SECOND GRADE > 2.OA.2 > TEACHER GUIDE

## TEACHER GUIDE TO CLARIFICATION

###### FLUENTLY ADD AND SUBTRACT WITHIN 20 MENTALLY

2.OA.2 mentions the word fluently when students are adding and subtracting numbers within 20. Fluency means accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (using strategies such as making 10 or breaking apart numbers). Research indicates that teachers’ can best support students’ memorization of sums and differences through varied experiences making 10, breaking numbers apart and working on mental strategies, rather than repetitive timed tests.

Kansas Association of Teachers of Mathematics (KATM) Flipbooks.

Questions or to send feedback: melisa@ksu.edu.

Retrieved from Math Flipbooks.

This standard builds upon the mental math strategies in Grade 1

(Below are 4 strategies named in standard 1.OA.6)

Example: 9 + 5 =___

Student 1

Counting On

I started at 9 and then counted 5 more. I landed on 14.

Student 2

Decomposing a Number Leading to a Ten

I know that 9 and 1 is 10, so I broke 5 into 1 and 4. 9 plus 1 is 10. Then I have to add 4 more, which gets me to 14.

Example: 13 - 9 =__

Student 1

Using the Relationship between Addition and Subtraction:

I know that 9 plus 4 equals 13. So, 13 minus 9 equals 4.

Student 2

Creating an easier problem using compatible numbers:

Instead of 13 minus 9. I added 1 to each of the numbers to make the problem 14 minus 10.

I know the answer is 4. So 13 minus 9 is also 4.

Kansas Association of Teachers of Mathematics (KATM) Flipbooks.

Questions or to send feedback: melisa@ksu.edu. Retrieved from Math Flipbooks.

Daily Discussions is a great way to practice these strategies and to utilize Math Practice 3 – Construct viable arguments and critique the reasoning of others.

This is a great definition of how fluency can look in the CC math classroom

The deep extended experiences students have with addition and subtraction in Kindergarten and Grade 1 culminate in Grade 2 with students becoming fluent in single-digit additions and the related subtractions using the mental Level 2 and 3 strategies as needed.2.OA.2

Common Core Standards Writing Team. (2013, September 19).

Progressions for the Common Core State Standards in Mathematics(draft). K-5 Counting and Cardinality and Operations and Algebraic Thinking. Tucson, AZ: Institute for Mathematics and Educations, University of Arizona.

For some definitions of Level 2 problem solving refer to pg. 37 of the KCC –OS Progression Document.

Common Core Standards Writing Team. (2013, September 19).

Progressions for the Common Core State Standards in Mathematics(draft). K-5 Counting and Cardinality and Operations and Algebraic Thinking. Tucson, AZ: Institute for Mathematics and Educations, University of Arizona

Check out how a third grade class adds mentally. 2nd graders would use numbers within 20.

https://www.teachingchannel.org/videos/third-grade-mental-math

###### 2.OA.2

Add and subtract within 20

2.OA.2 Fluently, add and subtract within 20 using mental strategies. By the 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

###### Coherence and Connections: Need to Know

Fluency Standard

So fluency in adding and subtracting single-digit numbers has progressed from numbers within 5 in Kindergarten to within 10 in Grade 1 to within 20 in Grade 2. The methods have also become more advanced. The word fluent is used in the Standards to mean “fast and accurate.” Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. It is important to push sensitively and encouragingly toward fluency of the designated numbers at each grade level, recognizing that fluency will be a mixture of these kinds of thinking which may differ across students. The extensive work relating addition and subtraction means that subtraction can frequently be solved by thinking of the related addition, especially for smaller numbers. It is also important that these patterns, strategies and decompositions still be available in Grade 3 for use in multiplying and dividing and in distinguishing adding and subtracting from multiplying and dividing. So the important press toward fluency should also allow students to fall back on earlier strategies when needed. By the end of the K–2 grade span, students have sufficient experience with addition and subtraction to know single-digit sums from memory; 2.OA.2 as should be clear from the foregoing, this is not a matter of instilling facts divorced from their meanings, but rather as an outcome of a multi-year process that heavily involves the interplay of practice and reasoning.

