 Addition
and subtraction should be taught concurrently in order to develop
understanding of the inverse relationship.
 The
problemsolving process is enhanced when students:
 create their own story problems;
 visualize
the action in the story problem and draw a picture to show their thinking;
and
 model the
problem using manipulatives, representations, or number sentences/equations.
 The least
number of steps necessary to solve a singlestep problem is one.
 In problem solving, emphasis should be placed on
thinking and reasoning rather than on key words. Focusing on key words
such as in all, altogether, difference, etc.,encourages students to perform a particular operation rather than make
sense of the context of the problem. A keyword focus prepares students
to solve a limited set of problems and often leads to incorrect solutions as well as challenges in upcoming grades
and courses.
 Provide
practice in the use and selection of strategies. Encourage students to
develop efficient strategies. Examples of strategies for developing the basic
addition and subtraction facts include:
 counting on;
 counting
back;
 “one more
than,” “two more than”;
 “one less
than,” “two less than”;
 “doubles”
(e.g., 6 + 6 =__);
 “near
doubles” (e.g., 7 + 8 = (7 + 7) + 1 =
or (8 + 8) – 1);
 “make ten”
(e.g., 7 + 4 can be thought of as 7 + 3 + 1 in order to make a 10 );
 “think
addition for subtraction” (e.g., for 9 – 5 = __, think “5 and what number
makes 9?”);
 use of the
commutative property (e.g., 14 +3 is the same as 3 + 14);
 use of
related facts (e.g., 14 + 3 = 17 , 3 + 14 = 17, 17 – 4 = 13, and 17 – 13 =
4);
 use of the
additive identity property (e.g., 14 + 0 = 14); and
 use
patterns to make sums (e.g., 0 + 15 = 15, 1 + 14 = 15, 2 + 13 = 15, etc.).
 Students at this level are not
expected to use the parentheses or to name the properties.
 Students
should develop fluency with facts to 10 and then use strategies and known
facts to 10 to determine facts to 20.
 Flexibility
with facts to 10 should be applied to facts to 20 (e.g., when adding 4 + 7,
it is appropriate to think of 4 as 3 + 1 in order to combine 3 and 7 to make
a 10 whereas adding 4 + 8, it is appropriate to think of 4 as 2 + 2 in order
to combine 8 and 2 to make a 10).
 Extensive research has been
undertaken over the last several decades regarding different problem types.
Many of these studies have been published in professional mathematics
education publications using different labels and terminology to describe the
varied problem types.
 Students
should have exposure to a variety of problem types related to addition and
subtraction. Examples are represented
in the chart below. It is important to
note that Join Problems (with start unknown), Separate Problems (with start
unknown), Compare Problems (with larger unknown – using “fewer”) and Compare
problems (with smaller unknown – using “more”) are the most difficult and
should be mastered in grade two.
GRADE 1: COMMON ADDITION AND
SUBTRACTION PROBLEM TYPES

Join
(Result
Unknown)

Join
(Change
Unknown)

Join
(Start
Unknown)

Sue had 9
pencils. Alex gave her 5 more pencils.
How many pencils does Sue have altogether?

Sue had 9
pencils. Alex gave her some more
pencils. Now Sue has 14 pencils. How
many did Alex give her?

Sue had
some pencils. Alex gave her 5
more. Now Sue has 14 pencils. How many pencils did Sue have to start
with?

Separate
(Result
Unknown)

Separate
(Change
Unknown)

Separate
(Start
Unknown)

Brooke
had 10 cookies. She gave 6 cookies
to Joe. How many cookies does Brooke
have now?

Brooke
had 10 cookies. She gave some to Joe. She has 4 cookies left. How many cookies did Brooke give to Joe?

Brooke
had some cookies. She gave 6 to Joe. Now she has 4 cookies left. How many cookies did Brooke start
with?

PartPartWhole
(Whole
Unknown)

PartPartWhole
(One
Part Unknown)

PartPartWhole
(Both
Parts Unknown)

Lisa has
4 red markers and 8 blue markers.
How many markers does she have?

Lisa has
12 markers. Four of the markers are
red, and the rest are blue. How many
blue markers does Lisa have?

Lisa has
a pack of red and blue markers. She
has 12 markers in all. How many markers
could be red? How many could be blue?

Compare
(Difference
Unknown)

Compare
(Bigger
Unknown)

Compare
(Smaller
Unknown)

Ryan has
7 books and Chris has 2 books. How many more books does Ryan have than Chris?
Ryan has 7 books. Chris has 2 books. How many fewer books does Chris have than Ryan?

Chris
has 2 books. Ryan has 5 more books than Chris. How many books does Ryan have?
Chris has 5 fewer books than Ryan. Chris
has 2 books. How many books does Ryan
have?

Ryan has
2 more books than Chris. Ryan has 7 books. How many books does Chris have?
Chris has 5 fewer books than Ryan. Ryan
has 7 books. How many books does Chris
have?

