Addition and Subtraction

1
Addition and Subtraction Word Problems and Strate
gies
Susan Wilson and Marilyn Powers Elementary Math
Curriculum Specialists
2






3
MATH FRAMEWORK APPENDIX CLASSIFICATION OF WORD
PROBLEMS

4
Dan
Join Result Unknown
1
2
3
4
5
6
7
8
9
10
11
12
13
Connie had 5 marbles. Juan gave her 8 more
marbles. How many marbles does Connie have
altogether?
13 marbles
Direct Modeling Joining All
5
Carla
Strategy Counting (Counting on from first)
8
13
9
12
7
6
11
10
Connie had 5 marbles. Juan gave her 8 more
marbles. How many marbles does Connie have
altogether?
13 marbles
6
Curtis
Strategy Counting (Counting on from largest)
11
12
10
9
13
Connie had 5 marbles. Juan gave her 8 more
marbles. How many marbles does Connie have
altogether?
13 marbles
7
Denise
Strategy Derived Fact
13
5
8


5
5 3
10
3
13
Connie had 5 marbles. Juan gave her 8 more
marbles. How many marbles does Connie have
altogether?
13 marbles
8
Richard
Strategy Recalled Fact
13
5
8



Connie had 5 marbles. Juan gave her 8 more
marbles. How many marbles does Connie have
altogether?
13 marbles
9
Dan
Separate Result Unknown
1
2
3
4
5
6
7
8
Connie had 13 marbles. She gave 5 to Juan.
How many marbles does Connie have left?
8 marbles
Direct Modeling Separating From
10
Donna
Strategy Counting Down
10
11
9
12
8
Connie had 13 marbles. She gave 5 to Juan. How
many marbles does Connie have left?
8 marbles
11
Denise
Strategy Derived Fact
13
5
8

-
3 2
13 - 3 10
10 - 2 8
Connie had 13 marbles. She gave 5 to Juan. How
many marbles does Connie have left?
8 marbles
12
Richard
Strategy Recalled Fact

13
5
8
-
Connie had 13 marbles. She gave 5 to Juan. How
many marbles does Connie have left?
8 marbles
13
Dan
Part-Part-Whole Whole Unknown
6
7
8
9
10
11
12
13
1
2
3
4
5
Connie has 5 red marbles and 8 blue marbles.
How many does she have?
13 marbles
Direct Modeling Joining All
14
Carla
Strategy Counting (Counting on from first)
8
13
9
12
7
6
11
10
Connie has 5 red marbles and 8 blue marbles.
How many does she have?
13 marbles
15
Curtis
Strategy Counting (Counting on from largest)
11
12
10
9
13
Connie has 5 red marbles and 8 blue marbles.
How many does she have?
13 marbles
16
Denise
Strategy Derived Fact
13
5
8


3 2
8
10
3
13
Connie has 5 red marbles and 8 blue marbles.
How many does she have?
13 marbles
17
Richard
Strategy Recalled Fact
13
5
8


Connie has 5 red marbles and 8 blue marbles.
How many does she have?
13 marbles
18
Dan
Compare Difference Unknown
1
2
3
4
5
6
7
8
Connie has 13 marbles. Juan has 5 marbles.
How many more marbles does Connie have than Juan?
8 marbles
Direct Modeling Matching
19
Tom
Strategy Counting On To
7
6
12
8
11
13
9
10
Connie has 13 marbles. Juan has 5 marbles. How
many more marbles does Connie have than Juan?
8 marbles
20
Tammy
Strategy Counting Down To
11
12
6
10
7
5
9
8
Connie has 13 marbles. Juan has 5 marbles. How
many more marbles does Connie have than Juan?
8 marbles
21
Denise
Strategy Derived Fact
8
13
5

-
10 3
10
5
- 5
3
5
8
Connie has 13 marbles. Juan has 5 marbles. How
many more marbles does Connie have than Juan?
8 marbles
22
Richard
Strategy Recalled Fact
-
13
5
8

or
13

5
8

Connie has 13 marbles. Juan has 5 marbles. How
many more marbles does Connie have than Juan?
8 marbles
23
Dan
Join Change Unknown
8
9
10
11
12
13
6
7
2
3
4
5
6
7
8
1
Connie has 5 marbles. How many more marbles
does she need to have 13 marbles altogether?
8 marbles
Direct Modeling Joining To
24
Tom
Strategy Counting On To
7
6
12
8
11
13
9
10
Connie has 5 marbles. How many more marbles
does she need to have 13 marbles altogether?
8 marbles
25
Denise
Strategy Derived Fact
13
8


