DIVIDE WITH DECIMALS
INTRODUCTION
The objective for this lesson on Divide with Decimals is, the student will divide using decimals to the thousandths place in mathematical and real-world situations.
The skills students should have in order to help them in this lesson include, dividing whole numbers and place value.
We will have three essential questions that will be guiding our lesson. Number One, what does division of decimals mean? Number Two, what happens to the decimal point when decimals are divided? And Number Three, what happens to the value of decimals when they are divided?
Begin by completing the warm-up for this lesson on multiplying decimals to prepare for the lesson on division of decimals.
SOLVE PROBLEM – INTRODUCTION
The SOLVE problem for this lesson is, Maurice and his father are building a dog house. They are using long pieces of wood and cutting them into smaller pieces. They are working on the shorter pieces of wood on the dog house door. If they have a piece of wood that is three and six tenths feet long, how many seventy five hundredths foot lengths can they cut from the longer piece of wood?
In Step S, we Study the Problem. First we need to identify where the question is located within the problem and underline the question. The question for this problem is, how many seventy five hundredth foot lengths can they cut from the longer piece of wood?
Now that we have identified the question we need to put this question in our own words in the form of a statement. This problem is asking me to find the number of seventy five hundredth foot lengths of wood that can be cut from the longer piece of wood.
During this lesson we will learn how to divide decimals to complete this SOLVE problem at the end of the lesson.
DIVIDING WITH DECIMALS TO TENTHS WITH PICTORIAL REPRESENTATIONS
What does the model represent? Ten tenths or one whole.
If you wanted to divide the model by two tenths, how could you represent the answer on the model? Draw lines around groups of two tenths.
Let’s circle the groups of two tenths.
How many groups of two tenths are in one whole? One, two, three, four, five. There are five groups of two tenths in one.
How would this problem be written in numerical form with the quotient? One divided by two tenths is equal to five.
If you wanted to work with six tenths and divide it by three tenths, how many groups of three tenths would be separated?
What is the value of the dividend? Six tenths
What does the divisor represent? Three tenths represents the size of the groups.
If you wanted to work with six tenths and divide it by three tenths, how many groups of three tenths would be separated?
What does the quotient represent? Two represents the number of groups of three tenths. One, two
How would this problem be written in numerical form with the quotient? Six tenths divided by three tenths equals two.
DIVIDING WITH DECIMALS TO HUNDREDTHS WITH PICTORIAL MODEL
What does the model represent? Hundredths
Let’s divide the model into groups of twenty five hundredths. Circle the groups of twenty five hundredths. One group, two groups, three groups, four groups
How many groups of twenty five hundredths are in one whole? Four
How would this problem be written in numerical form? One divided by twenty five hundredths is equal to four.
If you wanted to work with thirty two hundredths and divide it by eight hundredths, how many groups of eight hundredths would be separated?
What does the dividend, thirty two hundredths, represent? The area to be divided.
What does the divisor, eight hundredths, represent? The size of the groups.
If we want to work with thirty two hundredths and divide it by eight hundredths, how many groups of eight hundredths would be separated? One, two, three four. Four groups
If you wanted to work with thirty two hundredths and divide it by eight hundredths, how many group of eight hundredths would be separated?
How can we write our problem in numerical form? Thirty two hundredths divided by eight hundredths is equal to four.
PATTERNS WITH DIVING DECIMALS.
Let’s look at our chart that has the Patterns with Dividing Decimals. We have our Dividend, Divisor, Quotient, How many places did the decimal point move in the answer? Which direction did the decimal point move? And why?
Take a look at the fourth row in the chart which shows fifteen and thirty five hundredths divided by one.
What is the quotient? Fifteen and thirty five hundredths
Explain the position of the decimal point in both the dividend and the quotient. They are in the same place.
How many decimal places did the decimal point move in the answer? Zero
Which direction did the decimal point move? It did not move.
Explain why the decimal point did not move. Dividing any number by one will not change the value.
When we divided fifteen and thirty five hundredths by one our quotient remained the same.
We moved the decimal point zero places, it did not move, because when we divide by one there is no change.
Take a look at the third row in the chart which shows fifteen and thirty five hundredths divided by ten.
What is the quotient? One and five hundred thirty five thousandths.
How many decimal places did the decimal point move in the answer? One
Which direction did the decimal point move? To the left.
Explain why the decimal moved one place to the left. Because we are dividing by a power of ten, the digits in the quotient are the same as the dividend, but the decimal point moves to the left one place.
When we divide by ten our quotient is one and five hundred thirty five thousandths.
