one section on contexts and applications which focuses on students’ ability to apply mathematical knowledge. This will allow teachers to focus on the problem solving skills of students rather than entirely on rote learning and practising algorithms for answering exam questions. The teachers in the 24 pilot schools have been very positive about this change in emphasis.

The State Exams Commission (SEC) trialled a sample paper at each syllabus level in October 2009 from which it developed the official sample papers. These sample papers can be viewed on the SEC website at www.examinations.ie (follow the link for Project Maths). NCCA provided a Pre-Leaving set of exam papers with solutions and mark schemes for the 24 schools and these are now available at www.ncca.ie/projectsmaths.

Junior Certificate and Leaving Certificate exams remain. When the change in mathematics is complete there will not be a choice of questions in examinations. This will ensure full coverage of course material and the same mathematical experience for all students. These changes ensure no major topic area will be ignored. Questions will test students ability to think, problem solve and apply mathematical knowledge. Take a look at the sample papers on www.examinations.ie and follow the link for the report of the trialling to see comments on some examples of student work.

In the classroom

The changes brought about by the teachers in methodology in the initial 24 schools has been received in a positive way by students, particularly by junior cycle who would have been used to active methodologies in primary school.

A bridging framework is being put in place to allow teachers to connect with what students have learned in primary and to give a lens to primary teachers whose students in 5th and 6th classes are starting to think in terms of second level.”We’re using dice, coins and cards in our probability class,” explains 16-year-old Rebecca Evans of Moate Community School, one of the 24 pilot schools in the Project Maths programme. “Two of us roll the dice 50 times each and record our findings. It’s great to be working in teams in maths class.”
(Article published in Irish Times 10/12/08)”The change in teaching methodology is bringing the class alive for the students… It’s more active as there’s greater student participation. The students are actually saying it’s ‘fun’, so different to the way that they’re used to,” says Helen Lambe, Maths teacher at St Patricks College for Girls, Cork, one of the initial twenty four schools.
(Article published in Evening Echo 13/2/09)There is a Common Introductory Course for all students who begin maths at second level. Research tells us that students experience difficulty in maths when transferring to second level -this common course will ease this transition.
Partnership

This project has succeeded in bringing together all expertise in the teaching of maths in Ireland. The DES and SEC are working directly with NCCA. The National Centre for Excellence in Maths and Science Teaching and Learning (NCE-MSTL) are providing training in strand 1 and strand 2 directly for teachers through summer courses, from which additional resources for teachers are developed. They also trained local facilitators who, in collaboration with the Irish Maths Teachers Association (I.M.T.A), can deliver supplementary courses nationally on a part-time basis.

Resources

NCCA has developed resources which are available on line. These resources are for Junior Certificate and Leaving Certificate students studying strand 1 and strand 2.

On-line tutorials for students are available on NCCA’s Action website at www.action.ncca/projectmaths

The Project Maths Development Team (PMDT) have a dedicated website at www.projectmaths.ie which has a range of resources for both students and teachers.

NCCA has briefed the publishers of maths text books on a regular basis and they are preparing textbooks which will be available shortly.

Consultation

Project Maths will place Irish students in a more favourable position internationally. The syllabus development draws on consultation and research conducted in Ireland and internationally.

Review of Mathematics Education, a discussion paper outlining some of the issues of concern, was published by NCCA in 2005. A questionnaire sought the views of students, teachers, principals, parents, lecturers and employers.

Independent research on trends in post-primary mathematics education was commissioned by NCCA in 2005 and a report by Conway and Sloane was published in 2006 (International Trends in Post-Primary Mathematics Education).

Good practice in mathematics teaching in other countries was also examined. The focus was on the countries that perform better in international studies (PISA, TIMSS). These countries are Finland, South Korea, Holland and Japan.

NCCA has brought together best practice from around the world and tailored it for the modern Irish school. We have retained what is seen as valuable from the past and blended it with what is viewed as essential for the future.

Part of this process has included taking into consideration the perspectives of third level institutions in Ireland, IBEC, Engineers Ireland and multi-nationals operating in Ireland. The NCCA’s representative structures mean that many of these organisations are directly represented on Council and/or its committees.

It is the stated aim of Project Maths to raise the mathematical ability of students at second level in Ireland both in a national and international context.

It is expected over the lifetime of the project to see participation levels increase at higher level for both Junior Certificate (the target is 60%) and Leaving Certificate (a target of 30%). This is ambitious but, with a robust syllabus, authentic assessment and an enthusiastic cohort of teachers, these levels are attainable.

## Information on the Inception of Project Maths

Information on the Inception of Project Maths
Information on the Inception of Project Maths
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.

