Addition and Subtraction with Decimals
Fifth Grade Teacher Notes
Addition and Subtraction of Positive Rational Numbers
(Whole Numbers and Decimals)
Table of Contents
|Topic | |Page |
|Addition and Subtraction |Addition and Subtraction of Whole Numbers |1-8 |
| |Action Poster note-taking page |9 |
| |Addition and Subtraction with Decimals & Whole Numbers |10-18 |
| |Student Copy of Examples | |
| |Guided Practice |19-20 |
| | |21-23 |
| | | |
| | | |
| | | |
| | | |
| | | |
Addition and Subtraction Whole Numbers
5.3 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational numbers computations in order to solve problems with efficiency and accuracy.
(A) The student is expected to estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. (S)
(K) The student is expected to add and subtract positive rational numbers fluently. (R)
Vocabulary: sum, difference, minus, regroup, join, put together, take away, compare, missing part, expression, number sentence, equation, inverse operations
Materials: action poster note taking page, students’ copy of examples
*See District Addition and Subtraction PowerPoint- The PowerPoint in iXplore will illustrate the action posters, model drawing, and give students an opportunity to practice problems. The note taking page may be used with the PowerPoint for students to have the opportunity to take notes or practice problems.
IMN: action poster note taking page could be cut apart and glued into IMN
Example 1
Use the windowpane to complete the four-step process.
Discuss with the students how to summarize the question into a few important words. The use of abbreviations and symbols is encouraged.
Now begin filling in the details by determining the who and what. Each who and what should have equal sized unit bars.
NOTE: There is no need to add Martin into the details since he is not needed to find the amount Sally’s school collected. Some students may add a unit bar for Martin and not use it.
Now complete the details section by reading the story problem one “chunk” at a time pausing at the words “AND” and “OR” and also at each period.
Discuss with students which school collected more. Since Riley’s school collected more, that means Sally’s school collected less. Students will need to adjust Sally’s unit bar to be smaller.
The students would not need to add anything to their details if they determined that Martin was not needed to find your answer. However, if students made a unit bar for Martin they would need to add extra to their bar and label it 6,000.
Students can draw an arrow to show the relationship between the two amounts. Sally is 1,889 less than Riley. The question mark needs to be added to the unknown section in Sally’s unit bar.
Discuss with students what action they are showing. Ask students “how do you know we are subtracting?”
Students will now need to solve the problem in the strategy section of the windowpane.
Last, students will complete the How/Justify section of their windowpane.
Note: student responses may vary.
Possible How/Justify:
1. Drew unit bars to show relationship between R & S
2. Subtract 1,889 from 3,600 with re-grouping
3. Found the difference of 3,600 and 1,889
Example 2:
Use the windowpane to complete the four-step process.
Discuss with students how to summarize the question into a few important words. The use of abbreviations and symbols is encouraged.
Now begin filling in the details by determing the who and what. Give each who and what equal sized unit bars.
Now complete the details/known section by reading the story one “chunk” at a time pausing at the words “AND” and “OR” and also at each period or comma.
There is nothing to add to the unit bars since the first sentence does not give any information needed to solve the problem.
Students will need to add an extra piece to Plant B’s unit bar since 1,362 is greater than 852.
Students will need to shade in part of Plant C’s unit bar to show that 749 is smaller 852.
Students will now use a bracket to connect all 3 unit bars to show the action of “put together.” Then they need to place a question mark outside the bracket.
Since we know that the action of put together requires us to use the addition algorithm, we would complete the following in the strategy section of the windowpane.
Last, students will complete the How/Justify section of their windowpane.
Note: student responses may vary.
Possible How/Justify:
1. Drew unit bars to show the relationship between plants
2. Added 852, 1,362, and 749
3. Found the sum of 852, 1,362, and 749
Addition and Subtraction with Decimals and Whole Numbers
5.3 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational numbers computations in order to solve problems with efficiency and accuracy.
(A) The student is expected to estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. (R)
(K) The student is expected to add and subtract positive rational numbers fluently. (S)
Vocabulary: sum, minus, regroup, join, put together, take away, compare, missing part, expression, number sentence, equation, decimal point, whole number, inverse operations
Materials: Student copy of Example 3 and 4, Guided Practice, student copy of windowpane with decimal place value chart in strategy section
IMN: foldable in iXplore – MATH_5_A_ADDSUBTRACTDECIMALSIMN_RES
Example 3
The following chart shows the number of meters of butcher paper each 5th grade class used for a school project.
|Class Teacher |Number of Meters of Paper |
|Mrs. Marquez |1.2 |
|Mrs. White |1.03 |
|Mrs. Garza |2 |
|Mrs. Depp |.985 |
|Mr. Henry |1.65 |
How many meters of paper did the classes of Mrs. White, Mrs. Garza and Mrs. Depp use?
Use the windowpane to complete the four-step process.
