Second Grade Operations and Algebraic Thinking Tasks

Add and subtract within 20. (2.OA.2)

2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. (See standard 1.OA.6 for a list of mental strategies.)

As a mathematics community, we have learned a great deal about helping children become fluent with their facts. This knowledge has helped us to understand that timed tests and particular drill techniques are not effective. We now know that students need to use relationships between numbers to develop efficient strategies for fact retrieval. These relationships are developed as students solve meaningful word problems as noted in 2.OA.1.

The tasks provided in this section are designed to assess a student's fluency with strategies that students have begun using in problem-solving settings. Therefore, it is important to carefully select tasks below to align with a particular strategy with which the student has demonstrated an understanding of and has begun using to solve word problems. With this careful alignment between the student and the strategy, efficient mental processes are further developed as students become fluent with addition and subtraction within 20.

*The following strategy categories and premise for the Student Forms has been informed by Van de Walle & Lovin (2006) Teaching student-centered mathematics, Grades K-3. Boston: Pearson. For instructional strategies regarding these strategies, please see Chapter 4 of this resource.



Facts Assessed

Student Form

One-more-than Facts
Two-more-than Facts
(0 to 9) + 1
(0 to 9) + 2

Facts with Zero
(0-9) + 0

(0 to 9) doubles

Doubles Plus One
(0 to 9) doubles + 1

Make Ten Facts
8 + (1 to 9)
9 + (1 to 9)

Doubles Plus Two
(0 to 9) doubles + 2

Make-Ten Extend
7 + (3 to 9)


Before working on fluency with subtraction facts, determine if a student has begun making connections between addition and subtraction when solving problems. This can be determined as students solve word problems and when students solve equations in which subtraction facts are included with the corresponding addition facts.


Student Form

Connecting Addition and Subtraction

Once students have demonstrated connections between addition and subtraction, the following strategies can be used.


Student Form

Build Up Through 10

Back Down Through 10

The remaining facts can be solved using Think Addition, as discussed in the Unpacking Document:
NOTE: Before students can use Think-Addition effectively, they need to have mastered the addition facts first.

For more information about fluency, timed tests, and learning basic facts see:

Burns, 2007, About Teaching Mathematics K-8
Fosnot & Dolk, 2001, Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction
Van de Walle & Lovin, 2006, Teaching student-centered mathematics, Grades K-3