Mathematics Grade 1
Strand: NUMBER AND OPERATIONS IN BASE TEN (1.NBT) Standard 1.NBT.4
Mathematics Grade 1
Strand: NUMBER AND OPERATIONS IN BASE TEN (1.NBT) Standard 1.NBT.6
Invitation to Learn
Two and Three Digit Addition Strategies
Additional Resources
Books
Principles and Standards for School Mathematics, by National Council of Teachers of Mathematics; ISBN 9 780873534802
Developing Number Concepts; Place Value, Multiplication, and Division, by Kathy Richardson; ISBN 0769000606 21882
Elementary and Middle School Mathematics; Teaching Developmentally, by John A. Van De Walle; ISBN 020538689X
Mall Mania, by Stuart Murphy; ISBN 9780060557775
Mission Addition, by Loreen Leedy; ISBN 0823414124
A Fair Bear Share, by Stuart Murphy; ISBN 0064467147
Flexible or invented methods of computation require a student to have a good understanding of place value, compatible numbers, and operations and properties of the operations. Invented methods require students to take apart and combine numbers in a variety of ways. Students have to use their number sense to solve problems, and look at numbers as a composite number rather than a single digit. Invented strategies rely on the students' understanding. Students who have an opportunity to work with invented strategies will have an easier time understanding the traditional algorithm. Research shows that students that are taught the standard algorithms too early use the algorithms as a substitute for thinking and common sense.
There are many different inventive strategies for addition, but in this lesson we will discuss three different ways that students often use to solve problems. The first strategy will be referred to as "Expanded Form." Students write the numbers in expanded form first and then add the different place values. The answers from each of the places are then added together.
Example:
36  →  30  + 6  80  
+ 57  →  50  + 7  + 13  
80  13  93 
The second strategy will be called "Partial Sums." In this strategy students still think about the numbers as composite numbers and not just digits. Students can start to add with the ones place or the hundreds place, but they must remember that they are adding 200 plus 300 not 2 plus 3 when they record their answers.
Example:
36 
+ 57 
80 
+ 13 
93 
The third strategy we will discuss will be named "Opposite Change." Students should be familiar with "making tens" as a strategy for adding basic addition facts. In this strategy students subtract or add from one of the numbers to make compatible numbers, usually tens because they are easier to add. Whatever operation I use on the first addend, I have to use the opposite operation on the second addend to keep the problem the same.
Example:
36  3 Think: Because I added 3 to 57, I have to subtract 3 from 36 to keep the problem the same. 36 subtract 3 is 33.  
+ 57  + 3 Think: if I add 3 to 57 it will make it 60. 
33  
+ 60 

93 
1. Demonstrate a positive learning attitude.
2. Develop social skills and ethical responsibility.
Invitation to Learn
Write the following story problem on the board and ask students
to solve the problem using base ten blocks or any other method that
they choose. Problem: Chelsea bought 26 pieces of bubblegum
and 19 jawbreakers at the store. How many pieces of candy did she
have altogether? After students have had an opportunity to solve the
problem using their manipulatives, ask students to share how they
solved the problem. Did some of the students use similar methods?
Do the strategies make sense to other students? Write the steps on
the board as students explain their methods.
Instructional Procedures
Directions to make an Addition/Subtraction Mat
Partner Spin and Add
Two and Three Digit Addition Strategies
Partner Roll and Add
Curriculum Extensions/Adaptations/ Integration
Family Connections
Research Basis
Burns, M., (November 07). Nine Ways to Catch Kids Up: How do we help floundering students who lack basic math concepts? Educational Leadership. 65(3) 1621.
In this article, Marilyn Burns discusses nine essential strategies that help struggling mathematics learners become successful. Although all of the strategies are helpful, there are two strategies that I would like to focus on. The first strategy is building a routine of support. Burns discusses a fourstage lesson process that supports the students' learning and understanding of the concept before they are asked to work independently. Secondly, she discusses the importance of fostering student interaction with each other about their math knowledge either through sharing with the whole class, partners, or table groups.
Strong, R., Thomas, E. Perini, M. & Silver, H. (February 2004). Creating a Differentiated Mathematics Classroom. Educational Leadership. 61(5) 7378.
The researchers in this article state that students acquire math using four different styles. Although students can work in all four styles, most find one or two styles comfortable and work within them. The four styles are: Mastery, Understanding, Interpersonal, and Self Expressive. The authors also explain the importance of using the nine effective teaching strategies. Mathematical differentiation and students' achievement can take place when educators design units that include all four dimensions of mathematical learning, use a variety of teaching strategies and create assessments that correspond with the learning styles.