Main Curriculum Tie: Mathematics Grade 1 1.NBT.C Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Materials: Invitation to Learn
 Addition/Subtraction Mats
 Base Ten Blocks
 Spin and Add
 Transparent spinners
 Math journals
Two and Three Digit Addition Strategies
Partner Roll and Add
 Math journals
 Place Value cubes
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
Attachments
Background For Teachers: 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:
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 

Intended Learning Outcomes: 1. Demonstrate a positive learning attitude.
2. Develop social skills and ethical responsibility.
Instructional Procedures:
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
 Divide a 11" X 14" piece of cardstock on the 14" side into four
sections each measuring 3 ½".
 Draw lines with a black marker to separate the four sections.
 Glue a 3 ½" X 11" piece of colored cardstock in the third
section.
 Label the sections as follows: 1) First Addend 2) Second
Addend 3) Thinking Area (different color cardstock) 4) Sum.
 Turn the cardstock over to make the subtraction mat. Divide
the cardstock into four 3 ½" sections.
 Glue a 3 ½" X 11" piece of colored cardstock in the second
section.
 Label the sections as follows: 1)Minuend 2)Thinking Area
3)Subtrahend 4)Difference.
Partner Spin and Add
 Organize students into partner groups. Pass out an Addition/
Subtraction Mat to each student. To each partnership, pass out base ten blocks and a Spin and Add template with a transparent
spinner. Students need their math journals to record their
strategies.
 Have each player spin the spinner. The highest number goes
first.
 The first student spins the spinner, and both students model the
number using their base ten blocks on their Addition/Subtraction
Mat.
 The second student spins the spinner and again both students
model the number on their mats using the base ten blocks.
 Each player writes the equation in his/her journal and then
writes or draws pictures explaining how he/she solved the
problem. Students share their answer and method with each
other. If students get the same answer they celebrate and
continue with a new problem. If they get different answers then
they need to go back and work the problem out together.
 When students have completed the activity and cleaned up
their materials, have them bring their journals with them to the
rug for math meeting. Call on students to share some of their
solution strategies with the other students by either drawing on
the whiteboard or verbally explaining.
Two and Three Digit Addition Strategies
 Pass out the Addition Strategies Foldable to each student.
Explain how to fold the paper and where to cut the flaps.
 Model together an addition problem using “expanded form.”
Then, have the students make up a problem on their own, write
it on the opposite side of the flap, and solve it using the same
method. Continue using “partial sums,” and “opposite change”
strategies.
Partner Roll and Add
 Organize your students into partner groups. Pass out both a
tens and a ones number cube to each partnership.
 Students take turns rolling both cubes to create a twodigit
number. After both numbers have been created then the
students write the addition equation in their journals.
 Have the students practice solving the problems using expanded
form, partial sums, or opposite change strategies for addition.
Attachments
Extensions: Curriculum Extensions/Adaptations/
Integration
 Provide larger numbered spinners or a hundreds place cube for
advanced learners during these activities.
 Provide smaller numbered spinners and allow learners with
special needs to continue using manipulatives to assist them in
solving the problems.
 Have special needs students orally explain their thought process
to you if writing is a struggle.
Family Connections
 Write a note home to family members explaining that you will
be teaching to their children different strategies for addition
before you teach the standard algorithm. Give parents some
examples and ask them to support you by helping their children
learn these strategies too.
 Have students take a copy of the Spin and Add spinner home
and play with a family member using an assigned strategy.
Assessment Plan:
 Walk around the room while students are participating in
the activities. Are they able to model the numbers correctly?
Do they understand place value, and are they lining up their
equations properly? Are they able to solve the problems? What
strategies are they using most often?
 Ask a partner group to explain their thoughts and strategies to
you.
 Look at students’ journals and evaluate their work to see where
students are struggling.
Bibliography: 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.
Author: Utah LessonPlans
Created Date : Jul 07 2008 17:56 PM
