Introducing Multiplication
Strand: Number
Outcome: 11
Step 3: Plan for Instruction
Guiding Questions
- What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?
- What teaching strategies and resources should I use?
- How will I meet the diverse learning needs of my students?
A. Assessing Prior Knowledge and Skills
Before introducing new material, consider ways to assess and build on students' knowledge and skills related to multiplication. For example:
- Have students use skip counting in a concrete situation, such as counting money or counting out a snack to arrive at a total amount.
- Have students use counters or pictures to figure out a multiplication situation, such as how many treats would they need if they were having a party for five students and each student was going to get three treats. Are they able to conceive of this kind of a situation and arrive at an answer using concrete modelling and counting?
- Have students write a mathematics journal entry describing what they know about multiplication.
If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student's level of skill and understanding. See Sample Structured Interview: Assessing Prior Knowledge and Skills 
.
B. Choosing Instructional Strategies
Consider the following guidelines for teaching about multiplication:
- Use an "Assessment for Learning" approach to ensure that students understand the learning intentions for all activities, understand what distinguishes quality work, receive descriptive feedback about their progress and have opportunities for self and peer assessment. For example, have students write about their understanding of a multiplication situation and notation both before and after learning about multiplication, and have them compare their answers to see what they have learned. (This activity is adapted from About Teaching Mathematics: A K–9 Resource (p. 203) by Marilyn Burns, Copyright 2000 by Math Solutions Publications.)
- Invite students to estimate answers before solving problems and to reflect on their predictions after a task has been completed.
- Teach multiplication through a problem-solving approach. Use contexts that are real or relevant to your own students. Make sure each student understands multiplication in a story context or as an investigation of a real-life problem, and relates numbers and symbols to concrete objects and relationships, before moving on to abstract representations of multiplication using just numbers and symbols outside of a context.
- Use different contexts for multiplication, including equal grouping problems, multiplicative comparison problems (something is a number of times as large as something else), combinations and area or array problems.
- Encourage students to think about, discuss, act out or explain the situation in a problem before beginning to solve it.
- Encourage learners to model problems with objects or draw pictures, diagrams or charts to represent the elements and relationships in problems in order to help them build connections between visual and kinesthetic understanding and abstract mathematical understanding.
- Encourage students to write equations that first describe the way they have already represented the action in a problem and solved the problem, and later translate a problem into an equation in order to solve it.
- Plan a significant amount of time for students to compare strategies and approaches with the rest of their class at the end of a problem-solving lesson. During this time, ask questions about the efficiency and mathematical thinking of particular responses in order to encourage greater abstraction and mathematical elegance.
- Differentiate multiplication problems by allowing students to use different solution strategies, starting with counting for students who are just beginning to develop an understanding of what multiplication is, to skip counting, repeated addition, repeated doubling and building on known facts as students develop multiplicative understanding.
- If necessary, differentiate tasks by substituting smaller or larger numbers.
- Use student’s literature to teach about equal groups; for example, use Each Orange Had 8 Slices: A Counting Book, by Paul Giganti (1992, HarperCollins) or What Comes in 2s, 3s & 4s, by Suzanne Aker (1990, Aladdin Paperbacks). Lessons can be planned around these or similar books that involve students solving problems suggested by the books, students making individual pages to be compiled into a similar class book (What comes in 5s, 6s, 7s and 8s?), or students devising problems based around some of the examples in the books for their peers to solve.
C. Choosing Learning Activities
Learning Activities are examples of activities that could be used to develop student understanding of the concepts identified in Step 1.
Grade 3
