Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

Pin it!
Google Plus

Exploring Adding with Sets

Pre-K-2
1
Number and Operations
Grace M. Burton
Location: unknown

This lesson builds on the previous two lessons and encourages students to explore another model for addition, the set model. This model is similar to the counting model in the first lesson, because it is based on counting. Reading a related counting and addition book sets the stage for this lesson in which students write story problems, find sums using sets, and present results in the form of a table. In the discussion of the table, the students focus on the order property and the effects of adding 0.

To set the stage for this lesson, you may wish to read The Hershey’s Kisses Addition Book, or a similar book. Then ask the children to write an addition story problem that uses sets. Encourage them to share their problems and to put them in their portfolios.

Then provide groups of children with dominoes and a work mat. Tell them that they will consider the number of spots on each side of the domino as a set. Ask them to choose a domino and record the number of spots on each side as well as both sides combined. Next, tape up a large piece of chart paper that displays a recording table featuring columns that you have labeled “Number of Spots on the Left Side,” “Number of Spots on the Right Side,” and “Number of Spots in All.”

Number of Spots
on the Left Side
Number of Spots
on the Right Side
Number of Spots
in All
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Display a 5+4 domino and have the students suggest what will go in each column (e.g., 5, 4, 9). Then have them work in pairs to create new entries for the table. When they have identified the sum, help them enter their findings on the class chart. Allow the children time to make several entries, then call them together and review the terms “addend” and “sum.”

A partially completed (sample) chart is shown below.

Number of Spots
on the Left Side
Number of Spots
on the Right Side
Number of Spots
in All
addend
addend
sum
5
 
4
 
9
 
3
 
5
 
8
 
0
 
6
 
6
 
2
 
2
 
4
 

Call on a volunteer to read one row of the chart. Then call on other volunteers to read the other rows. When several have been read, ask the children if they see any similarities among the entries. Repeat with other volunteers. If examples of the order property are not mentioned, prompt them to notice such entries. Also call attention to rows where at least one addend is zero. Encourage students to also notice rows in which the last column shows the same number.

Alternatively, students may record their domino information on the Number of Spots Activity Sheet.

pdficonNumber of Spots Activity Sheet 

Finally, ask the students to choose one of the rows from the chart and draw a picture (using dominoes or something personal to them) illustrating that number fact. They may wish to display these in the classroom or in a more public place.

360 Dominos

For the example above, students would write 4 + 5 = 9.

Reference

Pallotta, Jerry. The Hershey’s Kisses Addition Book. New York: Scholastic, 2001.


 

  • The Hershey’s Kisses Addition Book (or another appropriate book)
  • Dominoes
  • Work mats, such as construction paper
  • Chart paper
  • Number of Spots Activity Sheet 
 

Assessment Options 

  1. The suggested Questions for Students may assist you in understanding your students’ level of knowledge, but others may suggest themselves as you dialogue with your students.
  2. You may find it helpful to add to your recordings on the Class Notes sheet that you began earlier in this unit. This data may be helpful as you plan strategies for regrouping students and for remediation or extension activities.
Extension
Move on to the next lesson, Balancing Discoveries.

Questions for Students 

1. How many spots are on the left side of this domino? On the right? How many in all?

[Answers will depend upon the dominoes in question.]
2. Which sum that we listed was the greatest? What addends were used? Do you think we could get a larger sum with this set of dominoes? How?
[Answers will depend upon the dominoes used in the lesson.]

3. Suppose you had a domino with a “5” and a “0.” What would be the sum? How about a “0” and a “5?”

[5; 5.]

4. Look at this row. Does any other row have the same sum? The same two addends?

[Answers will depend upon the rows in question.]

5. Would you get the same thing if you had a “4” on the left and a “3” on the right as you would if the “3” were on the left and the “4” on the right? Can you show why?

[Yes; 4 + 3 = 7 and 3 + 4 = 7 also.]
 
Teacher Reflection 
  • Which students met all the objectives of this lesson? What extension activities are appropriate for these students?
  • Which students did not meet the objectives of this lesson? What misconceptions did they demonstrate?
  • Can most of the students justify the sum when one addend is “0?”
  • What parts of the lesson went smoothly? Which parts would you change the next time that you teach this lesson?
 
349icon
Number and Operations

Counting to Find Sums

Pre-K-2
This lesson focuses on the counting model for addition and begins with reading a counting book. Students model the numbers with counters as the book is read. Then they count the spots on each side of a domino and write, in vertical and horizontal format, the sums suggested by dominoes. Finally, the students illustrate a domino and record a sum it represents.
355icon
Number and Operations

Hopping on the Number Line

Pre-K-2, 3-5
In this lesson, students generate sums using the number line model. This model highlights the measurement aspect of addition and is a distinctly different representation of the operation from the model presented in the previous lesson. The order (commutative) property is also introduced. At the end of the lesson, students are encouraged to predict sums and to answer puzzles involving addition.
364icon
Number and Operations

Balancing Discoveries

Pre-K-2
This lesson encourages students to explore another model of addition, the balance model. The exploration also involves recording the modeled addition facts in equation form. Students begin to memorize the addition facts by playing the “seven-up game.”
368icon
Number and Operations

Seeing Doubles

Pre-K-2
In this lesson, the students focus on dominoes with the same number of spots on each side and on the related addition facts. They make triangle-shaped flash cards for the doubles facts.
349icon
Number and Operations

Finding Fact Families

Pre-K-2
In this lesson, the relationship of subtraction to addition is introduced with a book and with dominoes. Then students explore the concept of missing addends.

Learning Objectives

Students will:

  • Explore the results of adding sets.
  • Review the order (commutative) property.
  • Define and use the terms “addend” and “sum.”
  • Explore the effects of adding 0.
  • Construct a table showing addends and sums.

NCTM Standards and Expectations

  • Count with understanding and recognize "how many" in sets of objects.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.
  • Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.1
    Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.2
    Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.5
    Fluently add and subtract within 5.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.4
    Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.5
    Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.6
    Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.C.4
    Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit 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 two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 2, Algebraic Thinking

  • CCSS.Math.Content.2.OA.B.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.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.5
    Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.6
    Add up to four two-digit numbers using strategies based on place value and properties of operations.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.7
    Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.9
    Explain why addition and subtraction strategies work, using place value and the properties of operations.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP1
    Make sense of problems and persevere in solving them.
  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP6
    Attend to precision.