Common Core Standards Writing Team. (2013, September 19).

Progressions for the Common Core State Standards in Mathematics(draft). K-5 Counting and Cardinality and Operations and Algebraic Thinking. Tucson, AZ: Institute for Mathematics and Educations, University of Arizona.

This cluster is connected to the Second Grade Critical Area of Focus #2, Building fluency with addition and subtraction.

This cluster is connected to Represent and solve problems involving addition and subtraction and Add and subtract within 20 in Grade 1, and to Use place value understanding and properties of operations to add and subtract in Grade 2.

Kansas Association of Teachers of Mathematics (KATM) Flipbooks.

Questions or to send feedback: melisa@ksu.edu. Retrieved from Math Flipbooks.

When teaching these mental math strategies the approach the teacher takes is just as important. A recommendation is to let students solve the problem in any way that works for them, and then elaborate on how they solved the problem. Given the problem 13 + 5 students can solve the problem a few different ways. It is up to the teacher to recognize how they solved it and then identify that strategy to the other students. This promotes student-discovery learning. The teacher then truly becomes a facilitator of learning.

This standard is strongly connected to all the standards in this domain. It focuses on students being able to fluently add and subtract numbers to 20. Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

Mental strategies help students make sense of number relationships as they are adding and subtracting within 20. The ability to calculate mentally with efficiency is very important for all students. Mental strategies may include the following:

* Counting on

* Making tens (9 + 7 = 10 + 6)

* Decomposing a number leading to a ten ( 14 – 6 = 14 – 4 – 2 = 10 – 2 = 8)

* Fact families (8 + 5 = 13 is the same as 13 - 8 = 5)

* Doubles

* Doubles plus one (7 + 8 = 7 + 7 + 1)

The use of objects, diagrams, or interactive whiteboards, and various strategies will help students develop fluency.

Kansas Association of Teachers of Mathematics (KATM) Flipbooks.

Questions or to send feedback: melisa@ksu.edu.

Retrieved from Math Flipbooks.

Example of Major Within-Grade Dependencies

Knowing single-digit sums from memory (2.OA.2) is the basis for adding and subtracting multi-digit numbers fluently and efficiently in general (cluster 2.NBT.B).

Examples of Opportunities for Connections among Standards, Clusters or Domains

Students’ work with addition and subtraction word problems (2.OA.1) can be coordinated with their growing skill in multi-digit addition and subtraction (2.OA.2, cluster 2.NBT.B).

PARCC Draft Model Content Frameworks: Mathematics Grades K-2

In this grade level, the conceptual understanding is being developed. In grade 3, students will learn the standard algorithm with regrouping.

Grade Below

1.OA.6

Grade Level

2.OA.2

2.NBT.5

Grade Above

###### Additional Resources

Card game that allows students to add or subtract numbers in order to get close to 20.

http://www.insidemathematics.org/problems-of-the-month/pom-gotyournumber.pdf

Howard County Wiki

https://grade2commoncoremath.wikispaces.hcpss.org/Assessing+2.OA.2

K-5 teaching resources – scroll down to 2.OA.2 – many activities, good center ideas

http://www.k-5mathteachingresources.com/2nd-grade-number-activities.html

North Carolina Wiki

http://commoncoretasks.ncdpi.wikispaces.net/2.OA.2+Tasks

Illustrative Math

https://www.illustrativemathematics.org/2

###### HOT Questions

1. Jean solved the addition problem below. Can you think of another way to solve it?

7 + 8 = 15

Jean: I know that 7 + 7 equals 14 and one more from the 8 makes 15

2. True or False – explain how you know

9 + 6 = 10 + 5

3. Solve 13 – 8 two different ways. Be prepared to share your strategy with a partner.

###### Classroom Resources

This power point will give the teacher addition and subtraction problems that allow students to solve in multiple ways and to utilize their mental math strategies. Sample answer are in the notes of the ppt., however, students may use a variety of ways to solve.