1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction
within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10
+ 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 =
9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4
= 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g.,
adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Unpacked
This standard is broken up into 2 parts: Students will be expected to become
proficient at solving addition and subtraction equations within 20. The
second part of this standard deals with Computational Fluency. Students use
computational fluency to solve problems accurately, efficiently, and by
quickly using mental strategies such as making 5 or making 10.
It is important for students to relate a given number to other numbers. The
10 is a landmark number for this.
For both parts of this Standard, the use of objects, diagrams, or interactive
whiteboards and various strategies will help students develop both
computational fluency and mental strategies for solving all addition and
subtraction equations with efficiency. It is important for students to be able
to use a variety of strategies when adding and subtracting numbers within
20. Students should have ample experiences seeing these strategies modeled
and practiced with pencil and paper before working on computational
fluency. *The most important model for exploring the relationship between
numbers is a ten frame.
The emphasis of this standard is not as much on the tasks that are required of
the student as on the strategies and thought processes that the student uses to
arrive at a solution. Although the tasks will often resemble the traditional
ones from the textbook and worksheets, the work produced by the student
should look very different. Students will work with concrete objects and
drawings to develop their strategies. Through questioning, such as “Is there a
way you could arrange these numbers to make them easier to add?” teachers
can lead students to make groups of ten. Teachers should ask questions to
encourage students to express and clarify their thinking while they work,
such as “How will it help with this subtraction if you know how many you
need to add to 5 to get 9?” etc.
Wherever the word fluently appears in a content standard, the word means
quickly and accurately. It means more or less the same as when someone is
said to be fluent in a foreign language. To be fluent is to flow: Fluent isn’t
halting, stumbling, or reversing oneself. A key aspect of fluency in this sense
is that it is not something that happens all at once in a single grade but
requires attention to student understanding along the way. It is important to
ensure that sufficient practice and extra support are provided at each grade to
allow all students to meet the standards that call explicitly for fluency.
(PARCC MCF, v3.0, p. 9)
Fluency is not meant to come at the expense of understanding but is an
outcome of a progression of learning and sufficient thoughtful practice. It is
important to provide the conceptual building blocks that develop
understanding in tandem with skill along the way to fluency; the roots of this
conceptual understanding often extend one or more grades earlier in the
standards than the grade when fluency is finally expected. (PARCC MCF,
v3.0, p. 12)
Students need a variety of strategies for solving addition and subtraction
problems within 20 including those that can be computed mentally. These
strategies will provide students with a variety of choices when deciding the
best way to solve problems. This skill contributes to a more thorough
understanding of the relationships and properties between numbers.
Counting on should be seen as a thinking strategy, not a rote method. It
involves seeing the first addend as embedded in the total, and it involves a
conceptual interplay between counting and the cardinality in the first addend
(shifting from the cardinal meaning of the first addend to the counting
meaning). Finally, there is a level of abstraction involved in counting on,
because students are counting the words rather than objects. Number words
have become objects to students.
Counting on can be used to add (find a total) or subtract (find an unknown
addend). To an observer watching the student, adding and subtracting look
the same. Whether the problem is 9 � 4 or 13 _ 9 , we will hear the student
say the same thing: “Niiiiine, ten, eleven, twelve, thirteen” with four head
bobs or four fingers unfolding. The differences are in what is being
monitored to know when to stop, and what gives the answer.
Make 10 Strategy

The most important strategy for students to know is the Make 10
strategy, or the combinations of 10. Story problems using two
numbers that make 10 or that ask how many are needed to make 10
can assist this process.
 The ten frame is a very useful tool for creating a visual image for
students. Placing counters on a one ten frame and ask, “How many
more to make 10?” (Van de Walle)
 Knowing number combinations that make 10 not only helps with
basic fact mastery but builds foundations for working on addition with
higher numbers and understanding place-value concepts. For
example, 36 + 6, using the Make 10 strategy, students can add 4 to 36
and get 40, then 2 more for 42.