Comparing Decimals to the Thousandths Free Lesson Plan and Activities

The lesson that I am sharing today is comparing in ordering decimals to the thousandths. In previous grade levels, students have compared and ordered decimals using models and they compared and ordered whole numbers using <, >, and =. This standard scaffolds into higher grade where students need to compare and order all rational numbers. Since rational numbers can be converted into decimals if students have a strong foundation and understanding decimals in their value than it will help them with the higher level comparing. 

The TEKS this lesson covers says "compare and order decimals to thousandths and represent comparisons using symbols >,<, and =."  The common core standard states "students will compare two decimals to thousandths based on meanings of the digit in each place using >, <, and = symbols to record the results of comparisons."

When you work with students comparing in ordering decimals you see what types of misconceptions they have pretty soon in the lesson a lot of students may feel that 0.49 is less than 0.432 because the second number has more digits. 

Anytime students are comparing two numbers I like to use a number line. Students have used number lines before and have placed numbers on the number line and I believe it is important for them to be familiar and fluent with how to place numbers on a number line. You can start by providing students with teacher created number lines but I think it is more beneficial for students to eventually create their own number lines. This lesson begins with students looking at a number line and placing numbers on the number line. 

You can download the lesson for free here. I left the actual lesson plans in Word form so you can edit it as need. 

If you would like any more resources for comparing decimals to come back to this topic for review throughout the year, you can check out these items in my TpT store. 

Rational Numbers Cards FREEBIE Small Group Instruction Ideas

One things I consistently used every year was random numbers written on cards. Usually, I would take some index cards, cut them in half, and write random numbers on them right before class started. 

Once small groups started, I pulled students over and depending on the topic, gave them random numbers to work with. 

I used these number cards for classifying numbers, ordering and comparing numbers, converting between fractions, decimals, and percents, and rational number operations. 

By the end of going through 3-4 groups per class, over 3 classes over 2 day, those cards got a lot of use out of them. 

So, I wanted something that would last longer, and where I wouldn't have to use brain power to come up with random numbers on the spot. (Have you ever made yourself come up with random numbers on the spot? Eventually I can't think of anything!)

I created these cards with lots of numbers so I could laminate them on pretty colored paper and use them over and over again without scrambling to write down numbers real quick. 

Here are some ideas on how you can use them in small group instruction:

• For ordering numbers, students pull 5 random cards and order them least to greatest, greatest to least (use all the vocabulary here)
• For classifying numbers, students pull 10 random cards. Create a large Venn Diagram on butcher paper and students will classify numbers. 
• For converting numbers, give students a fraction, decimal or percent and ask them to generate two equivalent numbers. 

Of course, you can differentiate for each student. You can give them random cards or you can choose specific cards to give them depending on what kind of practice they need. 

I find that in the best small group instruction, students need to do most of the talking. So as they are completing the tasks above I ask them questions. 

"Why did you put this number there?" "Explain the process you used for this." "Why isn't this number an integer?"...

Posts I Love--Part 7

I love reading math blogs. I like reading what math teachers try in their classroom and reading their reflection on how it went.

Here is a collection of blog posts I love!

Fraction Ordering Activities from Math Fireworks-- The students will be practicing ordering rational numbers this week.This activity from Math Fireworks only talks about fractions, but I would like to expand it to include decimals and percents. I like the ideas of having students share their reasoning and discuss mistakes with each other.

I found this game which is a very basic but necessary beginning practice for graphing in all four quadrants. Stock the Shelves

I Speak Math shared this game. I will have it as a small group station to practice integer operations and absolute value. All I'll need is a deck of cards.

Finally, I love this activity about volume over at No. 2 Pencils.  She poses the question "How many starburst can fill our classroom?" and students go about measuring and formulating plans to figure out the answer. Definitely a thing I want to try.

Hopefully you are inspired to try something new!

Blog Posts I Love--Part 6

Doing these blog posts help me remember the great ideas that I have read and helps me plan for how I will use them in my classroom.

1. I have wanted to set up a large number line in my classroom for a while and this blog post gave me the push. Mr Elementary Math posted about a number line that is geared towards younger elementary. To make it appropriate for my 6th graders, I will mix fractions, decimals, percents for students to place on the number line. I want to have this as a station that students can rotate into.

2. Another post from Elementary Math Coach--Math Pictionary. This is the second time I have posted about this and I am actually going to make something for a math station. Students will get an integer operation problem and will draw the algebra tiles that model that problem which their team mates will have to name.

3. The growth mindset is something I am going to talk to my students about the day we get back from winter break. This is one blog posts at Edudemic on the importance of having a growth mindset. I have a bulletin board that focuses on growing in math and I want to make sure I am talking to my students about it.

4. When my students take tests, I do not let them turn it in early. I give them a time and tell them they need to be working on the test until then. My students don't try to turn in the test early, but they will close their test and just sit there until it is time. I ask them to go back and check their work and some students will say "I already did" and others will go through and check that they did all the problems.

I experimented with one class one day and briefly looked through their tests when they said they were done and said "It's not a 100." All of the students went through and some found at least one mistake and changed their answer.

At Who's Who and Who's New,  this post explains the levels of checking your work. Something I want to share with my students. There are three levels from make sure you check that you have an answer, checking that your answer is reasonable, and solving the problem again.

Card Clutter

Another FREE app. Algebra Card Clutter.  At first glance, it seems very basic. But it provides good ordering practice for students. 

Basically, students order numbers as fast as they can. It start pretty simple with just natural numbers, but then it gets progressively harder adding different types of numbers. 

Students are timed as they go and work up the levels.