Multiplication and Division Part B

Strand: Number
Outcomes: 6, 7

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

The students who have difficulty solving problems by estimating and using a personal strategy for multiplication or division 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 understanding that each student already has 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 student's interest; 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).

If the difficulty lies in estimating products and quotients, use the following strategies:

use the base ten materials to focus on the place values of the numbers and the relationship among the place values
use smaller numbers initially and connect them to larger numbers; e.g., connect 30 to 300 to 3000
convince the student of the need for estimating by citing many real-world examples of where estimating is needed
review number facts and place value
emphasize flexibility in estimating, capitalizing on the student's methods and fine tuning them for correctness and efficiency
take small steps, using a range of acceptable estimates with closer estimates as the students become more comfortable with the process.

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 students to think and ask questions to clarify 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' language
post various personal strategies in the classroom for the students to share and critique
encourage the student to check the reasonableness of the answer using a given personal strategy by comparing the answer to the estimated answer provided earlier.

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