1.OA.A.2
Solve word problems that call for addition of three whole numbers whose sum is less
than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for
the unknown number to represent the problem.
Unpacked
First Grade students solve multi-step word problems by adding (joining) three numbers
whose sum is less than or equal to 20, using a variety of mathematical representations.
Fosnot and Dolk (2001) point out that in story problems, children tend to focus on
getting the answer. “Context problems”, on the other hand, are connected to children’s
lives, rather than to school mathematics. They are designed to anticipate and to develop
children’s mathematical modeling of the real world.
Critieria for Mathematical Problems
1 There is a perplexing situation that the student understands.
2 The student is interested in finding a solution.
3 The student is unable to proceed directly toward a solution.
4 The solution requires use of mathematical ideas.
When students are doing word problems they are building their understanding of the
operations and their ability to think algebraically. When students are doing rich problems
that involve extended thinking, they are also building mathematical understanding, but
additionally their ability to think and reason. The point is not whether students should be
doing word problems or problem solving, but rather, as teachers we need to have clearly
in our minds the kinds of problems we are presenting to students and why we are
presenting them. We need to look carefully at published materials and lesson ideas we
use in our classrooms to make the best choices to meet the goals for any given day for our
students.
Notice that in the examples below, the standard algorithm is not represented. The use
of the standard algorithm for multi-digit addition and subtraction is not
mentioned in the standards until 4th grade.
Example: Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6
gingerbread cookies. She needs to figure out if she has enough cookies so that all of
her students can have one. She has 15 students. Can you help her figure this out?
Student A:
I put 4 counters on the Ten Frame for the oatmeal raisin cookies. Then, I put 5 different
color counters on the ten frame for the chocolate chip cookies. Then, I put another 6 color
counters out for the gingerbread cookies. Only one of the gingerbread cookies fit, so I
had 5 leftover. Ten and five more makes 15 cookies. Mrs. Smith has 15 cookies. Yes she
has enough for her students.
Student B:
I used a number line. First I jumped to 4, and then I jumped 5 more. That’s 9. I broke up
6 into 1 and 5 so I could jump 1 to make 10. Then, I jumped 5 more and got 15. Mrs.
Smith has 15 cookies. She has enough.
Student C:
I wrote: 4 + 5 + 6 = . I know that 4 and 6 equals 10, so the oatmeal raisin and
gingerbread equals 10 cookies. Then I added the 5 chocolate chip cookies. 10 and 5 is 15.
So, Mrs. Smith has 15 cookies.
To further students’ understanding of the concept of addition, students create word
problems with three addends. They can also increase their estimation skills by creating
problems in which the sum is less than 5, 10 or 20. They use properties of operations and
different strategies to find the sum of three whole numbers such as:
 Counting on and counting on again (e.g., to add 3 + 2 + 4 a student writes 3 + 2 + 4 = ?
and thinks, 3, 4, 5, that’s 2 more, 6, 7, 8, 9 that’s 4 more so 3 + 2 + 4 = 9.
 Making tens (e.g., 4 + 8 + 6 = 4 + 6 + 8 = 10 + 8 = 18)
 Using plus 10, minus 1to add 9 (e.g., 3 + 9 + 6. A student thinks, 9 is close to 10 so I
am going to add 10 plus 3 plus 6 which gives me 19. Since I added 1 too many, I need to
take 1 away so the answer is 18.)
 Decomposing numbers between 10 and 20 into 1 ten plus some ones to facilitate
adding the ones
 Using doubles
 Using near doubles (e.g. 5 + 6 + 3 = 5 + 5 + 1 + 3 = 10 + 4 =14)
Students may use document cameras to display their combining strategies. This
gives them the opportunity to communicate and justify their thinking. (MP 3)
Misconceptions to consider:
Many children misunderstand the meaning of the equal sign. The equal sign means “is
the same as”, but most primary students believe the equal sign tells you that the “answer
is coming up” to the right of the equal sign. This misconception is over-generalized by
only seeing examples of number sentences with an operation to the left of the equal sign
and the answer on the right. First graders need to see number sentences written
multiple ways, for example 5 + 7 = 12 and 12 = 5 + 7.
A second misconception that many students have is that it is valid to assume that a key
word or phrase in a problem suggests the same operation will be used every time. For
example, they might assume that the word left always means that subtraction must be
used to find a solution. Providing problems in which key words like this are used to
represent different operations is essential. For example, the use of the word left in this
problem does not indicate subtraction as a solution method: Seth took the 8 stickers he
no longer wanted and gave them to Anna. Now Seth has 11 stickers left. How many
stickers did Seth have to begin with? Students need to analyze word problems and
avoid using key words to solve them. (MP 1)
Speaking
Level 2
Emerging
Identify
possible
ways to
solve word
problems
that call for
addition of
three whole
numbers
whose sum
is less than
or equal to
20 by
providing an
explanation
using math
tools with a
partner.
Level 3
Developing
Identify
possible
ways to
solve word
problems
that call for
addition of
three whole
numbers
whose sum
is less than
or equal to
20 by
providing an
explanation
using visuals
or graphics
such as a
number
line,10
frame, or
base 10
blocks.
Level 4
Expanding
Identify
possible
ways to
solve word
problems
that call for
addition of
three whole
numbers
whose sum
is less than
or equal to
20 by
producing
and
describing
original
equations in
a small
group.
Level 5
Bridging
Identify
possible
ways to
solve word
problems
that call for
addition of
three whole
numbers
whose sum
is less than
or equal to
20 by
explaining
the process
or procedure
used to solve
the word
problem.
ELD Standard #3: English Language Learners communicate information, ideas,
and concepts necessary for academic success in the content area of
Mathematics.
Level 6 Reaching
Level 1
Entering
Identify
possible
ways to solve
word
problems
that call for
addition of
three whole
numbers
whose sum is
less than or
equal to 20
by
describing
illustrations,
diagrams, or,
drawings
with teacher
support.