Introducing Multiplication
Strand: Number
Outcome: 11
Curriculum Focus
The changes to the curriculum targeted by this sample include:
- The general outcome for the number strand in the revised program of studies states simply that the goal of this entire strand is to "develop number sense." The number strand is no longer divided into "number concepts" and "number operations." Number sense includes, for example, the ability to partition numbers and the ability to reason multiplicatively. These abilities apply to both numbers and operations.
- In the previous program of studies, general outcomes at each grade level specified magnitudes of numbers and particular operations, implying that number sense develops in a linear fashion. A more current understanding of student's mathematical development is that number sense deepens over time. Students' understanding of even 1-digit numbers is not fully developed until they are able to think of numbers abstractly (as quantities that do not necessarily refer to specific objects or as progressions on a scale).
- Two specific outcomes from the previous program of studies referred to both multiplication and division. In one outcome, students were to demonstrate the operations of multiplication and division; in another outcome, students were to calculate products and quotients using estimation and mental mathematics strategies. A different outcome dealing with the recall of addition and subtraction facts also required the recall of multiplication facts to 49. In the revised program of studies there is an outcome requiring students to demonstrate their understanding of multiplication in a variety of specified ways, and a similar outcome for division. Although students are required to be able to relate multiplication and division, the separation of multiplication and division into discreet outcomes supports students' understanding of these two separate processes.
- Whereas the previous program of studies specified products to 50, the revised program of studies specifies multiplication to 5 x 5. The priority at Grade 3 is for students to construct a solid understanding of the process of multiplication, which will be the basis for problem solving as well as recall and mental mathematics strategies in later grades.
- The revised program of studies requires that students relate multiplication to division and division to multiplication, again ensuring that understanding is in place before students are expected to use inverse operations to verify solutions.
- The revised program of studies includes relating multiplication to repeated addition, ensuring that students connect multiplication to their prior knowledge, and recognizing that most students in Grade 3 think additively rather than multiplicatively. This outcome prepares students for the transition from additive reasoning to multiplicative thinking that will begin for some of them as early as Grade 3.
- Similarly, students are exposed to multiplication both as equal groupings, which can be interpreted additively, and arrays, which support the transition to multiplicative thinking.
- Understanding of the process of multiplication is supported by the requirement that students create, as well as solve, problems.
Introducing Multiplication addresses the following outcomes from the Program of Studies:
What is a Planning Guide?
Planning Guides are a tool for teachers to use in designing instruction and assessment that focuses on developing and deepening students' understanding of mathematical concepts. This tool is based on the process outlined in Understanding by Design, by Grant Wiggins and Jay McTighe.
The following steps will help you through the Planning Guide:
See Bibliography for reference information.
Grade 3