## Practical Parenting for the Junior Cert and Leaving Cert

Practical Parenting Advice-LC/JC General

The following is some General advice for you as a Parent of a Leaving/Junior Certificate student:

• Pushing your anxiety onto them is not helpful for your child
• It affects their confidence
• Most put themselves under so much pressure anyway, they don’t need any extra pressure
• They need support, space, reassurance and recognition that they are working hard
• They also need extra encouragement (fuel for motivation)
• When they get home from school, give them a transition period adjusting to being at home again before asking questions about their day etc

Your child may have:

• A fear of failure
• Not enough time for the volume of work that is being laid on for them
• A Study plan will help them break it into manageable chunks
• Little rewards for themselves will always help
• They should alternate 40 minutes study with 10 minutes break
• A fear of not being accepted if they don’t perform well
• A fear of doing badly (You hear them say sometimes “I’m gonna fail”)

…….and they may be ultimately afraid that they won’t be loved as a result

You need to communicate in such a way saying “it’s not all about school”

• The car can be a great time to communicate with your child – side on communication is excellent to get  through to teenagers

During the LC, they need active relaxation, they also need:

• Rest
• Timeouts
• Sport/Exercise – Recommended is 20/30 minutes per day – Helps keep serotonin levels balanced
• Could you buy them two months gym membership during their exam year
• Checkout Steve covey – The 7 habits (time management)
• Study plan
• Eat well
• Someone to listen

Deep abdominal breathing is a great technique for helping you and your child deal with the Exams and the Junior/Leaving cert in general. It also works for stressful situations.

Little gestures like the following are great for your child:

• Cleaning their room
• Favourite dinners
• Treats
• Buy their favourite magazine
• Bring them on an surprise evening out

Good Luck Parents!!!!

## Practical Parenting for the Junior Cert and Leaving Cert

Practical Parenting for the Junior Cert and Leaving Cert
Practical Parenting for the Junior Cert and Leaving Cert
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.

## A little Project Maths Information for Parents

A little Information for Parents who have a child for doing a Maths Exam

In case of a Maths Emergency, it’s a good idea to have the following at home for your child:

• Copies
• Red and Blue Pens
• Make and Model of the calculator your child always uses
• Log Tables
• Mathematical Set

The Gender Divide

In general, most students experience a slight dip in maths results during second year due to the increase workload and other external factors. The girls dip is not as pronounced as the boys. There is also a dip in fifth year but it is not as extreme as the second year one. In relation to project maths, girls don’t tend to be as good at taking a chance when answering questions. With the new phrasing of project maths papers, you need to be willing to take risks which suits boys better since they are less conscious of what they are writing on the paper and not as afraid of being wrong. In my opinion, girls need to learn to express their opinion in a free and open manner in order to improve their grades. It will be important for the girls not to get overly upset if they cannot get a certain part of a question out perfectly.  It is important just to keep going with the paper in this case

Facts about the New Points System

D1 – LCH English – 55 Points

D1 – LCH Maths – 80 Points

A1 – LCH Accounting – 100 Points

B3 – LCH Maths – 100 Points

Students who pass (Get a D3 or above) Honours Leaving Certificate Maths will receive an extra 25 bonus points.

Other Information of Note

The average teacher is struggling to get the course finished as the general consensus out there, as the curriculum exists, is that there is too much material on the Leaving Cert course.

It is more difficult to get a grade A now due to the fact there is no choice on the paper. It is important to remember that the marking scheme is stacked in the favour of all students except those who are chasing an A. The last two years have shown statistics of 97% and 98% of people passing the exam.

There is approximately 5,000 students extra doing honours Maths now every year since the advent of Project Maths.

## A little Project Maths Information for Parents

A little Project Maths Information for Parents
A little Project Maths Information for Parents
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.

## Why our Students Can’t Read a Math Textbook

Wh? ?ur Students ??n’t Read ? Math Textbook

Most Algebra ? students us? th??r math textbook f?r ? single purpose, ? source f?r homework problems. ??m? math instructors ?sk th??r students t? read th??r book ?s ??rt ?f th??r assignment, m?st d? n?t! Instructors kn?w students find th? task ?f reading th??r math textbook ? difficult ?n?, f?r s?m? ?n impossible ?n?. ?h?r? ?r? specific math reading skills th?t ?r? d?ff?r?nt fr?m ordinary reading skills ?nd w? ?r? n?t teaching ?ur students t? identify ?nd us? math-reading skills. ?h? purpose ?f th?s article ?s two-fold: (1) identify f?v? differences b?tw??n math reading skills ?nd ordinary reading skills, ?nd (2) discuss wh?t sh?uld b? d?n? t? help students read th??r math textbook.

