N3A3TNp19

Students should have plenty of experiences working with number combinations that provide students with opportunities to see or discuss strategies that involve using facts to find unknown facts. These opportunities do more than help students memorize facts; they help students build number sense. This does not necessarily involve teaching these strategies in direct instruction, but rather, capitalizing on and labeling the strategies that students will naturally use when presented with the task of finding an answer.

Answer to Problem 19:

They are both right. You get the same answer when you multiply 12 ´ 8 as you do when you add 8 twelve times. The answer is 96.

DEFINITION:

develop fluency—developing the ability for efficient and accurate methods of computing and being able to demonstrate flexibility in computational methods chosen which result in students being able to explain their methods and produce accurate answers.[1]

Teacher Notes:

Throughout third grade, students should rely less and less on counting strategies to compute the basic multiplication and division relationships. Students should begin to use strategies such as skip counting, arrays and using known facts to solve unknown facts. By the end of third grade, most students should “know” the multiples for 2, 5, 10, and any other multiple where any number that is 5 or less is one of the factors.

Teachers can help students increase their understanding and skill in single-digit multiplication and division by providing tasks that (a) help them develop the relationships within multiplication and division combinations, (b) help students build models for the relationships, such as arrays, and (c) elicit the use of known multiples to find unknown multiples.