5
10
5
5


13
10
3


Connie has 5 marbles. How many more marbles
does she need to have 13 marbles altogether?
8 marbles
26
Richard
Strategy Recalled Fact
13

5
8

or
-
13
5
8

Connie has 5 marbles. How many more marbles
does she need to have 13 marbles altogether?
8 marbles
27
Dan
Separate Change Unknown
1
2
3
4
5
1
2
3
4
5
6
7
8
Connie had 13 marbles. She gave some to Juan.
Now she has 5 marbles left. How many marbles
did Connie give to Juan?
8 marbles
Direct Modeling Separating To
28
Tammy
Strategy Counting Down To
11
12
6
10
7
5
9
8
Connie had 13 marbles. She gave some to Juan.
Now she has 5 marbles left. How many marbles
did Connie give to Juan?
8 marbles
29
Denise
Strategy Derived Fact
5
8
-

13
10
3
13
-

5
10
5
-

Connie had 13 marbles. She gave some to Juan.
Now she has 5 marbles left. How many marbles
did Connie give to Juan?
8 marbles
30
Richard
Strategy Recalled Fact
-
13
5
8

or
13

5
8

Connie had 13 marbles. She gave some to Juan.
Now she has 5 marbles left. How many marbles
did Connie give to Juan?
8 marbles
31
Dan
Part-Part-Whole Part Unknown
1
2
3
4
5
6
7
8
Connie has 13 marbles. 5 are orange and the
rest are blue. How many blue marbles does
Connie have?
8 marbles
Direct Modeling Separating From is
sometimes used
32
Tom
Strategy Counting On To
7
6
12
8
11
13
9
10
Connie has 13 marbles. 5 are orange and the
rest are blue. How many blue marbles does
Connie have?
8 marbles
33
Tammy
Strategy Counting Down To
11
12
6
10
7
5
9
8
Connie has 13 marbles. 5 are orange and the
rest are blue. How many blue marbles does
Connie have?
8 marbles
34
Denise
Strategy Derived Fact
8
13
5

-
I know 13 take away 3 is 10 and take away 2
more is 8.
Connie has 13 marbles. 5 are orange and the
rest are blue. How many blue marbles does
Connie have?
8 marbles
35
Richard
Strategy Recalled Fact
13
5
8
-

or
5
8


13
Connie has 13 marbles. 5 are orange and the
rest are blue. How many blue marbles does
Connie have?
8 marbles
36
Dan
Compare Quantity Unknown
9
10
11
12
13
1
2
3
4
5
6
7
8
Juan has 5 marbles. Connie has 8 more than Juan.
How many marbles does Connie have?
13 marbles
Direct Modeling Joining All is
sometimes used
37
Strategy Counting On
8
13
9
12
7
6
11
10
Juan has 5 marbles. Connie has 8 more than Juan.
How many marbles does Connie have?
13 marbles
38
Denise
Strategy Derived Fact
13
5
8


I know 5 and 5 is 10 and 3 more is 13.
Juan has 5 marbles. Connie has 8 more than Juan.
How many marbles does Connie have?
13 marbles
39
Richard
Strategy Recalled Fact
5
8
13


Juan has 5 marbles. Connie has 8 more than Juan.
How many marbles does Connie have?
13 marbles
40
Dan
Compare Referent Unknown
1
2
3
4
5
1
2
3
4
5
6
7
8
Connie has 13 marbles. She has 5 more marbles
than Juan. How many marbles does Juan have?
8 marbles
Direct Modeling Separating From is
sometimes used
41
Donna
Strategy Counting Down
10
11
9
12
8
Connie has 13 marbles. She has 5 more marbles
than Juan. How many marbles does Juan have?
8 marbles
42
Denise
Strategy Derived Fact

