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Some Special Sums

  • Lesson
Number and Operations
Grace M. Burton
Location: unknown

Students practice doubles and doubles-plus-one addition facts. They record their current level of mastery of the addition facts on their personal addition charts.

Call two students to the front of the room and ask the class how many noses they see. Ask for a volunteer to write the number sentence that shows that on the board. [1 + 1 = 2.] Now ask the class how many eyes they see, and call for a volunteer to write that number sentence [2 + 2 = 4] on the board directly under the previous equation. Now, have each of the two students in the front of the room hold up three fingers, then have a volunteer record the relevant number sentence [3 + 3 = 6]. Then ask both students to hold up four fingers, then five fingers, and then six fingers. Call on a volunteer to write each number sentence on the board.

Ask the class what these kinds of facts are called. [Doubles.] Then point to the calendar and ask how many days are in two weeks, then add the doubles fact 7 + 7 = 14 to the list on the board. Next, call on eight students to wave their arms and ask someone else in the class to tell how many hands the class can see. Record 8 + 8 = 16 on the board. Finally, put 9 + 9 = on the board and ask the students what the answer will be [18]. Then, repeat with 10 + 10 =. Ask the students to look at the sums to see whether they notice a pattern. [Possible answers are that all the sums are even or that the sums increase by 2.]

Next to 2 +2 = 4, write 2 + 3 =, and ask the students what the answer will be [5]. Call on volunteers to explain how they know. Repeat with other doubles-plus-one facts up to 9 + 10 =. Encourage the students to say both the doubles and doubles-plus-one facts aloud.

510 doubles

Now assign the students to groups of four students each, and give each group two number cubes and a copy of the Tossing Sums activity sheet. Tell them to take turns rolling the number cubes and making an X in the column that shows which sum they rolled, beginning at the bottom of the sheet. As they play, you may wish to move around the room, noticing which students can name the sum immediately, which students count on their fingers, and which students need to use counters or other external aids, such as manipulatives.

pdficon   Tossing Sums Activity Sheet  

After the students have played for several minutes, call the students together and ask them what sums came up most often. Then have them identify the sums that can be obtained only by getting doubles [2 and 12]. Now, assign each group one of the other even sums (4, 6, 8, or 10) and have them list all the ways they could get that sum. Then, ask them to circle the double. Encourage them to share their work with the class. Repeat with odd sums, having them circle doubles-plus-one sums.

Next, ask them to return to their seats and take out their personal addition charts. Ask them to add to their charts any facts that they now know from memory. Then have pairs of students exchange charts and ask each other the facts that are marked on the chart. If a student misses a fact, ask the partner to make a small dot or check mark by the fact to indicate that he or she needs to practice it further.

As a record of this lesson, have the students write two addition facts that they have recently learned and two facts that they wish to learn next.     


  1. Asking the Questions for Students is one means of gathering data about the students' current level of functioning.
  2. Document student progress on the Class Notes recording sheet.

Questions for Students 

1. What sums can you get when both numbers are the same? What are these facts called? How can knowing doubles help you learn the addition facts?

[The sums are both even; they are called doubles.]

2. What happens when one addend is one more than the other? What do we call these facts?

[The sum is odd; these are called doubles-plus-one facts.]

3. What is the sum when one addend is zero? How can knowing this help you learn the addition facts?

[The sum is the other addend.]

4. What is alike about 6 + 5 and 5 + 6? What is different?

[The addends and the sum are the same; the order of the addends is different.]

5. Write the sums you say when you skip count by twos to 20.

[2, 4, 6, 8, 10, 12, 14, 16, 18, 20.]

Teacher Reflection 

  • Which students have only a few addition facts learned? What activities should I plan for them?
  • What extension activities are appropriate for the students who have learned all or almost all their addition facts?
  • What adjustments will I make the next time that I teach this lesson?
Number and Operations

Finding Addition Patterns

A game encourages students to find the sums of two one-digit numbers. Students explore commutativity and examine addition patterns. Then they record known facts on a personal addition chart.
Number and Operations

Finding Sums to Six

In this lesson, students discover the role of the additive identity and explore sums to six. They continue to complete their personal addition charts.
Number and Operations

Addend Pairs to 12

Students practice their addition facts for sums up to 12 by playing a game. They add to their personal addition charts. Students are encouraged to practice the facts that they have not yet mastered. Finally, triangular flash cards help students practice addition facts.

Wrapping up the Unit

In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.

Learning Objectives

Students will:

  • Identify doubles and doubles-plus-one addition facts
  • Practice selected addition facts
  • Add new facts (as appropriate) to their personal addition charts

Common Core State Standards – Mathematics

-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.MP6
    Attend to precision.