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Balancing Discoveries

Number and Operations
Grace M. Burton
Location: unknown

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.”

In this lesson, the balance model for addition will be demonstrated using an actual balance beam or pan balance. If you use a balance beam, you will hang weights from positions in the arms; if you use a pan balance, you will need to enclose sets of weights in plastic bags (and you may want to write on the bags the amount of weights in each). To use a balance beam, display it and review with the students how it operates. Then ask a volunteer to hang a weight on the “3” position of the left arm of the balance beam and then another weight from the “2” position. Next ask “Where would we need to place a weight on the other side so that the beam balances?” If you use a pan balance and weights in plastic bags, put a bag with three weights and a bag with two weights on the left side and ask how many loose weights would be needed to balance them. Accept and model all student responses. When the response “5” is given, ask students to record this using the equation 3 + 2 = 5. Continue with other weights until the children are comfortable with the process.

You may wish to introduce the children to the online Pan Balance— Shapes Tool as another way to practice.

appicon Pan Balance— Shapes 

When they have had time to explore, suggest that they write a portfolio entry about how a balance can help them find sums. Note that because the shapes have different values, when using the online balance, only one shape weight should be used throughout the session.

Next put the children into pairs and give them a set of Double 6 dominoes to share equally between themselves.

364 Domino box

Have them place their dominoes upside down so that the spots are not visible.

Explain the rules of the “seven-up game:”

  1. Each player turns over one domino and finds the total number of spots on it.
  2. If it is 7, the domino is placed on end on that player’s side of the desk and the player who turned it over writes the appropriate equation.
  3. If the domino has any other sum, it is removed from the pile.
  4. Then once all the dominoes have been turned over, the player who turned over the most dominoes with a sum of 7 lines up his or her dominoes and pushes them to make them fall over.

You may wish to display the Rules for the Seven Up Game Overhead so students have them handy.

overhead Rules for the Seven-Up Game 

Allow the students to play the Seven Up Game until the class period is nearly over. Then call them together to discuss their experiences using the following, or other, guiding questions.

Assessment Options

  1. The Questions for Students will elicit information that will help you assess the students’ current level of knowledge about addition.
  2. As a new model for addition has been added today, you may wish to make more entries on the Class Notes sheet begun earlier in this unit.


  1. You may extend the Seven Up Game as follows. For those who are ready, you may wish to suggest a related game where the sum of 10 is the goal.
  2. Move on to the next lesson, Seeing Doubles.

Questions for Students 

1. When you modeled an equation on the balance beam, what did you do first? Then what? How did you record this? 

2. Suppose you put a weight on the “1” and on the “2” on the left hand side of the beam and that you wanted to put a weight on the right hand side to balance the scale. Where would you put it? 

3. What equation could you write to show what you did? Can you write another addition equation with the same addends? 

4. How could you use the balance beam to complete this number sentence: 3 + _ = 5?

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 instructional experiences do they need next?
  • Which students have mastered sums of 7? Which are still counting to find these sums?
  • What parts of the lesson went smoothly? Which parts would you change 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

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.
Number and Operations

Finding Fact Families

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 balance model of addition.
  • Write the addition modeled on balances in equation form.
  • Find sums of 7.

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, 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.