Division of School Improvement – Number Operation Examples

Students should have plenty of experiences working with number combinations that are selected to provide opportunities to see or discuss strategies of plus-one and minus-one combinations, doubles, and facts to ten. This does not necessarily mean “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. This also means asking students to find the sum of more than two single-digit numbers. Let’s say you roll a die or number cube three or four times, and ask students to find the sum of the numbers rolled (such as 3 + 5 + 3 + 5). Rather than instructing or expecting students to combine the numbers in order from left to right, ask them if there are other ways in which the numbers can be combined. Some students will choose to combine the two 5s to get 10 and the two 3s to get 6 for a sum of 16. Some students may choose to separate the problem into 3 + 5 and 3+ 5 thus leading to 8 + 8.

DEFINITION:
develop fluency: developing fluency means the process of memorizing some combinations or—having command of some combinations—not having to count, use manipulatives or draw pictures to find the sum or difference; fluency means that students are able to compute efficiently and accurately with single digit numbers.[1]

Throughout first grade, students should rely less and less on counting strategies to compute basic number relationships. Students should begin to use strategies such as doubles, doubles plus 1, sums of 10s. By the end of first grade, most students should “know” the doubles combinations, plus 1 and minus one combinations, and sums and differences of 10s.

“Students should develop strategies for knowing basic number combinations (the singe-digit addition pairs and their counterparts for subtraction) that build on their thinking about, and understanding of, numbers.

Teachers can help students increase their understanding and skill in single-digit addition and subtraction by providing tasks that (a) help them develop the relationships within subtraction and addition combinations and (b) elicit counting on for addition and counting up for subtraction and unknown-addend situations.”[2]

[1] National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (p. 84). Reston, VA: Author.

[2] National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics (p. 9). Virginia: Author.