# Comparing Decimals

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## Objective

Students will be able to compare to numbers with decimals into the thousandths.

#### Big Idea

Think of it like a grid!

## Opener

10 minutes

Today’s lesson will focus on creating models from hundreds grids to compare decimals.  In fifth grade students will have pretty good understanding of what it means to compare a whole number but as we move to comparing numbers with decimals they get a little confused.  My goal is to show students what a decimal looks like using a hundreds grid and then apply that knowledge to compare numbers with decimals with places further than the hundredths.

I open the lesson by having students write some numbers with decimals into expanded form.  This is part of a Powerpoint that I used in a previous lesson.  I display each number and have the students write the expanded form on their whiteboards.  For this lesson I ask students to use the fraction form of expanding the numbers.  For example, if the number is 9.5, the students should write 9+5/10 instead of 9+0.5.

After allowing the students a few moments for the first number, I ask them to raise their board.  I look around the room for a correct response to highlight.  Once I have found a student that has a correct response I identify them to the class and have them explain their answer as others look and listen to the response.  I then display the answer on the Powerpoint.  I continue in this fashion for the remainder of the slides.

## Practice

20 minutes

As we move into the practice portion of the lesson I really want students to gain a flexible understanding of what decimal places represent.  To do this I use a sheet pulled from commonsheets.com.  It includes tenths and hundredths comparing problems using a hundreds grid for each number.  The students have to determine the decimal number from a hundreds grid example and then have to compare the numbers to each other in sets of four.

My students have a lot of prior experience with using base ten blocks in math and when I am using a hundreds grid for decimals it is important to make the distinction to them that this grid represents the number 1.  I don’t want them to think of the grid as tens and ones; I want them to think of it as a square that represents one and if we divide up the square we can use fractions of one.  Before passing out and starting the worksheet I explain this concept to students.

Alright, I’m going to draw a square on the board.  How many squares do I have on the board?  Since I have one square we can think of this as one whole.  What if this square was the playground outside and I wanted to split it up into parts to run a race between ten of you?  Could I split this square into ten equal parts?

Students quickly understand that I am able to split the square into ten parts by drawing lines all in one direction on square to create the running lanes.  I have them help me label the ten parts as I continue to emphasize that the square is one.  Each part of the square is then labeled 1/10.

Now think back to our examples we just did with expanded form.  If this part is one tenth as fraction written one over ten, what would one tenth be as a standard number?  Talk to your neighbor.

I allow the students some time to think about this question with their neighbor.  My hope is they are able to see the connection between 1/10 as a fraction and 0.1 as a decimal using their knowledge of expanded form.  I bring students back to a whole group and ask for responses and then move into using the worksheet.

I complete the first row of the worksheet with the students.  The first step for this worksheet should be writing the name for each decimal.  While determining the answer to each grid I emphasize the square being one again.  I have students write the decimal underneath the grid for each square first.  After they complete that, I ask them to compare the decimals and order them least to greatest.    I allow the students time to work with their group for solving the remaining grid sets.

## Closer

20 minutes

To wrap up today’s activity I give students a quick quiz using a Powerpoint presentation with six questions.  I have students write down the answers on a scrap piece of paper as they take the quiz individually and self-grade at the end.  Before starting the quiz I remind students to think of decimals as grid.

While the students are self-grading the quiz I ask them to think about how they did.  I encourage them to come and see me if they need more help on comparing decimals.  To gauge the successfulness of today’s lesson I have students show me with their hand on their chest how many questions they got wrong.  I look around the room to identify students who struggled.