Download Lesson 8 - BGRS - Engaging Students

Math 5
Unit 1
Lesson 8
Adding Decimals
Rainfall in Calgary
Researching and learning about a certain city or area can be very
interesting. You can learn about its history, interesting places to visit and
also about its weather. If you look in an atlas about Calgary you can find
the data collected about temperature, snowfall and rainfall amounts. You
can also find many other measurements.
The table shows the average rainfall amounts in Calgary. Study the
following table:
Month
Rainfall Amount
January
February
March
April
May
June
July
August
September
October
November
December
1.27
1.016
1.524
2.54
5.33
7.62
7.112
4.826
4.826
1.524
1.27
1.27
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
Which month(s) has the most rain? If you said July you are correct.
Which month(s) have the least rain? If you said February you are correct again!
How can you find out how much total rain Calgary gets in one year? If you
add all 12 months together you will have the answer.
1.27 + 1.016 + 1.524 + 2.54 + 5.33 + 7.62 + 7.112 + 4.826 + 4.826 +
1.524 + 1.27 + 1.27 = 40.128 cm
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Math 5
Unit 1
Lesson 8: Adding Decimals
Reflection
After studying the information in the table, in
your opinion when would be the best time to
begin growing a garden?
Objectives for this Lesson
In this lesson you will explore the following concepts:
• Add decimals to thousandths
Go online to watch the Notepad Tutor: Adding Decimals (to hundredths).
Adding Decimals
Remember that you add decimals the same way that you add whole
numbers. You will need to make sure that the place value of each number
is lined up in the correct place before adding each column. You always
use the decimal as a guide.
Tens
Ones
.
Tenths
Hundredths
1
2
.
0
4
5
.
2
5
7
.
2
9
1
Here you see a sample of 12.04 + 5.25. The place values are lined up and
then added.
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Math 5
Unit 1
Lesson 8: Adding Decimals
If you are asked to add, and each number has a different number of
places, simply line up the decimals and fill in the holes with 0:
Ones
.
Tenths
Hundredths
2
.
3
4
4
.
7
6
Thousandths
2
2.34 + 4.762
For addition:
1
1
2.340
+ 4.762
7.102
As you can see, as long as the decimals are lined up, you will add the
proper place values.
Example 1
Write a number sentence for the following problem. Solve.
Lisa has 2 pieces of fabric measuring 2.451 m and 3.237 m.
How many metres of fabric does she have?
Write a number sentence for the problem:
2.451 + 3.237
Use the decimals to line up the place values:
Ones
.
Tenths
Hundredths
Thousandths
2
.
4
5
1
3
.
2
3
7
The place value chart becomes:
2.451
+ 3.237
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Math 5
Unit 1
Lesson 8: Adding Decimals
Add the columns from right to left, starting with the thousandths place.
2.451
+ 3.237
5.688
Be sure to bring down the decimal in the appropriate position.
Lisa has 5.688 metres of fabric.
This is just like basic addition but there will be times when you will need
to regroup. When you need to regroup you can use place value instead
of traditional form to help you solve the problem. Using visual models is
one way to understand this.
Pictorial Models
You can also use picture models to understand addition of decimals.
By taking one hundredth and dividing it into ten equal pieces you can
create thousandths:
This creates one thousand pieces of the whole since 100 x 10 = 1 000.
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Lesson 8: Adding Decimals
Example 2
Add 4.567 + 8.318
1. Model 4.567. You can use Hundred Squares in the back of your Workbook.
4 ones
5 tenths
6 hundredths
7 thousandths
2. Model 8.318
Math 5
8 ones
3 tenths
1 hundredth
8 thousandths
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Lesson 8: Adding Decimals
3.Add. Start with the thousandths:
You will need to regroup: Seven thousandths + eight thousandths
Create 10 thousandths by adding 3
thousandths from the second to the first:
This gives us 1 hundredth and 5 thousandths.
The thousands will stay and the
1 hundredth will be added next.
4.Add the hundredths. You are bringing one hundredth and five
thousandths from number 3:
Becomes
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6 hundredths, 1 hundredth and 1 hundredth
=
8 hundredths
Math 5
Unit 1
Lesson 8: Adding Decimals
5. Add the tenths. You are bringing no tenths from number 4.
Becomes
5 tenths plus 3 tenths
=
8 tenths
6. Now add all the ones:
8 ones plus 4 ones
4.567 + 8.318 = 12.885
=
12
Another way to look at adding decimals is with expanded notation. Look
at the following example to understand further.
Example 3
Add using expanded notation.
6.278 + 1.943
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Math 5
Unit 1
Lesson 8: Adding Decimals
1. Look at the place value of each number:
Ones
.
Tenths
Hundredths
Thousandths
6
.
2
7
8
1
.
9
4
3
2. Write each number in expanded notation
6 + .2 + .07 + .008 and 1 + .9 + .04 + .003
3. Line up the values according to place value and add from left to right:
6 + .2 + .07 +.008
+ 1 + .9 + .04 +.003
7 +1.1 + .11 + .011
Sometimes this type of regrouping may feel strange at first. If you learn
better through listening, say the following out loud:
a. eight thousandths plus three thousandths equals eleven thousandths
b. seven hundredths plus four hundredths equals eleven hundredths
c. two tenths plus nine tenths equals eleven tenths
d. six ones plus one one equals seven ones
4. Add all four numbers together:
7 + 1.1 + .11 + .011
7 + 1.1 + .11 + .011 = 8.221
The traditional method for adding decimals is the same one that you used
with adding large numbers. You regroup by carrying the place value to
the top of the problem.
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Lesson 8: Adding Decimals
Example 4
Add 3.528 + 6.389
1. Line up the decimals for addition:
3.528
+ 6.389
2. A
dd the thousandths place first. 8 + 9 = 17 so you will need to carry
the 1:
1
3.528
+ 6.389
7
3. N
ow add the hundredths place. The 1 that you carried is part of it now so
you will add 1 + 2 + 8. Again, you will have to carry since the sum is 11:
1 1
3.528
+ 6.389
17
4. A
dd the tenths place. You will not need to carry since it is 1 + 5 + 3 = 9.
This is a good time to bring down the decimal:
1 1
3.528
+ 6.389
.917
5. Add the ones place.
1 1
3.528
+ 6.389
9.917
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Lesson 8: Adding Decimals
Let’s Explore
Exploration 1: Let’s Go Shopping!
Materials: Unit 1, Lesson 8, Exploration 1 page from your Workbook, Pencil
Your mom has given you $10.00 to spend at the store. You can buy
anything that you want as long as it costs less than $10.00. The items
that you like are shown below:
Yo-yo: $3.95
Balls: $4.25
Book: $2.50
Answer the following questions. Show your work.
1. What combinations of items can you buy for $10.00?
2. How many yo-yos can you buy for $10.00?
3. How many sets of balls can you buy for $10.00?
4. How many books can you buy for $10.00?
5. How many pretzels can you buy for $10.00?
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Pretzel: $1.25
Math 5
Unit 1
Lesson 8: Adding Decimals
Let’s Practice
Go online to watch the Notepad Tutor: More on Adding Decimals.
• In your Workbook go to Unit 1, Lesson 8 and complete 1 to 21.
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Math 5
Unit 1
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Lesson 8: Adding Decimals