How to Teach Halving


HALVING SHAPES

Before teaching a child to halve a number, make sure that they can halve a shape.   Most children find it easy to halve a shape and don’t realise that halving means the same as splitting into 2 equal parts. So before teaching your child how to halve a number, please make sure that they have understood the following common misconceptions:

1.  When you half a shape, you must make sure that it is split in the middle.  This teaches the child that halving must be fair and that both halves must look the same.

2.  There is more than one way to half a shape.  Ask your child to halve a rectangle or square in as many ways as possible.  This should include diagonally as well.

3.  Draw and inaccurately half some shapes so that some are split unequally, some are split into three or more pieces.  then ask your child to find out if they have been halved.

HALVING NUMBERS

There are many ways to explain the term of “half of”; sharing equally between 2 people, counting in 2’s, dividing by 2, opposite of doubling and splitting down the middle.

Different ways of working out half of a (2)

Therefore, there are a variety of ways of teaching halving.  Choose a method that your child finds easy, and stick to it.  Once they are confident with that method, try to teach a different way of halving.

I always start off teaching a child how to share equally.  I usually use counters and draw 2 smiley faces on a whiteboard or piece of paper representing me and the child.  The child has to share the counters between the smiley faces.  Sometimes you have to teach a child “one for you, one for me” and once they have learnt this they find it quite easy.  Make sure that once all the counters have been shared between the 2 smiley faces, that they have been shared equally.  the child needs to check every time. “How many do you have and how many do I have” seems to work well.  What if the counters have not been shared equally?  The child can repeat again or if they have caught on, they will be able to move some counters around to make the distribution fair.  I use this method for up to 24 counters.

For numbers larger than 24, using counters can be time-consuming and often ends up with the child miscounting.  By now the child should know half of 2, 4, 6, 8, and 10 without working them out. So I break down larger numbers into manageable chunks, and then ask the child to share equally between 2 smiley faces.

Example 1:  Draw 2 smiley faces.  Half of 30 = 10+10+10 Draw three 10’s in circles at the side as in diagram below.

How To half 30
How to half 30

Then share as in the diagram below, the smiley faces will get 10 each and then, there will be 10 left which will have to be split into 5’s.  So each person gets 15.

Halving 30
How to halve 30

The same method can be used for bigger numbers and it’s easy and simple.

half of 34 = 10+10+10+4

half of 50 = 10+10+10+10+10

Do try this with your children and let me know if it works.

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It Takes 66 Days to Form a Habit


During the long summer break, I decided to drink a glass of water first thing in the morning whether I need it or not. And since I have been doing this daily for the last 2 months, it has become a part of my routine. In fact if I forget, then I feel as if something is missing; it bugs me.

Experts say that on average it takes 66 days to form a habit, if the new habit/behaviour is repeated every day. The length of time depends on the habit, the person and how consistent the person is. Also, if it takes longer to form a habit, then it will be stronger.

The same rules apply when forming learning habits in children (and adults).  Some of the learning habits that we encourage our literacy students to adopt are:

  • to plan a piece of written work before writing it

  • to check their work for mistakes

  • to remember to start sentences with capital letters and end with full stops

  • to remember to use quotes correctly and to explain them.  This is called the PQE technique in English (point quote explain)

  • to underline keywords in exam questions

  • to read every day

  • to brainstorm words and ideas for used in a story

And some of the learning habits we teach our numeracy students are:

  • to show working out when doing a maths question

  • to touch every single object when counting

  • to write out the formula they are going to use

  • to search for patterns in maths calculations

  • to set out calculations in the correct way

These learning habits cannot always be acquired in the classroom because there isn’t enough opportunity for repetition.  Planning is taught, but maybe only for a week and then the school teacher would move onto a new topic.  To create a habit you need to repeat the behaviour in the same situation. It is important that something about the setting where you perform the behaviour is consistent so that it can cue the behaviour.  Eventually the behaviour will becomes automatic and then the child can apply it in other situations.  So a child may punctuate correctly at Kip McGrath, but not necessarily remember to do so at school.  This would happen once the behaviour has become automatic and the child does so without thinking.

So be patient with children, when they are trying to learn a new skill.  New habits do not stop the old habits from existing; they just have to become stronger influences on behaviour.

Good habits formed at youth make all the difference    ………………………Aristotle

When Private Tuition Is Not Enough


I did an assessment on a year 12 pupil yesterday (age 17), who will be sitting her GCSE Maths in 9 teaching week’s time. She wanted to get a C grade, but when I tested her, she was working at a low E grade.

She was also re-taking her GCSE and got an F the first time round. That meant that she had only improved by 1 grade since starting her course 7 months ago and that’s with approximately 4 hours of maths per week at college. So it’s not difficult to do the numbers here. It’s plain and simple that 9 weeks of tuition (an 80 minute session per week) is not going to get her that C! In fact it would be nothing short of a miracle if she did. And that’s exactly what I told her.

From all my years of teaching experience, I have learnt that to pass maths you need to

  1. Learn the different methods of working out maths problems

  2. Memorise formulas

  3. Practice using these methods and formulas

  4. Go over past exam questions

Revision and learning is like building a wall. One brick at a time is laid and cemented together to make a wall. But if those bricks are not solid enough or the cement hasn’t had time to set, then the wall will be weak and inevitably break. So don’t leave your revision to the last minute or think that having a few extra lessons is going to be enough to pass your exams. It takes hard work, organisation and dtermination!