During my years of teaching, I always realise one obvious but constantly made mistake among my students when they attempt this topic that involves figures, circles and triangles… yes, Area & Perimeter.
Many a times, my students feel that they are similar because both formulas require the use of length and breadth (for Squares/Rectangles), base and height (for Triangles), radius and π (for Circles). The tricky part that many fellow educators and parents face is that it is difficult to explain to their children or students that Area and Perimeter are related yet different in their own ways.
My students always tell me this:
“Mr. Marc, they both use breadth and length! (for a rectangle) They are the same right?”
“Mr. Marc, area and perimeter have the ‘same’ units! Only area does not have the ‘2’ on top!”
I am sure this sounds familiar to many of you.
This always tells me one thing…my students only know the formulas for area and perimeter by memorising it. They do not understand how this concept correlates to one another. This can make the difference between scoring 5 marks or 0 marks in a problem sum.
Here’s a simple yet effective trick that I use to explain this confusing situation to my students.
Imagine you are a farmer today…
Area is the amount of space you have to plant crops (i.e. vegetables, carrots, etc.)
This is the amount of space in the field that I have to plant my crops. Many students mistake area as a length. By knowing that it is the amount of space inside a field, my students tell me that this helps them recall easily the concept that area is a space, and not a length. Thus, area being a space reminds them that units would have to be in cm2 / m2.
Now comes the confusing part about Perimeter and why it is different from Area!
Perimeter is the distance that I have to run around the field. (No taking of shortcuts here!)
No matter what the given figure is, here are the steps to minimize missing out any sides of the figures when finding the perimeter.
Step 1 : Mark out with an ‘X’ a start point
Step 2: From the ‘X’, imagine you are running around the field (figure) with no shortcuts to be taken in a clockwise manner
Step 3: When you arrive back at the ‘X’, this means you have completed running around the field arriving back at your start point.
Simple right? :)
This also helps my students from missing any sides and ensures that they have covered all ‘ground’ along the path of the figure. With this, my students are normally able to tell me now that Perimeter is a distance and hence, the units are in cm / m .
Give it a try and let me know if you face any problems!
I hope this resource has been useful for you and your child as it has been useful for my students. Do feel free to drop me a comment below if you have any questions or need any clarifications that you need. Your question might be of help to others too !
To allow your child to have an easier time recalling these tricks, I have created a FREE Revision Card which I am giving away. Simply join our mailing list now to download the FREE Revision card and other learning resources in the future!
“Ah boy(Son), have you done the assessment/revision for your exams? You must do Practice More and Do More so that you can do well for your exams and go to a good school in future.”
I’m sure most of you parents hear yourselves saying this or a variation of this more than half the time before exams. Now this is what we call the “Old School” way of revision – Practice More and Do more.
What we at Lexis Education Asia believe in is not simply Practicing More and Doing More BLINDLY. In fact stop doing this! It drives your children and you crazy and frustrated.
Now what I am going to share with you is 3 simple tips to revise for Maths :
1) Ensure your child understands the basics of the topics to be covered before jumping STRAIGHT into Problem Sums – even though problem sums might be important. If your child does not understand the basics/foundation of at least 70% of the topic, it is almost impossible to even attempt problem sums.
SOLUTION – Work on the MCQ/Short answer type questions of each topic 1st!
2) Have a cheat sheet/formula sheet created for your child for each individual topic so that there is something he can refer to when he first starts off his revision and while he is doing his revision. After the 1st round of revision, progressively reduce the use of this cheat sheet and have him/her practice on from his/her own. This is also to help him revise on the day before the exam – a quick look through of all the important pointers for each topic.
SOLUTION - If you can’t do it yourself, head down to POPULAR bookstore and purchase the book “SAP – Learning Maths”. It comes with a set of notes.
P.S : Children do not like to flip through the whole text book to find out something. It is a total waste of time as well. Give them a cheat sheet, we say.
3) When practicing for Problem sums, stop BLINDLY doing it. What do we mean by this? There are many books in the market which have broken down and categorized Problem solving into Different Model Concepts and Heuristic Skills. Use these to help your child individually understand and learn each individual concept/skill before attempting Past Exam Papers, etc.
SOLUTION – Head down to POPULAR bookstore and pick up one of these books :
i) FAN-MATH Process Skills
ii) Marshall Canvendish – Problem Solving Beyond the class room
If there are any other questions, do write to me in the comment box below ! :)
Chief Trainer Marc
Did you know mistakes can be classified into 3 Major types? (Part 1)
Did you know that mistakes aren’t simply mistakes if you analyse them?
Type 1 – The blank answer
The type 1 mistake a child makes is if he/she does not understand the question at all and normally would leave it totally blank.
For this type of mistakes, it would be best to read through with your child the question and prompt questions regarding various key points so as to ensure he/she understands what is stated/written in the question. It is most commonly a case of the child totally not understanding the question given, hence, leaving it totally empty.
Only after carrying out the steps above should you go on to have your child try working on the question. If at this point, after ensuring he/she understands the information provided in the question, he/she still does not know how to do it, can we say that he/she probably doesn’t know how to apply the concepts learnt for that particular topic.
