www.everydaymathonline.com Lesson 2 7 119 Advance Preparation Plan to spend a total of two days on this lesson. Place quarter-sheets of paper near the Math Message. If students need computation grids in Part 1, make copies of Math Masters, page 403 or 404. Teacher’s Reference Manual, Grades 4–6 pp. 119–122, 256–261 Key Concepts and Skills • Identify places in whole numbers and the values of the digits in those places. [Number and Numeration Goal 1] • Apply extended addition facts. [Operations and Computation Goal 1] • Use the partial-sums and column-addition algorithms to solve multidigit addition problems; choose an appropriate paper-and-pencil algorithm to solve multidigit addition problems. [Operations and Computation Goal 2] • Make ballpark estimates for multidigit addition problems. [Operations and Computation Goal 6] Key Activities Students make ballpark estimates for addition problems. They use the partial-sums and column-addition methods for addition. Ongoing Assessment: Recognizing Student Achievement Use journal page 42. [Operations and Computation Goal 2] Key Vocabulary partial-sums method column-addition method ballpark estimate Materials Math Journal 1, pp. 42 and 43 Student Reference Book, pp. 10 and 11 Study Link 2 6 Math Masters, p. 403 or 404 (optional) quarter-sheet of paper base-10 blocks (optional) Playing High-Number Toss Student Reference Book, p. 252 Math Masters, p. 487 per partnership: 1 six-sided die Students practice comparing numbers. Math Boxes 2 7 Math Journal 1, p. 44 Students practice and maintain skills through Math Box problems. Study Link 2 7 Math Masters, pp. 57 and 58 Students practice and maintain skills through Study Link activities. READINESS Solving Addition Number Stories Math Masters, pp. 59 and 405 base-10 blocks 3-section paper dinner plates (optional) Students use base-10 blocks to model the partial-sums method for addition. ENRICHMENT Writing Addition Number Stories Students write and solve addition number stories. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 140 Students add the term ballpark estimate to their Math Word Banks. Teaching the Lesson Ongoing Learning & Practice 1 3 2 4 Differentiation Options Addition of Multidigit Numbers Objectives To review the partial-sums algorithm used to solve multidigit addition problems; and to introduce a column-addition method similar to the traditional addition algorithm. eToolkit ePresentations Interactive Teacher’s Lesson Guide Algorithms Practice EM Facts Workshop Game™ Assessment Management Family Letters Curriculum Focal Points Common Core State Standards
Transcript
www.everydaymathonline.com
Lesson 2�7 119
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Advance PreparationPlan to spend a total of two days on this lesson. Place quarter-sheets of paper near the Math Message. If students
need computation grids in Part 1, make copies of Math Masters, page 403 or 404.
Teacher’s Reference Manual, Grades 4–6 pp. 119–122, 256–261
Key Concepts and Skills• Identify places in whole numbers and the
values of the digits in those places.
[Number and Numeration Goal 1]
• Apply extended addition facts.
[Operations and Computation Goal 1]
• Use the partial-sums and column-addition
algorithms to solve multidigit addition
problems; choose an appropriate
paper-and-pencil algorithm to solve
multidigit addition problems.
[Operations and Computation Goal 2]
• Make ballpark estimates for multidigit
addition problems.
[Operations and Computation Goal 6]
Key ActivitiesStudents make ballpark estimates for addition
problems. They use the partial-sums and
column-addition methods for addition.
Ongoing Assessment: Recognizing Student Achievement Use journal page 42. [Operations and Computation Goal 2]
Have students share their solution strategies. Tell them that in this lesson they will review the partial-sums method and explore the column-addition method. To support English language learners, explain the meaning of the word partial. Some students may have used these algorithms to solve the Math Message problems.
� Making Ballpark Estimates WHOLE-CLASS ACTIVITY
Remind students that they should always check their answers to see whether they make sense. This is true for number stories and for computation problems like those in the Math Message.
Whether done in advance or as a final check, it is often desirable to make a rough ballpark estimate of the answer. One way to estimate a sum is to change the addends to “close-but-easier” numbers and then add them. To support English language learners, discuss the mathematical as well as the everyday meanings of the terms ballpark and estimate.
Ask students to give ballpark estimates rather than exact answers for sums. (See examples on page 121.) Have them tell how they arrived at their estimates. Encourage students to use terms such as closer to, between, and a little more than to refine their estimates. Note that often more than one estimate is acceptable.
ELL
ELL
Getting Started
Math Message Solve the problems on a quarter-sheet of paper. Show your work.
