Addition with Three or More Addends

Addition with Three
or More Addends
Objective To guide children as they solve number stories
having three or more addends.
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Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Use basic facts to solve extended fact
problems. [Operations and Computation Goal 1]
• Solve addition number stories with three
or more addends. [Operations and Computation Goal 2]
• Use a parts-and-total diagram to solve
addition number stories involving three
or more addends. [Operations and Computation Goal 6]
• Practice adding three or four numbers
in a convenient order. [Patterns, Functions, and Algebra Goal 4]
Key Activities
Children practice adding three or four
numbers in a convenient order. They solve
number stories having three or more
addends, including stories with missing
addends.
Key Vocabulary
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Math Masters, p. 451
Student Reference Book, pp. 299
and 300
per group: 4 each of number cards
0–10 and 1 each of number cards
11–20 (from the Everything Math
Deck, if available)
Children practice writing number
sentences.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Masters, page 451. [Number and Numeration Goal 4]
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Adding with Base-10 Blocks
Math Masters, p. 412
4 each of number cards 1–10 and 1 each of
number cards 11–20 (from the Everything
Math Deck, if available) base-10 blocks
Children explore addition using base -10
blocks.
ENRICHMENT
Solving Addition and Subtraction Puzzles
Math Masters, pp. 58 and 59
Children solve addition and subtraction
puzzles.
Math Boxes 2 9
Math Journal 1, p. 53
Children practice and maintain skills
through Math Box problems.
Home Link 2 9
Math Masters, pp. 56 and 57
Children practice and maintain skills
through Home Link activities.
addend
Materials
Math Journal 1, pp. 51 and 52
Home Link 28
transparency of Math Masters, p. 44
(optional)
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 pp. 225–229
Lesson 2 9
147
Mathematical Practices
SMP1, SMP2, SMP4, SMP6, SMP8
Content Standards
Getting Started
3.OA.8, 3.NBT.2
Mental Math and Reflexes
Math Message
Children write answers on slates as you pose
higher-decade fact-extension problems. For example:
The ostriches in the zoo had
4 clutches this year. They laid
13 eggs, 9 eggs, 7 eggs, and
11 eggs. How many eggs were
laid in all? 40 eggs
= 11 6
= 21 16
= 51 46
9
17 = 8 +
37 = 8 +
29
67 = 8 +
59
= 15 7
8+
88 +
= 105 17
118 +
= 175 57
5+
5+
5+
Unit
eggs
Home Link 2 8
Follow-Up
Have partners share their answers and strategies
before turning in their work.
1 Teaching the Lesson
Math Message Follow-Up
Total
T
Part
Part
Part
Part
13
9
7
11
148
Unit 2 Adding and Subtracting Whole Numbers
WHOLE-CLASS
DISCUSSION
Algebraic Thinking Discuss the Math Message by asking questions
such as the following:
●
What do you understand from the Math Message number
story? We need to find out the number of eggs laid in all. We
know that ostriches laid clutches of 13, 9, 7, and 11 eggs.
●
What did you do to find the answer? add
●
What kind of number story is this? Parts-and-total
●
What might a parts-and-total diagram for the problem look
like? Draw a parts-and-total diagram on the board and have
children write the number of eggs in the Parts boxes. Explain
that a letter can be used in place of a question mark to
represent what we want to find out. Since the total number of
eggs is what we want to find out, write a T in the Total box.
●
Can anyone suggest a number model for the problem? Sample
answer: 13 + 9 + 7 + 11 = T
●
Did everyone add the numbers in the same order? Remind
children that numbers in an addition problem are called
addends. Can someone suggest another way to combine the
addends to make the addition easier? For example, someone
might first add 13 and 7, totaling 20; then add 9 and 11, also
totaling 20; and finally add 20 and 20.
●
Does it matter in which order the addends are written? no
Explain to children that they can add the numbers in any order
because of the Commutative Property of Addition (the
turn-around rule) and the Associative Property of Addition,
which states that numbers can be added in any order without
changing the sum.
●
Does your answer make sense in the original story? yes How
can you tell? The total number of eggs is more than the number
in any one clutch.
Student Page
Date
Time
LESSON
Number Stories with Several Addends
29
●
Does your answer make the number model true? yes Write a
summary number model on the board: 13 + 9 + 7 + 11 = 40.
1.
José bought milk for 35 cents, apple juice
for 55 cents, grape juice for 45 cents,
and orange juice for 65 cents.
