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Assessing Students' Levels of Understanding Multiplication through Problem Writing

Using a Journal Article as a Professional Development Experience
Number and Operations 


Recommended Grade Level:  Teachers of grades 3 - 6

Title:          Assessing Students’ Levels of Understanding Multiplication through Problem Writing
Authors:    Mizell Drake, Jill and Angela T. Barlow
Journal:     Teaching Children Mathematics
Issue:        December 2007, Volume 14, Issue 5, pp. 272- 277

Procedures:Session One 

  1. Facilitator asks participants to write a story problem that could be represented by 4 x 8.
  2. Have participants read pages 272 through the top of 273, ending with the section General Model of Multiplication.
  3. After reading the article ask participants if they would like to rewrite their story problem or write another one.  Then allow time for them to do so.
  4. Have participants, working in groups of 3 or 4, share their problems.  Have the group examine the problems to assure that:
    • They show that they understand multiplication and can verify how they know.
    • They know the class of multiplication model they wrote.
    • They can identify the multiplier, multiplicand, and product in each problem.
    • The question goes with the problem.  Have them suggest ways that students might check this- e.g. have a partner solve their problem,
    • They do not confuse multiplication with division.
    • They are realistic problems.
  5. Have the groups share their findings.
  6. Working in groups, design a lesson for students to write problems.  Share these with other participants.
  7. If they haven’t already done so, have participants in their groups write an area model and Cartesian product model multiplication story problem.  (Although the students in the article did not write these types of story problems, their students may write them.)
  8. Ask participants to read pages 274 through 276.  Assign one of the problems in Figures 2 – 6 to each of the groups. Groups share if they agree with the evaluation of the student’s work and the intervention recommended.  If they do or do not agree with the recommended intervention they should give either an alternative intervention or an additional intervention.


  1. Participants have students in their classrooms write story problems for the multiplication problem 4 x 8 and share work with the class.  Discussion should be guided by the features to look for as outlined in Step 4, above.
  2. Participants classify the problems according to type: repeated addition, rate, area model or Cartesian product model. (Depending upon time,this may be done with the students in class.)
  3. Participants develop an intervention for at least two students based on the errors in their story problems.
  4. Participants work with these two students, recording what was successful and what they would do differently next time.

Session Two 

  1. Participants share and discuss at least one of their students’ story problems, intervention plans, and how they implemented their plans.
  2. Participants share what new teaching idea they have gained from this sharing.

Connections to Other NCTM Publications 

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