13
5
-
Student may use known facts to find (derive) the
solution to an unknown fact.
Connie has 13 marbles. She has 5 more marbles
than Juan. How many marbles does Juan have?
43
Richard
Strategy Recalled Fact
13
5
8
-

or
5
8


13
Connie has 13 marbles. She has 5 more marbles
than Juan. How many marbles does Juan have?
8 marbles
44
Dan
Join Start Unknown
?
1
2
3
4
5
6
7
8
6
7
8
9
10
11
12
13
8
9
10
11
12
9
10
Connie had some marbles. Juan gave her 5 more
marbles. Now she has 13 marbles. How many
marbles did Connie have to start with?
8 marbles
Direct Modeling Trial and Error is
sometimes used.
45
Tom
Strategy Counting On To
7
6
12
8
11
13
9
10
Connie had some marbles. Juan gave her 5 more
marbles. Now she has 13 marbles. How many
marbles did Connie have to start with?
8 marbles
46
Tammy
Strategy Counting Down To
11
12
6
10
7
5
9
8
Connie had some marbles. Juan gave her 5 more
marbles. Now she has 13 marbles. How many
marbles did Connie have to start with?
8 marbles
47
Denise
Strategy Derived Fact
Student uses relations between numbers to find
(derive) the solution.
Connie had some marbles. Juan gave her 5 more
marbles. Now she has 13 marbles. How many
marbles did Connie have to start with?
48
Richard
Strategy Recalled Fact
5
8


13
or
13
5
8
-

Connie had some marbles. Juan gave her 5 more
marbles. Now she has 13 marbles. How many
marbles did Connie have to start with?
8 marbles
49
Dan
Separate Start Unknown
?
1
2
3
4
5
1
2
3
4
5
6
7
8
Connie had some marbles. She gave 5 to Juan.
Now she has 8 marbles left. How many marbles did
Connie have to start with?
13 marbles
Direct Modeling Trial and Error is
sometimes used.
50
Strategy Counting On
13
9
12
7
6
11
10
Connie had some marbles. She gave 5 to Juan.
Now she has 8 marbles left. How many marbles did
Connie have to start with?
13 marbles
51
Denise
Strategy Derived Fact
Student uses relations between numbers to find
(derive) the solution.
Connie had some marbles. She gave 5 to Juan.
Now she has 8 marbles left. How many marbles did
Connie have to start with?
52
Richard
Strategy Recalled Fact
5
13
8
-

or
5
8
13


Connie had some marbles. She gave 5 to Juan.
Now she has 8 marbles left. How many marbles did
Connie have to start with?
13 marbles
53
(No Transcript)
54
(No Transcript)
55
Class Journal
Problem Type Join Change Unknown
Kameron and Amy Direct Modeling Joining To
Justin Strategy Counting On To
56
Mary had 5 balls. Her friend gave her some More
balls. Now Mary has 8 balls. How Many balls
did Marys friend give her?
What problem type is this question?
Join Change Unknown
57
Mary had 5 balls. Her friend gave her some more
balls. Now Mary has 8 balls. How many balls did
Marys friend give her?
Direct Modeler
Strategy Joining To
58
Mary had 5 balls. Her friend gave her some more
balls. Now Mary has 8 balls. How many balls did
Marys friend give her?
Strategy Counting On To
59
(No Transcript)
60
Class Journal
Problem Type Join Result Unknown
Amy, Noah, and Harlan Direct Modeling Joining To
61
Student Journal
Problem Type Join Result Unknown
Invented Strategy Combining Hundreds, Tens
and Ones
62
(No Transcript)
63
Reflection Questions

• What type of problems are my students
• solving?
• Are the problems related to students lives?
• Are students allowed free choice of and use
• of materials?
• Do I ask students to explain their thinking?
• Do students have the opportunity to explain
• their thinking with the class, small group, or
  
• partner?
• Do I know the strategy(s) a student uses?

64
Contact Information
Susan Wilson Math Curriculum Specialist susan.wils
on_at_thelearninginstitute.net 501-760-5525x1008
Marilyn Powers Math Curriculum Specialists marilyn
.powers_at_thelearninginstitute.net 501-760-5525x1010