How much money did he spend?
Total
T
Part
Adding Three or Four Numbers
35 + 65 + 55 + 45 = T
$2.00
Answer the question:
Part
Part
35 55 45 65
Number model:
WHOLE-CLASS
ACTIVITY
Part
(unit)
Check: How do you know your answer makes sense?
in Any Order
Sample answer: The answer has to be more than 100 cents
because only two of the amounts add up to at least 100, so
all four must be more than that.
Write additional sets of three and four numbers on the board.
Children decide which order is easiest for them to find the sums.
Suggestions:
2. Michelle drove from Houston, Texas to
Total
Wichita, Kansas. On the first day, she
drove 245 miles. On the second day, she
drove 207 miles. On the third day, she drove
158 miles and arrived in Wichita.
How many miles did she drive in all?
9 + 8 + 21 9 + 21 = 30; 30 + 8 = 38
T
Part
Part
Part
245 207 158
Number model:
245 + 207 + 158 = T
610 miles
15 + 25 + 18 15 + 25 = 40; 40 + 18 = 58
Answer the question:
(unit)
8 + 13 + 7 + 22 8 + 22 = 30; 13 + 7 = 20; 30 + 20 = 50
Check: How do you know your answer makes sense?
16 + 14 + 1 + 5 16 + 14 = 30 and 30 + 1 + 5 = 36;
or 14 + 1 + 5 = 20 and 20 + 16 = 36
so when you add the last amount, it will be more than 500.
Sample answer: The first two amounts will be more than 400,
Math Journal 1, p. 51
Using the Guide to Solving
WHOLE-CLASS
ACTIVITY
EM3MJ1_G3_U02_30-54.indd 51
12/29/10 4:35 PM
Number Stories
Total
(Math Masters, p. 44)
19
Algebraic Thinking Guide children through the problem-solving
steps for the following number story:
Part
Over the summer, 3 children read a total of 19 books. One child
read 6 books, and another child read 9 books. How many books did
the third child read?
6
Part
Part
9
P
1. What do you understand from the story?
●
What do you want to find out? The number of books read by
the third child
Student Page
Date
Time
LESSON
●
What information do you know from the number story? A
total of 19 books were read. One child read 6, and another
read 9.
Number Stories with Several Addends
29
3.
Zookeepers watched a clutch of 54 python
eggs. On the first day, 18 eggs hatched. On
the next day, 11 more hatched. How many
eggs did not hatch?
Total
54
Number model:
18 + 11 + P = 54
or 18 + 11 = 29, 54 − 29 = P
2. What could you do to find the number of books read by the
third child? Find the total number of books read by the two
children, then subtract that sum from the total number of
books read.
●
●
●
What kind of a number story is this? Parts-and-total, with
2 parts and the total known and 1 part unknown
Draw a parts-and-total diagram on the board, or display a
transparency of Math Masters, page 44, and have children
write 6 and 9 in the Parts boxes and 19 in the Total box.
Remind children that a letter can be used to represent what
we want to find out. In this case, since we don’t know one of
the Parts, write the letter P in the third Parts box.
Ask volunteers to suggest number models for the story. Sample
answer: 6 + 9 + P = 19
Answer the question:
continued
Part
Part
Part
18
11
P
25 eggs
(unit)
Check: How do you know your answer makes sense?
Sample answer: The amount of unhatched eggs has
to be less than the total amount of 54. More than 20
hatched so less than 30 have not hatched.
4.
Carl has $2.50 for juice or milk
at lunch. On each of 2 days, he buys
grape juice for 45 cents. On the third
day, he buys milk for 40 cents.
How much money does he have left?
Number model:
TotalTotal
250
Part
Part
Part
Part
45
45
40
P
45 + 45 + 40 + ? = 250
or 45 + 45 + 40 = 130, 250 − 130 = P
Answer the question:
$1.20
(unit)
Check: How do you know your answer makes sense?
Sample answer: The answer has to be less
than $2.50. He spent more than $1.00 so
he’ll have less than $1.50 left.