Solution : Revise with your child the basics of that particular chapter and see if he grasps the basics 1st before moving on to the more advanced level type of questions.
Type 2 – The Half-correct Answer
The Type 2 mistake is typically made when a child understands the question, tries to attempt it and gets lost/stuck at a certain stage of the working.
For this type of mistakes, your child normally understands about 50-70% of a question (depending on the number of steps he/she has gotten right).
It is only at a certain stage of his/her working where he gets lost. Find out which part this is from the steps he has attempted. From there, prompt your child with some questions to help your child understand why this step should not be done in this particular way or give him/her hints to look out for clues on what the right step to take next is.
Solution : By helping to pin-point where your child has made these mistakes during his steps, it would help him/her with understanding the steps from which he has made mistakes.
Type 3 – The correct Method with the wrong Answer (‘aka’ “The Careless Mistake)
The Type 3 mistake is described by many parents as the “pulling your hair” type of mistake. This mistake is typically made when your child rushes through and doesn’t check his work. He/she has done all the steps correctly but ends up with a carelessly calculated wrong answer (either by way of pressing the wrong numbers on the calculator or a mistake done in his/her working”
Solution : The almost full-proof way of reducing mistakes by at least 60-70% is to write all workings legibly even if it’s in the working column. It doesn’t mean that the working column has to be a ‘chaotic warzone’. Why? This helps to eradicate mistakes made through the recognition of wrong digits during manual workings.
Now, by knowing all the 3 Major Types of mistakes, don’t you think helping your child with his/her revision would be 300% more EFFECTIVE and 300% less Frustrating? Your kid would thank you for not PILING on the massive amounts of assessments too! :D
Do leave me your thoughts at the end by commenting ! :)
Enrich, Develop & Excel!
Julie believed she was a total failure and would never be able to change anything in her life. Julie also felt all her shortcomings were her own fault.
Where, I ask myself, did such a young person acquire this negative and fatalistic thinking?
The answer soon became apparent when I invited her parents into the session. They began discussing numerous life events and explaining them in ways that their children were learning. The car, for example, got dented because you can’t trust anybody these days; Mom yelled at brother because she was in a bad mood; you can’t get ahead in this world unless you know somebody, etc.
As a parent, your own thinking style is always on display and your children are listening intently!
The Importance of Optimism
Why should you want your child to be an optimist? Because, as Dr. Martin Seligman explains: “Pessimism (the opposite of optimism) is an entrenched habit of mind that has sweeping and disastrous consequences: depressed mood, resignation, underachievement and even unexpectedly poor physical health.”
Children with optimistic thinking skills are better able to interpret failure, have a stronger sense of personal mastery and are better able to bounce back when things go wrong in their lives.
Because parents are a major contributor to the thinking styles of their children’s developing minds, it is important to adhere to the following five steps to ensure healthy mental habits in your children.
How Parents Can Help
Step 1: Learn to think optimistically yourself. What children see and hear indirectly from you as you lead your life and interact with others influences them much more than what you try to ‘teach’ them.
You can model optimism for your child by incorporating optimistic mental skills into your own way of thinking. This is not easy and does not occur over night. But with practice, almost everyone can learn to think differently about life’s events – even parents!
Step 2: Teach your child that there is a connection between how they think and how they feel. You can do this most easily by saying aloud how your own thoughts about adversity create negative feelings in you.
For example, if you are driving your child to school and a driver cuts you off, verbalize the link between your thoughts and feelings by saying something like “I wonder why I’m feeling so angry; I guess I was saying to myself: ‘Now I’m going to be late because the guy in front of me is going so slow. If he is going to drive like that he shouldn’t drive during rush hour. How rude.’”
Step 3: Create a game called ‘thought catching.’ This helps your child learn to identify the thoughts that flit across his or her mind at the times they feel worst. These thoughts, although barely noticeable, greatly affect mood and behavior.
For instance, if your child received a poor grade, ask: “When you got your grade, what did you say to yourself?”
Step 4: Teach your child how to evaluate automatic thoughts. This means acknowledging that the things you say to yourself are not necessarily accurate.
For instance, after receiving the poor grade your child may be telling himself he is a failure, he is not as smart as other kids; he will never be able to succeed in school, etc. Many of these self-statements may not be accurate, but they are ‘automatic’ in that situation.
Step 5: Instruct your child on how to generate more accurate explanations (to themselves) when bad things happen and use them to challenge your child’s automatic but inaccurate thoughts. Part of this process involves looking for evidence to the contrary (good grades in the past, success in other life areas, etc).
Another skill to teach your child to help him or her think optimistically is to ‘decatastrophize’ the situation – that is – help your child see that the bad event may not be as bad or will not have the adverse consequences imagined. Few things in life are as devastating as we fear, yet we blow them up in our minds.
Parents can influence the thinking styles of their children by modeling the principals of optimistic thinking.
Enrich, Develop & Excel!
Kids are making headlines. But, the news isn't something to cheer about. Turns out they are becoming more overweight than ever before.
