## Counting to Find Sums

Pre-K-2
1

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.

To set the stage for learning, choose a counting book to read. Of the many available, a few are listed in the Bibliography of Counting Books.

Any book in which the pictures for the numbers are unambiguous will work, but a book that also presents the written or numerical form of the numbers is preferable. Ten Little Rabbits or Ten Black Dots are two books that use the number words; The M & M’s Counting Book uses both numerals and words for the numbers. As students listen to the story, have them model each number as it is mentioned with counters (or coated chocolate candies), then write the numeral and number word for each. This recording process will assist you in assessing the students’ current level of functioning.

Next put students in small groups and give each group a set of Double 6 dominoes. Hold up a domino (or display one on the overhead) and have the children count the total number of dots. Then ask them to look in their set to find a domino that has the same number of dots as yours does, one that has one more dot, and one that has one less dot.

Now ask the students to hold a domino vertically so that one side is over the other. Ask them to count the spots on the top part of the domino and write the number. Then have them count the spots on the bottom part and write it under the first number they wrote. Introduce the addition sign, if necessary, and have them draw a line under the bottom number. Then have them count the number of spots in all, record the sum, and read the addition statement to a friend.

Encourage the students to continue this procedure with several dominoes. Next, repeat this activity asking the children to rotate the domino a quarter turn so it is in a horizontal position. Then ask them to count the spots on the top first, then those on the bottom, and finally to record the sum in horizontal format.

When the students are ready, review some of the sums and the counting process that was used to get those sums. Ask the children to choose one domino to draw for their portfolio and to write the addition statement modeled in the domino in both vertical and horizontal format.

To conclude the lesson, students can play a Dominoes game. Children who have never played dominoes should be introduced to the game. Begin in a whole-group setting by showing the students a set of Double 6 dominoes.

Encourage the students to describe what they notice as they look at the tiles. Then ask for two volunteers to play a game while the other children watch. So that all students can follow the action, ask both volunteers to display all their tiles for this demonstration. The type of game you will want to teach the children is called a Draw Game (search the internet for "Dominoes Draw Game"). Explain that the Draw Game begins with a tile that is randomly chosen from the set of upside down tiles being placed right side up on the playing field. To determine the first player, the children each choose a tile from the set and compare the number of spots on their dominoes. The child whose domino has the most spots goes first. Then help the children play the game.

Assessment Options

1. Documenting information about students’ understanding and skills throughout the unit can help you focus on individual needs and strengths and foster appropriate additional learning opportunities. The recording format, Class Notes, has been provided for your use. You may find this information useful when discussing children’s progress toward learning targets with parents, administrators, colleagues, and the students themselves.
2. Collect the students' drawings and addition sentences from the lesson. Students will add to their portfolios throughout the unit.

Extensions

1. Put the students in pairs and have each pair turn a set of dominoes upside down. Then have each partner pick a domino from the set at the same time and compare the total number of spots. The child whose domino has the most spots writes the two addition sentences in horizontal format for both dominoes. If the number of spots is equal, each child writes one of the sentences. Have them continue the game until one child has written 10 addition sentences. Have them repeat the game, this time recording in vertical format.
2. Move on to the next lesson, Hopping on the Number Line.

Questions for Students

1. How many spots were on this part of the domino? On this part? In all?

[Student responses will depend upon the domino in question.]

2. Are there more or less on this next domino? How can you tell?

[Student responses will depend upon the domino in question.]

3. What is alike between the two ways we recorded the sums? What was different?

[They both contained the same numbers, but one was written horizontally and the other vertically.]

4. Can you find a domino with five spots? With ten?

[Students should be able to identify these specific dominoes.]

5. I am thinking of a domino with six spots. What could it look like? Could it look any other way?

[1+5 spots, 6+0 spots, 2+4 spots, 3+3 spots.]

6. What does the “plus” sign mean?

7. What is the largest number you can show on your fingers? What is the largest number modeled on a set of Double 6 dominoes? Which is greater?

[10; 12; 12 is greater.]

Teacher Reflection

• Which students met all the objectives of this lesson? What extension activities would be appropriate for those students?
• Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification?
• Which groups worked together well?
• What adjustments would you make the next time that you teach this lesson?

### 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.

Pre-K-2
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.

### 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.”

### 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.

### 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:

• Count to 12.
• Model numbers to 12.
• Count sums to 12.
• Write and recognize numerals to 12.
• Record sums in vertical and in horizontal format.

### NCTM Standards and Expectations

• Count with understanding and recognize "how many" in sets of objects.
• Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
• Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
• Use multiple models to develop initial understandings of place value and the base-ten number system
• 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, Counting & Cardinality

• CCSS.Math.Content.K.CC.A.2
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-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.

• 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.

• 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).

• 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.

• 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.

• 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.

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

• 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.