Math Journal 1, p. 52
EM3MJ1_G3_U02_30-54.indd 52
12/29/10 4:35 PM
Lesson 2 9
149
Home Link Master
Name
Date
HOME LINK
Time
NOTE Some children may suggest 19 - 6 + 9 = P. Although children will not
Three or More Addends
29
Family
Note
be introduced to grouping symbols until Unit 7, accept this number model and
write it with parentheses: 19 - (6 + 9) = P. Explain that the addition fact inside
the parentheses is calculated first, then the sum is subtracted from 19 to find
the missing part. Other children may suggest 2 separate number models:
6 + 9 = 15, then 19 - 15 = P. This is also acceptable.
This Home Link provides practice in looking for combinations that make addition easier.
Guide your child to look for combinations that add up to 10, 20, 30, 40 and so on.
Then add the rest of the numbers.
Please return this Home Link to school tomorrow.
Remember that when you add:
The numbers can be in any order.
Some combinations make the addition easier.
3. What is the answer? The third child read 4 books. Have
children share their solution strategies.
Add. Write the numbers in the order you added them. Tell someone at home
why you added the numbers in that order.
Sample answers:
Example:
2.
1. 6 + 18 + 14 =
50
50
5 + 17 + 25 + 3 =
38
I added in this order:
I added in this order:
55 +
+ 25
25 +
+ 17
17 +
+3
6 + 14 + 18
125 + 13 + 75 = 213
3. 15 + 6 + 14 + 5 =
4. Go back to the question in the number story. Does the answer
make sense? yes How can you tell? The number of books the
third child read has to be less than the number of books read
by all three children.
40
I added in this order:
I added in this order:
125 + 75 + 13
15 + 5 + 6 + 14
70
4. 33 + 22 + 8 + 7 =
●
5. 150 + 215 + 300 + 50 + 200 =
915
I added in this order:
Does your answer make the number model true? yes Write a
summary number model on the board: 6 + 9 + 4 = 19.
I added in this order:
33 + 7 + 22 + 8
150 + 50 + 300 +
200 + 215
Solving Number Stories
Math Masters, p. 56
EM3MM_G3_U02_036-063.indd 56
1/5/11 3:41 PM
PARTNER
ACTIVITY
Having Three or
More Addends
PROBLEM
PRO
PR
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
LV
VIN
ING
(Math Journal 1, pp. 51 and 52)
Links to the Future
Algebraic Thinking Give partners time to work on the journal
pages. Circulate and use guiding questions such as those modeled
in this lesson. Then bring the class together to share solution
strategies. As you discuss strategies, fill in the displayed
parts-and-total diagram.
The use of parentheses in number models
is introduced in Unit 7. Recognizing that
numeric expressions can have different
values depending on the order in which
operations are carried out is a Grade 3 Goal.
Evaluating numeric expressions containing
grouping symbols and inserting grouping
symbols to make number sentences true is a
Grade 4 Goal.
Home Link Master
Name
HOME LINK
29
Date
Playing Name That Number
Time
Three or More Addends
2 Ongoing Learning & Practice
continued
(Math Masters, p. 451; Student Reference Book,
pp. 299 and 300)
Solve these number stories.
6. Nico’s baby brother has a basket of wooden
blocks. 18 blocks are red, 15 are blue, and
22 are yellow. How many red, blue, and
yellow blocks are in the basket?
Number model:
18 + 15 + 22 = T
Answer the question:
55
Total
T
Part
Part
Part
18
15
22
blocks
Total
7. Marianna has 3 days to read a 58-page
book. She read 17 pages on Monday
and 22 pages on Tuesday. How many
more pages does she need to read to
finish the book?
58
17 + 22 + P = 58
or 17 + 22 = 39, 58 - 39 = P
SMALL-GROUP
ACTIVITY
Part
Part
Part
17
22
P
Children practice writing number sentences by playing Name
That Number. For game directions, see Student Reference Book,
pages 299 and 300. Have children record the number sentence(s)
from their best round on Math Masters, page 451. Encourage
children to write each of their calculations on separate lines.
Number model:
Answer the question:
19
pages
Ongoing Assessment:
Recognizing Student Achievement
8. Make up a number story with three or more addends.
Answers vary.
Answer the question:
(unit)
[Number and Numeration Goal 4]
Check. Does my answer make sense?
Math Masters, p. 57
150
Use Math Masters, page 451 to assess children’s progress toward writing
equivalent names for numbers. Children are making adequate progress if they
write a number sentence using at least two of the five faceup cards and the
target card as the sum or difference. Some children may write number sentences
using more than two cards or more than one operation.
