Download C6 LESSON 6

Level C Lesson 6
Place Value - Rounding
In lesson 6 the objective is, the student will use knowledge of place value to round whole
numbers to the nearest 10 or 100.
The skills students should have in order to help them in this lesson include knowledge of
place value through hundreds.
We will have three essential questions that will be guiding our lesson. Number 1, when
is it useful to round whole numbers to the nearest 10 or 100? Number 2, how can we
round whole numbers to the nearest 10? And number 3, how can we round whole
number to the nearest 100?
The SOLVE problem for this lesson is, Albert’s class is working with estimation and
rounding. Albert has 186 baseball cards. His teacher wants him to round this number to
the nearest hundred. What is186 rounded to the nearest hundred?
We will start by S(ing) the problem. First we want to identify where the question is
located within the problem. Then we will underline the question. What is 186 rounded
to the nearest hundred? Next we will put this question into our own words in the form of
a statement. This problem is asking me to find the number 186 rounded to the nearest
hundred.
Throughout this lesson students will be working together in cooperative pairs. All
students should know their role as either partner A or partner B before beginning this
lesson.
We will be learning how to round numbers in this lesson. Rounding means taking a
number and making it simpler by using zero’s in place of some digits. This skill is used
with SOLVE when working word problems to estimate the answer to a problem. It also
makes computation problems easier when adding, subtracting, multiplying or dividing.
Rounded numbers are close to a number but not an exact representation.
In our first problem we want to round the number in our Place Value Chart to the nearest
10. The number we will be rounding is 63. The digit in the tens place is a 6. This
represents 60 or 6 tens. Notice on our number line that we start with the value of 60 and
go up to the value of 70, because 63 is between 60 and 70. Our scale is in increments of
1. We will place a bean on our number line at 63. Now let’s look to see if 63 is closer to
60 or closer to 70. 63 is closer to 60 on our number line, so we will place another bean at
60. So 63 rounded to the nearest 10 is 60. The place value to the right of the digit to
which we are rounding decides whether we will move higher or lower on our number
line. The ones digit became a 0 as a place holder because we rounded to the nearest tens
value. Notice that the tens value stayed the same in this example. And the ones value
which was 3 has become a 0.
In our next example we will round the number 68 to the nearest ten. Notice that 68 is the
value that’s been given to us in the Place Value Chart. There are 6 tens, which represent
the number 60, so our number line starts at 60 and goes up to 70, because the value 68 is
between 60 and 70. Our scale is again in increments of 1. We will place a bean on the
number 68, on our number line. Is 68 closer to 60, or closer to 70? 68 is closer to 70, so
we will place a second bean on the number 70. This means that 68 when rounded to the
nearest ten is 70. The place value to the right of the digit to which we are rounding
decides the move. The ones digit became a 0 as a place holder, because we rounded to
the nearest tens value.
In our next example we will round to the nearest hundred. Looking at our Place Value
Chart we have the number 423. The 4 is in the hundreds place, so we will start our
number line at 400 and go up to 500, because the number 423 is between 400 and 500.
Notice that our scale is now in increments of 10. We will place a bean roughly where the
number 423 would be located on our number line. 423 is going to be between 420 and
430. A little bit closer to 420, so this is where we will place the bean. Is 423 closer to
400 or closer to 500? 423 is closer to 400, so we place a second bean on the value 400.
423 rounded to the nearest hundred is 400. The place value to the right of the number to
be rounded decides the placement. The ones and tens digit became 0’s, because we
rounded to the nearest hundreds value.
Let’s do one more example rounding to the nearest hundred. This time our Place Value
Chart gives us the number 468. Again, our number line will start at 400 and will go up to
500, because the number 468 is between 400 and 500. We will place a bean roughly
where 468 is located on our number line. Since our number line is in increments of 10,
we will place our bean between 460 and 470. A little bit closer to 470. Is 468 closer to
400 or closer to 500? This will tell us if we are going to round up or round down. 468 is
closer to 500, so we will round up to 500, and place a bean on 500. Our rounded number
is 500. The place value to the right of the number to be rounded decides the placement.
The ones and tens digits became 0, because we rounded to the nearest hundred’s value.
