Showing posts with label Practical Maths. Show all posts
Showing posts with label Practical Maths. Show all posts

Mathematics Exam Resources Website for PNG students and teachers

Your initiative (Mathematics Examination Resources website) is welcomed as an approach students can prepare themselves well ahead of examinations.

Consequently, the issues and challenges are briefly discussed to deepen members of the public perceptions of the examination papers, examination, teaching and learning, school curriculum, memorisation and thinking strategies.

Readers' note: The comments are by/from the former PNG Education Department Secretary Dr Michael Tapo in response to the new initiative we spearheaded - making online resources for teachers and students. We thank Dr Tapo for reaching out and for the comments below.
The math resource website is called Mathematics Examination Resources (MER). Here is why (The Reason) we created this Maths resource website. Take a look and let us know what you think.

An in-depth article from Dr Tapo was published on the PNG Insight parent website titled 'Thinking Strategies' Help Students Solve Problems' - read here.  

Immediate challenges in educational approaches

Central to all of the approaches taken, the century-long learning phenomenon of Thinking versus Memorising of facts in the late 1960s -1980s is worth revisiting. Approaches such as:

  • students were routinised memorising of facts, and
  • learn to remember and then display this in Grade 6, Grade 8, and Grade 10 examinations. 
When they fail to understand the examination questions and cannot remember the facts they fail to meet the achievement level for high school or tertiary and university education.

Problem Solving and Thinking Strategies

School education examination in Papua New Guinea (PNG) from 1975 to 2020 and beyond is all about Knowledge Gathering and Remembering and is significant and very much dependent on the quantity of teaching, quality of teaching, and teacher quality.  

The problem has been and continues to be so and is an urgent and acute problem associated very much to Problem Solving or best described as Thinking.

Almost all high and secondary school education in Papua New Guinea failed to focus Problem Solving Strategies. And have limited teaching and learning strategies that address the scientific approach (of teaching thinking strategies) required to solve problems.  Hence, its an apparent strategy and definite means to know the facts from knowledge and skills taught and learned in primary, high and secondary examinations.

We know revising for exams is important because it helps to stop anxiety and stress. We created a Maths website where you can download Grade 8, Grade 10 and Grade 12 General Maths and Advanced Maths Exam Papers. GET THEM HERE.

Importance of teaching the syllabus 

The amount of time spent in teaching and learning mathematics, Science and Grammar is interconnected to the number of multiple practices each child assumes in class in these subjects is significant to avoiding dependency on past and recent examination papers. 

The current culture of schooling and learning is dependent on schools and teachers must teach children more and make them work harder to increase their information on the level of knowledge and skills planned around the subject learning being learned.  

Foremost, the level of individual child intelligence and termly achievements in a subject learning area must be corrected with the facts (knowledge and skills acquisition). Students primarily learn best if they can remember these facts. 

Knowledge and skills being examined 

The ambiguity of language and phrases used in the past and more recent examination papers indicate the facts of knowledge and skills being examined can or could lead to confusion.

Some questions can mislead students to select or choose to answer a question in future examinations because of a similar question and answer from the past examination papers and likely answer that is expected in the 2020 or 2021 examination papers.

The quest for high and secondary examinations is placing more emphasis on the thinking strategies which lead children to creativity, problem-solving, inquiry, and critical approach to thinking in a subject learning area being learned. 

Expectations and clarity of examinations 

Papua New Guinea children in the 21st Century must be encouraged and have a voice in determining what is taught in the National Curriculum, what is examined and the rules applied to assessing and measuring of facts in knowledge and skills in examinations.

Quality of teaching and teacher quality needs major shifts towards thinking strategies and say goodbye to the current heavily dependent ideology of the 'chalk-talk and certainty principle which is central to the there is a right and wrong answer to every question! 

Dr Michael F Tapo, EdD 

EXAM RESOURCE FOR GRADE 8, 10 and 12 STUDENTS | Download Old Exam Papers

We know times are hard. Schools have been struggling this year. That is why we made this website - PNG Maths Exam Resources (MER) Website.

Exam questions and Answers

PNG Insight created this website to give teachers and students the opportunity to access materials - especially revision materials  old exam papers for Mathematics Examinations - with ease. It is a community service as such the resources are made available for FREE.

