In maths, an equation is a representation of two things which are equal, so it’s generally two expressions related by an equals sign. Equations can be solved using both symbols and numbers. When solving numerically, then only numbers are admitted as solutions. However, if you are solving equation symbolically then expressions can be used to represent the solutions.
What is the importance of math equations and why do kids need to learn it?
Equations are useful in daily life since various disciplines in the real world depend on maths and equations. Electricians, builders and engineers all use equations as part of their daily activities. Even every day tasks like doing the shopping require simple solving skills.
Computer chips and other modern gadgets/machines we use in our daily lives are based on mathematical equations and algorithms. Therefore, it is essential for kids to properly learn the concepts of solving equations.
Usually, math teachers instruct students to solve equations at grade school but even kindergartens can learn a bit of simple equation solving using basic arithmetic. The most important thing is for them to develop the skills they need to solve numerical problems using computational methods.
Kids are often given equational problems with a number missing, for example 50 + ___ = 90 – 2. Students need to be aware of the process involve in solving this problem and they must know how to use inverse. In fact, they must know what they should add to 50 to come up with 88.
Learning basic concepts is essential for students so they will be able to solve more complex quadratic equations as well as understand several topics like curve sketching and finding the maximum and minimum values of an equation.
Why do basic concepts get lost when more complex concepts are learnt?
Some students forget basic concepts when they are tackling more complex equations like quadratics. They often forget to use to use the both sides method as they are bombarded with the null factor law and the quadratic equation, along with various methods of factorisation.
We need to help student integrate what they learn from the past with the new methods they recently acquired. Therefore, teachers must be able to assess the current method they are using and remind them that they must also apply some basic concepts to solve difficult equations. I like to create a flow chart for my students so that they can learn when to use each method of solving depending on the question type. To simplify, I tell students that if only one term has the unknown, then the both sides method is the most simple and practiced method to use. If multiple terms have an unknown (for example; 5x and 2x2) the equation must first be made equal to zero, then factorised or put into the quadratic formula.
Students will master these methods through constant practice, so teachers must provide them with lots of opportunities to practice their skills conceptually.
Overall, students must understand the importance of basic concepts in solving equations. Maths continuously builds to new levels of difficultly but basic concepts are always still important to remember when learning more advanced solving techniques. Given that students have only just started learning in schools again, it is even more important to revisit the basics
Some parents experience an uphill battle when it comes to encouraging their child to improve their maths skills and understanding. You may need to engage your children at home by playing some active maths games, and I don’t mean apps or games on their mobile devices.
In fact, your kids will enjoy these games without even realising that they are learning some important concepts along the way. You may also customise most of these games based on what skills you want your kids to learn, so it wouldn’t hurt to pick a few to try. Your kids will beg for more once they try some of these maths games.
Overall, these games are engaging and fun and will teach your children some valuable maths concepts that they can use to improve their skills. Even though onsite learning has now resumed, experts are predicting that many students may have fallen behind with the events of 2020 lockdowns in Victoria, so extra practice at home will surely help your children get to the expected level.
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:
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:
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.
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.
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.
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:
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:
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.
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.
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:
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.
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.
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.
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.
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.
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.
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.