Square roots are found in many science and maths problems, and students must know the basics of square roots to tackle many questions. Square roots are indispensable in various fields like calculus, engineering and virtually every career path of the modern world. Solving equations involving square roots is an important skill in algebra, so kids must understand the simple square root concept.

Basically, the square root is a number that when multiplied by itself provides the original number. For example, the square root of 100 is 10 and the square root of 0 is 0. Also, every root has a positive and a negative answer, so the square root of 4 = 2 and also -2. This is because 2 squared is four and -2 squared is also 4. But most kids tend to remember the positive answer only. So, √4 = ±2, with the ± standing in for “plus or minus.” Although answering just 2 is acceptable in many cases, particularly when a negative answer does not make sense for the intended application. For example, if the solution to the square root is the answer to a question involving dimensions of a prism, only the positive solution is applicable.

Why is this simple concept so often forgotten?
A lot of kids forget this concept since they are introduced to negative numbers later on in their schooling and different topics are segregated in primary school and early high school. This makes it hard for students to integrate topics as they progress to more advanced levels of mathematics. My theory is, students learning about surds will no doubt be explicitly taught about the plus/minus answer and remember to apply it, but then set that knowledge aside when learning about polynomials or algebra.

How to help students remember this outside of its direct teaching?
It is essential for us to remind our kids that the answer to a positive number's square root will always have both a positive and negative solution.

As students tackle problems independently, they are likely to make mistakes by omitting neative solutions. As they study, they are likely to learn from these mistakes and begin to make them less often. This is why it is so essential for students to learn and practice a variety of study techniques as part of their homework routine from a young age. With the recent return to school, teachers can begin introducing positive study techniques and habits into their daily classroom routine.


Similarly, we should emphasise that negative number do not have real square roots, because a real number cannot yield a negative value when multiplied by itself. Therefore, a negative square root of a positive number is often ignored. For example, they will give an answer for the square root of 361 as 19 rather than -19 and 19.

It is important for students to understand that the negative root exists, but the positive answer is often the preferred choice.

Overall, kids often forget this concept, so parents and teachers must make an extra effort to remind that every number will always have two roots – a positive and negative. It is then up to them to answer the question with consideration to the practical application.

Education Minister James Merlino announced the reopening of schools on Monday 12th of October. The decision to return to onsite learning was based on the updated public health advice and the current situation in Victoria, where experts see the region’s progress in defeating the second wave of Covid-19.

Since October 5th, students in specific year levels begun the transition to onsite learning. Yesterday, all primary students in years P-6 returned to school. Students in years 7,11 and 12 arer also returning to school this week, though schools have the option to stagger the return depending on local circumstances.

However, based on Victoria’s reopening roadmap, it is expected that all students in Prep to 6, Year 7, 11, and 12 will be back onsite by Friday 16th of October.

How to help your child transition back to school
Due to the coronavirus, returning to school this October feels very different. In fact, parents and children are expected to feel overwhelmed with greater levels of stress and anxiety, especially when there’s a threat of contracting and spreading Covid-19 at school.

While stress and anxiety levels may be high, it’s essential for parents to help their children cope with this transition and reduce their worries. There are several ways to encourage a positive back-to-school transition, and these will include the following:

• Have an honest and open discussion with your children

It’s important for parents to have an honest, factual and open conversation with your children, especially when it comes to Covid-19 and the implications of the return to school. You should also reiterate their role in staying safe, like washing hands, avoiding touching their face, using hand-sanitizer, and keeping distance from other students when in school.

• Identify fears to tame fears

Parents should also use the name-it-to-tame-it strategy wherein they will identify the current concerns of their children and what they should do about it. With this strategy, you should label your child’s fears and the things they can do to avoid or at least lessen the impact this fear has on their lives. You should also acknowledge that there are things that are out of our control, and it’s best to just focus on what we can control.

• Model a calm behaviour

It’s okay for us parents to be worried, but we must always show a calm and confident attitude to our children. When they’re returning to school, it’s best to give your children some positive messages since this can encourage them to have a cheerful attitude. Talk to them about the clusters of cases and how unlikely it is that the virus will reach their school. But, for extra safety, they just need to follow the standard health protocols in their school.

