In Lesson 9 the Objective Is, the Student Will Add Decimals to the Hundredths Place

Level E Lesson 9
Add Decimals

In lesson 9 the objective is, the student will add decimals to the hundredths place.

The skills students should have in order to help them in this lesson include adding whole numbers and knowledge of decimal place values to hundredths.

We will have three essential questions that will be guiding our lesson. Number 1, why is it important to know how to add decimals? Number 2, how can you add decimals with different place values? And number 3, when would you add decimals in real life?

The SOLVE problem for this lesson is, Talisha and her friend, Moni, went to the mall to shop. They had a total of ten dollars and twenty cents between them. Talisha spent four dollars and twenty four cents on snacks, and Moni spent fifty cents on pencils. How much did the girls spend altogether?

We will begin by Studying the Problem. First we want to identify where the question is located within the problem and we will underline the question. How much did the girls spend altogether? Now that we have identified the question, we want to put this question in our own words in the form of a statement. This problem is asking me to find the total amount the girls spent.

During this lesson we will learn how to add decimals to the hundredths place. We will use this knowledge to complete this SOLVE problem at the end of the lesson.

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.

Let’s start this lesson by taking a look at the decimal addition models that have been shaded for us. First let’s identify how many sections are in each grid. There are ten sections on each grid. What is the name of each of those ten sections? We call each of these sections tenths. How many sections are shaded on the first grid? On the first grid we have five shaded sections. We call this, five tenths. Five tenths is our first addend. Let’s record five tenths into our graphic organizer which is a place value chart provided on this page. We will place a five in the tenths column and use a zero as a place holder in the ones column. Let’s take a look at the second grid. The second grid represents three tenths. This is our second addend and we want to record this addend into our place value chart. We will place a three in the tenths column and use a zero as a place holder in the ones column. To find the sum first we want to bring down the decimal point into our answer. Now we want to add starting in the column furthest to the right, which in this case is the tenths column. Five plus three equals eight, and in the ones column we have zero plus zero which is zero. Zero is our place holder in the ones column. Our sum is eight tenths. We can record this example as a number sentence. We started with five tenths and we added three tenths to that. Five tenths plus three tenths equals eight tenths.

Let’s take a look at another example together. Let’s identify how many sections are in the first grid. There are ten sections in the first grid. Each of those ten sections are called tenths. There are seven sections that are shaded on the first grid. This means that we have seven tenths as our first addend. Let’s record seven tenths on our place value chart. We will place a seven in the tenths column, and a zero in the ones column to hold this place. On the second grid we also see that there are ten sections. Each of these ten sections represents one tenth. Two of these sections are shaded. So our second grid represents two tenths. Let’s record our second addend into our place value chart. We will place a two in the tenths column and a zero as a place holder in the ones column. To find the sum we want to bring down the decimal point into our answer. And we will add starting with the place value furthest to the right. In this case it is the tenths place. Seven plus two equals nine. And in the ones place we have a zero as our place holder. Seven tenths plus two tenths gives us a sum of nine tenths. We can record this as a number sentence. We started with seven tenths and added to it, two tenths. So we record this as seven tenths plus two tenths equals nine tenths.

In our next example we have an additional grid. How many sections are shaded in the first grid? There are ten tenths that are shaded. We can also refer to this as one whole. On the second grid we have four shaded sections. This represents four tenths. Our first addend is one and four tenths. We can record this in our place value chart by placing a one in the ones column and a four in the tenths column. Let’s look at our second addend. Here we have four tenths that are shaded. Our second addend is four tenths. We can record this addend into our place value chart by placing a four in the tenths column and a zero as a place holder in the ones column. We want to make sure that our decimals are lined up. And we will bring our decimal down into our answer. To find the sum we start at the place value furthest to the right, which in this case is the tenths place. Four plus four equals eight. And in the ones place one plus zero equals one. One and four tenths plus four tenths gives us a sum of one and eight tenths. Let’s record this example as a number sentence. For our first addend we had one whole and four tenths and our second addend was four tenths. Our number sentence is one and four tenths plus four tenths equals one and eight tenths.

