The ordering decimals game
There are lots of ways that you can go about teaching ordering decimal numbers by size.
Developing pupils’ understanding of where decimals sit on the numberline is one approach. Getting them to understand that if we want to put a number on the numberline between 3.4 and 3.5, that we need a second decimal digit to do this is one way to develop their understanding of place value. If they understand this concept they will avoid the classic misconception that 3.45 is bigger than 3.5 because “45 is bigger than 5”. They’ll understand that 3.45 is between 3.4 and 3.5. I’ve seen nice posters produced from this kind of work that show pictures of repeatedly zooming in on the numberline, each time adding a new decimal digit.
Secondly, Ten Ticks have a lovely worksheet that gets pupils thinking about place value; tenths, hundredths etc in a visual way. It centres around colouring in proportions of squares which are made from 100 smaller squares (10×10 grid). The sheet starts by saying ‘this is one tenth’ and shows ten squares shaded (one vertical column). It then says ‘this is one hundredth’ showing one small square shaded. It gives examples of numbers like 0.62, showing six columns of small squares (10 in each column) and two extra small squares coloured in. The sheet works up to getting pupils to shade in proportions of squares for five different numbers and then asks them to order them by size by thinking about how much of the squares are shaded. This is a lovely activity for getting pupils to understand place value with decimals and why tenths are much larger than hundredths etc.
Thirdly, you can go down the route of asking pupils why ‘Andrews’ comes after ‘Anderson’ in the phone directory. This route develops the understanding to sort by units digits first, then tenths, then hundredths etc.
Fourthly, another method you can teach is an algorithmic approach. If the decimals have the same units digits you line them up vertically and ‘make them the same length by adding zeros’. For example, ordering 3.45, 3.7 and 3.012 you line them up like this:
Then you cover up the units digits and decimal points, leaving just the decimal digits which you then order by size. 012 is smaller than 450 which is smaller that 700 etc. You then write out the original numbers in this order, removing the extra trailing zeros you added before. Whilst not great conceptually, there is a time and place for such approaches in my opinion if other strategies have failed.
Regardless of which route you go down to get your pupils to understand how to order decimals, The Decimal Game makes a nice AfL plenary. The idea is that you show a grid of decimal numbers on the board. They may look like this:
Divide your class into two teams who then take it in turn to choose decimal numbers from the grid. After they choose a number, cross it off the grid. Each time they choose numbers they also write them on a whiteboard, lining them up so they can do some column addition with them. Once all numbers have been chosen each team sums their decimal numbers and the team with the highest total is the winner. The correct strategy is to always choose the largest remaining decimal number on the board. When the game is over you can look down the columns of decimal numbers that each team recorded and they should be ordered from largest to smallest. If not, some interesting discussions can arise and you can get a gauge as their teacher how well your pupils have learned the skill of ordering decimal numbers. You can create variations on the game, making it a two, three or four player game rather than a whole class game. Winner stays on etc… Who will be class champion?!