# Striving for Subtraction (or Division) Fluency

### Striving for Subtraction (or Division) Fluency

While we often think of fluency as the goal, the study of basic math facts begins with a focus on understanding. Exploring basic math facts is our opportunity to build number sense, strengthen students’ understanding of operations, and support computational fluency.

Students make sense of math facts by looking at patterns in the facts, connecting fact sets to each other (e.g., in addition they connect doubles and doubles plus 1 facts or in multiplication they connect x2 facts with x4 or x8 facts), creating models to show the facts, and discussing the facts through problem contexts that help them understand what each number represents.

The understanding of inverse operations is critical for students’ ultimate fluency with subtraction and division facts.

• Creating models of the equations allows our students to see the connection between addition and subtraction as they move 4 and 5 cubes together to make 9 and then separate the 9 cubes into a group of 4 and a group of 5.
• Students might construct an array by building 4 rows of 3 tiles to see 12 total tiles (4 x 3 = 12) and then divide that array by separating the 12 tiles into 4 rows and find that 3 are in each row (12 ÷ 4 = 3).

And then observing the related equations allows them to make observations about the connections between the numbers in the equations.

Once understanding occurs and students can utilize strategies to find a set of sums or products (e.g., 4 + 5 = 4 + 4 + 1, so the sum is 8+1 or 9 since it is like thinking about doubles plus 1), students begin to work on fluency (automaticity). Through interactive games that repeatedly pose doubles plus 1 facts, students begin to gain fluency with these addition facts, but students often have a difficult time moving from addition (or multiplication) fluency to subtraction (or division) fluency.

For most people, subtraction facts are recalled by “thinking addition” which means subtraction fluency is grounded on both