In this next example, we’re going to round to the nearest ten. In our Place Value Chart
we are given the number 22. Since we will be rounding to the nearest 10, let’s look at the
tens column. In the tens column is the digit 2, which means that the tens column has a
value of 20. So our number line starts at 20 and goes up to 30, because the number 22
falls between 20 and 30. Our scale is in increments of 1. Let’s place a bean on the
number 22. Since we don’t always have a bean or another object available to us to place
directly onto our number line, let’s replace our bean with a point to represent the number
22. Our point is closer to 20 than it is to 30. So rounding 22 to the nearest ten is 20. The
2 in the ones place became a 0, because we rounded to the tens place.
In our next example, notice that our number line looks a little bit different. It has not
been scaled or numbered. We will need to identify and label the numbers on the number
line. In this example we will be rounding to the nearest hundred. In the hundreds place
is the digit 7. So we know that our number line will start at 700. The next hundred up
from 700 is 800. So our number line will go from 700 to 800. There are 10 spaces in our
number line. So will need to label in increments of tens; 710, 720, 730, 740, 750, 760,
770, 780, 790, and then 800. Now let’s plot the number 750 on our number line. Notice
that 750 is exactly in the middle our number line. The digit that places the value in the
middle is the 5 that is in the tens place. When looking at a digit to decide which way to
round if the digit is 5 or above we will round up to the nearest ten or hundred, if the digit
is 4 or below the number will round down to the nearest ten or hundred.. In this case we
are rounding to the nearest hundred and the digit in the tens place is a 5 we will need to
round up to the nearest hundred. Rounding up to the nearest hundred will be 800. So
let’s look at the steps that we completed to find our rounded number. First we rounded to
the nearest hundred; to do that we found that the number 750 is between 700 and 800.
We circle the digit to be rounded, label the number line and plot the point. Then we
underlined the digit that will tell which way to go. We learned that if it’s 4 or below, it’s
way to low. And if it’s 5 or above, then up you go. Our rounded number for this
example was 800.
In this next example, we are rounding to the nearest hundred, the number 592. Since we
do not have a Place Value Chart in this example we need to figure out what number is in
the hundreds place. The number 5 is in the hundreds place. So we will need to label our
number line, starting at 500 and going up to 600, because 592 is between 500 and 600.
Since we have 10 sections in our number line we know that our scale is going to be by
tens. So we will count by tens to label our number line. Now that we have our number
line labeled, we can plot a point at the number 592. 592 is going to be between 590 and
600. A little bit closer to 590. The digit in the tens place will determine the rounding of
the hundreds digit. The tens digit is greater than 5, so the number 592 is rounded to 600.
Let’s complete these steps together on our graphic organizer. First we had to figure out
to what number we were rounding. We were rounding to the nearest hundred. We know
that the number 592 is between 500 and 600. And we circle the digit to be rounded. We
then labeled the number line and plotted the point. Then we underline the digit that tells
us which way to go. Remember our saying, if it’s 4 or below, it way to low. If it’s 5 or
above, then up you go. Since our number in the tens place was 5 or above we went up to
600. Our rounded number was 600.
Next we are going to round the number 39. Notice that this time we do not have a
number line to help us. But we can use the steps that we have included in our graphic
organizers to remind us what we need to do. First we know that we need to round to the
nearest ten. The number 39 is between 30 and 40. So we circle the digit to be rounded.
Next, we will underline the digit that tells which way to go. Remember our saying, if it’s
4 or below, it’s way to low. If it’s 5 or above, then up you go. Since our number is 9 we
know that we will be rounding up, so our rounded number is 40.
Let’s now examine the steps that we use for rounding, whether we’re rounding to the
nearest ten or hundred. First we identify the number. Next, we decide to what place you
will round, either the tens or the hundreds. Third, decide between what two numbers the
number is between. Fourth, we circle the digit to be rounded. Fifth, we underline the
digit that tells, which way, whether we’re going to round up or if we’re going to round
down. Step 6, is to think. If it’s 4 or below, its way to low, if it’s 5 or above, then up you
go. And then in Step 7, we write the rounded number.
Let’s look at the example where we round 873 to the nearest hundred. We do not have
our graphic organizer, we do not have our number line, and we do not have our place
value chart to help us. What we do have are the steps that we have written out at the top.