Main Idea:
After finding the main idea, students may realize that not all teachers from the chart are needed in their windowpane.
Details:
Strategy: Discuss with students what operation will be used. The story is wanting to find the meters of paper used by all 3 teachers’ classes. This is the addition action of putting together.
Make a place value chart with the numbers from our Details.
Strategy
| |Ones |Tenths |Hundredths |Thousandths |
|White | | | | |
|Garza | | | | |
|Depp | | | | |
|Total | | | | |
Just as with whole numbers, we will add the different sections together, starting with the smallest place value , the thousandths place, and working to the left.
|Strategy |
| |Ones |Tenths |Hundredths |Thousandths |
|White | | | | |
|Garza | | | | |
|Depp | | | | |
|Total | | | | |
Now, group all the hundredths together making 11 hundredths.
Trade 10 hundredths for 1 tenth.
|Strategy |
| |Ones |Tenths |Hundredths |Thousandths |
|White | | | | |
|Garza | | | | |
|Depp | | | | |
|Total | | | | |
Next, group all the tenths together making 10 tenths. Trade the 10 tenths for 1 whole.
|Strategy |
| |Ones |Tenths |Hundredths |Thousandths |
|White | | | | |
|Garza | | | | |
|Depp | | | | |
|Total | | | | |
Finally, add all the ones to the whole we have just made. Now we have 4 wholes, giving a total of 4.015
|Strategy |
| |Ones |Tenths |Hundredths |Thousandths |
|White | | | | |
|Garza | | | | |
|Depp | | | | |
|Total | | | | |
We now review the step we took to put these meters together and record this in the How.
Example 4
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall, and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Use the windowpane to complete the four-step process.
Discuss with the students how to summarize the question into a few important words. The use of abbreviations and symbols is encouraged.
Now begin filling in the details by determining the who and what. Give each who and what equal sized unit bars.
NOTE: There is no need to add Jack into the details since the question is about Ben and his father.
Some students may add a unit bar for Jack and not use it.
Now complete the details section by reading the story problem one “chunk” at a time pausing at the words “AND” and “OR” and also at each period.
The students would not add anything to their details if they determined that the question was not about Jack. Some students might have a unit bar for Jack in which case they would label the bar with 1.75 m.
Students will need to adjust the father’s unit bar to be longer since 1.9 m is greater than 1.62.
Students will now place a question mark to indicate what they are looking for.
Since we know that finding a missing part action requires us to use the subtraction algorithm we complete the following concretely while showing the algorithm in the strategy section of the windowpane.
Build the number 1.9
We will be subtracting 1.62 from the manipulatives starting with the smallest place value. Since we do not have any hundredths in our numbers we will add the imaginary zero in the hundredths place.
Trying to take 2 hundredths away, we will need to trade 1 tenth for 10 hundredths.
Now we can subtract the 2 hundredths from 10 hundredths leaving 8 hundredths.
Next, take away the 6 tenths from the 8 tenths remaining – leaving 2 tenths.
Finally, take away the 1 whole leaving 0 wholes.
Our answer becomes: 0.28 m
Possible How/Justify:
1. Missing part so subtract.
2. Line up decimal points and places.
3. Put in imaginary zeros.
4. Subtract with re-grouping.
Note: Each student’s response will be different.
Example 1
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
Example 2
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Example 3
The following chart shows the number of meters of butcher paper each 5th grade class used for a school project.
|Class Teacher |Number of Meters of Paper |
|Mrs. Marquez |1.2 |
|Mrs. White |1.03 |
|Mrs. Garza |2 |
|Mrs. Depp |.985 |
|Mr. Henry |1.65 |
How many meters of paper did the classes of Mrs. White, Mrs. Garza and Mrs. Depp use?
Example 4
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall, and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Guided Practice
1. Barry purchased a classic car that had 113,528 miles on it. He drove it another 32,487 miles before he decided to sell it. At that point, how many miles did the car have on it?
2. According to current figures published by the Environmental Protection Agency, in 2009, Americans generated 243,000,000 tons of trash. That same year, 4,000,000 tons of paper trash were generated. Which expression can be used to determine how many tons of trash were placed in landfills if 82,000,000 tons of trash were recycled or composed?
A. 82,000,000 - 243,000,000
B. 82,000,000 – 4,000,000
C. 243,000,000 – 82,000,000
D. 82,000,000 + 243,000,000
3. From 2000-2013, Drew Brees had 51,081 yards passing and Tom Brady had 49,149 yards passing. How many more yards passing does Drew Brees have than Tom Brady?
4. The following is a list of city populations in Texas in 2013.
|City |Population |
|Plano |274,409 |
|Lubbock |239,538 |
|McAllen |136,791 |
|Frisco |136,639 |
What is the combined population of these cities?
5. Karen found a piece of string that measured 1.06 meters long. Dennis found a string that was 1.7 meters long. Susanne found a piece of string that was 1.726 meters long. What is the combined length of all three strings?
