Know your Place ……..Value!
Post date: Aug 27, 2013 9:38:32 PM
On the surface, Place Value probably seems like it should be one of the easiest topics to teach; it’s usually the first topic a class tackles each year and often it may appear to a teacher that the class has got it…..especially when they’re getting all the correct answers in their books. It’s usually only later, when difficulties start to arise, often with operations, that you might start asking yourself did they really get it?
Read on for hints, tips and suggestions on how to ensure they do get it!
Make sure you allow yourself plenty of time to explore Place Value at the beginning of the school year – many people can be in a rush to move on, afraid that they will fall behind on what they had planned to do. Indeed, if you spend sufficient time on meaningful activities now, it may reduce the potential hurdles later on.
Furthermore, if you can keep this going throughout the year, then the children will have ample opportunities to continuously revise and reinforce their understanding. One way to do this is to have a number of the day to explore everyday. Check out my Number of the Day washing line posters here on my TpT Store
Concrete materials! Concrete materials! Concrete materials!
Being a strong advocate of the Bruners CPA approach as evident in Singapore Maths, to me, concrete materials are key to the children developing a good conceptual understanding of place value. They need lots of opportunities, in all classes but particularly 1st-4th to explore and manipulate a variety of Base Ten materials. These should be introduced in the following order:
Groupable materials that the children can physically put together in collections of tens and physically take apart. These include lollipop/bundling sticks, straws (counting or ordinary drinking), unifix/multilink cubes, ten frames and counters etc.
Grouped materials: Materials already put together as tens, units etc. where the ten is ten times bigger than the unit and the hundred is ten times bigger than the ten etc., e.g. Base Ten Blocks/Dienes, cardboard representations of these, dot strips, ten frame flash cards with removable dots
Other materials that operate on a base-ten system, while not increasing/decreasing in size by 10 e.g. money, place value disks/cubes. These are particularly valuable in the older classes when trying to show ten thousands plus. For money, it is necessary to make up some cheques for €1,000, €10,000 etc. Commercial place value disks, as used in Singapore Maths, are not readily available here in Ireland, although you can make your own very simply using counters or unifix cubes and a permanent marker (check out my post on DIY concrete materials for Place Value for more ideas).
Other equipment that is sometimes used to demonstrate place value includes the abacus and notation boards with dots. These can be useful, but I would also advise using them with caution; a child may use these accurately, without having a good conceptual understanding of place value, rather they are just recording the number of beads/dots in each place.
10 times bigger, 10 times smaller
Another thing to consider when teaching Place Value is what happens to numbers when we multiply or divide them by a power of 10. Often children are told to add a zero when multiplying by 10; which works fine until you are you move on to decimals and get this: 5.5 X 10 = 5.50! When I was in school we were told, incorrectly, to move the decimal point to the left or right to make numbers 10 times bigger or smaller; rather than being shown how it is the digits that are moving. Moving Digits: is a very visual Interactive Teaching Program (ITP), that clearly shows how the digits move when we multiply/divide them by 10/100, and how zeros are used as place holders, when necessary.
Don't be limited
Be aware of the number limits for your class level but don’t feel obliged to stick rigidly to them. The curriculum specifies a limit of 99 in first class 199 in second, 999 in third and 9,999 in fourth class. Interestingly, there are no specified number limits in 5th and 6th classes (although most textbooks tend to only go to 99,999 in 5th and 999,999 in 6th), so the sky, or rather infinity, is your only limit. I’d recommend that when working with bigger numbers that you do try to use numbers from real life so that the children see a purpose to them.
For bigger numbers, using place value houses, as in the image above can be beneficial. This way, the children come to understand that once they can read a three-digit number they should be able to read any multi-digit number, once the scan ahead for the number of commas.
Place Value in the environment
To further reinforce the real-life importance of larger numbers, ask the children to bring in examples of place value from the environment. This could include photographs of numbers in the school grounds or locality e.g. car registration numbers, distances on road signs. It could also include examples of numbers from print media e.g. newspapers, magazines. In the older classes you could challenge them to find an example of a very large number and/or one with the most places of decimals.
Things to do with these:
o Make a display for the classroom with the examples, in order of size
o For each example the children find, they must write out the number in word and expanded form (it will probably be in standard form)
o Round the number to the biggest place ie if the number is 312 round it to the hundreds, if it’s 0.012 round it to the hundredths etc.
Playing with Place Value
To bring in the fun element, there are lots of simple games that the children can play to reinforce place value; check out some of these links for ideas:
Place Value Activities: Including games, teaching ideas and loop cards (I have; who has) from Mathswire
More Place Value Activities: again from Mathswire
Place Value Games: using dice or cards, simple and adaptable to most classes
There are also quite a number of online games and activities; ones I’d particularly recommend are:
Place Value Games: Whole suite of online games, some of which also look at bigger numbers
Rounding numbers: Interactive self-checking activity, rounding to 1, 10 and 100.
The Stations of the Place
If you were considering trying out station teaching as a methodology in maths this year, Place Value lends itself quite well to this. You could set up a variety of activities at various stations, which could include some games (above) and activities on PCs/laptops/tablets etc. Check out NZ Maths Number Knowledge: for a whole suite of mini-lessons and this Place Value Activity Pack that has a plenty of teaching ideas, games etc. Or for some ready-made maths stations check out these Place Value Maths Stations from my TpT Store.
For these and other Place Value tips and ideas please don't forget to check out my Place Value Board on my Pinterest page
Interactive Base blocks: can be used to teach place value, from Math Learning Centre
Place value cards: allow you to explore place value up to 9,999
Number line: Customisable
100 bead string: Counting on and back along a 100 bead string
Place Value Charts: Interactive activities involving making a given number, from 10 digit numbers to 9 decimal places.
Place Value and Partitioning Games: a varied selection of games, clearly outlined.