1. Reading speed: Suppose ??u ?r? reading ? novel ?nd find ? word th?t ??u d?n’t understand. D? ??u g?t ??ur dictionary, search f?r th? meaning ?f th? word ?nd write s?m? notes r?g?rd?ng th? meaning? Readers d?n’t expect th? unknown meaning ?f ?n? word t? spoil th? plot th? novel. Wh?n students ?r? reading ? math book ?nd find ? key word th?t ?s unknown, ? lack ?f understanding ?f th? key word m?? spoil th??r success ?n th? problems ?t th? ?nd ?f th? s??t??n. ?n fact ?t m?? spoil th? plot ?f th? s??t??n ?nd ??ss?bl? th? plot ?f th? entire chapter! Ordinarily ? proficient reader ?s ?ls? ? fluent reader. ?n mathematics, ? sufficient reader ?s ?ls? ? deliberate reader. Y?u m?? h?v? t? read ? passage s?v?r?l times. Y?u must search f?r th? meaning ?f ???h key word utilizing ? math textbook.

2. Reading directionality: Fr?m early learning, th? concept ?f print directionally f?r reading ?s taught fr?m left t? r?ght. Wh?n reading math ??u d?n’t ?lw??s read fr?m left t? r?ght, ?n fact ??u m?? h?v? t? resist th? urge t? read fr?m left t? r?ght. Consider th? math expression: 3 + 2 ? 4

Reading fr?m left t? r?ght: 3 + 2 ? 4 = 5 ? 4 =20

Reading mathematically: 3 + 2 x 4 = 3 + 8 = 11

Notice ??u g?t ? completely d?ff?r?nt result wh?n ??u read fr?m left t? r?ght compared w?th reading mathematically. ?n th?s case ??u, ??u must resist th? urge t? read fr?m left t? right.

3. Read w?th pencil ?nd paper: Reading w?th pencil ?s ? math reading skill th?t ?s critical t? problem solving. ?h?s skill helps students m?k? ? connection b?tw??n th? g?v?n ?nf?rm?t??n ?nd wh?t th? problem ?s ?sk?ng th?m t? find. ??n? word problems h?v? hidden ?nf?rm?t??n, wh??h ?s ?nf?rm?t??n ?n? n??ds t? solve th? problem but ?s n?t g?v?n ?n th? problem. ? student n??ds t? read w?th pencil ?nd paper wh?n searching th??r textbook f?r hidden ?nf?rm?t??n. Reading w?th pencil ?nd paper ?s ?n? ?f th? m?st ?m??rt?nt math reading skills.

4. Symbol interpretation: ??n?? mathematics ?s ? symbolic language ?n? must b? careful h?w th?? interpret math symbols, th? meaning ?f ? symbol depends ?n th? placement ?f th? symbol. Students incorrectly interpret exponent notation ?nd m?k? common math errors ?v?r ?nd ?v?r ?g??n. ??n? students m?k? errors wh?n th?? enter symbols ?nt? ? calculator, b???us? th?? d?n’t differentiate b?tw??n ? division symbol ?nd th? symbol f?r ? fraction bar. Wh?n faced w?th ?n incorrect answer th?? lack th? math reading skills t? find ?nd correct th? error.

5. Independent learning: ? student must possess good math reading skills ?n order t? b???m? ?n independent learner ?f mathematics. ?s technology advances, ?t plays ? larger roll ?n education; m?r? students ?r? t?k?ng online math courses ?s?????ll? ?t th? college level. ? b?l??v? ??u n??d t? b? ?n independent learner t? succeed wh?n t?k?ng ?n online course. ?? b???m? independent learners, ?ur math students n??d t? read math w?th understanding. ?n addition, th?? sh?uld b? ?bl? t? find ?nd eliminate common math errors.

If w? expect ?ur math students t? improve th??r problem solving skills ?nd b???m? independent learners, ?ur mathematics curriculum n??ds ? n?w emphasis. ?ur math Ireland education programs n??d t? train prospective math teachers h?w t? teach th??r students t? read math w?th understanding. Identifying math reading skills ?nd h?w t? apply th?s? skills sh?uld b? ?n integral ??rt ?f ?ur math curriculum.

## Why our Students Can’t Read a Math Textbook

Why our Students Can’t Read a Math Textbook
Why our Students Can’t Read a Math Textbook
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.

## Maths Teaching Tip #1-Remembering Whats Its Like Not to Know

Math Teaching ??? #1 – Remembering Wh?t It’s L?k? ??t t? Know

I h?d b??n t? London ? f?w times b?f?r?, s? ? knew m? w?? ?r?und pretty well. ??v?rth?l?ss, ? ?lw??s carried ? map. ?? ? felt sur? th?t ? w?uld n?t h?v? ?n? trouble finding m? w?? t? m? appointment w?th ? local education official-especially s?n?? h? h?d g?v?n su?h good directions: “??k? th? Northern L?n?; g?t ?ff ?t th? Elephant ?nd Castle; g? straight ?ut th? door ?nd cross t? th? ?th?r side ?f th? road; g? u? th? f?rst street ? couple hundr?d meters; ?ur office ?s ?n th? left, ?ust b?f?r? th? park. Y?u ??n’t m?ss it.”