Number model:
EM3MM_G3_U02_036-063.indd 57
Math Masters
page 451
12/29/10 5:57 PM
Unit 2 Adding and Subtracting Whole Numbers
Math Boxes 2 9
Student Page
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 53)
Date
Time
LESSON
29
䉬
Math Boxes
Use addition or subtraction to
solve these problems on your
calculator.
Enter Change to
How?
1.
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 2-5 and 2-7. The skill in Problem 6
previews Unit 3 content.
3,291
10,538
12,201
Home Link 2 9
(Math Masters, pp. 56 and 57)
39
49
72
INDEPENDENT
ACTIVITY
out
42
65
203 204
Fill in the tag. Write at least 5
names for that number.
4.
Answers vary.
A 500
PROBLEM
PR
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
IN
IN
NG
G
Rule
Subtract 7
Answers vary.
18, 19,
264
In 5,639,
the 5 means
.
Fill in the circle next to the best
answer.
3.
Home Connection Children look for number
combinations to solve addition problems having three
or more addends.
24
909
in
7
17
32
14
⫹500
⫺3,000
291
10,138 ⫺400
15,201 ⫹3,000
409
“What’s My Rule?”
in
out
2.
B 5,000
C 50
D 5
18 19
Jack answered 29 questions. José
answered 37 questions. How many
fewer questions did Jack answer
than José?
Quantity
5.
37
8
29
?
Difference
3 Differentiation Options
yardstick
ruler
thermometer
thermometer
Height of the ceiling yardstick
ruler
Length of your thumb
Temperature
Quantity
questions
14 15
Which tool would you use to
measure the following?
6.
258
Math Journal 1, p. 53
READINESS
Adding with Base-10 Blocks
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, p. 412)
To explore addition using a concrete model, have children solve
addition problems with base-10 blocks. Children generate three
addends by turning over three cards. They represent each addend
by placing longs and cubes on Math Masters, page 412. The
problem 14 + 5 + 6 = ? might be represented as shown in the
margin. Encourage children to look for combinations that
make tens.
ENRICHMENT
Solving Addition and
SMALL-GROUP
ACTIVITY
14 + 5 + 6 = ?
Teaching Master
Name
LESSON
29
䉬
5–15 Min
Subtraction Puzzles
Date
When children understand what to do, they work in small groups
to solve the remaining puzzles. Volunteers may share their
solution strategies. Math Masters, page 59 provides additional
blank puzzles for children to complete.
Time
Addition and Subtraction Puzzles
Study the examples. Can you figure out what must be done to solve
this type of puzzle?
Example 1:
Example 2:
SUBTRACT
(Math Masters, pp. 58 and 59)
To apply children’s understanding of addition and
subtraction, have them solve the puzzles on Math Masters,
page 58. Ask children to study the examples on the page
and tell what must be done to solve this kind of puzzle. Add
going across, and subtract going down. The final sum and final
difference are the same: This means there is a “check number” for
each puzzle.
14 + 6 + 5 = ?
20 + 5 = 25
A
D
D
27
8
15
3
12 5
SUBTRACT
35
18
A
D
D
17
40 46
20
9
20 37
86
29
57
Solve these addition and subtraction puzzles.
1.
2.
3.
SUBTRACT
A
D
D
48 18
12
8
36 10
66
20
A
D
D
46
22
8
14
6
8 2
30
20
5.
55 40 95
28 8 36
27 32 59
Answers vary.
6.
SUBTRACT
A
D
D
A
D
D
10
Make up addition and subtraction puzzles of your own.
4.
SUBTRACT
SUBTRACT
SUBTRACT
SUBTRACT
A
D
D
A
D
D
Math Masters, p. 58
Lesson 2 9
151
Name
HOME LINK
29
Date
Time
Three or More Addends
continued
Solve these number stories.
6. Nico’s baby brother has a basket of wooden
blocks. 18 blocks are red, 15 are blue, and
22 are yellow. How many red, blue, and
yellow blocks are in the basket?
Total
Part
Part
Part
Number model:
Answer the question:
blocks
Total
7. Marianna has 3 days to read a 58-page
book. She read 17 pages on Monday
and 22 pages on Tuesday. How many
more pages does she need to read to
finish the book?
Part
Part
Part
Number model:
Answer the question:
pages
Copyright © Wright Group/McGraw-Hill
8. Make up a number story with three or more addends.
Number model:
Answer the question:
(unit)
Check. Does my answer make sense?
57