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Post date: Nov 6, 2016 3:36:56 PM
Counting is a vital aspect of numeracy in all classes and especially in the junior classes:
Junior Infants should be counting to 10 (although they only analyse numbers to 5)
Senior Infants should be counting to 20 (although they only analyse numbers to 10)
First class should be counting, reading, writing and ordering numerals from 0-99
Second class should be counting, reading, writing and ordering numerals from 0-199
Essentially the focus should be on the children developing an understanding of the number word sequences ie "nineteen, twenty, twenty-one, ....." etc.
Here are some ways and tools that I would suggest to achieve these learning outcomes
See it, say it.
When introducing a less familiar or unfamiliar section of numbers to children, the children should have the opportunity to see the numbers in sequence and to become aware of their positioning in relation to each other ie the children need to see the actual numerals first and recite them. Then, through a process of saying out loud the numbers they see, they should begin commit those numbers to memory. Some tools that would be useful for this:
An interactive hundred square that could be shown up on the class IWB eg use this interactive Number Grid or Operation Maths users could use the 100 square eManipulative, pictured at top and accessible at http://www.edcodigital.ie/ ; I find that this eManipulative is easier to use and has more possibilities
An interactive number line that could be shown up on the class IWB; my favourite is the Number Line app from the Math Learning Centre
When counting out loud, don't always count forward starting at 0; have various starting points and count backwards also from various points.
And be aware of potential hurdles: decuples/decades and teen numbers can be often confused eg fifty Vs fifteen. Make sure the children are aware of the differences in how to verbalise these numbers and how to represent them. Two good lessons from NZ Maths that explore this further are Teen numbers and Ty numbers (for any teachers doing stations with 1st or 2nd class there some good suggestions here). I also find arrow cards or place value strips quite useful when exploring Teen Vs Ty; this interactive programme also shows it quite effectively.
Say it, See to check.
Once comfortable with the first stage, the children can progress to where they say out loud a numeral that is hidden and then reveal what's hidden to check if they were correct. This use of blank/partial number sequences promotes children’s ability to visualise numbers.
To do this you can use the same interactive hundred square and/or number line as used before, but progress to hide an increasing number of numerals so that the children must rely on their visual and aural memories. The children can also be asked to say the numeral that would be 2 before/after, 10 before/after etc. For the hundred square, I find the Operation Maths eManipulative the easiest to use as you can hide/reveal entire columns/rows at once, as well as individual squares, whereas many other interactive hundred squares only allow you to hide/reveal do a square at a time.
If the internet or projector fails, you could quickly write/draw up a targeted section of a number line on the board, add the numbers, with help from the class, and then hide them using a strategically placed shapes/pieces of paper that could be re-positioned to reveal the hidden numbers.
Also related (but not as customisable) is this great game called Estimate. You have to estimate to what number on the number line the arrow is pointing, based on its position in relation to the known numbers. There are lots of different levels, therefore it'd be useful in all primary classes.
Just count!
At this stage the children just count orally, with no visual supports. Sometimes referred to as rehearsal, oral chanting, choir of number, etc, these oral counting activities should form a regular part of your oral starters routine. Again don't forget, have various starting points and count backwards also.
For extra practice...
Writing and ordering:
Get the children to write numbers on a selection of mini-whiteboards (MWBs) and then order the numbers by ordering the MWBs
Use blank number lines (like the one opposite). Write a suitable number at the start and get the children to fill in the rest. To make it more challenging (differentiation), write a number in the middle and/or end and ask the child to complete it.
Relate the counting to real-life contexts:
Locating a specific page in a book or catalogue
Counting height/length in cm (linkage - measures)
Identifying years on a time line (Integration - History)
Games e.g. snakes and ladders.
If you're teaching a senior class...
While the specific activities above are targeted at the junior classes, the number line suggestions can easily be differentiated for the older classes eg they can be customised go up in intervals of tens, hundreds, twos, fours, 25 etc., and can be used for fractions, decimals, percentages, positive and negative numbers.
Further reading...
Another important point worth making, is that number lines should be used regularly as part of maths in all classes, not just in the junior classes. Current evidence suggests that, while teachers appreciate greatly the benefits of concrete manipulatives and exploration, we can often move children from this stage, straight to the abstract stage of just using numbers, symbols and digits. Rather, we should progress from Concrete to Pictorial (Representational) to Abstract (also know as CPA approach, based on research by Bruner and as found in Singapore Math).
Number lines are an ideal strategy to use as part of this pictorial/representational stage and can be used very effectively in both the junior and senior classes, as can be seen in this fantastic InTouch article Keeping Numbers on Track . Personally, I use blank/open number lines all the time when teaching elapsed time and also for making change in money.
The counting stick (see Going Mental! Part 2) is in itself a concrete example of a blank/open number line. Also related are hundred squares, which are simply an adaptation of the traditional horizontal number line, and can be used in much the same way.
For further ideas on both number lines and hundred squares, check out Using number lines and hundred squares: A Maths to Share article from NCETM
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