Multiplication and Division Part A

Strand: Number
Outcomes: 4, 5

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

If the student appears to be having difficulty with using mental strategies to determine basic multiplication facts to 9 x 9 and related division facts, provide guidance in understanding the operations by nesting the number facts in problem situations that relate to the student's experiences. Assessment by observing a student solving problems will provide valuable data to guide further instruction. By accommodating the individual learning styles, success will follow.

As the student solves a problem using a multiplication or division fact, provide guidance and prompts as follows:

Diagnose the student's understanding of place value by having the student explain the meaning of a number, such as 25, and represent it visually. Provide activities to develop understanding of place value if necessary, such as adding 5 to 25 or 8 to 16, using base ten materials and their symbolic representations.
Diagnose the student's understanding of number relationships by having the student write the number, such as 7 in a variety of ways; e.g., 1 + 6, 2 + 5 and 3 + 4. Provide activities to develop understanding of number and the various representations using counters and their symbolic representations.
Build on prior knowledge by posing problems that use the number facts for multiplication to 5 × 5 and the related division facts. See the folded cards strategy described in the activities.
Review the meaning of multiplication and division by having the student verbalize whether the numbers in the problem represent the part(s) or the whole and whether the unknown is the part or the whole.
Review the commutative property for multiplication so that the students are successful in applying a mental strategy that works for a given fact, such as 3 × 4 to another fact in which the order is reversed; i.e., 4 × 3. Use arrays to show this relationship as well as the relationship between multiplication and division.
Have counters and tiles available for the students to use in building arrays to represent the multiplication or division fact in the problem.
Think aloud how you would use a mental strategy to solve a given problem. Use counters and/or diagrams to help the student understand what you are saying. Connect the visual display to the symbolic representation and explain why these symbols make sense.
Focus on one type of mental strategy, such as doubling—choose a mental strategy that is developmentally appropriate for the student's background. Use a variety of problems with number facts that can be solved using this mental strategy; e.g., 4 × 3, 4 × 5, 6 × 7,
6 × 8 and so on. Use arrays to visually represent the strategy.
After the student can explain clearly one mental strategy for a given number fact, encourage him or her to try another mental strategy that would work for that problem. For example, 4 × 9 can be solved using doubling or patterns in the 9s facts.
Have the student decide which mental strategy is best for him or her in solving a given multiplication or division fact.
Provide practice in using the mental strategies and selecting which strategy is best to use for a given multiplication or division fact.

B. Reinforcing and Extending Learning

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

Strategies for Reinforcing and Extending Learning