The website is mobile friendly and interactive, which means you can take some tests online and get the scores and feedback at the end of the test. 

Features of PNG Insight's MER

 We had some great features to enhance math exam revision. Some of them include:

  • Old Exam Papers for Grades 8. 10 and 12 students to download
  • Online Practice Test Questions with Answers. Feedback is also provided at the end of each test.
  • Teachers Mathematics revision resources for use with students 
  • Education department Apps and Links to on-demand webpages
  • Maths Examinations Tips and Guides

Latest features of MER: Online Skill Practice Test and Answers

There are two latest additions to the MER website. First, the Basic Numeracy Skill Online Test/Assessment. It is basically a check-point of the functional ability (learnt skill) of students at upper primary and lower secondary schools - Grades 5 - 8. 

There are 50 multiple choice questions arranged by difficulty level from low to high. The test is split into 4 parts - each takes less than 5 minutes to do. See it here.
Online skill test revision

Latest features of MER: Free Download of Grade 10 Old Exam Questions & Answers (2010 - 2014 Math Exam Qtn Compilation)

 The second feature is the compilation of 2010 - 2014 Math Exam Questions by Unit. Free to download and use. Great for both teachers and students at Grade 10 

If your child, a sibling, friend or someone you know is in Grade 10 encourage them to check out the past exam papers and revision materials on the *new* website, MER
math exam questions and answers PDF

The resource booklet is 33 pages, but quick to download as the PDF was compressed to just 3.45 MB (from a 16.9 MB). 

It is watermarked to protect the originality of the document. If you want to remove the watermark and use it in class or for other educational purposes, please email us at

Visit the Grade 12 General math and Advanced math old exam papers pages here> GM/AM revision materials

Please do share the work or leave a comment. Enjoy!

8th Grade Math Test Paper with Answers

The 8th Grade math test paper with answers PDF is useful. It contains classroom tests questions on Algebra.

(This is an updated version of our US visitor)

You can download the free test paper at our Math Resource Website. First, here are some important points that you should know when revising for your math tests.

8th Grade math test paper with answers PDF

What to expect in your test?

Your math teacher often sets the test from the easiest question to the hardest. Where there are short-answer questions, you’ll see the easier ones at the top and the harder ones at the bottom. Here are some quick tips:

  • The one-mark questions need no working out. Always write the answers clearly and include the units where necessary. 
  • Most questions will need working out whereas others will ask you to give reasoning. Take time to do the higher-order questions if they carry 3 - 5 marks.
  • The 8th Grade math tests marks can range from 30 – 50. You should be able to complete them in one period, 40 or 50 minutes. Some end-of-the-year tests do often have more than 50 marks and can take up to two periods in duration time.

Read the instruction carefully

Your teacher will expect you to do certain things. These expectations are often given in the instructions. So, it is important to read the instructions and know what you must do to get full marks.

Here is an example of instructions you are likely to see on your 8th Grade math test papers:

  • You may use a calculator.
  • Read all questions carefully.
  • You will need a ruler.
  • You have 50 minutes to complete this test.
  • Show all you working in the space provided.
  • 8th Grade math test best practices

Do not spend too much time on one question if you find it very hard to do. Move on and attempt the other test questions. Return to the hard question/s when you have time in the end.

For example, if you have 50 minutes to do 40 test questions, that is 1.25 minutes per question. Some questions may take less time, but all in all, you should NOT spend 2 minutes or more on one question. By doing this, you’ll have time to answer all the questions.

Using the 8th Grade math test paper with answers PDF

This is a real test for Year 8 students. It’s on Algebra. The questions are ideal for Year 8 students from the UK and Australia. 

If you are an 8th Grade student from the US, you'll find these Algebra questions useful too.

Get the 8th Grade Algebra test paper with answers PDF

Where to get more 8th Grade math test questions and topics PDF?

The resources on our math website are free of charge. We’ve created it to help students who need these math resources to do well in tests and exams. 

What’s more, we want to ensure that math questions are available to students when they need them.

Get the 8the Grade Algebra test paper with answers PDF

Here are resources that will help you to prepare for Year 8 tests and exams. You can get them via the links below.

8th Grade math test papers PDF

All in all, if you are an 8th Grade parent or student, we hope you find these math test questions useful.