46 233 + 37 + 158
83 391
Study Link 2�6 Follow-UpHave partners compare answers. Ask students to share the estimated time they spend watching TV each week. Have them compare their estimates to 20
1
_ 2 hours, the average viewing time reported by the
World Almanac 2004 for children 2–11 years old.
Mental Math and Reflexes Pose extended addition-facts problems. Suggestions:
the Partial-Sums Method for Addition(Student Reference Book, p. 10; Math Journal 1, p. 42)
The partial-sums method (algorithm) for addition was introduced in Second Grade Everyday Mathematics. Discuss the example of the partial-sums method that appears on page 10 of the Student Reference Book. It involves more steps than some standard algorithms, but it is also more explicit; for this reason, it might be easier to use. Addition is performed from left to right and column by column. The sum of each column is recorded on a separate line. The partial sums can be added following each step or at the end.
NOTE Addition by the partial-sums method can be performed from right to left.
The advantage of working from left to right is that this is consistent with the
approach used in estimating sums.
Write several 2-digit and 3-digit addition problems on the board. Have volunteers use and describe the partial-sums method to solve these problems. Remind students that the value of each digit is determined by its place in the numeral. Thus, they should keep in mind what numbers they are adding. For example, in the first problem below, they should think “40 + 30,” not “4 + 3”; in the second problem, they should think “200 + 100,” not “2 + 1,” and “30 + 50,” not “3 + 5.”
Lesson 2�7 121
NOTE An algorithm is a step-by-step set of
instructions for solving a problem. In class-
room discussion, simply refer to algorithms as
“methods.” The partial-sums algorithm is an
example of what is sometimes called a “low-
stress” algorithm. Such algorithms are not
necessarily the most efficient, but they are
easy to use, and they reveal important
underlying concepts.
Addition Using the Partial-Sums Method 46 + 37
Add the 10s: 40 + 30 → 70
Add the 1s: 6 + 7 → + 13
Add the partial sums: 70 + 13 → 83
233 + 158
Add the 100s: 200 + 100 → 300
Add the 10s: 30 + 50 → 80
Add the 1s: 3 + 8 → + 11
Add the partial sums: 300 + 80 + 11 → 391
Adjusting the Activity
Have base-10 blocks readily available for students to use while solving the addition problems.
AUDITORY � KINESTHETIC � TACTILE � VISUAL
ELL
Whole Numbers
Larger numbers with 4 or more digits are added the same way.
Note
Use base-10 blocks to add 248 + 187.
The total is 300 + 120 + 15 = 435.
248 + 187 = 435
Addition Methods
Partial-Sums MethodThe partial-sums method is used to find sums mentally or with paper and pencil. Here is the partial-sums method for adding 2-digit or 3-digit numbers:
1. Add the 100s. 2. Add the 10s. 3. Add the 1s.
4. Then add the sums you just found (the partial sums).
Add 248 + 187 using the partial-sums method.
Use base-10 blocks to show the partial-sums method.
Ask students to turn to journal page 42. Have computation grids available (Math Masters, page 403 or 404) for those students who prefer to use them to help keep the digits in the proper columns. Assign Problems 1–7 for students to complete on their own.
Have students share their solutions to Problem 7 and indicate thumbs-up if they agree with an answer.
Ongoing Assessment: Journal
page 42 �
Problems 4–6Recognizing Student Achievement
Use journal page 42, Problems 4–6 to assess students’ ability to solve
multidigit addition problems. Students are making adequate progress if they
are able to use a paper-and-pencil algorithm to calculate the correct sums.
Some students may be able to use more than one method to solve the problems
or demonstrate how the relationship between + and - can be used to check their
answers.
[Operations and Computation Goal 2]
� Discussing and Practicing WHOLE-CLASS ACTIVITY
the Column-Addition Method(Student Reference Book, p. 11;
Math Journal 1, p. 43)
Column addition is another method for adding numbers. It can become a reliable method for students who are still struggling with addition. Column addition is similar to the traditional addition algorithm that most adults know.
Discuss the example of the column-addition method that appears on page 11 of the Student Reference Book. In this algorithm, each column of numbers is added separately in any order.
� If this results in a single digit in each column, the sum has been found.
� If the sum of any column is a 2-digit number, that column sum is adjusted by “trading” part of the sum into the column to the left.
� The concept of trading is equivalent to the idea of carrying in the traditional algorithm. In some cultures, the words used to describe what we call trading translate into making and breaking. For example, when you have ten 1s, you make a 10. When you need more 1s, you break a 10.
Write several 2-digit and 3-digit addition problems on the board. Have volunteers use and describe the column-addition method to solve these problems.
