For children of all mathematics ability, working with their parents in a fun and relaxed way, free from the peer pressures they encounter in the classroom, can only be a good thing! In fact, any mathematics done outside the classroom is invaluable for a child's development. It's about looking for opportunities.
Up to the age of about 11, a majority of children are taken to school either walking, or via the 'school run' - and then trips to cinema, shopping, holidays, etc. As a way of practising and reinforcing the various maths objectives, use the numbers found on car number plates as a starting point. Example - AT 16 DTP
Read that number. Can you count on in ones? in steps of two? 3? 5? ......
Read that number. Can you count back in ones? in steps of two? .....
What do you add to 6 to make 10? 20? 100?
What is 10-6=? 20-6=? 100-6=?
What is double 6? half of 6? three times 6? ten times 6? 100 times 6?
What is 6+7=? 6+9=? 6+5=? .......leading to 6+8=? 6+18=? 6+28=? ...6+78=? etc
What do you add to 16 to make 20? 50? 100?
What is 20-16=? 50-16=? 100-16=?)
What is double 16? half of 16? ten times 16? 100 times 16?
What is 6 divided by 10? by 100?
What are the factors of 6? 16? (or is it a prime number?)
In all these examples, regular practice makes perfect - your child will become very proficient and gain huge self-esteem. And hopefully, you will have fun at the same time. These are just a few questions, covering some of the important maths objectives which you can ask your child. There is a high probability that you will think up many of your own - when you get into the habit!
For young children.
If your child is very young, and doesn't yet understand the abstract concept of number, it will be helpful if you ask questions in a more 'concrete' manner. For example; I have 6 apples, how many more do I add to have 10 apples? If you have 6 apples, and share them equally between you and your friend, how many will you each have?
Thursday, 28 July 2011
Friday, 15 July 2011
Counting and Sequencing for Very Young Children - and Not So Young
As a primary teacher (ages 7-11), I've found that invariably the most confident and able of my young mathematicians are those who have a good understanding of pattern and sequencing of numbers. This allows them to master their number bonds and times tables more quickly - the foundation on which to build.
In School many hours are devoted to the learning of number patterns, but how can parents support and aid this learning inside and outside the home, and perhaps also give their children a head start?
In principle the answer is easy - knowing which sequences are important, looking for opportunities to practise with your child - and making this a habit!
If you put your mind to it, there are endless opportunities, but perhaps the most useful are in conjunction with walking, counting each step. So teaching your little one in earnest can begin as they make their first steps!! But also hopefully continue into their school years. Climbing the stairs at home, walking from the car to the front door, steps in the shopping mall, underpass, walking the length of the supermarket aisle, garden, etc, etc.
I must stress here that although your 18 month old child may be able to count perfectly to 20 or beyond! they are most unlikely to be understanding the whole concept of number. But it is this repetition and memory of sequences that will enter their sub-conscious - to be understood at later stages of their development.
1,2,3,4,5,6,7.......Don't stop there!
The first sequence to be mastered is counting in ones; 1, 2, 3, 4, 5, 6, 7,
and just about every parent in the world does this. But don't stop there! You will usually be the best judge, so when you feel the time is right, encourage and help your child to;
Count in steps of two; 2, 4, 6, 8, 10, 12, (reinforce even numbers and 2x tables)
Count in steps of ten; 10, 20, 30, 40, 50, (important to pass the 100 point)
Count in steps of five; 5, 10, 15, 20, 25, (has a nice rhyming feel to it)
Count in steps of two to recognise odd numbers; 1, 3, 5, 7, 9, 11, 13, etc
As your child gets older, help to recognise patterns in the various times tables by counting on in different jumps; three, four, six, seven, eight, etc. Whenever possible, keep the sequences going to pass the 100 point.
Challenge! On longer walks - can they continue the sequence past 1000?
It's also very beneficial to count backwards down to zero from a particular point in these sequences.
Other important sequences could include.....
Square numbers; 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Prime numbers; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, etc
Triangular numbers; 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, etc
Fraction sequences; zero, half, one, one and a half, two, etc
zero, one third, two thirds, two, two and one third, etc
Decimal sequences; 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, etc
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, etc
Have fun!
In School many hours are devoted to the learning of number patterns, but how can parents support and aid this learning inside and outside the home, and perhaps also give their children a head start?
In principle the answer is easy - knowing which sequences are important, looking for opportunities to practise with your child - and making this a habit!
If you put your mind to it, there are endless opportunities, but perhaps the most useful are in conjunction with walking, counting each step. So teaching your little one in earnest can begin as they make their first steps!! But also hopefully continue into their school years. Climbing the stairs at home, walking from the car to the front door, steps in the shopping mall, underpass, walking the length of the supermarket aisle, garden, etc, etc.
