Question: Why do the assessments of the multiplication facts in Grade 3 include a time limit?
In Investigations, the overwhelming majority of students’ work with the facts is focused on making meaning of the operation of multiplication, building connections between problems and images that represent them (e.g. problems about things that come groups, arrays), and using what they know to solve what they don’t (e.g. how can knowing that 3×4=12 help with 6×4?). This work happens in Ten-Minute Math Activities like Counting Around the Class; during games, activities, and class discussions; when students write clues and practice with the Multiplication Cards; and on Daily Practice and Homework pages. In Investigations, fluency with the facts stems from frequent use, sense-making, and understanding.
Third graders are expected to demonstrate fluency with the multiplications facts up to 10×10 by the end of the year. This work is benchmarked in two of the three multiplication units. At the end of Unit 1, students are assessed on the x1, x2, x5 and x10 facts. The remainder of the facts are assessed at the end of Unit 5. In both cases, students are asked to solve 30 problems in 3 minutes.
Why a time limit?
As explained in the Teacher Note: Learning the Multiplication Facts, “Fluency means that facts are quickly accessible mentally, either because they are immediately known or because the calculation that is used is so effortless as to be essentially automatic (in the way that some adults quickly derive one fact from another).” (3U1, p. 205) Given this definition of fluency, it seemed that some sort of time limit was required. A student who is skip counting on their fingers for every problem would likely not finish in the suggested time. This is important information for the teacher, as that student is not yet fluent.
In both assessments of the multiplication facts, the text – shown below – suggests asking students to pause after 3 minutes, circle the problems they have not yet done (or change the color of their writing utensil), and then complete the assessment. This gives useful information to both students and teachers about students’ progress.
In addition, a Teaching Note is included to help teachers think about how timed situations might cause stress, and to suggest ways to talk with students to alleviate it.
A Differentiation suggestion is included as well, suggesting ways to adapt the assessment task if needed.
When we have been asked about the reasoning behind the time limit, the questions have often been phrased as “why a timed test?” While there are two assessments of multiplication facts that include a suggested time limit, to us, this phrase conjures images of classrooms where regular timed tests (ala Mad Minutes or Around the World) are the way to teach the facts. In Investigations, the time limit is used—at the end of extensive periods of in-depth work focused on sense-making and understanding—to assess students’ fluency with the facts. While some may see this as semantics, to us, it is a critical distinction.