Visitors note:

We produced a lot of math resources like this - let us know what you are looking for and we will direct you to the right pages to access them.

If you have any questions about the 8th math test papers with answers PDF, please leave a message below. 

Online Maths Games for Kids and Toddlers

Giving children an early start in education is every parent's wish. Many studies have supported the fact that preparing children early - before they start school - sets the foundation for future success in school.

For keen parents wanting to give their children a better start, there are many educational programs (and smartphone apps) available for free; as well as those that are purchasable. 

But, knowing the right option, age-appropriate for younger children can be a hassle. 

This post identifies one highly recommended learning program for children - Reading Eggs.

Online Maths Games for Kids and Toddlers

The Reading Eggs is a fun-filled educational software for children ages 3 years old to 13 years old. 

Parents of children who've used the software have seen *significant* improvement in their children's ability to read and write and learn about numbers.

Why Reading Eggs?

The Maths Factor is another learning program available, but I am also a fan of the Reading Eggs. One of the best features of Reading Eggs is the *Reward*. 

The Reading Eggs reward system motivates kids to keep exploring and learning.  My kids have used it since they were 3 years old – fantastic learning program, highly recommended. 

Here is a brief citation from Reading Eggs:

“Children love the games, songs, golden eggs and other rewards which, along with feeling proud of their reading, really motivate children to keep exploring and learning.” Reading Egg (accessed 23/11/2017)

Reading Eggs Maths Online Games

Many parents of young children have recommended Reading Eggs. Your children can have fun and learn to read, early, both at home or when you are out and about.

Perhaps giving children the best start early in life is the best thing to do as parents. This paves way for both academic success and success in life - reading is a life skill and every child should know how to read. 

The best way to learn how to read is to learn about LETTER SOUNDS. Find out how you can help your child learn letter sounds as the first of the 5 steps of learning to read by following the link.

Reading Eggs Fun

The 5 points are the main reasons why Reading Eggs is proven to be popular among many parents:
  • 1.  Cater for children ages 3 – 13 years old;  
  • 2. Highly interactive and reward-based – children play, earn points and learn;  
  • 3. Accessible via Personal (Home) Computers and Smartphones;  
  • 4. *Free* online trial permitted - no need to enter bank card details prior to the unlimited free trial; 
  • 5. Over 90% of parents indicated noticeable *improvement* in their children.

DIY: Build a Bookshelf And Save, Customised To Meet Your Preference

If you have lots of books and wanting a bookshelf, the obvious choice would be to buy one. Take a look at the prices of bookshelves at Courts. I bet the other retailers have the same prices, if not more. You may not have the time to build one. That is okay. All you have to do is buy it. But any DIY person would know the satisfaction that comes with building something.
Courts' Price at March 2016
I spent K157.20 to build this bookshelf - 110 cm (H) x 30 cm (W) x 140 cm (L).  Such a size bookcase would, ideally, cost around K500. Despite the fact that it may not be professionally done, it is practical, stable and above all met the need.

Six stands (taken from a crate) providing lift to slot nicely into back wall; rope attachment at the back as 'stopper'

Perhaps the important fact behind DIY idea was that I saved more than K300. Additionally, I now have materials (nails, off-cut timbers), tools and knowledge and skills to make the next one better.  I only have to buy good quality timbers to make it look great.

It would be smart to paint the finished shelf. I have decided to use wood stain or vanish, but I considered them to be too expensive. That is why the first bookshelf has not been given any TLC. I planned to build a couple more. Hopefully they will get the Tender Love and Care they deserve…

I’ll provide some tips (with photos illustration) for building a bookshelf in my next post (a step-by-step guide). So, if you would like to get some inspiration, join me on Google+Twitter or Facebook for update. 

Here are some vital materials, tools and information I used in the making of the first bookshelf shown in the above photo.

Materials used
1.       Nails: One, two and three inch nails
2.       Timbers: 4x1 , 1x1, 2x1 (some of the timbers & nails are taken from a used crate)

Tools used
1.       Hammer
2.       Hand Saw
3.       Tape Measure
4.       Square
5.       Nail punch (option: use a 5 inch nail)

Other useful info
-          You can ask for the timbers to be cut to length at the timber yard before taking them away. Instead of using your hand saw, the electric saw they use at the timber yard gives a fine cut, ensuring perfect fit.
-          Always take the off-cut with you. They are useful.
-          POM residents, hire vehicles are usually on stand bye at most timber yards. Keep an eye out for them if you need help with transporting timbers.
-          The timbers have been sourced from UAA Timbers, behind Big Rooster, opposite TST Boroko 4 Mile.