That sounded pretty easy. ? h?d ridden th? Northern L?n? ?f th? Underground dozens ?f times, ?lth?ugh ? h?d n?v?r g?tt?n ?ff ?t th? Elephant ?nd Castle. ?? ? g?t ?ff th? Tube ?t th? correct st?? ?nd w?nt u? th? escalator, thinking t? head straight ?ut th? door. That’s wh?n m? troubles began. Wh?n ? g?t t? th? top ?f th? escalator, th?r? w?s n?t ? door t? g? straight ?ut from-there w?r? f?v? doors, ?ll distributed ?r?und th? circumference ?f ? circular-shaped exit/entry area! ?h? official hadn’t mentioned th?t. ? h?d n? idea wh??h direction t? exit. ?? mu?h f?r “g? straight ?ut th? door!”

But ?ll w?s n?t lost. ? h?d m? trusty map, ?nd ? knew th? n?m? ?f th? street ? w?s headed f?r, s? ? ?ust headed ?ut th? nearest door t? l??k f?r th? street sign. ?s ? emerged, ? discovered th?t th? tube st?? w?s ? round island surrounded b? s?v?r?l wide lanes ?f swirling traffic, w?th streets radiating ?ut ?n s?v?r?l directions. ?h? street signs ?n London ?r? embedded ?n th? walls ?f th? buildings, ?nd n?n? ?f th?m ??uld b? s??n fr?m wh?r? ? stood. (Wh?t ?s th? practicality, ? wondered, ?f street signs th?t ?r? ?nl? visible ?n?? ??u’v? ??tu?ll? turned ?nt? th? street? D? th?? serve t? offer reassurance t? people wh? ?lr??d? kn?w wh?r? they’re going?!)

It t??k ? long time f?r m? t? wander ?r?und th?t circus (well, th?t ?s wh?t th?? call ?t) unt?l ? finally f?und th? r?ght street. ? finally arrived ?t m? appointment s?m?wh?t late ?nd r?th?r perturbed. ?ut th? experience w?s n?t lost ?n m?. ?h? man h?d g?v?n m? directions th?t described exactly wh?t h? d?d ?v?r? day. ?ut h? failed t? t?k? ?nt? account th?t ? h?d n?v?r b??n th?r? b?f?r?. ?nd th? fact th?t h? d?d n?t remember wh?t ?t w?s l?k? t? b? th?r? f?r th? f?rst time caused h?m t? omit ?m??rt?nt ?nf?rm?t??n, wh??h rendered h?s directions meaningless t? m?. ?h?? w?uld ?nl? m?k? sense t? ? person wh? h?d ?lr??d? b??n th?r?! “Y?u ??n’t m?ss ?t,” indeed.

It struck m? ?s ? left m? appointment th?t th?s w?s ? perfect metaphor f?r wh?t ?ft?n g??s wrong w?th math education. ? ?n?? heard ? teacher introduce fractions t? h?s class b? pronouncing “numerator,” ?nd “denominator,” writing th?m ?n th? board, quizzing h?s pupils ?n th? correct spelling ?f th? w?rds, ?nd th?n verbally defining th??r meaning. Wh?l? h?s presentation w?s technically correct, ?nd w?s ?n accurate description ?f h?w h? thought ?f fractions ?v?r? day, th? lesson w?s meaningless t? m?n? ?f h?s students b???us? ?t provided n? connection t? physical ?r visual experience. ?h? instructor h?d forgotten wh?t ?t w?s l?k? n?v?r t? h?v? s??n ?r considered ? picture ?f ? fraction b?f?r?, ?r t? h?v? divided ?n object ?r groups ?f objects ?nt? fractional parts. ?? h?d forgotten wh?t ?t w?s l?k? t? n?t kn?w ?b?ut fractions. ?s ? consequence, h?s instructions w?uld m?k? sense m??nl? t? students wh? ?lr??d? knew ?b?ut fractions; but th? lesson w?uld g? r?ght ?v?r th? heads ?f ?th?r students, ?v?n wh?n they’re diligently paying attention.

