## Repeating Decimal Lesson Plan: You've Never Seen a Better Explanation

By Raphael Kohlberg

After your students are familiar with decimals, get them to extend their thinking. In this lesson students will discover why a repeating decimal repeats!

Give the students a division problem with an answer with a repeating decimal. For instance: 658 ÷ 3 (the answer will be 219.333333333 or 219.3 ̅)

When they divvy up the blocks, each plate gets 219 blocks, and we have 1 leftover.

The leftover single block “unpacks” to 10 tenths, and each plate gets 3 of the tenths, with 1 tenth leftover. (Not familiar with decimal blocks? checkout our introduction to decimal lesson plan)

The leftover tenth block “unpacks” to 10 hundredths, and each plate gets 3 of the hundredths with 1 hundredth leftover.

The students can explain what will happen each time we open the leftover block. They also understand that this pattern will continue infinitely. They explain to me what a repeating decimal is!

Similarly, 100 ÷ 3 is a fun problem. Some advanced students are able first to explain/draw/write about what will happen with the blocks. Then they can physically model the problem with blocks to check their answer.