I must stress here that although your 18 month old child may be able to count perfectly to 20 or beyond! they are most unlikely to be understanding the whole concept of number. But it is this repetition and memory of sequences that will enter their sub-conscious - to be understood at later stages of their development.
1,2,3,4,5,6,7.......Don't stop there!
The first sequence to be mastered is counting in ones; 1, 2, 3, 4, 5, 6, 7,
and just about every parent in the world does this. But don't stop there! You will usually be the best judge, so when you feel the time is right, encourage and help your child to;
Count in steps of two; 2, 4, 6, 8, 10, 12, (reinforce even numbers and 2x tables)
Count in steps of ten; 10, 20, 30, 40, 50, (important to pass the 100 point)
Count in steps of five; 5, 10, 15, 20, 25, (has a nice rhyming feel to it)
Count in steps of two to recognise odd numbers; 1, 3, 5, 7, 9, 11, 13, etc
As your child gets older, help to recognise patterns in the various times tables by counting on in different jumps; three, four, six, seven, eight, etc. Whenever possible, keep the sequences going to pass the 100 point.
Challenge! On longer walks - can they continue the sequence past 1000?
It's also very beneficial to count backwards down to zero from a particular point in these sequences.
Other important sequences could include.....
Square numbers; 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Prime numbers; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, etc
Triangular numbers; 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, etc
Fraction sequences; zero, half, one, one and a half, two, etc
zero, one third, two thirds, two, two and one third, etc
Decimal sequences; 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, etc
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, etc
Have fun!
Thursday, 31 March 2011
Asking Questions
A good teacher is not one who can ask lots of questions (admittedly this is important), but one who can elicit their students to ask lots of questions. The main purpose of a question is to elicit a verbal response - from both the teacher and the student. It is therefore in the teacher’s best interests, to teach how to ask relevant questions and to differentiate between the types of questions available.
Asking and answering questions are important parts of effective learning and teaching. The types of questions you ask should capture the students’ attention, arouse their curiosity, reinforce key points, and encourage active learning. Here is a list of question types based on Benjamin Bloom’s six cognitive levels:
Knowledge (identification and recall of information):
• “Who, what, when, where, how…?”
• “Describe…”
Comprehension (organization and selection of facts and ideas):
• “Retell…”
• "Summarize..."
Application (use of facts, rules and principles):
• “How is…an example of…?”
• “How is…related to…?”
• “Why is…significant?
Analysis (separation of a whole into component parts):
• “What are the parts or features of…?”
• “Classify …according to…”
• “Outline / diagram…”
• “How does…compare / contrast with…?”
• “What evidence can you list for…?”
Synthesis (combination of ideas to form a new whole):
• “What would you predict / infer from…?”
• “What ideas can you add to…?”
• “How would you create / design a new…?”
• “What might happen if you combined…?”
• “What solutions would you suggest for…?”
Evaluation (development of opinions, judgments, or decisions):
• “Do you agree…?”
• “What do you think about…?”
• “What is the most important…?”
• “Place the following in order of priority…”
• “How would you decide about…?”
• “What criteria would you use to assess…?”
Asking and answering questions are important parts of effective learning and teaching. The types of questions you ask should capture the students’ attention, arouse their curiosity, reinforce key points, and encourage active learning. Here is a list of question types based on Benjamin Bloom’s six cognitive levels:
Knowledge (identification and recall of information):
• “Who, what, when, where, how…?”
• “Describe…”
Comprehension (organization and selection of facts and ideas):
• “Retell…”
• "Summarize..."
Application (use of facts, rules and principles):
• “How is…an example of…?”
• “How is…related to…?”
• “Why is…significant?
Analysis (separation of a whole into component parts):
• “What are the parts or features of…?”
• “Classify …according to…”
• “Outline / diagram…”
• “How does…compare / contrast with…?”
• “What evidence can you list for…?”
Synthesis (combination of ideas to form a new whole):
• “What would you predict / infer from…?”
• “What ideas can you add to…?”
• “How would you create / design a new…?”
• “What might happen if you combined…?”
• “What solutions would you suggest for…?”
Evaluation (development of opinions, judgments, or decisions):
• “Do you agree…?”
• “What do you think about…?”
• “What is the most important…?”
• “Place the following in order of priority…”
• “How would you decide about…?”
• “What criteria would you use to assess…?”
Saturday, 26 March 2011
Easter Chatterbox Activities
It's approaching Easter, if you're a teacher looking for something different for your little darlings, try these.
Based on the timeless childrens' playground game - the 'Fortune Teller', these worksheets involve a bit of cutting, followed by a bit of folding - origami style, leading to a fun interactive activity with the children asking and answering questions.
Easter Story http://embedit.in/C8Ltt5yWqK.swf
Easter Jokes http://embedit.in/5jfMEGo3tr.swf
Based on the timeless childrens' playground game - the 'Fortune Teller', these worksheets involve a bit of cutting, followed by a bit of folding - origami style, leading to a fun interactive activity with the children asking and answering questions.
