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Finding Fact Families

Number and Operations
Grace M. Burton
Location: unknown

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.

To review the concept of subtraction, read Ten Sly Piranhas. Ask the children to act out with counters what is happening in the story and to write the related subtraction sentence for each page. Then call out a sum and have each child show you a domino with that many spots. Encourage the students to write the addition equation suggested by the domino.

372 6-4 domino

In the example above, students may suggest the following addition equation:

6 + 4 = 10


Next, choose two dominoes with the same number of total spots, then display them with one crossed over the other so that both parts of the upper domino but only one part of the bottom domino is visible. Now tell the children that both dominoes have the same number of spots and that they are to guess how many spots are covered on the bottom domino. When a correct response is given, display the domino and ask the students to explain how they knew.

Model the activity a few more times, being sure to include one example of what happens when one domino has 0 spots on one side. Then place the students in pairs and have them take turns being the teacher. This activity will help them focus on the relationship of subtraction to addition. Finally, ask the pairs to sort the set of Double 6 dominoes by the sums that the dominoes represent. Ask the students to write a sentence about this exercise for their portfolios.

Now call the children together and ask a volunteer to choose a domino that is not a double and write the four number sentences (two addition and two subtraction) that the domino suggests. You may wish to repeat this exercise with other volunteers.

372 4-5 Domino

For the domino above, the following addition and subtraction sentences are suggested:

4 + 5 = 9
5 + 4 = 9
9 - 5 = 4
9 - 4 = 5

As the lesson concludes, remind the students that they need to practice the addition facts and that making more triangle-shaped flash cards will help them to do so.


  •  Wise, William. Ten Sly Piranhas. New York: Dial, 1993.
  • Book: Ten Sly Piranhas, by William Wise
  • Dominoes
  • Index cards

Assessment Options

  1. The Questions for Students help students focus on their current level of understanding and of fact mastery.
  2. You may wish to add more documentation to the Class Notes chart. These notes will be valuable as you plan appropriate remediation and enrichment opportunities.

Questions for Students 

1. What is missing when I say “2 + ‘something’ = 5?” Can you write the complete addition sentence?

[3 is missing; 2 + 3 = 5.]

2. What about when I say “6 + ‘something’ equals 6?” What addition sentence would show that?

[0 is missing; 6 + 0 = 6.]

3. What addition and subtraction facts can I write if I pick a 3+4 domino? Suppose I pick a 3+0 domino? A 3+3 domino?

[Answers may include any of the following:
3 + 4 = 7
7 - 4 = 3
3 + 0 = 3
3 - 0 = 3
3 + 3 = 6
6 - 3 = 3.]

4. How could you help a friend find a subtraction fact related to 5 + 4 = 9?

[Student responses may vary, but they may say 9 - 4 = 5.]

Teacher Reflection 

  • Which students have some of the facts memorized?
  • Did most students remember the effects of adding by 0? Did most recall the order property?
  • Which students met all the objectives of this lesson? What extension activities are appropriate for those students?
  • Which students are still having difficulty with the objectives of this lesson? What additional instructional experiences do they need?
  • What will you do differently the next time that you teach this lesson?
Number and Operations

Counting to Find Sums

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.
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.
Number and Operations

Exploring Adding with Sets

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.
Number and Operations

Balancing Discoveries

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.”
Number and Operations

Seeing Doubles

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.

Learning Objectives

Students will:

  • Find missing addends.
  • Review the additive identity.
  • Relate subtraction to addition.

NCTM Standards and Expectations

  • Understand the effects of adding and subtracting whole numbers.
  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • 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.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, Algebraic Thinking

  • CCSS.Math.Content.1.OA.D.8
    Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

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.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.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.
  • CCSS.Math.Practice.MP6
    Attend to precision.