Let’s look at another example together. How many sections are shaded in the first grid? There are a total of twenty three sections that are shaded. This represents twenty three hundredths. Our first addend twenty three hundredths can be recorded in our place value chart by placing a two in the tenths column and a three in the hundredths column. The zero in the ones column holds this place. Let’s look at our second grid. Our second grid represents our second addend. We can see that there are a total of seventy one shaded sections. Our second addend is seventy one hundredths. We can record this into our place value chart by placing a seven in the tenths column and a one in the hundredths column. We use a zero as a place holder in the ones column. To find the sum we need to make sure that the decimals are lined up. We will place a decimal into the sum lined up underneath the decimals in both addends. Now we need to add starting in the place value furthest to the right. In this case it is the hundredths place. Three hundredths plus one hundredth equals four hundredths. In the tenths place two tenths plus seven tenths equals nine tenths. And in the ones place we have a zero. The zero will hold the ones place. Twenty three hundredths plus seventy one hundredths gives us a sum of ninety four hundredths. Let’s record this as a number sentence. Our first addend is twenty three hundredths. And our second addend is seventy one hundredths. Twenty three hundredths plus seventy one hundredths equals ninety four hundredths.

In our next example how many sections are shaded in the first grid? There are fourteen sections shaded in the first grid. Our first grid represents fourteen hundredths. We can record our first addend into our place value chart by placing a one in the tenths place and a four in the hundredths place. Zero holds the ones place. For our second addend there are forty five shaded sections. This represents forty five hundredths. To record our second addend into our place value chart we will place a four in the tenths column and a five in the hundredths column, making sure to use a zero as a place holder in the ones column. Now to find our sum we need to make sure that our decimals are lined up, and we need to bring our decimal down into our sum. We will add starting in the place value furthest to the right, which is the hundredths place. Four hundredths plus five hundredths equals nine hundredths. One tenth plus four tenths equals five tenths and we will use our zero to hold the ones place. Fourteen hundredths plus forty five hundredths gives us a sum of fifty nine hundredths. Let’s record this example as a number sentence. Our first grid represents fourteen hundredths and our second grid represents forty five hundredths. Our first addend is fourteen hundredths plus our second addend is forty five hundredths which equals a sum of fifty nine hundredths.

We will continue in this next example to use the gridded models that are provided to help us in completing the addition problems. Our first grid has ten sections. Three of these sections are shaded. Our first addend is three tenths or zero point three. On the second grid we have one hundred sections. Of these one hundred sections twenty one sections have been shaded. Our second addend can be represented as twenty one hundredths or zero point two one. We want to write the decimals in the place value chart by lining up the decimal points. How many decimal places are in the first addend? There is one decimal place in the first addend. How many decimal places are in the second addend? There are two second places in the second addend. All addends should have the same number of decimal places. Zero can be used as a place holder. We can represent three tenths by placing a three in the tenths column on our place value chart. Three tenths is the same as thirty hundredths. We can add a zero to the hundredths column to represent thirty hundredths. We will use a zero in the ones column as a place holder. We can show on our model that three tenths is equivalent to thirty hundredths. As we still have the same shaded region if we represent this using hundredths instead of tenths. For our second addend we already have two decimal places. We will place our second addend into our place value chart by placing a two in the tenths column and a one in the hundredths column. We will use a zero to hold the ones place. We can now find the sum of our two addends. Our decimal point is lined up and we will bring that down into our sum. Now we need to go to the hundredths place which is the place value furthest to the right in our place value chart and add from right to left. We have zero hundredths plus one hundredth which give us one hundredth. Three tenths plus two tenths equals five tenths and a zero holds the ones place. Thirty hundredths plus twenty one hundredths gives us a sum of fifty one hundredths. Now let’s record our number sentence for this example. Our first addend was three tenths and our second addend was twenty one hundredths. Three tenths plus twenty one hundredths, we saw that it works best when we have the same number of decimal places in both addends. And we found that three tenths is equals to thirty hundredths. Thirty hundredths plus twenty one hundredths equals fifty one hundredths.