Fortunately, m?st teachers n?w kn?w better th?n t? ?r?s?nt ? fraction lesson l?k? that-although th?t style ?f presentation ?s st?ll pretty mu?h th? norm ?n algebra classes! ?? introduce fractions, ?t ?s m?r? typical f?r th? teacher t? b?g?n b? drawing ? circle ?n th? blackboard, drawing vertical ?nd horizontal diameters thr?ugh ?t, shading three ?f th? f?ur r?sult?ng parts-and th?n proceed t? t?ll th? students th?t s?n?? th?r? ?r? f?ur parts altogether, ?nd three ?f th?m ?r? shaded, w? call th?s “three fourths.” ? f?w teachers m?ght consider th?s ?n? illustration sufficient t? define ?ll fractions. ?ut m?st teachers w?uld provide s?v?r?l pictures ?f d?ff?r?nt fractions, ?nd th?n ?sk volunteer students t? n?m? th?m properly. ?h?? th?n consider th??r introduction complete.

This type ?f presentation s??ms t? m?n? teachers t? cover ?ll th? bases, s? th?? ?r? surprised ?nd dismayed t? discover l?t?r th?t ? couple ?f th??r students st?ll h?v? n? understanding ?f basic fractions whatsoever. Naturally, teachers feel ? n??d t? account f?r th?s “? taught it-but th?? d?dn’t learn ?t” situation. ?n days g?n? b?, teachers w?uld simply label th?s? students ?s stupid, lazy, ?nd incompetent; th?? w?r?n’t paying attention, th?? w?r?n’t f?ll?w?ng directions, th?? w?r?n’t tr??ng hard ?n?ugh, th?? w?r?n’t focused, th?? d?dn’t care. Nowadays, ? d?ff?r?nt label ?s invoked: th? students d?dn’t learn th? lesson b???us? th?? h?v? learning disabilities.

But th?r? ?r? ?th?r reasons wh? th?s seemingly effective presentation ?s v?r? mu?h l?k? telling ? first-time visitor t? London t? g?t ?ff ?t th? Elephant ?nd Castle ?nd g? “straight ?ut th? door.” ?f th? teacher ?s d??ng ?ll th? drawing ?n th? board, th? teacher owns th? drawings, n?t th? students. ??m? pupils m?k? better sense ?f th? teacher’s drawings wh?n th?? copy th?m ?nt? th??r ?wn paper. F?r th?m, feeling th? ?nf?rm?t??n thr?ugh th??r ?wn fingers ?s m?r? effective th?n m?r?l? l??k?ng ?t s?m??n? else’s pictured thought. ?ut ?v?n wh?n th? lesson requires students t? copy th? teacher’s drawings, s?m? students copy th? drawings incorrectly, b???us? th?? fail t? notice ?m??rt?nt details, ?r fall b?h?nd ?nd b???m? confused ?r flustered. ?? th?? st?ll d?n’t learn th? lesson th?t ?s supposedly b??ng taught.

Even ?f th??r drawings ?r? perfect, pupils ??n st?ll fail t? connect th? pictures t? th? fraction nomenclature voiced b? th? teacher. Wh?l? th? teacher ?s proclaiming “…?nd that’s wh? w? call ?t three fourths…” s?m? students ?r? busy studying th? picture, noticing th?t three sections ?r? shaded ?nd ?n? ?s n?t. Wh?l? th??r minds ?r? completely occupied w?th t?k?ng ?n th?s visual ?nf?rm?t??n, th?? m?? n?t ?v?n hear th? teacher’s voice ?t ?ll. ?t ?s easy f?r teachers t? assume th?t b???us? th?? s??d s?m?th?ng, ?v?r??n? heard ?nd understood wh?t w?s said-forgetting h?w m?n? times ? day th??r students fail t? respond t? th? sound ?f th??r voice telling th?m t? ?ut th??r books ?w??, ?r t? ?ut th??r pencils d?wn, ?r t? b? quiet. ?v?n ?f th? students d? hear wh?t ?s s??d, th? teacher’s w?rds ??n s?m?t?m?s provoke n?th?ng but confusion: “Wh? ?s h? calling ?t three fourths, wh?n ?n? ??rt ?s white ?nd three parts ?r? shaded? ?h?t d??sn’t m?k? sense!”

And th?r? ?s st?ll m?r? th?t ??n g? wrong, ?v?n wh?n th? students understand th?t th?? sh?uld count h?w m?n? parts th?r? ?r? altogether, ?nd h?w m?n? ?f th?t total ?r? shaded. Wh?n writing th? fraction, th? learners m?? write th? total number ?f parts ?n top, ?nd th? number ?f shaded parts ?n th? bottom. ?r th?? m?? write th? fraction correctly, but read ?t fr?m th? bottom u?, ?nst??d ?f fr?m th? top d?wn. ?r th?? m?? us? th? ordinal number terminology incorrectly: “third fourth,” “three fours,” “thirds f?ur,” ?t?. ?h?r? r??ll? ?r? f?v? doors ??u ??n g? ?ut ?t th? Elephant ?nd Castle-and ?v?n m?r? ways t? misconstrue ? simple introductory lesson ?n basic fraction identification.

