I think this was one of the hardest things for my students to grasp at the beginning of the year. When I taught it in fifth grade it always seemed to be some portion not understood. Even in sixth grade I see it playing out in students not understanding place value.

It is something that needs to be practiced and seen over and over for some students.

This one subject spans many grades but I will attack it from 4th through 6th grade.

In 4th Grade: Compare and order decimals using concrete and visual models to the hundredths.

In 5th Grade: Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =.

In 6th Grade: Order a set of rational numbers arising from mathematical and real-world contexts,

As you can see it builds off each other leading to a deeper Understanding. If one portion is missed then it hurts our students as they progress through different grades.

What are some of the misconceptions we see when dealing with ordering and comparing decimals?

Students will often believe that a thousandth is larger than a hundredth because they know that a thousand is larger than a hundred. The way we work around this is by practicing and seeing this applied in different ways. This really plays out in sixth grade when students start working with positive and negative numbers.

Students will often think that .348 is larger than .35 because they see 348 being larger than 35. Again this is where we want to see students understanding place value and using number lines and other graphic organizers to see the value of each place value.

Students will attempt to place a tenths in the tens place value. This is one area where expanded notation can really help. Have them write several numbers in expanded notation. I wrote an article on expanded notation

I already mentioned it above but students need to realize just because a number looks larger does not mean it is larger in value.

Students will not equate .5 as the same as .50. They do not see the equivalence.

When it comes to ordering and comparing decimals the one thing I have always done is have them add a zero. For example:

This allows them to see the numbers in a different way. With your struggle learners it will help them a lot.

I put together a resource on comparing and ordering decimals. You can find it by clicking on the image below.