6. Matthew found an electrical wire that was 1.3 feet long. He measured the section of wire that had its protective coating and found it to be 1.032 feet long. How much of the wire did not have protective coating?
Use the chart for questions 7 and 8.
The following chart shows the number of meters of butcher paper each 5th grade class used for a school project.
|Class |Number of Meters of Paper |
|Mrs. Marquez |1.2 |
|Mrs. James |1.03 |
|Mrs. Davis |2 |
|Mrs. Peters |.985 |
|Mrs. Canatella |1.654 |
7. How many meters of butcher paper were used by Mrs. Davis, Mrs. James, and Mrs. Canatella’s class?
8. How many more meters of butcher paper did Mrs. Canatella’s class use than Mrs. Marquez’s class?
-----------------------
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Questions
Main Idea
Strategy
How/Justify
Details/Known
# BT Sally school collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
# BT Sally school collect?
Riley BT
Sally BT
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
# BT Sally school collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
3,600
Riley BT
Sally BT
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
# BT Sally school collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
3,600
Riley BT
Sally BT
1,889
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
Riley’s school collected 3,600 Box Tops. This is 1,889 more Box Tops than Sally’s school. Martin’s school collected 6,000 Box Tops. How many Box Tops did Sally’s school collect?
# BT Sally school collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
3,600
Riley BT
Sally BT
1,889
?
?
# BT Sally collect?
Questions
Main Idea
Strategy
How/Justify
Details/Known
3,600
Riley BT
Sally BT
1,889
9
10
10
5
3,600
- 1,889
1,711
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Plant A mm
Plant B mm
Plant C mm
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Plant A mm
Plant B mm
Plant C mm
852
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Plant A mm
Plant B mm
Plant C mm
852
1,362
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Plant A mm
Plant B mm
Plant C mm
852
1,362
749
Romina and Naja were measuring the heights of different sunflower plants at Lowe’s for a science experiment. Plant A measures 852 millimeters, Plant B measures 1,362 millimeters, and Plant C measures 749 millimeters. What is the combined length of all three plants?
Questions
Main Idea
Strategy
How/Justify
Details/Known
Combined length of 3 plants?
Plant A mm
Plant B mm
Plant C mm
852
1,362
749
?
1 1 1
852
1,362
+ 749
2,963
Subtraction
Addition
Questions
Main Idea
Strategy
How/Justify
Details/Known
Details/Known
Questions
Main Idea
Meters for White, Garza and Depp
How/Justify
Strategy
Details/Known
Questions
Main Idea
Strategy
White 1.03
Garza 2.00
Depp
1.03
2.00
.985
Meters for White, Garza and Depp
?
How/Justify
Algorithm
1.0 3
2.
0. 9 8 5
Line up numbers according to their place value and write in imaginary zeros
Algorithm
1.0 3 0
2.0 0 0
0. 9 8 5
5
(5)
Algorithm
1
1.0 3 0
2.0 0 0
0. 9 8 5
1 5
(5)
Algorithm
1 1
1.0 3 0
2.0 0 0
0. 9 8 5
.0 1 5
(5)
(1)
Algorithm
1 1
1.0 3 0
2.0 0 0
0. 9 8 5
4 .0 1 5
(5)
(1)
(4)
(0)
Details/Known
Questions
Main Idea
White
Garza
Depp
1.03
2.00
.985
[pic]
Meters for White, Garza and Depp (add)
How/Justify
Strategy
1. Lines up the decimal points
and numbers in columns.
2. Add zeroes.
3. Add starting with the thousandths column and regroup.
(see above steps)
Questions
Main Idea
Strategy
How/Justify
Details
# Ben needs to grow to = father’s height
Questions
Main Idea
Strategy
How/Justify
Details
# Ben needs to grow to = father’s height
Ben height
Father height
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Questions
Main Idea
Strategy
How
Details
# Ben needs to grow to = father’s height
Ben height
Father height
1.62 m
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Questions
Main Idea
Strategy
How
Details
# Ben needs to grow to = father’s height
Ben height
Father height
1.62 m
1.9 m
Ben is 1.62 meters tall. His brother Jack is 1.75 meters tall and his father is 1.9 meters tall. How much will Ben need to grow to be as tall as his father?
Questions
Main Idea
Strategy
How
Details
# Ben needs to grow to = father’s height
Ben height
Father height
1.62 m
1.9 m
?
Strategy
Algorithm
1.9
Ones
Tenths
Line up 1.62 under the corresponding place value
1.9
- 1.62
Add the imaginary zero.
1.9
- 1.62
81
1.90
- 1.62
Ones
Tenths
Hundredths
Ones
Tenths
Hundredths
Ones
Tenths
Hundredths
x
x
81
1.90
- 1.62
8
81
1.90
- 1.62
.28
81
1.90
- 1.62
0.28
Ones
Tenths
Hundredths
Ones
Tenths
Hundredths
................
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