What differences to expect in schools
All students will now be required to wear masks and do frequent hand washing when inside the school premises. Some schools might also limit the number of students per classroom, so this means that they might re-arrange the sections or extend school hours in order to implement the social distancing rules set by the government.

What to do if you or your child feel unwell
The first thing to do if you or your child feel unwell is to call your healthcare provider in your area as soon as possible. It’s also recommended that you organise a test for Covid-19 and quarantine your child and yourself inside your home while you wait on results. This will prevent any possible transmission and determine the cause of your child’s illness.

You or your child may also get a flu vaccine which can reduce the likelihood of being sick or hospitalised.

Overall, it’s essential to help your child to cope with the challenges brought upon by this pandemic. Therefore, you’ll need to have a proactive mindset as you support them though the return to onsite learning. If your child is in need of a tutor for Maths in Melbourne, contact us today!

If you’re preparing for VCE, it’s essential to know which maths subject to select. In fact, the subjects you’ll be choosing may influence your options beyond high school. You’ll need to set your goal, and what knowledge and key skills a particular subject can provide, especially if it’s required in the career you are pursuing.

You must also know if the maths subject you’re taking will be relevant to the areas or fields within your career path.

Here are some of the things you’ll need to know when choosing maths subjects within the VCE curriculum:

• Foundation Mathematics

Foundation maths is for students who want to develop their mathematical skills and use it in practical contexts, which is required in everyday life in the community, at study, and at work. Also, if you do not intend to undertake Unit 3 and 4 studies in VCE mathematics, then this is the viable path for you.
Another thing to remember about Foundation Maths is its strong emphasis on areas that include shape, space, design, patterns and numbers, measurement, and data. Students will tackle various techniques, processes, and routines involving real and rational arithmetic, lists and tables, diagrams, geometric constructions, equations and graphs.

Therefore, by undertaking these units, students are expected to use by-hand and mental approaches to computation and estimation. They should also have developed graphical, numerical, symbolic, and statistical functionality of technology for learning and teaching mathematics.

• General Mathematics

General Mathematics is designed to prepare students to undertake unit 3 and 4 Further Mathematics. The areas of study covered within this subject will include arithmetic and number, algebra and structure, discrete mathematics, trigonometry and measurement, geometry, statistics, arithmetic and number, graphs of non-linear and linear relations.

In addition, content covered in this subject is a clear progression of knowledge and skills from Unit 1 and Unit 2. So, students are expected to be able to use estimation, computation, by-hand, and mental approaches to solving problems.
 

• Mathematical Methods Unit

Mathematical methods units 1 and 2 provide an introductory study of several areas, which includes probability, statistics, algebra, calculus, function of a single real variable, and their applications in various theoretical and practical contexts. These are also designed to prepare students for Mathematical Methods Units 3 and 4, which contain assumed knowledge from these units.

In units 2, the focus is more on simple transcendental functions and calculus of simple algebraic functions. At the end of units 2, students are expected to have learned the content outlined in these units, and they must be able to apply the techniques, routines as well as processes they have covered in this subject.

• Specialist Mathematics Units 1 and 2

Specialist Maths is for students who wish to acquire an in-depth knowledge of mathematics. This subject will provide a course of study with emphasis on concepts and skills as well as processes that are related to modelling, mathematical structure, problem-solving, and reasoning.

So, if you have an interest in the discipline of mathematics and to have a sound background for further studies in maths and its related fields, then you should take this subject.

Overall, be sure to choose the subject(s) that interest and challenge you, but are not so difficult that they consume all of your study time, causing anxiety over poor grades or failure. 

Do you need to know when to start preparing for exams? Click the link to learn more

Maths and science are frequently associated with each other because mathematics assists in our understanding of biology, chemistry, geology, astronomy, physics, and psychology. In fact, students are required to master foundational mathematics in order to read scientific charts and graphs.

More complex maths like algebra, geometry, and calculus can help students solve problems in chemistry and understand planets' behaviour in astronomy. Mathematics is also important in practical sciences such as computer and engineering science since students will be required to solve equations when developing algorithms and writing intricate computer programs.