How many places did the decimal point move in the answer? One
Which direction did the decimal point move? To the left.
And why? When we divide by ten we have a change in the value.
Complete the second row and then the first two of the chart using one hundred and then one thousand as divisors.
Take a look at the fifth row in the chart.
What is fifteen and thirty five hundredths divided by one tenth? One hundred fifty three and five tenths.
How many places did the decimal point move in the answer? It moved one place.
What direction did the decimal point move? To the right.
Why did the decimal point move one to the right? Dividing by one tenth will make the answer larger.
When we divide by one tenth our quotient is one hundred fifty three and five tenths.
How many places did the decimal point move in the answer? One
What direction did the point move? To the right.
Why? When we divide by one tenth the value changes.
Complete the rest of the chart.
What is the problem asking us to find? How many groups of eight tenths are in thirty two hundredths?
In order to divide decimals, we must first “jump the decimal point” in the divisor to the right to make the divisor a whole number.
Now we must “jump the decimal point” in the dividend the same number of spaces it jumped in the divisor. Let’s jump the decimal point in thirty two hundredths to the right one place.
Now we can bring the decimal point straight up and then divide.
Since thirty-two divided by eight is equal to four, we should place a four directly above the two in the dividend and write a zero in front of the decimal point as a place holder.
What is the problem asking us to find? How many groups of eight hundredths are in thirty two hundredths?
How is this problem different from Problem One? Problem Two is the same as Problem One, except that the divisor is in hundredths now instead of tenths.
We will “jump the decimal point” in eight hundredths to the right two spaces to make the divisor eight.
We must “jump the decimal point” in the dividend the same number of spaces it jumped in the divisor. Let’s jump the decimal point two spaces to the right.
Now bring the decimal point straight up and divide.
Since thirty-two divided by eight equals four, we should place a four directly above the two in the dividend.
DECIMAL FOLDABLE – DIVISION
Label the top of the fourth column “Divide Decimals.”
Determine the steps used for dividing decimals.
SOLVE PROBLEM – COMPLETION
We are now going to go back to the SOLVE problem from the beginning of the lesson. The question was, Maurice and his father are building a dog house. They are using long pieces of wood and cutting them into smaller pieces. They are working on the shorter pieces of wood on the dog house door. If they have a piece of wood that is three and six tenths feet long, how many seventy five hundredths foot lengths can they cut from the longer piece of wood?
In the S Step, we Study the Problem. We underline the question and we complete this statement, this problem is asking me to find the number of seventy five hundredths foot length of wood that can be cut from the longer piece of wood.
In the O Step, we Organize the Facts. First we identify the facts. We go back to our original problem and we place a vertical line or a strike mark at the end of each fact. Maurice and his father are building a dog house./ They are using long pieces of wood and cutting them into smaller pieces./ They are working on the shorter pieces of wood on the dog house door./ If they have a piece of wood that is three and six tenths feet long,/ how many seventy five hundredth foot lengths/ can they cut from the longer piece of wood?
After we identify the facts we eliminate the unnecessary facts. Maurice and his father are building a dog house. We can strike that fact because it will not help us determine how many of the smaller pieces of wood we need. We can also strike the second fact. We can also strike the fact that we’re using pieces of wood on the dog house door.
After we eliminate the unnecessary facts we list our necessary facts. The longer piece of wood is three and six tenth feet long, and the shorter length is seventy five hundredths foot long.
In the L Step, Line Up a Plan. First we write in words what your plan of action will be. We’re going to divide the larger length by the smaller cuts.
Then we choose an operation or operations. Our operation will be division
In the V Step, we Verify Your Plan with Action. First we estimate your answer. About five lengths.
Carry our your plan. Three and six tenths divided by seventy five hundredths is equal to four and eight tenths lengths.
E, Examine your Results.
Does your answer make sense? Compare your answer to the question. Yes, because we are look for the number of seventy-five hundredth foot length.
Is your answer reasonable? Compare your answer to the estimate. Yes, it is close to our estimate of five lengths.
Is your answer accurate? Check your work. Yes.
Write your answer in a complete sentence. There are four and eight tenths pieces of seventy-five hundredth foot lengths of wood that can be cut from the longer piece of wood.
CLOSURE
Now let’s go back and discuss the essential questions from the lesson.
Our first question was, what does division of decimals mean? Separating part of a whole into equal groups or separating part of a part into equal groups.
Number Two, what happens to the decimal point when decimals are divided? The decimal point in the dividend must be moved to the right to match the exact number of decimal values in the divisor.
And Number Three, what happens to the value of decimals when they are divided? The quotient, or answer, is larger than the divisor and/or dividend.