Before students solve each problem, ask for and record ballpark estimates.
Partial-Sums AdditionLESSON
2 � 7
Date Time
10
Write a number model for a ballpark estimate. Solve Problems 1–3 using the partial-sums method. Solve Problems 4–6 using any method. Compare your answer with yourestimate to see if your answer makes sense. Sample estimates:
7. Name three 4-digit numbers whose sum is 17,491. Sample answer:� � � 17,491 1,4918,0008,000
1.
76� 38
Ballpark estimate:
80 � 40 � 120
114
2.
647� 936
Ballpark estimate:
650 � 940 � 1,590
1,583
3.
1,672� 3,221
Ballpark estimate:
1,700 � 3,200 � 4,900
4,893
5.
736� 645
Ballpark estimate:
700 � 600 � 1,300
1,381
6.
7,854� 4,550
Ballpark estimate:
7,900 � 4,600 � 12,500
12,404
4.
66� 28
Ballpark estimate:
70 � 30 � 100
94
Try This
� � �
Math Journal 1, p. 42
Whole Numbers
Add 248 + 187 using the column-addition method.
100s 10s 1s
2 4 8+ 1 8 7
Add the numbers in each column. 3 12 15
Two digits in the ones place.Trade 15 ones for 1 ten and 5 ones.Move the 1 ten to the tens column. 3 13 5
Two digits in the tens place.Trade 13 tens for 1 hundred and 3 tens.Move the 1 hundred to the hundredscolumn. 4 3 5
248 + 187 = 435
Column-Addition MethodThe column-addition method can be used to find sums with paperand pencil, but it is not a good method for finding sums mentally.
Here is the column-addition method for adding 2-digit or 3-digit numbers.
1. Draw lines to separate the 1s, 10s, and 100s places.
2. Add the numbers in each column. Write each sum in its column.
3. If there are 2 digits in the 1s place, trade 10 ones for 1 ten.
4. If there are 2 digits in the 10s places, trade 10 tens for 1 hundred.
Ask students to solve Problems 1–3 on journal page 43, using the column-addition method. They can do the remaining problems using any method they choose. Bring small groups of students together to share solutions.
Have students use base-10 blocks to model the meaning of trading in
the context of addition.
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
2 Ongoing Learning & Practice
� Playing High-Number Toss PARTNER ACTIVITY
(Student Reference Book, p. 252; Math Masters, p. 487)
Students play High-Number Toss to practice comparing numbers.
Have students play High-Number Toss in groups of three or more to
practice ordering numbers. Have them adjust the scoring accordingly.
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
� Math Boxes 2�7 INDEPENDENTACTIVITY
(Math Journal 1, p. 44)
Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 2-5 and 2-9. The skill in Problem 6 previews Unit 3 content.
Writing/Reasoning Have students write a response to the following: Shaneel said, “I can draw a rhombus, rectangle, square, or kite for Problem 4.” Do you agree or disagree?
Explain your answer. Sample answer: I disagree. A parallelogram has two pairs of parallel sides. A rhombus, rectangle, and square have two pairs of parallel sides, but a kite doesn’t have any parallel sides.
ELL
Lesson 2�7 123
Math Boxes LESSON
2 � 7
Date Time
1. A number has3 in the millions place,1 in the ones place,8 in the thousands place,9 in the ten-thousands place,0 in the tens place,6 in the hundred-thousands place, and 5 in the hundreds place.
Write the number.
, , 1058963
3. Write �, �, or � to make each number sentence true.
a. 16 � 11 47
b. 206 602
c. 150 � 50 100
d. 62 � 10 � 10 62 � 10 � 10
e. 423,726 413,999 �
�
��
�
5. Measure these line segments to thenearest �
12� centimeter.
a.
About cm
b.
About cm4.5
5.5
6. Multiply mentally.
a. 5 � 8 �
b. 2 � � 16
c. 7 � � 21
d. � 9 � 54
e. 8 � 3 � 246
38
40
4. Draw a parallelogram. Label the verticesso that side AB is parallel to side CD.
149
148 149
128 16
99 100
4
2. Write five names for 100. Sample answers:
A
CD
BSample answer:
100
10 � 10216 � 1161,000 10
90 � 20 � 1027 � 28
Math Journal 1, p. 44
Student Page
Column AdditionLESSON
2 � 7
Date Time
Write a number model for a ballpark estimate. Solve Problems 1–3 using the column-addition method. Solve Problems 4–6 using any method. Compare your answer withyour estimate to see if your answer makes sense.
11
Sample estimates:
1.