Even medical subjects require mathematics like how to precisely calculate dosages or create medical charts that record an individual’s clinical status, history, and caregiver involvement.

How maths comes into play when learning science
Physics and maths are closely connected subjects, and mathematics, particularly calculus, is commonly used to solve scientific problems. In fact, electromagnetism and classical mechanics are all related through calculus. The movement of objects and its inertia, including the total energy of objects can be found using several concepts in calculus.
 
In chemistry, math can be used for a variety of tasks like balancing the equation of a chemical reaction. Mathematical calculations are also essential to explore concepts in chemistry like utilising the dimensional analysis to get the reactions of various elements and the concentration of chemicals in a solution.
 
Chemistry also required calculations for the compression of a gas, energy released in reactions, or the amount of chemicals needed to reach the desired concentration, and quantities of reactants to added.
 
In addition, mathematics also plays a key role in biology, especially in the creation of mathematical models. These are mathematical equations and formulas that can describe or predict natural events. A good example is the behaviour of a particular organism or the changes in their population over time.
 
These mathematical models can be utilised in a variety of ways, but the main goal is to effectively measure a phenomenon without relying too much on raw, numerical data. Even the spreading rates of diseases and frequencies of gene expression can be calculated using mathematical models.
 
Psychology is another subject that needs mathematics, especially statistics since students must interpret tables, graphs, and statistical analyses. They also need to design quantitative research studies as well as reporting results. Statistical knowledge is also vital for critical and analytical skills that psychologists need to understand and study complex human behaviour.
 
Overall, students must learn and understand several maths concepts since these are essential in learning science. Therefore, one must complete several learning activities in each subject so they can develop a better understanding of both subjects.
 
If they pursue a career in science, they will eventually use mathematics in real-world practices, especially in their work.

If your child is looking for guidance in either maths or science, check out our online tutoring options.

Mathematics has a specific language, and students must learn and understand it so they can apply this knowledge when solving mathematical problems. Therefore, students must be able to interpret this language in a range of mathematical contexts before they can develop a deep understanding of it.
There are three required types of vocabulary that students need to be able to solve word problems, and these will include the following:

• Descriptive vocabulary
• Procedural vocabulary
• Mathematic vocabulary

It is essential for students to explicitly learn these types of vocabulary since it will give them the proficiency to move between written, symbolic notation, oral language, and graphs and visual displays. This will develop their familiarity with mathematical grammatical patterns, use of synonymous verbs, logical relationships.
 
How to effectively develop an understanding of mathematical language
There are various strategies that teachers can use to develop the literacy and understanding of their students when it comes to mathematical language. These will include:

• Translating from words to symbols - students must recognise terms or phrases that can be translated into mathematical symbols. In fact, they should be able to effectively perform this translation, especially in situations where symbols are predictable, and scaffolding is provided. Another situation is when they must decide on which prior knowledge must be implement (without scaffolding).

That is why teacher-led discussions must be implemented because this will provide students the opportunity to read worded problems and identify which words can be translated. However, it is important for teachers to explicitly share their thinking and decision-making as they identify crucial mathematical translations and how this translation should be done.

• Helping students understand mathematical terms and notation – teachers must effectively teach various conventions since students must have learned this before they can interpret letters correctly in context. Therefore, these concepts should be explicitly taught to students during the learning and teaching cycle so they can adequately build their knowledge around it.

 

• Mathematical versus everyday words – the aspect of mathematical language may confuse students as it may create ambiguity between several terms used in a maths classroom. Teachers must be able to clarify when they encounter a range of common words that have different meanings in mathematics. A good example is the word ‘square’ which is a special ‘rectangle’, even though some students may classify a square as a rectangle. Also, the word ‘sum’ might be referred to as a calculation, but teachers must clarify that ‘sum’ formally means addition.

Using the power of storytelling and narrative to bolster students’ insights
In math classes, students usually approach challenging word problems by annotating, reading, and writing to get their meaning. Therefore, students must learn how to break the problems down into smaller parts so they can master difficult concepts.