-          Price and receipt attached (Take note of the Unit Price)
Unit price: K2.50/m 20x20cm | K4.80/m 4x1 inch

What Can Papua New Guinea Curriculum Developers Learn From Singapore’s Maths Mastery Lessons

Researchers in the article (shown on the right) compared mathematics ‘teaching methods’ in the UK to the Singaporean method. Their finding revealed that ‘students taught using problem solving strategy learn faster than their counterparts – ‘making an extra month of progress in a calendar year’.  That’s impressive.

Another point worth reiterating is that student’s ability to do well in maths can be enhanced by tweaking it at certain time. 

The report highlighted that ‘even a small enhancement at age 10 yields long term economic benefits for individual and the country’.

Singapore’s maths mastery concentrates on problem-solving

If PNG students were to do well in mathematics, maths teachers have to look at ways to create resources targeted at developing student’s problem-solving skills, ideally students between the ages of 9 and 16 years. 

Take a look at Singapore’s mastery class. A good example has been indicated – using three wooden bars to find three consecutive numbers that add up to 42. Papua New Guinean (and English, US, NZ and Australian) teachers would solve this by trial and error or by using algebra.

Method one: By trial and error - choose 3 numbers at random. Start at 10, 11, 13 (=34); 11, 12, 13, (=36); 12, 13, 14 (=39) and 13, 14, 15 (=42)

Three numbers are 13, 14 and 15

Method 2: By using algebra - let the first number be x, second number x + 1 and third number x + 2

            x + x + 1 + x + 2 = 42
             3x + 3 = 42
             3x       = 39
                       x       = 13

Three numbers are 13, 14 and 15

Maths Mastery Lessons Singapore

Importance of Maths Mastery Lessons 

This is not about a complete shift in teaching styles. This is about enhancement – creating ‘power lesson’ effective enough to enrich students ability on a weekly or monthly basis.

The importance of helping students to learn faster and think for themselves is far superior to preparing students for examinations. There has to be a balance between building strong problem-solving skills and preparing students to achieve good grades. 

What Singaporean schools have done can also be done in Papua New Guinea. Giving students the best possible opportunity to improve their maths skills on a regular basis, and above all, prepare them for life.

Practical Mathematics: 4 Easy Skills To Aid Mental Calculations And Beat Non–calculator Exam Questions

Here are four mathematical skills you can use in any situation when shopping or dealing with everyday numbers. In fact, having these skills can make you a better maths student – also will help to add, subtract, multiply and divide accurately. 

1. Easy Adding


Skill: Separating numbers into parts, then add

If you can see parts like 20, 20 and 10 (add to 50) and the other 50 make an easy 100. 

Also, 7and 3 (=10) and 8 and 2 (=10) gives 20. By doing this you can get 120 (100 and 20) without having to use a calculator. 

2. Easy subtracting 


Skill: Ensure last digits end with the same number (353 and 33), then subtract in parts
The idea is that the same numbers result in zero, making calculation easier.  

3. Easy Multiplying 


Skill: Separate on number (usually the smaller number) into parts, multiply each out, then add. 

3. Easy dividing 


Skill: Identify a multiple of the divisor (24 is a multiple of 12 closest to 33), and simplify


Many changes are happening in PNG's education system. Change in structure (in 2016) and change in the curriculum (2015, OBE to SBE) are two significant educational changes. The changes must be equally complimented by good learning content (syllabus).  

Methods above are examples of creating effective learning contents, especially when introducing mathematics in class. 

Traditional mathematics and practical mathematics are still grey areas in PNG mathematics syllabus. The examples I gave above are illustrations of practical mathematics – you can do a mental calculation using those skills when shopping or doing other everyday math. 

Traditional mathematics skills are those that you may require a pen and paper to work out the answers.  Our parents are very good at such working out. But, if we are to make a nation of quick thinkers, we’ve got to introduce practical mathematics for everyday use – not just to help in tests and exams. 

Take above as examples of how mathematics in the classroom can be streamlined to prepare students for life. 



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