One imprtant key t? avoiding th?s? instruction land-mines ?s f?r th? teacher t? remember wh?t it’s l?k? n?t t? kn?w. Wh?t ?s ??t?nt??ll? confusing ?b?ut th? subject? Wh?t ??n g? wrong? Wh?t steps ?f learning ?r? prerequisite t? ?th?r steps? ?t ?s helpful f?r th? teacher t? adopt th? attitude ?f ?n actress ?n ? stage play. ??f?r? th? f?rst performance, th? actress rehearses h?r ??rt thoroughly-and naturally, sh? kn?ws h?w th? play ends. ?ut wh?n ?t ??m?s time t? perform ??t ?, Scene ?, sh? acts ?s ?f sh? d?dn’t ?lr??d? kn?w th? outcome ?f th? play. ?h? acts ?n ? w?? th?t ?s appropriate f?r th? b?g?nn?ng ?f th? play.

So th? math teacher sh?uld guide h?r students ?t th? b?g?nn?ng ?f th? lesson w?th th? attitude ?f s?m??n? wh? d??sn’t ?lr??d? kn?w wh?t ?t ?ll m??ns. ?n guiding h?r students’ exploration ?f th? subject, th? teacher’s w?rds sh?uld g?v? voice t? th? questions th?t ?r? emerging ?n th? students’ mind-or th?t ?ught t? b?. ?h? students’ attention must b? skillfully directed w?th simple commands ?nd questions. ??r? ?s ?n example ?f h?w t? d? th?s w?th ? lesson th?t introduces fractions.

The teacher hands ?v?r? student ? copy ?f ? ??g? th?t h?s m?n? pictures ?f fractions (th?r? ?r? m?n? ways t? d? th?s, but pictures ?f “pizzas” will d? f?r n?w). ???h pizza h?s ?nl? ?n? shaded slice, n? matter h?w m?n? slices th?r? ?r? altogether. ?h? f?rst pizza ?s ? picture ?f “?n? fourth.” ?h? teacher s??s, “?v?r?b?d? touch th? f?rst pizza ?n ??ur ??g?. Count ?ll th? slices. Y?s, count th? shaded slice, t??. ??w m?n? slices ?r? th?r? altogether? Write th?t number ?n ? piece ?f scratch paper.” ?h? teacher writes th? number ?n th? board ?nd l??ks t? m?k? sur? th?t ?v?r??n? h?s f?ll?w?d th? directions precisely. “??w draw ? l?ttl? l?n? ?v?r th? f?ur.” ?h? teacher models h?s instruction ?n th? board, ?nd qu??kl? inspects th? students’ work, offering guidance t? students wh? h?v? s?m?h?w managed t? draw th??r l?n? und?r th? f?ur ?nst??d ?f ?v?r ?t. “??w count h?w m?n? slices ?r? shaded… Y?s, ?ust ?n?. ??w write th?t number ?b?v? th? l?n? ??u drew. ?v?r?b?d? touch th? top number ?nd s?? ‘one.’ ??w touch th? bottom number ?nd s?? ‘fourth.’ Wh?t d? w? call th?s fraction? That’s r?ght: ‘one fourth.’ Good. ??w let’s l??k ?t th? n??t pizza.”

[By h?v?ng th? students count ?ll th? parts f?rst ?nd th?n th? shaded ??rt, th? teacher h?s sh?wn h?w t? determine th? denominator ?nd th? numerator-even th?ugh th? specific nomenclature h?s n?t ??t b??n introduced. ?f th? students h?d counted th? non-shaded ??rt f?rst, s?m? ?f them-in spite ?f verbal instructions-would h?v? automatically counted th? shaded ?n?s n??t, r?th?r th?n th? total amount. Task order ?s ?m??rt?nt ?n shaping th? direction th?t th? students’ thinking takes.]

Continuing th? lesson, th? teacher g?v?s exactly th? s?m? directions f?r th? n??t f?ur ?r f?v? pizzas. ?h?n h? tells th? students, “??w turn ??ur pencil ?r?und s? ?t l??ks l?k? you’re going t? write w?th ??ur eraser. Count ?ll th? slices ?n th? n??t pizza. Pretend t? write th?t number ?n ??ur scratch paper. ??w draw ?n imaginary l?n? ?v?r th? number. ??w m?n? slices ?r? shaded? ?h?n write ?n imaginary ‘one’ ?v?r th? l?n?. Wh?t ?s th?s fraction called?” ?w? ?r three s?m?l?r examples follow.

“Now ?ut ??ur pencils d?wn. Count h?w m?n? slices th?r? ?r? altogether ?n th? n??t pizza. Pretend t? write th?t number w?th ??ur finger, ?nd draw ? l?n? ?v?r ?t. ??w m?n? ?r? shaded? Pretend t? write th?t number ?b?v?. Wh?t ?s th? n?m? ?f th?s fraction?”