In a classroom setting, teachers must read the problem, then students read and paraphrase the problem. Together, and then individually, the whole class can break problems down, as well as translate them to aide in their interpretation. This method will foster both individual and group learning and bolster their insights.

Lastly, the teacher must also provide an opportunity for students to discuss their reasoning since this can enhance their understanding of the mathematical language, and point out some misconceptions that the teacher can correct along the way.

As educators, our tutors have a good understanding of maths literacy and how to help students learn and apply associated skills. Learn more about our remote tutoring options

In all successful teaching and learning relationships, the relationship between the tutor and student must be built on trust and mutual respect. The main focus of the lesson is tailored to one person’s needs, interests and abilities, so the tutors understanding of each of these aspects is paramount. This also provides an opportunity for the tutor to try a variety of teaching techniques that might help the student to understand a topic effectively.

These are the strategies we’re going to discuss on this blog post, and I’m sure it will provide tutors some inspiration, especially when it comes to alternative and sometimes complementary ways of tutoring.

1. Build rapport and get to know your student well (including interests and preferred learning styles)

Rapport is the glue that makes the tutor/student relationship productive. So, the main aspect of a tuition session is to be able to read your student and make them feel at ease. It’s recommended that you talk to them in a plain but respectful way and ask them about their interests and learning styles. Once rapport is established, students can easily open up, and they may even tell you their struggles, especially when it comes to their academics.

1. Get an idea of the topic which will be a focus so you can prepare

The key to an effective tuition session is a well-prepared and individualised lesson plan, and this can only be accomplished when you know the concepts that your student wants to work on about. That is why collaboration and communication are essential to your success since you’ll need to reach out to your student as well as their parents and map a better plan for learning.

1. Teamwork

Ask your students to highlight, underline or write down any questions or concepts they don’t understand. This way, you won’t waste time trying to assess their prior learning and get straight to the concepts and ideas they are struggling with. If all questions are similar, you might be able to create a summary together after helping them work through the tough questions.  

1. Summarize each idea conceptually with an emphasis on when to use this skill

An effective tutor will always summarise each concept they have discussed with their student. This will emphasise the importance of each idea and when they can use them in solving problems. It could also be useful to link each concept with others that are relevant or may be used in parallel.

1. Demonstrate a variety of revision techniques for your students to use for test and exam preparation

There are various revision techniques, but each student is unique, so one method might be useful while others may not apply to your student. That is why you should demonstrate a variety of techniques to your student and let them use the method that is more suited to them. 

Learn more about our tutoring services here: ​https://www.mathstutorsmelbourne.com.au/online-tutoring.html

If you're planning to become a maths tutor, you need to understand that exceptional math skills are not enough. You might also be good at conveying maths lessons to other people, but there are many things to consider before you become a qualified and proficient maths tutor.

We will discuss all these factors in this article, so I urge you to read on. Before you decide to become a maths tutor, you must first answer these questions:

• Why do you want to be a tutor?

You'll need to get your intentions right before you embark on your journey as a tutor. If your main goal is to make a positive difference in students' lives, so this means you will work with both children and young adults teaching, supporting, and empowering them to achieve their full potential, then becoming a maths tutor is the right path for you.

In fact, if you have aspirations to become an educator, you will most likely succeed as a tutor because you already have the right mindset and traits to become a good teacher.

• Do you have the right credentials/qualifications?

A tutor must have the right credentials and qualifications, so being enrolled in or having an undergraduate education degree is a must. This will give you a significant edge over tutors who have no aspirations to become educators. If you are not yet a qualified teachers, you'll need to apply for a working with children check since this is a requirement for anyone who work with or care for children in Victoria.

Lastly, as a qualified teacher, you will need to register with the Victorian Institute of Teaching, because teachers, who are practising in Victoria are required to register with VIT.

• How do you market yourself or apply for jobs?

There are several ways to get a job in Victoria if you're a maths tutor. You can register on various job portals for tutors like Tutor Finder, GumTree, Airtasker, AllJobs, and Australian JobSearch. Make sure to list all your qualifications, credentials, and experience as well as proofread your bio; you'll want to make a good first impression to your potential employers.

