Combining and Partitioning

Use this dialog to guide a discussion about addition strategies.

Save the Sorting Mats students used to sort the sums for use in Lesson 8. Students will use the mats again to sort subtraction cards.

The addition cards in this lesson are not intended to be used as flash cards or for rote memorization. That is why the sums are not written on the back of the cards. In Adding It Up, a publication of the National Research Council, the authors state, "Practicing single-digit calculations is essential for developing fluency with them. This practice can occur in many different contexts, including solving word problems. Drill alone does not develop mastery of single-digit combinations. Practice that follows substantial initial experiences that support understanding and emphasize "thinking strategies" has been shown to improve student achievement with single-digit calculations." Inappropriate practice of procedures and skills too soon can interfere with learning as students may not be able to make sense of the procedures later (Hiebert, 1999).

The activities in this lesson provide opportunities for students to practice and develop strategies for the addition facts with sums of ten or less in different contexts with a variety of tools. Learning the facts with sums of ten and becoming flexible with the strategies for using these known facts to find other facts will serve as building blocks for applying similar strategies to sums with larger numbers.

Research has shown that an approach to learning the math facts that is built on a foundation of work with strategies and concepts leads to more effective learning and better retention. In this way, students are not forced to rely on rote memorization and instead become confident that they can select from a range of strategies to solve a fact problem quickly.

Give students who may be overwhelmed with the task of sorting all 36 cards a smaller set. The sums on the three pages of the Addition Cards for Small Sums increase in size from pages 1 to 3. Some students may be more successful sorting only the first 24 sums.

Some students may already know the addition facts with sums of ten or less. There are several ways to extend the lesson for these students. Challenge them to explain to other students good strategies for finding the sums. Do not be satisfied with the response, "I just know it." Communicating their reasoning and strategies will deepen their understanding. As you discuss students strategies for placing sums in particular groups, you can also challenge students to use the same strategies with larger numbers and sums. Finally, ask students to look for patterns in the number of sums in each group. That is, ask students to find the number of sums in each of the first six groups and then predict the number of sums in the seventh group. Then check their prediction. Finally, ask students to predict the number of combinations of 11 (if turn-around facts are not allowed as in the activity.)