“Now ? h?v? ? challenge f?r ??u. Wh? ??n n?m? th? f?rst f?v? fractions?” ?h? teacher calls ?n ? volunteer. ?h?n ?n?th?r volunteer names th? n??t f?v? fractions. “??w ? n??d tw? volunteers wh? will ??t ?s partners.” ?h? teacher hands ?n answer key t? ?n? ?f th? partners ?nd s??s t? th? ?th?r partner, “??m? ???h fraction. Y?ur partner will check ??ur accuracy w?th th? answer key. Wh?n ??u answer correctly, sh? will s?? ‘Yes.’ Wh?n ??u ?r? wrong sh? will s??, ‘Try again,’ ?nd ??u will h?v? t? figure ?ut th? r?ght answer.” ?ft?r th? partners model th? n?w activity, th? teacher g?v?s ?n answer key t? ???h pair ?f students, ?nd t?g?th?r th?? practice proving th??r mastery ?f th? n?w lesson.

A lesson su?h ?s th?s us?s commands ?nd questions t? engage students’ natural ability t? notice. ?nd th? noticing ?s directed ?n su?h ? w?? ?s t? avoid potential points ?f confusion. ?h? strategies ?r? simple ?nd learner-friendly: Wh?t d? ??u count? Wh?t d? ??u call ?t? Supervised practice ?s undertaken ?mm?d??t?l?, providing th? teacher w?th ?lm?st instant assessment-and ?t involves ?v?r? single student, r?th?r th?n ? f?w vocal volunteers. Practice ?s safeguarded b? ?mm?d??t? peer feedback, wh??h demands ?mm?d??t? student self-correction. ? lesson su?h ?s th?s m?k?s sur? th?t ?v?r? student finds th??r w?? ?ut th? r?ght exit ?t th? Elephant ?nd Castle.

## Maths Teaching Tip #1-Remembering Whats Its Like Not to Know

Maths Teaching Tip #1-Remembering Whats Its Like Not to Know
Maths Teaching Tip #1-Remembering Whats Its Like Not to KnowMore details about Joe as a Maths Tutor for Junior Cycle and Leaving Certificate (2022), ACE Maths Assessments and Solution Books via the links below.

## How to Improve your Maths Skills

??w t? Improve Y?ur Math Skills

Very f?w people ?r? aware th?t mathematics ?s ? branch ?f science; science enhances technology ?nd technology m?k?s life easier. ?n fact, ?f ??u compare ?ur lifestyle t? th?t ?f th? previous generations, w? ??n call ?urs?lv?s luxurious. Y?u h?v? math t? th?nk f?r th?t, b???us? th? r?ght ingredients ??n b? destructive wh?n us?d ?n wrong amounts.

If th?t ?s n?t ?n?ugh reason f?r ??u t? w?nt t? improve ??ur math skills, th?n let’s zoom ?n t? ??ur personal life. ??th?ng ?n th? market ?s f?r free. ?s?d? fr?m th? basic addition, subtraction, multiplication, ?nd division ??u perform ?n designating ??ur budget, th?r? ?r? discounts t? consider ?nd promos t? join. ??w m?n? miles ??n th? gas ?n ??ur car tank t?k? ??u? ??w m?n? yards sh?uld th? carpet ??u h?v? t? buy b?? D?d ??ur secretary compute yesterday’s expenditures correctly? ??w ??n ??u check? Y?u s??, th?r? ?r? plenty ?f reasons ??u sh?uld invest time ?n improving ??ur math, b???us? ?t will g?v? ??u m?r? confidence ?n dealing w?th numbers ?n daily activities. ??, ??u d?n’t h?v? t? throw ??urs?lf b??k ?n college ?r ?n review centers. ?h?r? ?r? simple ?nd effective ways ??u ??n d? th?s w?th?ut th? additional stress ?r expenses.

An Early Math Challenge

We’re n?t sur? wh?r? th? wacky alarm clock ideas originated fr?m (w? bet th? Japanese influenced th?m ?n?w??) but th?t d??sn’t r??ll? matter ?s mu?h ?s th? fact th?t th?? work. ?n? ?f th?s? ideas ?s t? require th? sleepy-head t? answer ten sets ?f equations ?n basic mathematics f?r th? alarm t? st?? ringing. ?h?? ??n g?t annoying, ?s?????ll? ?f ??u ?r? n?t ? morning person, s? ?ust concentrate ?n ?ts benefits. F?rst ?nd foremost, b? th? time ??u finish ?nd silence resumes, ??ur brain w?uld b? t?? awake t? b? seduced b??k t? sleep.