You can also take advantage of social media sites like Facebook where you can find various community groups to connect with. LinkedIn is also a good site for job seekers since you can create a public and private resume or connect with potential clients and employers.

• How do you prepare your maths lessons?

 Once you are hired as maths tutor, you'll want to make a positive first impression and get your students underway on their learning journey. It is essential to find out as much as you can about your student and the math topics and concepts they need help with.

Lessons must be prepared a few days before the actual tuition session so you can adjust the topics needed by your students. The important thing here is to guide your students as best as possible by determining their learning needs and helping them cope with their schoolwork.

Overall, a maths tutor is a fulfilling vocation because you're helping students help themselves by guiding them until they reach their academic goals or become proficient with maths. Click here if you need help determining how much to charge.

Many students dread calculus because they think it’s a subject that is hard to learn and understand. In reality, the main struggles of most students are not with calculus itself, but their lack of understanding with foundational trigonometry and algebra concepts that are commonly applied to calculus.

This is the main reason why it is essential to review past math classes and notes to truly understand the foundational maths concepts that you’re required to know before you take on calculus.

In this article, we’re going to simplify calculus. Get ready to discuss key concepts from trigonometry and algebra, as well as definitions and symbols you must understand.

• Know the definitions

Knowing the different terms and their definitions is essential in calculus since you will be learning things called derivatives, limits, integrals, and other terms that have a conceptual definition. Therefore, you need to understand that one problem can be phrased in various ways. Knowing definitions is essential to your correct interpretation of problems and subsequently, your reasoning and understanding.

• Taking one step at a time

Calculus concepts are taught in a very specific order. We start with limits, derivatives, integrals, series, higher dimensions, and progress to more advanced concepts. The reason for this is that all concepts are grouped together like a ladder, so everything you learn will be based on a previous topic.

It’s recommended that you don’t breeze on a particular topic like limits since it’s the foundation of calculus and everything else will depend on it. You will need to understand the conceptual meaning behind a limit to fully understand next concept.

• Know the symbols

Calculus is full of arrows, S’s, and Greek letters- it’s like you’re reading a foreign language! That is why you’ll need to know all the symbols to properly solve a problem. If you can’t determine their meanings, then will not understand what the problems are asking. No Matter how naturally gifted you are in maths, it s impossible to work through problems if you do not know the symbols or terminology used.
After learning the symbols, you should also know when to use them. Therefore, it’s essential to know all the small details, or you’ll end up getting more confused.

• Start Thinking in 3D

Calculus is considered a journey into the world of three dimensions, so you’ll need to expand everything, and visualising will be your key to solve problems. Although you don’t need to be an artist to succeed, you are required to draw various 3D figures.

• Learn the rules

Like in any other subject in school, mathematics is bounded by rules and you need to follow them to be successful in this subject. One good example is the chain rule, product rule, the quotient rule, u-substitution, and integration by parts. If you don’t know these rules, then you will be limited in your ability to solve problems in calculus.

Overall, practice is the key to your success so solve a lot of problems everyday or as much as you can. Don’t give up, it will become easier once you get the hang of it. Most importantly, do all your homework following what your teacher has covered before the following lesson commences. If you need a tutor to help with your understanding and confidence, find out about their rates.

Holidays are the best time to refocus and recharge, but it’s also an ideal time to get your head around the curriculum. Studying over the holiday break will provide you an opportunity to get a head start when classes begins, so you won’t feel completely lost in class.

This is also essential for Year 12 since you’ll be shifting to higher education, and teachers will expect you to be more independent, so setting a study routine during the holiday will better prepare you for the Victorian Certificate of Education or Victorian Certificate of Applied Learning.

Here are some tips to consider when you’re setting your study routine during the holiday break:

• Set an ideal time to study per day

It’s best to set aside at least 3 to 5 hours a day to study, so you establish your rhythm. The important thing is that you’ve allotted enough time to for studying so it becomes the centrepiece of your day.

• Use a planner in outlining your daily goals

Setting goals is important in any type of endeavour, so we recommend that you list your daily, weekly, and monthly goals. This is best done in a planner where you can outline all your activities and the timeframe required for each task. Accomplishing goals will also motivate you to study and to stick with your daily study routine.

