Comparing and Ordering Decimals using Money

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SWBAT compare and order decimals by using money.

Big Idea

Using money can give the students a conceptual understanding of comparing and ordering money.

Whole Class Discussion

15 minutes

Today's lesson is comparing and ordering decimals using money.  This aligns with CCSS 4.NF.C.7 because the students compare two decimals to hundredths by reasoning about their size. The students record the results of the comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.  

I let the students know that before we begin the lesson, we will review place value.  I remind the students that we used money to learn about decimal place value.  On the Smart board, I have the Comparing and Order Decimals Using Money.pptx power point displayed.  I ask the students, "What place does the whole number begin?"  Student response:  2.  I remind the students that the ones place is the where the whole number begins.  In money, we said that the ones place is like dollars.  To the right of the decimal, we have the tenths place.  I point out that tenths ends with "ths."  I tell the students that when they see "ths" in place value it is to the right of the decimal.  This represents a fraction of a number.  I ask the students, "What money represents the tenths place?"  Student response:  dimes.  If the 4 in the table represented dimes, then we would have forty cents.  The 7 is in the hundredths place.  I ask the students to tell me what money represents the hundredths place.  Student response:  pennies.

To make this lesson relevant to their everyday lives, I ask, "When might you compare two decimals in the real-world?"  Student responses:  1) When I go to the store and buy something, I need to know how much it costs so I can compare it to how much money I have, 2) When I want to buy the cheapest candy bar.   

On the Smart board, problem 1 is displayed:

Teresa and Becky are comparing extra credit points earned on a test. Teresa earned .5 points.  Becky earned .25 points.  Who earned more extra credit points?  

 I ask the students to tell me who they thought had more extra credit points.  (I want to find out how the students were thinking early in the lesson.  It gives me an idea of how much time I need to dedicate to this skill.)  One student responded, "Becky has the most points because she has the biggest number."  I wanted to know his thinking, so I asked, "How do you know she has the biggest number."  His response, "25 is bigger than 5.  His response lets me know that the student is not considering decimal place value.  He is looking at these two numbers as whole numbers. 

I display a decimal place value chart on the board.  I put .5 on the place value chart under the tenths place.  Then, I put .25 on the place value chart.  I ask, "If the 5 is in the tenths place, how much money would it be if we are talking about dimes?"  Student response:  50 cents.  How much money is .25?  25 cents.  Who has more?  Student response:  Teresa.

I let the students know that they should justify their answer by using visual models.  On the Smart board, I display the hundreds grid.  First, we shade 5 rows, which is 50 pieces, to represent Teresa's extra credit points.  Next, we shade 25 squares to represent Becky's extra credit points.  This gives the students to visual to actually see that .5 is greater than .25.

On the next slide, it gives the students a visual model using money.  On the board, the students see 5 dimes to represent five-tenths.  Also, they see 2 dimes and 5 pennies that represent twenty-five hundredths. 

Based upon money, we discuss putting numbers in order from least to greatest.  I ask the students to tell me the value of each number as if it is money.  (I find that the students can relate to money.  It makes comparing and ordering numbers easier.)  The students put the numbers in order from least to greatest:  0.55, 4.37, and 6.98.

To give the students more practice, I let them guide me through problem 2.  Upon completing problem 2, the students practice the skill in centers.

Skill Building/Exploration

25 minutes

To give the students practice on the skill, they work on center activities.  The activities are designed based upon student skill levels.  The students are placed in groups according to their abilities.  I used the activities for the following levels:  Activities 1 and 2 were for average students; activity 3 was for advanced students, and activity 4 was for lower level students.

Activity 1:  Compare and order decimals listed in a table (Comparing and ordering decimals activity sheet1.docx).  Use the money to help you compare the decimals.  For example, if you are comparing .46 and .38, you should take out 4 dimes and 6 pennies for 46 cents, and 3 dimes and 8 pennies for 38 cents.  Justify at least 1 of your answers with a model using the hundreds chart.  Write >,<, or =.  On your notebook paper, write to explain how you know your answers are correct.


Activity 2: (Activity 2 Comparing and Ordering Decimals.docx)  Roll the number cube twice.  The first number is the tenths place.  The second number is the hundredths place.  Roll the number cubes two more times to get the second decimal.  Compare numbers in two ways (hundreds chart and money).  Write >, <, or =. Write to explain how you know your answers are correct.  


Activity 3:   What’s for Sale?

Use the sales paper to compare decimals from Fred's and Family Dollar.  Find an item that you want to purchase (such as potato chips) from each store.  Use money to display each decimal.  Compare the decimals using >, <, or =. Write to explain how you know your answers are correct.  Record you answers on notebook paper.


Activity 4:  Choose a site to compare and order numbers.

Site 1

Site 2

Site 3 

Early Finishers:  Choose 1:

1) Write a paragraph explaining what your learned today.  2) Math book page 286 Set A


15 minutes

To close the lesson, I bring the students back together as a whole class.  I feel that it is very important to let the students share their answers as a whole class.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work) (Student Work - Comparing Decimals.jpg), as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the activity will be addressed whole class. 

I collect all papers from the students.  All struggling students identified as I monitored during the activity will receive further instruction in small group.