Decimals challenge learners to understand a new form of notation to represent specific fractions. Both the decimal notation and the fraction concepts need to be well-developed for students to master the topic.
I like to use hands-on activities to allow students the opportunity to develop decimal concepts in their mind. I always begin with a decimal grid model for tenths and relate it to the hands-on fraction tiles we have used previously. We take some time to practice decimal word names, decimal notation, and the equivalent fraction notation for tenths before jumping into hundredths.
I strongly believe it is important for teachers and students to practice reading 0.7 as "seven tenths" instead of "zero point seven". Using the proper fraction-based name for the decimal helps our minds process the actual size of the decimal fraction.
Next, introduce the decimal grid model for hundredths. I like to take a tenths grid and draw new lines on it to change it into a hundredths grid so the learners can see it "transform". Once again, we take plenty of time to practice decimal word names, decimal notation, and the equivalent fraction notation for hundredths.
For students that have a firm grasp of money, you may talk about $1.00 being a "whole object", tenths being equivalent to a dime, and hundredths being equivalent to a penny. Using the decimal grids along with the money concepts will help students make comparisons between tenths and hundredths.
One of the activities we do during class is to color decimal grid models for 0.4 and 0.40. Then I have the students write a statement comparing the shading. Many of them do not immediately see that the same quantity of the whole object is shaded in each grid. Some students require a significant amount of time for this to make sense.
At this moment, the relationship with money can be handy. We talk about how 0.4 is the same as four-tenths or 4 dimes. Many are quick to answer that the value of 4 dimes is 40 cents. Then we discuss the fact that 0.40 is the same as forty-hundredths or 40 pennies. Again, many are quick to answer that the value of 40 pennies is also 40 cents. By now, most of them are convinced that 0.4 = 0.40, but it may take a little more time for some of your students to understand the connection. More time and practice will help these learners.
I have designed two different hands-on Decimal Mini-Books to help students practice basic decimal concepts. One is titled "My Book of Tenths" and the other is titled "My Book of Hundredths". The tenths book is FREE and you will find the hundredths book in my TPT store for a minimal price.
Click on the image below to download your FREE copy of "My Book of Tenths".