• Dedicate enough time to all your subjects

As you set your study routine, you will also need to divide your time between your subjects. This means you need to devote enough time to all your subjects so that you can cover all of the relevant content. Some subjects may require more study time if you find them especially challenging but be sure not to neglect others. It is particularly important to study for English, as it is considered as a prerequisite to pass your VCE and to enter most courses.

• Create an accountability group

We all know that there are many distractions during holiday breaks so it’s best to get someone to check on you once in a while. We recommend you create an accountability group or join a study group since they will surely remind you when you get together for your study session.

• Exercise daily

To keep your mind healthy, you will need to maintain a healthy body. Daily exercises will not only diversify your activities, but It will also provide you the endurance you need throughout the holiday break.

• Eat a balanced diet

Like exercising daily, you will also need a balanced diet to stay healthy. Therefore, eating nutritious food is essential to get the daily boost you need to continue with your work.

Lastly, don’t forget to spend time every day doing something you enjoy, like going out with your friends and family. It’s a holiday break, after all, so its’ best to relax and not get burnout, while also prioritising your studies.
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Overall, it is essential to establish a solid study routine, so you make the most of your holiday break and give yourself a better chance of achieving high marks during the coming assessment period. If you are becoming overwhelmed, it's best to seek help from a qualified tutor. Find our about the cost of tutors here.

How Much Do Tutors Cost? 
A private tutor is someone who believes they have expertise to teach a specific subject, and they offer their services to students who need academic help. Tutors are usually professors, industry professionals, undergraduate students and teachers who have robust experience in a particular subject area. Therefore, private tutoring rates will vary depending on the location, experience of the tutor, and frequency of the tuition sessions.

However, the tutoring industry is currently unregulated, so anyone can claim they are a tutor even if they don’t have the required expertise and qualification to teach a particular subject like maths and science. In fact, unqualified, unaccredited, and tutors with no experience often charge very low. Some of these tutors are still students who achieved high grades in a particular subject, but this doesn’t mean that they have the capability to guide your child to academic success.

Breakdown of cost depending on the type of tutor:

• Unqualified and inexperienced tutors

These tutors have no experience or aspirations within education, and they usually charge $20 up to $50 per hour. Usually, these are undergrad students who achieved high grades in a specific subject like maths, and they are confident enough to teach the same subject to other students. However, often this persons high grades have a lot to do with a strong natural ability in maths. Therefore, they struggle to break concepts down for struggling students. They also have their preferred algorithms, which they are confident with, but cannot offer alternative algorithms for students to use. We do not recommend that you hire an unqualified and inexperienced tutor because they lack the needed training and knowledge to teach your child.

• Education undergraduates

These budding teachers are not yet qualified to teach, but they have the teaching experience and aspirations to become full-time teachers. In fact, these education student tutors are passionate about teaching, and they have a good understanding of the curriculum. Most importantly, they are currently learning and practising various teaching methods that are explicitly intended to assist students, and they hold a working with children check. They will often charge from $50 to $70 per session.

• Qualified and experienced teacher

These tutors are qualified teachers, and they specialise in the subject area needed by your child. They have years of experience teaching in various private and public schools, which gives them the knowledge and expertise to guide your child in their respective subject in the most effective way possible. So, if you’re looking for an ideal tutor for your child, then you may want to consider hiring a qualified teacher. In most cases, they charge between $70 to $100 per hour.

• Specialist teacher

This group of tutors are also qualified and experienced teachers with a VIT accreditation, but they have an additional qualification in the area of need. For example, a specialist teacher might be trained and qualified to work with children with special needs. These tutors will most likely charge more so you can expect to pay between $90 to $120 per hour.
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As parents, we should provide our children with an ideal tutor that can help them achieve their academic goals. That is why we urge you to ensure the credibility and qualifications of a potential tutor before you make the final decision. Additionally, be wary of cheap tutors since they may not be the right tutor for your child. It’s best to spend a little more as long as you get the value for your hard-earned money.

If you are looking for one of Melbourne's top Maths Tutors, expect to pay $66 for an undergraduate and $88 for a fully qualified teacher through maths tutors Melbourne.