Using Money to Understand Decimal Place Value

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Objective

Students will be able to use place-value charts to read and write decimals in tenths and hundredths by using money.

Big Idea

The relationship among dollars, dimes, and pennies is a good model for decimal numeration.

Direct Instruction

10 minutes

The students have already learned place value for whole numbers.  In today's lesson, they will learn to use money to help understand decimal place value.  

I tell the students, "You know how to identify place value for whole numbers.  Today, you will use money to identify place value for parts of a whole. What exactly is $8.23?  Let's find out."

I bring the class to the carpet for a whole class discussion on using money to understand decimals.  The Using Money to understand decimals.pptx powerpoint is on the Smart board.  

Discussion:

I begin the lesson by reviewing the vocabulary:

Tenths – One of ten equal parts of a whole.

Hundredths – One part of 100 equal parts of a whole.

Decimal Point – A dot used to separate a dollar from cents or ones from tenths in a number.

 I let the students know that we can use money to help us understand decimals.  A dime can help you understand the tenths place.  It takes 10 dimes to make a dollar.

A penny can help you understand the hundredths place.  It takes 100 pennies to make a dollar.

To practice using money to help with decimals, we practice by using the following information in the table:

 

Dollars

(ones)

 

 

.

 

Dimes

(Tenths)

 

Pennies

(Hundredths)

 

 8

 

.

 

 2

 3

 

 

 

 

 

 

 

 

 

 

 

There is a 3 in the hundredths place.  The hundredths place is like having pennies.  If you have 3 pennies, how much money do you have? I call on a student for a response.  There is a 2 in the tenths place.  The tenths place is like having dimes.  If you have 2 dimes, how much money do you have? 

Which place is greater, the tenths or the hundredths?  Explain.

I find that it is very important to question students in the whole class discussion.  This allows me to check for understanding as I teach.

After determining how to use money to help understand place value, I show the students how to write numbers.  

I let the students know that we can write this number in 3 other ways:

1.    8 ones, 2 tenths, and 3 hundredths
2.    8 dollars, 2 dimes, and 3 pennies
3.    8 dollars and twenty-three cents

 

To give students more practice, I tell them that we will  practice together.  Help me write this number in three other ways.

Dollars

(ones)

 

 

.

 

Dimes

(Tenths)

 

Pennies

(Hundredths)

 

 7

 

.

 

6

 2

 

 

 

 

 

 

 

 

 

 

 

 

After the whole class discussion, the students go back to their seats for instruction about the group activity.

Group Activity/Exploration

20 minutes

Activity:  Are we Equal?

Students will have 3 different numbers written in either word form, standard form, or expanded form.  The purpose of the activity is to have students be able to recognize their number in any form.  They will have to find other students with their numbers written in a different form.  For example, the number $5.48 will be written as 1) 5 dollars + 4 dimes + 8 pennies, 2) 5 ones, 4 tenths, & 8 hundredths, and 3) five dollars and forty-eight cents.  When the student finds someone with their number, they must each write down the number (in its form), and then record it correctly in the place value chart. If one student disagrees with the other student, then the they must use Accountable Talk to justify why they think they have the correct number.  If the other student can counter their example, then the students must see the teacher to solve the disagreement.  The teacher will not tell the students the correct answer, but will lead the students to the answer by questioning the students to get them to understand for themselves.  

When the students find all 3 forms of their numbers, they must write a paragraph explaining how they know they have found the correct numbers.  Also they must explain the difference between the tenths and hundredths place (what money can help them with these places.)

Any students who complete the activity early, may go to the computers to practice the skill at the following site:

 http://www.kidsmathgamesonline.com/numbers/decimals.html

 

Independent Activity/Exit Ticket

15 minutes

I give each student an independent activity sheet. First, the students put numbers on a place value chart.  This shows me if the students understand decimal place value. In today's lesson, the students learned to write the numbers in 3 different ways.  On the independent activity, the students must do this to show mastery of the skill.  Also, the students must explain how the place value chart and money help with their solving of the problem.

This independent activity is very important because it gives me the opportunity to see if the students actually mastered the skill.  Group work excellent to build a classroom community, and hear how other's think.  However, I feel that independent work is essential to allow the teacher to assess whether all students mastered the skill.