In this next example we will use our grid models to help us to answer the questions in the graphic organizer and to find the sum for this example. Looking at our shaded grid models, first we want to write the first addend as a decimal. The first addend is shown as seven tenths. So we write this as a decimal zero point seven. Next we will write the second addend as a decimal. There are twenty three hundredths shaded in the second grid. So as a decimal we write this as zero point two three. Does either addend need a zero place holder? Yes, seven tenths is equal to seventy hundredths. Now that we have the same number of decimal places for both of our addends we can write the addition problem, seventy hundredths and twenty three hundredths. What happens to the decimal points when we place these decimal numbers into our place value chart? We see that they are lined up. Seventy hundredths plus twenty three hundredths show our decimal in the same place in both decimal numbers. Now we want to solve the problem. We will bring down the decimal into our sum first. Then we will add from right to left starting in the hundredths place. Zero hundredths plus three hundredths equals three hundredths. Seven tenths plus two tenths equals nine tenths and the zero holds the ones place. What happens to the decimal point in the sum? It is lined up with the decimal points in the addends. Seventy hundredths plus twenty three hundredths equals ninety three hundredths.

In this next example the first addend is fifty three hundredths. And our second addend is twenty eight hundredths. Remember that fifty three hundredths is equal to five tenths and three hundredths. So in our place value chart we will place a five in the tenths place and a three in the hundredths place, using a zero to hold the ones place. Twenty eight hundredths is equal to two tenths and eight hundredths. So we will place a two in the tenths place and an eight in the hundredths place, again using a zero to hold the ones place. Do we need to use a zero place holder for either of our addends? No, both tenths and hundredths values are recorded in each addend. To find the sum we want to line up the decimal in our answer with the decimal points in our addends. Then we will add starting in the hundredths place. Three hundredths plus eight hundredths equals eleven hundredths. We will need to regroup when adding the hundredths. Since eleven hundredths is one tenth and one hundredth a one will be written in the hundredths place and the one tenth will need to be regrouped to the tenths place. Now we will add the tenths place. Five tenths plus two tenths equals seven tenths plus our one regrouped tenth equals eight tenths. We will use our zero as a place holder in the ones column. Fifty three hundredths plus twenty eight hundredths equals a sum of eighty one hundredths. If we did not have our place value chart to help us in lining up our decimals we would write each of our addends making sure that the decimal points lined up with each other, fifty three hundredths plus twenty eight hundredths. We bring the decimal point down into our answer so that it lines up with the decimal point in both addends. Then we add beginning in the column furthest to the right, which is the hundredths place. Three hundredths plus eight hundredths equals eleven hundredths. We will need to regroup. We will place one in the hundredths column and a regrouped one to the tenths column. Five tenths plus two tenths is seven tenths plus our one regrouped tenth is eight tenths. We will use a zero as the place holder in the ones place. Fifty three hundredths plus twenty eight hundredths equals a sum of eighty one hundredths.

This next example is different from the other problems that we have solved as both addends have whole numbers. Let’s record the addends into our place value chart. Our first addend is one and five tenths. We can see that our second addend is going to go into the hundredths place. So when we record one and five tenths we need to use a zero as a place holder in the hundredths column. We will place a one in the ones place, a five in the tenths place, and a zero in the hundredths place. Our second addend is one and thirty seven hundredths. In our place value chart we will record our second addend, with a one in the ones place, a three in the tenths place, and a seven in the hundredths place. Now we can find the sum. We want to bring the decimal point down so that it lines up with the decimal point in both addends. Now we add starting in the hundredths column. Zero hundredths plus seven hundredths is seven hundredths, five tenths plus three tenths is eight tenths and one plus one is two. One and fifty hundredths plus one and thirty seven hundredths equals a sum of two and eighty seven hundredths. If we do not have the place value chart to help us we need to make sure that when we write the problem that we line up the decimal points in both addends, one and fifty hundredths plus one and thirty seven hundredths. We bring the decimal point down into our answer so that it lines up with the two decimal points in our addends. Then we add from right to left, zero plus seven is seven, five plus three is eight, and one plus one is two. One and fifty hundredths plus one and thirty seven hundredths equals a sum of two and eighty seven hundredths.