Going Mental! Part 2
Post date: Feb 19, 2014 4:08:22 PM
And welcome back to the second instalment! Here I'll look more closely at oral counting, the counting stick and the sound of a number.
As I mentioned in the first Going Mental post, mental maths is something that can be taught to children in a very structured and developmental way. In this post, I will outline some examples that a teacher could incorporate into their repertoire of oral and mental maths activities
Firstly, a great video clip that I'd recommend is Maths out Loud, produced a number of years ago by the PDST. It shows a cuiditheoir modelling oral and mental maths with a senior infants class, while being observed by the class teacher. And while the specific activities seen here are obviously chosen to suit a senior infants class, they could all be easily adapted to suit every class.
It is 30 minutes long in total and is worth viewing in its entirety. Usually, when I show it at courses, I'm often tight for time, so I just show some snippets to highlight the activities below (if you're also on a tight time allowance, I've indicated exactly how far into the video you can see the various activities in action).
Oral Counting (7:30-8:24 & 11:08-12:31 on video)
Also referred to in some literature as choral counting or the choir of number, these are probably the easiest and quickest type of oral and mental activities to do in any class as they require no specific equipment. Some of the ways to vary this:
Involve the whole class, groups, or individuals.
Incorporating movement: as seen in the clip, using hands, clapping, standing up sitting down etc. The specific movements you choose are irrelevant (so long as they're safe!) and not only does this refocus the children (if they're getting a bit distracted!) but it greatly suits the kinaesthetic learner. The use of props (e.g. the swinging item in the second clip) can also hold their interest for longer
Counting forwards & backwards, from various starting points, ie don't always start at 1. It's a bit like reciting a familiar poem; if you start off at the beginning you're usually able to ramble on, but if you try to start from somewhere in the middle you can often be stumped! We need to make sure the children aren't just rambling on from the starting point, like some sort of mantra. By forcing them to count forwards & backwards, from various starting points, the children really need to visualise the individual numbers and their positioning in relation to others. One simple game that incorporates this is Clap & Change; while the children count out loud the teacher claps and they then change direction eg ...6,7,8,9,10, CLAP, 9,8,7, CLAP, 8, 9, 10, 11... Again this game can be played with any class using content that suits that level.
The counting can be in ones (as seen in the video clip), tens, hundreds, twos, fours, multiples of any number; in other words anything that suits the class level and is relevant. Personally, I believe that children in the more senior classes, should (apart from the usual multiples covered in the basic facts) also know the multiples of 20, 25, 50, 200, 250, 500. These numbers have such a close relation to place value, measures, fractions, decimal fractions, percentages etc that even being able to remember (and recite) the first five or six multiples of each would be very useful to them in the long run.
Again to make it more challenging for the middle and senior classes you can count in fractions, decimal fractions, integers etc. One I've done with my own fifth class is this:
Everybody standing, sitting, standing, sitting, while counting on in eights i.e. one eighth, two eighths, three eighths, etc.
Then I ask "Is four eighths in its lowest term? What should it be when simplified?"
Next time we count, we replace four eighths with a half. I then ask what other fraction can be expressed in a lower term. We continue on 'till all possible replacement have been made. It really makes the children visualise the positioning of the numbers.
And while counting activities are completely valid as their own stand-alone activity, they could also be used to set up a different learning activity, as can be seen in this video clip.
Another point I would add is that it's better to have the children counting aloud something that they have already seen in print. This can be numbers on a number-line, hundred square etc. The more experiences they've had looking at and working with visual representations of the numbers, the easier it will be to visualise them mentally.
See also the paragraph on counting in Jan Pringles blog post on place value, for more ideas.
Counting Stick: (8:25-10:28)
The counting stick is another resource that is well used in my class. If you don't have a commercial stick you can make your own out of a variety of materials (eg a broom handle, cut to 1m length, with 10cm bands of contrasting insulating tape applied alternately, or you could colour in bands of contrasting colours on the back of a metre stick). You could also just use an image of one on your IWB or use this Virtual Counting Stick or these Interactive Counting Stick Activities.
A small finger puppet is an ideal accompaniment to the counting stick when using it with younger classes; your puppet can hiccup forward and sneeze backwards to add a variation. While you should not write numbers straight on the counting stick you could add some temporary cards with the required numbers initially, again to help the children visualise the numbers when the scaffolding of the cards is removed.
Like the oral counting, you can use the counting stick to count forwards & backwards, from various starting points, to count in ones, tens, hundreds, twos, fours, 25s, or multiples of any number. For this reason, it works especially well when reinforcing the basic number facts, as you can see in this video clip and in this one. However, I would stress that this abstract phase (ie numbers based), should only occur after extensive exploration of the relevant number facts in the concrete and pictorial phases.
It can also be used with fractions, decimals, integers etc. For integers (ie positive and negative numbers, also known as directed numbers), I prefer to start with the counting stick in a vertical position, as that way it's easier to relate these numbers to temperatures on a thermometer. And then we move it to a horizontal position as shown in this activity.
I also find the counting stick great for rounding numbers. For example, if we are learning to round to the nearest ten, I ask the children to show me where they think the number 62 would go on the counting stick. I then ask them to tell me what is the multiple of ten that comes before and after. The we can visually ascertain to which ten it is closer and round it to that number. In this same way, I might ask them to round the number 65 to the nearest multiple of ten. If they know their stuff they will tell me that 70 is closer but them if we look closely we realise that 70 is not closer, rather 65 is equidistant from 60 and 70. It is important to explain to children that we round up if it ends in five, because we needed to have a rule, same as we need rules to govern what side of the road we drive on. Otherwise there would be a lot more crashes, in both maths and on the road!
For other ways to use the counting stick check out these links:
Counting Stick: A Maths to Share article from NCETM
Counting Stick: Using it in the 10 min starter
Counting Stick: Using it to teach tables/number facts
Using the counting stick for mental maths: an article from An Seomra Ranga
The Sound of a Number: (10:29-11:07)
This is also a very simple activity that just involves dropping counters/beads/coins into an empty tin. As before each drop can represent ones, tens, hundreds, twos, fours, 25s or multiples of any number. This activity targets the children’s aural skills, illustrating how important is is that our oral and mental maths activities take a multisensory approach. On the video this was done in a very simple way, incorporating oral counting. A way this could be developed is to drop in an amount, pause and ask the children to hold that number in their heads, drop in more and ask for final total. To get a better sense of how individual children are doing, you could ask them to show you their final answer using digit cards, a number fan or by writing the number on a mini-white board (MWB)
Keep an eye out for the next Going Mental post, where I'll look at some other useful mental maths activities and resources.