Today, about 16 percent of children ages 6 to 19 are overweight, according to the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK), and the number is steadily increasing.
The dangers of being overweight in childhood are the same as in adulthood: heart disease, high blood pressure, high cholesterol, the precursors to type 2 diabetes and even some forms of cancer.
Experts say children need at least one hour of physical activity each day. Is your child this active?
Parents play a big role in shaping children's eating and physical activity habits. Helping your child maintain a healthy weight requires a long-term commitment with modifications the entire family should embrace.
Here are a few suggestions from the experts:
* Set a good example. Plan family activities, like hiking, biking, dancing or basketball. Include children in active chores like walking the dog, washing the car or mowing the lawn.
* Don't forget the fun factor. It is likely that younger kids will respond better to exercise if it doesn't feel like exercise. Try climbing a jungle gym, throwing a Frisbee or playing chase. For older children, encourage physical education classes or urge them to do activities that they like and will do every day.
* Cut down on screen time. Television viewing and other screen usage can hold your child's interest for hours, which may discourage physical activity and increase calorie consumption. Reduce your child's screen time by encouraging other behaviors such as playing outdoors or moving around during commercials. A few minutes of physical activity at a time can certainly add up.
Taking a pledge as a family to live a fit and healthy lifestyle is one of the best gifts you can provide your child.
One quick way to start is to start by factoring at least one such activity a week!
If time permits, increase the frequency of the activities.
Enrich, Develop & Excel!
Chief Trainer @ Lexis Education Asia
Allow me to paint you a picture. You and your teen talk about issues and rules as they come up. While you have disagreements that you resolve, you never have fights where one person wins and the other loses.
Sound impossible? Now, I am going to share 7 steps to lead you down the same path.
* If you want your child to talk with you, then give him a reason to trust you. Keep his confidence. Ask him if what he tells you is something between the two of you or if it is okay to share it with anyone, including family members. Honour his wishes.
* When you listen, be there 100%. Erase any other thoughts or postpone them until later. Let your mind be free to focus on what your teenager is communicating -- spoken and unspoken.
You can be there, fully at 100%, when you are not listening to that Little Voice in your head telling you about your child or what he is saying that is wrong or that you do not agree with. Instead you will actually be listening to the words of your child, his emotions and his complete message! Big difference. Huge impact for both you and for your teen.
You must be free from agendas to be there 100%. You have no idea what your teen is about to tell you nor do you have any idea what he wants in coming to you, so ask.
* Ask how your child wants to be listened to. Does he want an opinion, suggestions, advice, or does he just want to blow off steam? No guessing allowed! When you guess wrong, you frustrate him by going in a direction he does not want to go. He may see his effort to talk with you as a waste of time and decide not to make that mistake again.
* For accurate communication, ask questions -- not intrusive, prying ones, but check-ins to be certain you are hearing the message as your child intended you to hear and interpret it.
Be sure you are hearing what your teen means to say rather than what you want your teen to say or what you think your teen should say. Respond to a thought saying something like, "Is it accurate that you do not like it when X happens?"
If that is correct, he will say yes and if not, then he will state his thought differently. Check again -- you want to understand him.
When your child sees that you are truly available and paying attention he just may feel understood -- at least in that moment. The more moments he feels that way, the more frequently he will talk to you.
* Listen without judgement.
* Listen without expectation. When you have no attachment to what will be said or the outcome of what you hear, then you are free to pay attention to every word and every non-verbal clue.
Take all that information, check for your accurate understanding, then follow through with the request your child made for how he wants you to listen to him.
Your young adult may share things that surprise or scare you. He may do that to see your reaction -- or he may do that because he trusts you enough to be frank and honest. Your challenge is to listen honestly.
If you are surprised, it is okay and, in fact wise, to say so. Note that it is honest to share your feelings about what he said. However, telling him he is wrong or he should have done such and such differently is judging.
You might follow the judgement with a conviction and a sentence. Such actions could cause you to lose the trust that led to his coming to you in the first place. Then you are back to having a teenager who doesn't talk and likes to fight.
Consider that there is more than one way to do things and there is more than one solution to any problem. When your child tells you about something you cannot understand, ask about his thinking that led to that action. Ask as many questions as you need to so you can see his perspective.
Seeing his perspective is not the same as approving or agreeing with it. On the other hand, you may gain a fresh view on whatever the issue is.
*If your child has done something that breaks a law or a rule in your family, address that issue. Brainstorm for solutions together. Empower your teen to be responsible for every action he takes -- or fails to take -- in his life.
Pretending not to notice undesirable behaviours will not make them disappear. Follow the same brainstorming techniques to deal with such instances. You will be surprised how simple it is to create win-win outcomes. I did not say easy. I said simple. Success happens after doing it, doing it, doing it, until it becomes natural. Yes, that task may take effort and seem like work.
Actions and results, desirable and undesirable, reflect self esteem. To change behaviours, treat the cause not just the symptoms.
What are the hidden thoughts of your teen costing him -- and you?
Try it out. Leave us comments below if you have any queries!