Partition & rename numbers (standard & non-standard)
Theory
Partitioning and renaming numbers is a Year 3 place value skill: splitting a number into thousands, hundreds, tens and ones, writing it in standard and expanded form, and renaming it in non-standard ways. This Year 3 maths page explains how 324 can be shown as 3 hundreds, 2 tens and 4 ones, or renamed as 2 hundreds, 12 tens and 4 ones, how many tens or hundreds are in a number, and why renaming helps with subtraction. Curriculum: VC2M3N02, VC2M3N04 / AC9M3N01, AC9M3N03.
To partition a number means to split it into parts by place value. The usual way is standard partitioning: break the number into thousands, hundreds, tens and ones. For example, \(324\) is \(3\) hundreds, \(2\) tens and \(4\) ones, so \(324 = 300 + 20 + 4\). Written as a sum like this it is in expanded form. In \(7091\) there are no hundreds, so \(7091 = 7000 + 90 + 1\).
Non-standard partitioning splits the same number a different way, using more than \(9\) in a place. You can rename \(324\) as \(2\) hundreds, \(12\) tens and \(4\) ones, which is \(200 + 120 + 4\). The number has not changed, it is just grouped differently.
Renaming works because ten of one place makes one of the next: \(10\) ones \(= 1\) ten, \(10\) tens \(= 1\) hundred, and \(10\) hundreds \(= 1\) thousand. So a whole number can be counted in any place: \(5300\) is \(53\) hundreds or \(530\) tens altogether.
Renaming does not need formulas, but these place value facts are the ones to remember. Ten of one place always makes one of the next.
How to rename a number
- Partition first. Split the number into standard place value parts: thousands, hundreds, tens and ones.
- Trade a place. Swap \(1\) hundred for \(10\) tens, or \(1\) ten for \(10\) ones, wherever you need more. Ten of one place makes one of the next.
- Check the total. Add the new parts. They must still make the number you started with.
How to read non-standard blocks
- Find each value. Work out what each group is worth, for example \(14\) tens is \(140\).
- Add the values. Add the groups to get the number, then trade 10 for 1 to write it the standard way.
| \(476\) | \(=\) | \(4\text{ hundreds},\ 7\text{ tens},\ 6\text{ ones}\) |
| \(476\) | \(=\) | \(400 + 70 + 6\) |
Standard partitioning gives \(400 + 70 + 6\).
| \(7091\) | \(=\) | \(7000 + 0 + 90 + 1\) |
| \(7091\) | \(=\) | \(7000 + 90 + 1\) |
The 0 hundreds are left out, so \(7091 = 7000 + 90 + 1\). The 9 is in the tens place, so it is worth \(90\).
| \(2\text{ hundreds}\) | \(=\) | \(200\) |
| \(362 - 200\) | \(=\) | \(160 + 2\) |
| \(160\) | \(=\) | \(16\text{ tens}\) |
The blank is \(16\) tens, because \(200 + 160 + 2 = 362\).
| \(100 + 140 + 5\) | \(=\) | \(245\) |
| \(14\text{ tens}\) | \(=\) | \(1\text{ hundred},\ 4\text{ tens}\) |
The blocks make \(245\). Renamed the standard way, that is \(2\) hundreds, \(4\) tens and \(5\) ones.
(i) How many hundreds are there altogether?
(ii) How many tens are there altogether?
(iii) Write \(2480\) as hundreds and ones.
| \(5300\) | \(=\) | \(53\text{ hundreds}\) |
| \(5300\) | \(=\) | \(530\text{ tens}\) |
| \(2480\) | \(=\) | \(2400 + 80\) |
(i) \(53\) hundreds.
(ii) \(530\) tens.
(iii) \(24\) hundreds and \(80\) ones.
| \(92\,000 - 80\,000\) | \(=\) | \(12\,000\) |
| \(90\,000\) | \(=\) | \(80\,000 + 10\,000\) |
The gap is \(12\,000\). One ten thousand was renamed as 10 thousands.
| \(500\) | \(=\) | \(4\text{ hundreds},\ 10\text{ tens}\) |
| \(10\text{ tens} - 3\text{ tens}\) | \(=\) | \(7\text{ tens}\) |
| \(500 - 30\) | \(=\) | \(470\) |
Renaming \(500\) as \(4\) hundreds and \(10\) tens gives tens to subtract from, so \(500 - 30 = 470\).
Common pitfalls
Frequently asked questions
What does partition mean in maths?
To partition a number means to split it into parts by place value. For example, \(456\) partitions into \(400 + 50 + 6\).
What is non-standard partitioning?
Non-standard partitioning splits a number in a different way to the usual places. For example, \(456\) can be renamed as 3 hundreds, 15 tens and 6 ones, which is \(300 + 150 + 6\). It is still \(456\).
How do you rename a number in place value?
Trade one block of a place for ten of the next place down. One hundred becomes 10 tens, and one ten becomes 10 ones. The number stays the same, it is just grouped differently.
Why do we rename numbers before subtracting?
Renaming gives you enough in a place to subtract from. To work out \(500 - 30\), rename \(500\) as 4 hundreds and 10 tens, then take 3 tens from the 10 tens to get \(470\).
How many tens are in 5300?
There are 530 tens in \(5300\). Cover the ones digit and read what is left.
What is expanded form?
Expanded form writes a number as the value of each digit added together. For example, \(476 = 400 + 70 + 6\).