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# Place value

**Place value understanding** is used extensively in mental strategies.

A simple way to look at place value is counting.

Organising objects into groups of ten, one hundred, etc. is an easy way to keep track of counting a set.

Students need experiences of bundling individual objects (such as counters or icypole sticks) and linking the number of bundles and the extras to the written form of symbols.

- Applying the convenience of counting sets (using bundles of ten, one hundred, etc.) to addition and subtraction problems helps students to realise the usefulness of the system. Using groupings of tens and ones is more efficient than working in ones and makes learning about place value attractive to students.
- Renaming and decomposing units of ten (and later one hundred, one thousand, etc.) poses new challenges for students. This requires understanding the conservation of number (i.e. the number of objects stays constant during rearrangement).

Place value is a **multiplicative system**.

Students need to understand that the value of a digit in any numeral depends on the count it reflects (e.g. 4 means four of something) and the place it holds (e.g. if 4 is in the hundreds place then its value is 400). The significance of units is particularly important in solving multiplication problems. For example, 40 \(\times\) 30 has a relationship to 4 \(\times\) 3 = 12.