Illuminations: What's Left?

What's Left?
Triangular flash cards and dice games help students practice addition facts. Students modify their "Addition Chart" to record the facts they know at the immediate-recall level.

Learning Objectives
 
Students will be able to:
  • practice reciting addition facts
  • choose strategies to help them learn addition facts

Materials
 

Instructional Plan

Begin the lesson by having each student review his or her copy of the Addition Chart, adding known facts as necessary. Then display a large copy of an addition chart on the board or overhead. Call on volunteers to come to the front and circle one fact that they have studied so far.

When the students have circled all the facts that they have studied, direct their attention to the facts that are left: 4 + 9, 5 + 8, 5 + 9, 6 + 7, 6 + 8, 6 + 9, 7 + 6, 7 + 8, 7 + 9, 8 + 5, 8 + 6, 8 + 7, 8 + 9, 9 + 4, 9 + 5, 9 + 6, 9 + 7, and 9 + 8. Ask the class what they know that will help them learn fewer than 18 facts. [Encourage them to remember the commutative property.]

Remind the students that some of these facts belong to the doubles-plus-one group. Ask them to identify them. [These facts are 6 + 7, 7 + 8, and 8 + 9.] Now circle in another color the remaining six facts: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, and 7 + 9.

Place the students in pairs and assign each student three addition facts from the following: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, 7 + 9, as a set of demonstration facts. Have the students cut two triangular shapes from each of three file cards. Demonstrate how to make a triangular flash card by putting the two addends in two of the corners and the sum in the other corner [as in the example below].

Now ask the students to make triangular fact cards for the facts they choose, then trade the cards with their partner. Ask each student to cover the sum on one card with his or her thumb, show the card to the other student, and ask him or her to tell the sum.

When the students have had a chance to try all six cards, ask the students to play Cover Up the game they learned yesterday. After they have played the game for several minutes, have them return to their seats, take out their "Addition Chart," and cover any addition facts they have learned since yesterday.

Call the class together and ask them the Guiding Questions below. Then ask them to be sure that they have covered both facts in a commutative pair [For example, 6 + 7 and 7 + 6]. Finally, ask them to choose two facts and make triangular flash cards for them. Encourage the students to take those two new cards and the three they made in this lesson home to practice.

Mention that some students learn the facts by heart by writing them several times, other students by saying them out loud, and others by seeing them in their head. Now ask the students how they learn the facts by heart. Encourage them to list the facts that they still have to learn. [These will be the facts that are not blackened out on their addition charts.]

For their portfolios, have the students write two facts that they will learn next and their plan for doing so.

Questions for Students
 
  1. What pairs of numbers have a sum of 12? 18? Are any of these pairs doubles? What other doubles have you studied?
  2. What pairs of numbers have a sum of 13? Of 15? Of 17?
  3. What do you know about 6 + 7 if you know 7 + 6?
  4. What facts were the easiest to learn? Why?
  5. What strategies do you use when you set out to learn an addition fact? Is there another strategy you would like to try?
  6. What facts have you learned this week? What facts will you learn next?

Assessment Options
 

At this stage of the unit, it is important to know whether the students can do the following:

  • Describe the effects of the commutative property
  • Identify the addition facts that they know at the immediate-recall level
  • Explain the strategies that they use to learn addition facts

Your notes on students' progress will be helpful as you plan ways to ensure that each student has learned all the tables. You will find that daily five-minute review sessions, frequent chances to play the games, and establishment of a learning-buddy system will meet the needs of most of your students. Even for those students who need more intensive work with the facts, brief, focused, and frequent study sessions are most likely to lead to good memorization results.

Teacher Reflection
 
  1. Which students have improved in their ability to work in groups during this unit? What experiences will be helpful to the other students?
  2. Which students are able to identify the facts they have learned? How can others be helped to achieve this goal?
  3. Which students have only a few addition facts left to learn? What activities should I plan for them?
  4. What activities are appropriate for the students who have several facts left to learn?
  5. What adjustments will I make the next time that I teach this lesson?

NCTM Standards and Expectations
 
Number & Operations Pre-K-2
  1. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  2. Develop fluency with basic number combinations for addition and subtraction.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

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