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Multiplying and Dividing Whole Numbers

Strand: Number
Outcomes: 5, 6

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?

Students who have difficulty solving multiplication and division problems using a personal strategy with and without concrete materials will enjoy more success if one-on-one time is provided in which there is open communication to diagnose where the learning difficulties lie. Assessment by observing a student solving problems will provide valuable data to guide further instruction. Success in problem solving depends on a positive climate in which the students are confident in taking risks. By building on the existing understandings of each student and accommodating the individual learning styles, success will follow.

If the difficulty lies in understanding the problem, use the following strategies:

• Provide problems that relate to the students' interests; use the student's name in the problem.
• Use smaller numbers in the problem initially.
• Have the student paraphrase the problem.
• Guide the student to determine if the numbers refer to the whole, the number of groups or the quantity in each group.
• Ask the student if the unknown in the problem refers to the whole, the number of groups or the quantity in each group.
• Provide base ten materials for the students to represent the problem as needed.
• Have the student decide which operation should be used and why.
• Ask guiding questions to show the connections between multiplication and division and the possible option of using either operation in solving the problem.
• Provide a graphic organizer such as the K–N–W–S chart (see blackline master on page 29).

If the difficulty lies in using personal strategies to solve multiplication and division problems, use the following strategies:

• Use smaller numbers in the problems initially.
• Review place value and number facts.
• Provide base ten materials as needed.
• Think aloud a personal strategy that you would use to solve the problem and explain why this strategy is more efficient than another one that you describe.
• Emphasize flexibility in choosing a personal strategy; a strategy that is efficient for one student may not be efficient for another student.
• Build on the student's understanding of place value and number facts to guide him or her in finding a strategy that works.
• Provide ample time for the student to think and ask questions to clarify his or her thinking.
• Have the students work in groups so that they learn strategies from one another.
• Guide the students to critique various personal strategies to find one that can be used on a variety of problems efficiently.
• Have the students explain their personal strategies to the class so others can hear how they work in kid-friendly language.
• Post various personal strategies in the classroom for students to share and critique.
• Encourage the student to check the reasonableness of the answer by comparing the answer to the estimated answer provided earlier.

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.