First we’ll identify the number, 873. And then we need to decide to what place you will
round. This example tells us we will round to the nearest hundred. We need to decide
what 2 numbers the number is between. Since the number is 873 we know that we will
either round down to 800 or up to 900, but circle the digit to be rounded which is the 8,
and underline the digit that tells which way. Since the digit that tells which way is a 7 we
know that we will need to round up. 873 rounded to the nearest hundred is 900.
We are now going to go back to the SOLVE problem from the beginning of the lesson.
Albert’s class is working with estimation and rounding. Albert has 186 baseball cards.
His teacher wants him to round this number to the nearest hundred. What is 186 rounded
to the nearest hundred?
In Step S at the beginning of the lesson we studied this problem. First we underlined the
question. And then put the question into our own words in the form of a statement. This
problem is asking me to find the number 186 rounded to the nearest hundred.
In Step O we will Organize the Facts. We will start by identifying the facts. Albert’s
class is working with estimation and rounding, fact. Albert has 186 baseball cards, fact.
His teacher wants him to round this number to the nearest hundred, fact. What is 186
rounded to the nearest hundred? Now that we’ve identified the facts, we will eliminate
the unnecessary facts. Albert’s class is working with estimation and rounding. Knowing
that this is what there working on in class does not help us to find out what the value is of
186 when rounded to the nearest hundred, so we will eliminate this fact. Albert has 186
baseball cards. This is the number we want to round, so we will keep this fact. His
teacher wants him to round this number to the nearest hundred. Knowing how she wants
him to round the number is also going to be important, so we will keep this fact. Let’s
list the necessary facts. 186 baseball cards; round to the nearest hundred.
In Step L, we Line up our Plan. First we choose an operation or operations. Since we
cannot add, subtract, multiply or divide to find the answer to this problem, this part of
Step L is not applicable. Next we’ll write in words what your plan of action will be. We
will list the steps for rounding. And follow the steps using the number of baseball cards.
In Step V, we’ll Verify Your Plan with Action. First we’ll estimate your answer. Since
the number we’re rounding is 186, let’s estimate that our answer will be 200. Now we
will follow the steps using the number of baseball cards. First we need to, examine the
number. Our number is 186. Next, we will decide to what place you will round. The
question told us we wanted to round to the nearest hundreds. Third, we need to
determine, what two numbers the number is between. 186 is between 100 and 200.
Next, we will circle the digit to be rounded. In the number 186, the 1 in the hundreds
place is the digit to be rounded. Step 5, we will underline the digit that tells, which way.
In the number 186 the 8 in the tens place will tell us which way. Remember our saying,
if it’s 4 or below, it’s way too low. If it’s 5 or above, then up you go. Since the number
in the tens place is an 8 we will round up. Finally, we write the rounded number, 200.
In Step E, we will Examine Your Results. We need to ask ourselves three questions.
Does your answer make sense? Here we compare your answer to the question. The
question asks us to round the number 186. And in Step V, we rounded that number to the
nearest hundred. So we can say, yes our answer makes sense, because we are looking for
the number 186 rounded to the nearest hundred. Our next question is, is you answer
reasonable? Here we compare your answer to the estimate. Our estimate matched our
answer. So yes, our answer is reasonable, because it matches the estimate of 200. Our
third question is, is your answer accurate? Here we check our work. You can check your
work by completing the example in another area of your paper, talking to a partner. In
this problem, though, normally we could use a calculator we could not use a calculator to
help us round. 186 when rounded to the nearest hundred is 200. So our answer is yes.
Last we will write our answer in a complete sentence. The number 186 rounded to the
nearest hundred is 200.
Now let’s go back and discuss the essential questions from this lesson.
Our first question was, when is it useful to round whole numbers to the nearest 10 or
100? Estimation when computing whole numbers, makes numbers easier to work with.
Number 2, how can we round whole numbers to the nearest 10? We need to use the
following steps: Look at the number. Decide what two tens the number is between.
Circle the digit to which you are rounding. Underline the ones digit that tells, which way.
Think, if it’s 4 or below, it’s way too low. If it’s 5 or above, then up your go. And last,
write the rounded number.
Number 3, how can we round whole numbers to the nearest 100? Again, we want to use
the following steps. Look at the number. Decide what two hundreds the number is
between. Circle the digit to which you are rounding. Underline the tens digit that tells,
which way. Think, if it’s 4 or below, it’s way too low. If it’s 5 or above, then up you go.
And last we will write the rounded number.