Easter Story http://embedit.in/C8Ltt5yWqK.swf
Easter Jokes http://embedit.in/5jfMEGo3tr.swf
Thursday, 24 March 2011
Kids in the 50's, 60's and 70's
One of my favourite articles from a while back.
According to today's regulators and bureaucrats, those of us who were kids in the 50's, 60's, 70's and early 80's probably shouldn't have survived, because...
Our baby cots were covered with brightly coloured lead-based paint, which was promptly chewed and licked. We had no childproof lids on medicine bottles, or latches on doors or cabinets and it was fine to play with pans. When we rode our bikes, we wore no helmets, just flip flops and fluorescent 'clackers' on our wheels. As children, we would ride in cars with no seat belts or air bags. Riding in the passenger seat was a treat.
We drank water from the garden hose and not from a bottle - tasted the same. We shared one drink with four friends, from one bottle or can and no one actually died from this.
We ate dripping sandwiches, bread and butter pudding and drank fizzy pop with sugar in it, but we never got overweight because we were always outside playing.
We would spend hours building go-carts out of scraps and then went top speed down the hill, only to find out we forgot the brakes. After running into stinging nettles a few times, we learned to solve the problem.
We would leave home in the morning and play all day, as long as we were back before it got dark. No one was able to reach us all day and no one minded.
We did not have Playstations or X-Boxes, no video games at all. No 99 channels on TV, no videotape movies, no surround sound, no mobile phones, no personal computers, no Internet chat rooms. We had friends - we went outside and found them.
We played conkers, bulldog and street rounders, and sometimes that ball really hurt.
We fell out of trees, got cut and broke bones and teeth, and there were no lawsuits. They were accidents. We learnt not to do the same thing again.
We had fights, punched each other hard and got black and blue - we learned to get over it.
We walked to friend's homes.
We made up games with sticks and tennis balls and ate live stuff, and although we were told it would happen, we did not have very many eyes out, nor did the live stuff live inside us forever.
We rode bikes (some made from old frames from a local tip) in packs of 7 and wore our coats on by the hood.
Our actions were our own. Consequences were expected. The idea of a parent bailing us out if we broke a law was unheard of. They actually sided with the law. Imagine that!
This generation has produced some of the best risk-takers and problem solvers and inventors, ever.
The past 50 years have been an explosion of innovation and new ideas. We had freedom, failure, success and responsibility, and we learned how to deal with it all.
And you're one of them. Congratulations!
Our baby cots were covered with brightly coloured lead-based paint, which was promptly chewed and licked. We had no childproof lids on medicine bottles, or latches on doors or cabinets and it was fine to play with pans. When we rode our bikes, we wore no helmets, just flip flops and fluorescent 'clackers' on our wheels. As children, we would ride in cars with no seat belts or air bags. Riding in the passenger seat was a treat.
We drank water from the garden hose and not from a bottle - tasted the same. We shared one drink with four friends, from one bottle or can and no one actually died from this.
We ate dripping sandwiches, bread and butter pudding and drank fizzy pop with sugar in it, but we never got overweight because we were always outside playing.
We would spend hours building go-carts out of scraps and then went top speed down the hill, only to find out we forgot the brakes. After running into stinging nettles a few times, we learned to solve the problem.
We would leave home in the morning and play all day, as long as we were back before it got dark. No one was able to reach us all day and no one minded.
We did not have Playstations or X-Boxes, no video games at all. No 99 channels on TV, no videotape movies, no surround sound, no mobile phones, no personal computers, no Internet chat rooms. We had friends - we went outside and found them.
We played conkers, bulldog and street rounders, and sometimes that ball really hurt.
We fell out of trees, got cut and broke bones and teeth, and there were no lawsuits. They were accidents. We learnt not to do the same thing again.
We had fights, punched each other hard and got black and blue - we learned to get over it.
We walked to friend's homes.
We made up games with sticks and tennis balls and ate live stuff, and although we were told it would happen, we did not have very many eyes out, nor did the live stuff live inside us forever.
We rode bikes (some made from old frames from a local tip) in packs of 7 and wore our coats on by the hood.
Our actions were our own. Consequences were expected. The idea of a parent bailing us out if we broke a law was unheard of. They actually sided with the law. Imagine that!
This generation has produced some of the best risk-takers and problem solvers and inventors, ever.
The past 50 years have been an explosion of innovation and new ideas. We had freedom, failure, success and responsibility, and we learned how to deal with it all.
And you're one of them. Congratulations!
In the Beginning
Well, after reading several other blogs, nearly all discovered via Twitter, have decided to take the plunge and begin one of my own. No preconceived ideas of how it will pan out, but will try to keep a general focus on things educational. I reserve the right, however, to digress from time to time.
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