If I could choose one thing to teach in place value it would be…Renaming

If I could choose one thing to teach in place value it would be…Renaming

Over the years I have taught many Year 3-6 students who display a superficial understanding of our whole number place value system. This has not only held them back from mastering decimals, it has also hindered the development of their Number Sense. My research into place value identified the need to focus our teaching around six key aspects: Count, Calculate, Compare/Order, Make/Represent, Name/Record and Rename. While each of these aspects is important, the most critical is Renaming.

Essentially Renaming is rearranging a number into a different form without changing its value. For example, 345 can be renamed as 33 tens and 15 ones. The value of the number is the same, however the form it is presented has changed. Renaming is particularly difficult for students to master as it requires a deep understanding of our “10 of these is one of those” place value system. It also requires multiplicative thinking- something we know takes time to develop in students. Nonetheless, is important to persist with teaching this skill.

Renaming requires students to understand that there are smaller units “hiding within” larger units. For example, to rename 420 in term of tens, a student must understand there are 2 tens in 20 but there are also 40 tens “hiding inside” the 4 hundreds. When asked how many tens are in 420, children are accustomed to focusing their attention on the tens column, as they believe this is the only place the tens “live”. It is this narrow focus that leads students to become ‘Independent Column Thinkers’. Students who think in this way, fail to appreciate the multiplicative relationship between columns, making it near impossible to rename.

Without doubt renaming is a difficult concept to teach students. My experience has shown that visuals are critical. I like to introduce the idea of renaming using Russian Babushka dolls. These dolls allow students to see the smaller dolls hiding inside the larger, just like in place value where smaller units like tens ‘hide inside’ hundreds or thousands. I encourage students to look in each column in a number and consider which units are ‘hiding’. For example, in 420 I would ask:

 “Are there any tens in the ones column?”, No, they are too big to fit in there.

 “Are there tens in the tens column?”, Yes, there are two.

“What about the hundreds column?” Yes, there are 40 tens hiding.

Therefore, we can rename 420 as 42 tens. We want students to appreciate that the value of the number remains as 420, it is simply written in a different form. Analogies can be made here- ice is simply water in another form, melt the ice and the water returns- similarly, whether it is written as 42 tens or 39 tens and 30 ones, its value remains as 420.

We must also make students aware of the contexts where renaming is useful. One such context is when completing the formal algorithm. Teachers often use inaccurate terms like “borrow” or “carry” when modelling the algorithm. I always ensure I use the term ‘renaming’ when I complete an action like taking 1 ten and renaming it as 10 ones. The consistent use of this word allows students see how the algorithm links directly to the renaming work they have been doing in place value. Students also come to appreciate that when we rename a number in an algorithm we are not changing its value, we are writing it in a form that is simpler to compute.

In summary, if there was one skill I could encourage teachers to explicitly focus on when teaching place value it would, without doubt, be Renaming.