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## Seeing Doubles

Pre-K-2
1

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.

At this point, you may wish to read another of the books listed in the Bibliography of Counting Books, for example, What Comes in 2’s, 3’s and 4’s.

While students remain in their seats, ask them to name things that come in pairs. Record their responses and ask the children to say or write the addition equations the list of pairs suggests. Then ask a volunteer to choose a pair and state the addends and the sum.

You may also wish to discuss some examples from science, such as “If a starfish has 5 arms, how many arms will 2 starfish have?”

Or, ask students “If a flower has 4 petals, how many petals will 2 flowers have?”

Now ask the children to write an addition story problem that uses doubles. Encourage them to share their problem with a friend and add it to their portfolios.

When the students complete this activity, give groups of students a set of Double 6 dominoes, and ask them to put the tiles upside down. Tell the students to take turns picking a domino and finding the sum in any way they wish. If they pick a double (a domino with the same number of spots on both sides) they should write the equation it suggests. If the tile picked is not a double, it is simply removed from the pile and the next child draws. Play continues until all tiles are drawn. The winner is the child who drew the most doubles. As this game takes only a little time, the students may wish to play it more than once.

Next, provide the children with index cards from which 2 inches of the long side have been cut. Ask them to fold the 3-inch squares to make two right triangles and then to cut the triangles apart. Ask them “How many triangles will we need if we want enough for each doubles fact found on our dominoes?” If the answer “6” is given, remind them that there is a 0+0 domino also, and that they will each need seven cards. Then have children write one doubles fact on each triangle by writing the sum at the right angle and the addends across the hypotenuse, one in each corner. When the students are ready, call them together to display the cards that they created. Encourage them to practice their addition facts with doubles by having a friend cover the sum and show the addends only. You may wish to have the children draw a sample triangle fact card and write its associated addition facts as an entry in their portfolio.

### Reference

•  Aker, Suzanne. What Comes in 2’s, 3’s, & 4’s. New York: Simon and Schuster, 1990.
• Book: What Comes in 2’s, 3’s, & 4’s, by Suzanne Aker
• Dominoes
• Index cards

Assessments

1. The Questions for Students help students to focus on the mathematics studied in this lesson and provide information on the students’ current level of knowledge and skill.
2. Because this is the first lesson in which recall of facts is stressed, you may wish to document on the Class Notes sheet which facts each student has mastered.

Extensions

1. Ask the children this seemingly easy question: “How many dominoes will we need for a Double 6 set?” Encourage them to record how they found the answer. Then ask “How many would we need for a Double 9 set?” [The answers are 28 and 55, respectively.]
2. Move on to the last lesson, Finding Fact Families.

Questions for Students

[They are the same; It’s always an even number.]

2. What doubles did you find on the dominoes? Did you know any of the doubles facts by heart already?

[Student responses may vary.]

3. When we listed things that came in pairs, what equations did we write? Did you know any of these facts by heart?

[Student responses will depend upon the examples discussed in class.]

Teacher Reflection

• Did most children remember the effects of adding or subtracting 0?
• Which children met all the objectives of this lesson? What extension activities are appropriate for those children?
• Which children are still having difficulty with the objectives of this lesson? What additional instructional experiences do they need?
• Which children are most dependent upon the manipulatives? Which children are beginning to find the answers without them?
• What will you do differently the next time that you teach this lesson?

### 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.

### 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.”

### 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:

• Write equations using doubles.
• Review the terms “addend” and “sum.”
• Use equations to record doubles sums.

### 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.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.