Ask Marian

I don’t think there is a best manipulative, but one of the tools I find very valuable is a fraction tower.

This way, students can see many fraction comparisons and equivalences all in one spot, and they can see that unit fractions with a greater denominator are smaller than those with a smaller denominator.

If the focus is on relating fractions to percentages or to decimals, other manipulatives or visuals, such as a 100-chart, might be more useful.

A Rekenrek is designed to show numbers in groups of 10, but it also shows subgroups of 5.

Here is an example of a small one:

Here is an example of a larger one:

Just like with 10-frames, students are linking numbers both to multiples of 10 and to multiples of 5. But students might find it easier to just slide beads than to fish out and put down counters. From a mathematical point of view, however, they are very similar.

Different people will, of course, have different opinions on this. Asking students to occasionally write down their thinking is probably a good idea since we ultimately want them to communicate their thinking in writing. But if this is required too frequently, it may not be the best use of your instructional time since students are not really thinking about the math then; instead, they are thinking about how to record it. Furthermore, we may get an incorrect impression of their understanding since some students do understand but find it difficult to communicate their thinking in writing.