K.OA.A.1
Understand addition as putting together and adding to, and understand subtraction
as taking apart and taking from.
1. Represent addition and subtraction with objects, fingers, mental images,
drawings, sounds (e.g., claps), acting out situations, verbal explanations,
expressions, or equations. (Drawings need not show details, but should show the
mathematics in the problem. This applies wherever drawings are mentioned in the
Standards.)
Unpacked
Students demonstrate the understanding of how objects can be joined (addition) and
separated (subtraction) by representing addition and subtraction situations in various
ways. This objective is focused on understanding the concept of addition and
subtraction, rather than reading and solving addition and subtraction number
sentences (equations).
Common Core State Standards for Mathematics states, “Kindergarten students should see
addition and subtraction equations, and student writing of equations in kindergarten is
encouraged, but it is not required.” Please note that it is not until First Grade when
“Understand the meaning of the equal sign” is an expectation (1.OA.7).
Therefore, before introducing symbols (+, -, =) and equations, kindergarteners require
numerous experiences using joining (addition) and separating (subtraction) vocabulary in
order to attach meaning to the various symbols. For example, when explaining a solution,
kindergartens may state, “Three and two is the same amount as 5.”
This concept is the beginning of anchoring numbers to five and ten. The five frame is an
effective tool to help students see numbers to five. Using a five frame, explain that one
counter is put in each square. Ask the students to place three counters on the five frame.
Ask them what they notice about three - it is two away from five.
Once the five frame is understood, introduce the ten frame. The standard way to show
numbers on a ten frame is to fill up the top row, starting on the left, the same way you
read. When the top row is full, counters can be placed in the bottom row, starting at the
left. Ask students about the relationships of the number shown to five and ten. "Show me
7 on the ten frame. How many more to make ten? How many more than five?" Move to
representing the relationships with drawings to recording them through expressions.
Begin to talk about what happens if I take 2 away? How many do I have now? The use of
manipulatives to explore this idea is critical before any symbols are introduced.
Early learners need a wide assortment of visual cues to help them make the connection
between the abstract concept of addition and the concrete result. This can be
accomplished by providing them with situations where objects are added to an existing
set or two separate sets are combined.
Further, students need hands-on practice and visual cues for subtraction by taking from
a
set or taking a set apart.
Establishing the meanings of the vocabulary words “addition” and “subtraction” is
critical.
The use of manipulatives and technologies is very useful at this age: hands-on activities
make such an abstract concept more concrete in nature. For this standard, students will
benefit from the opportunity to put manipulatives together or take sets of manipulatives
apart.
Situations that involve real-life encounters or everyday objects will help students to
engage in the learning process.
Teachers need to provide opportunities for students to model with verbal and visual
cues,
such as drawings and the acting out of these situations.
Teachers should represent a situation with an expression or equation after it has been
modeled with manipulatives, a drawing, or a situation. This will help students make the
connection between real-world objects and the more abstract symbolic representation.
The chart below shows a representation of unknown quantity:
Speaking
Level 2
Emg
Demonstrate
an
understanding
of addition as
putting
together and
adding to and
subtraction as
taking apart
and taking
from
Level 3
Developing
Demonstrate
an
understanding
of addition as
putting
together and
adding to and
subtraction as
taking apart
and taking
from
Level 4
Expanding
Demonstrate
an
understanding
of addition as
putting
together and
adding to and
subtraction as
taking apart
and taking
from
Level 5
Bridging
Demonstrate
an
understanding
of addition as
putting
together and
adding to and
subtraction as
taking apart
and taking
from
using objects,
fingers,
mental
images,
drawings,
sounds (e.g.,
claps), acting
out situations,
verbal
explanations
or expressions
with objects,
fingers,
mental
images,
drawings,
sounds (e.g.,
claps), acting
out situations,
verbal
explanations
or expressions
with objects,
fingers,
mental
images,
drawings,
sounds (e.g.,
claps), acting
out situations,
verbal
explanations
or expressions.
with objects,
fingers,
mental
images,
drawings,
sounds (e.g.,
claps), acting
out situations,
verbal
explanations
or expressions.
with objects,
fingers,
mental
images,
drawings,
sounds (e.g.,
claps), acting
out situations,
verbal
explanations
or expressions.
orally in a
small group
with minimal
teacher
support.
orally
explaining to a
partner.
orally in a
cooperative
group.
orally with the
teacher.
orally with a
partner.
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
Demonstrate
an
understanding
of addition as
putting
together and
adding to and
subtraction as
taking apart
and taking
from