Introducing Multiplication

Strand: Number
Outcome: 11

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

Students, who have difficulty understanding multiplication, will benefit from ongoing experiences with mathematical narratives and contexts that involve multiplicative situations. These repeat experiences allow students to develop the understanding, moving on from counting and modelling strategies for solving problems, through skip counting, successive addition and doubling strategies, to true multiplicative thinking.

For example:

Have students make up their own problems to solve or make problems with or for a partner that involve personal details, such as their own names, birthdays, favourite foods, colours, toys, animals, characters, objects and ideas.
Encourage students, who are having difficulty, to dramatize and model multiplicative narratives so they can imagine multiplication in relationship to their lived experience.
Use small numbers, problems that can be solved using known skip counting sequences, simple contexts and no extraneous information. Introduce difficulty gradually, and reduce difficulty again if it becomes a block to understanding or diminishes confidence to the point where a student cannot proceed.
Allow students to solve problems without using equations and to answer using language instead of symbols until they are able to fully understand mathematical notation. Provide direct translation of their narrative answers into mathematical symbols, and do this on a repeated basis. If necessary, provide a written translation tool or chart for students to use.
Provide students with the opportunity to solve problems using a choice or any combination of models, objects, counters, drawings, oral language, written language and symbols. Do not restrict solution strategies at first. Observe students' solution strategies, and encourage solution strategies that are just a little more difficult; for example, moving from direct narrative modelling to using representative counters or tallies to represent objects, or from a counting all strategy to skip counting using known skip counting sequences.

B. Reinforcing and Extending Learning

Students, who have achieved or exceeded the outcomes, will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies, such as the following.

Provide students with contexts for using their multiplication skills, such as designing construction projects, planning a garden, designing visual patterns in arrays (e.g., using pattern blocks and calculating numbers of elements they need to make the array larger), planning events, taking a recipe, pattern or picture and making an enlargement using multiplication.
Have students use multiplication to solve area and volume problems that they model using tiles and cubes, but also describe using equations.
Introduce students to simple, everyday multiplication problems using rate, multiplicative comparison and combinations.