94� 47
Ballpark estimate:
100 � 50 � 150
141
2.
385� 726
Ballpark estimate:
400 � 700 � 1,100
1,111
3.
2,538 � 4,179
Ballpark estimate:
2,500 � 4,200 � 6,700
6,717
5.
469� 946
Ballpark estimate:
470 � 950 � 1,420
1,415
6.
4,614� 6,058
Ballpark estimate:
4,600 � 6,100 � 10,700
10,672
4.
49� 33
Ballpark estimate:
50 � 30 � 80
82
7. Name four 4-digit numbers whose sum is 15,706. Sample answer:� � � � 15,706 3,7065,0004,0003,000
Home Connection Students solve addition problems and show someone at home how to use the methods they used in this lesson. Note that this Study Link consists of two
pages—students use the partial-sums method on the first page and the column-addition method on the second page.
3 Differentiation Options
READINESS SMALL-GROUP ACTIVITY
� Solving Addition Number Stories 15–30 Min
(Math Masters, pp. 59 and 405)
To explore solving addition problems using a concrete model, have students solve parts-and-total number stories using base-10 blocks and Math Masters, page 405. For each number story, students put base-10 blocks in each of the Part sections, then move the Parts into the Total section to solve the problem.
Example:
The class had 43 blue crayons and 15 red crayons. How many crayons did they have in all? Students first put 4 longs and 3 cubes in one of the Part sections and 1 long and 5 cubes in the other Part section. To solve the problem, they move all of the base-10 blocks to the Total section.
NOTE Instead of Math Masters, page 405, consider using paper dinner plates
divided into three sections. Label each of the two smaller sections Part and the
larger section Total.
Total
Part Part 17. 16, 21, 26, , , , Rule: +5 18. , 52, , 104, 130, Rule:
To apply students’ understanding of addition algorithms, have them write and solve addition number stories. Then have them record a number model using a letter for the
unknown. Encourage students to write multistep number stories. Stories may look similar to the following:
� Ian is shelving books in the library. He shelves 25 science fiction books, 18 biographies, and 36 mystery books. How many books did he shelve in all? Answer: 79 books; Number model: 25 + 18 + 36 = b
Some students may be interested in writing and solving problems that involve distances, intervals of time, liquid volumes, masses of objects, or money. Stories may look similar to the following:
� Kendra bought some school supplies. She spent $1.75 on folders, $2.40 on pens, and $3.80 on notebooks. How much did she spend in all? Answer: $7.95; Number model: $1.75 + $2.40 + $3.80 = c
� Marco wanted to make three different kinds of cookies for the school bake sale. The first recipe called for 2 1 _ 2 cups of milk. The second called for 1 _ 2 cup of milk. The last called for 1 1 _ 2 cups of milk. How much milk did Marco need in all? Answer: 4 1 _ 2 cups of milk; Number model: 2 1 _ 2 + 1 _ 2 + 1 1 _ 2 = m
Provide opportunities for students to revise and share their writing. Then have partners solve each other’s problems.
ELL SUPPORT SMALL-GROUP ACTIVITY
� Building a Math Word Bank 5–15 Min
(Differentiation Handbook, p. 140)
To provide language support for estimation, have students use the Word Bank Template found on Differentiation Handbook, page 140. Ask students to write the term ballpark estimate, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information.
Planning Ahead
For Part 3 in Lesson 2-8, you will need several baseball caps with adjustable headbands—one cap to be used by each small group of students. Ask students to bring baseball caps to school if they can. To be on the safe side, bring in one or more caps.
Lesson 2�7 125
LESSON
2�7
Name Date Time
Addition Number Stories
Use Math Masters, page 405 and base-10 blocks to solve the number stories.
Record what you did in the parts-and-total diagrams.
Example:
The class had 43 blue crayons and 15 red crayons.
How many crayons did they have in all?
crayons58 ?
43 15
?
24 11
?
38 29
?
23 8
?
54 47
1. Auntie May had 24 fish and 11 hamsters.
How many pets did she have altogether?
pets
2. Jordan made a flower basket for his
mother that had 23 daisies and 8 roses.
How many flowers were in the basket?
flowers3135
3. Lucia had 38 cents and Madison had
29 cents. If they put their money together,
how much money would they have?
cents
4. Miguel has 54 baseball cards. Janet
gave him 47 more baseball cards. How
many baseball cards does he have now?
baseball cards 10167
EM3MM_G4_U02_038-071.indd 59 11/4/10 9:27 AM
Math Masters, p. 59
Teaching Master
PARTNER ACTIVITY
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