Understanding Place Value
- an understanding of using zeros as place holders
- knowing what numbers after a decimal point represent
- being able to order numbers in terms of size
- an ability to estimate and round numbers
- a true understanding of how multiplying and dividing by factors of 10 work
- why we 'carry' in column addition and subtraction
- and much more...
- If you can simply add a zero when multiplying 3 by 10 to get 30, why can't you just add a zero when multiplying 3.3 by 10 to get 3.30? Here, there is no understanding that the zero on the end makes no difference to the value of the number, as the rest of the numbers are still in the same position so represent the same value. There is also no sense of the value that a number after the decimal point represents.
- 564 rounded to one significant would be 6. I have seen answers like this numerous times, even after lengthy discussions of how rounding is giving a rough idea of the size of a number. The students do not understand that the 6 needs to remain in the same position of the number to keep its value and that you need two zeros after the 6 as place holders.
- 8 + 3 is 11 so 0.8 + 0.3 is 0.11. I have seen many students struggling with column addition of numbers (and not just decimals) as they do not understand why you carry numbers to the column to the left. A true understanding of place value would help them to understand this.
Use an abacus
I found a fantastic resource on primaryresources.co.uk that can be used if you do not have a real abacus to hand. What I really like about this pdf is that each ball has the value of the ball written on it (1, 10, 100, 0.1 etc.), helping kids to see the value that each ball represents just because of its position within the number. I would prefer the kids to come up with the value and write it on themselves (otherwise they are being led to the conclusion, rather than realising it for themselves) but I love the idea. The only trouble with this resource is the amount of cutting required!
- 6 beads - this task asks students to investigate the numbers that they can make using 6 beads on a tens/units abacus. This task really requires students to understand that putting a bead on the 10s means that it has a different value to putting it on the units.
- Five steps to 50 - this task requires students to move in jumps of 10s and 1s to get as close to 50 as possible in just 5 steps. Although it doesn't link directly to the position based number system, it gets kids thinking about 10s and 1s and the fact that adding a 10 makes a much larger difference than adding a 1.
- Largest Even - This task asks students to find the largest possible even number given specific numbered cards. It gets kids thinking about the fact that having a large number in the 10s column is much more important than having a large number in the units column, again leading kids to think about the different value that a number has depending on its position within the number.
Poly Plug Patterns
The Universal Abacus
I strongly believe that kids gaining a deep understanding of place value early on can help overcome so many difficulties in the future. We teach kids numbers and how to count, we teach them the patterns of our number system and how to write the numbers down. It is all too easy to miss the opportunity to teach them a true understanding of place value before they gain all their own ideas and misconceptions. Let’s get kids counting with an abacus, investigating our number system at a young age and leading their own learning towards a fundamental understanding of place value and our decimal system.