Second, ??u will b???m? m?r? alert th? longer ??u undergo th?s morning math surprise, ?nd third, ??u will master th? basics ?f math w?th?ut ?v?n knowing ?t. Time pressure ?nd noise will n? longer b? ?n?ugh t? distract ??u fr?m coming u? w?th th? correct solution.

Download th?s kind ?f applications ?nd install th?m ?n ??ur mobile phone. ??k? sur? ??ur thread ?f patience ?s long ?n?ugh b?f?r? ??u attempt th?s. ?th?rw?s?, ??ur poor phone m?ght ?nd u? ?n th? floor, crushed t? pieces.

The Advantages ?f Lending ? Hand

The n??t time ??ur son ?r daughter asks ??u t? help th?m w?th th??r math homework, s?? ??s ?nd g?v? ?t ??ur best shot. Learning m?r? ?b?ut math ?s n?v?r ? loss, ?nd ?n th?s instance, ??ur interest ?n numbers m?? influence ??ur child t? d? better ?t school.

Teenagers ??n offer after-school tutoring f?r free ?r f?r ? ??rt??n amount ?f money. G?tt?ng paid f?r assisting ?th?rs ?n math education ?n Ireland ??n b? ?n effective motivation t? study ?t furth?r. Y?u w?uldn’t w?nt t? teach ?th?rs th? wrong things, w?uldn’t ??u? ?h? people ??u teach m?? ?ls? add t? ??ur current bank ?f knowledge. Math ?s l?k? ? maze, th?r? ??n b? m?r? ways th?n ?n? t? g?t t? ??ur destination.

A Virtual Learning Experience

Math help n??d n?t b? boring, ?nd th? f?rst tw? examples ?r? proofs ?f th?t. ?h? worldwide web ?s ?n?th?ng but dull. Online mathematics courses create ? suitable playground f?r modern minds. Lessons ?r? commonly presented ?n th? form ?f game, puzzles, ?nd trivia, keeping users easily engaged. ??m?l?r t? th? approach ?f th? f?rst examples, ??ur attention ?s diverted fr?m improving ??ur math skills t? interacting w?th ?n entirely d?ff?r?nt ?nd enjoyable game.

During ??ur free time, ??u ??n boot u? ??ur laptop ?r bring ?ut ??ur mobile gadgets t? access th?s? math applications. Killing time h?s n?v?r b??n th?s fruitful.

The Brain ?s ? Powerful Tool

A computer system ?s patterned ?ft?r th? human brain. ?f ??u th?nk th? f?rm?r ?s impressive, th?n ??u sh?uld b? ?n awe ?f th? l?tt?r. ?ut t? maximize ??ur brain’s greatness, ??u h?v? t? exercise ?t. Avoid us?ng calculators wh?n d??ng ??ur grocery ?f summing u? ??ur monthly bills. Calculate mentally wh?n?v?r ??u ??n, ?nd bring ?ut ??ur gadgets ?nl? t? check wh?th?r ??u ?r? correct.

This practice m?k?s ??u l?ss reliant ?n tools ?nd m?r? confident ?n ??ur skills. ?t ?ls? saves time, energy, ?nd space ?n ??ur bag. ?h? n??t time ??u s?? numbers, g?t excited ?nd start jogging ??ur brain. Y?u will b? shocked b? th? results.

## How to Improve your Maths Skills

How to Improve your Maths Skills
How to Improve your Maths Skills
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.

## Log Tables

Click here to download the `Log Tables `

## Log Tables

Log Tables
Log Tables
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.

## Leaving Cert Mind Maps

Leaving Cert Mind Maps

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.

## Constructions 2013/2014

LC Students, here are the constructions you need to know for 2014 Exam

Construction List 2013_2014

16 Circumcircle of a triangle

17 Incentre of a triangle

18 Angle of 60 degrees

19 b. Tangent to a given circle at a given point on it.

20. Parallelogram, given the length of the sides and the measure of the angles

21. Centroid of a triangle

## Constructions 2013/2014

Constructions 2013/2014
Constructions 2013/2014
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.

## Geometry Theorems – JCH, LCO and LCH

Junior Cert Honours Level – Students need to be able to formally prove Theorems 4,6,9,14 and 19 and need to be familiar with 1-6, 9-15 and 19

Leaving Cert Ordinary Level – Students need to be familiar with Theorems 7-8, 11-13, 16-21 and Corollary 6

Leaving Cert Higher Level – Students need to be familiar with Theorems 7-8,16-18,20-21 and Corollary 6 and need to be able to Prove Theorems 11-13. Students also need to be able to prove Junior Cert Honours Level Theorems 4,6,9,14 and 19
Theorems 1-21
Theorems 1-21 Powerpoint

## Geometry Theorems – JCH, LCO and LCH

Geometry Theorems – JCH, LCO and LCH
Geometry Theorems – JCH, LCO and LCH
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.