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Fraction Error Pattern Analysis

Mr. Goldberg has been teaching a unit on fractions. He was pleased that all of his students seemed to quickly
master adding and subtracting two fractions. However, when he began teaching the students how to multiply
fractions, a small number of them did not readily learn the content. But after a quick mini-lesson, it appears that
all but three students seem to understand how to solve the problems. One of these students, Wyatt, seems to be
really struggling. Mr. Goldberg determines that he needs to collect some data to help him decide what type of error
Wyatt is making so that he can provide appropriate instruction to help Wyatt be successful. To do so, he decides to
evaluate Wyatt’s most recent independent classroom assignment.
! Assignment
1. Read the Introduction.
2. Read the STAR Sheets.
3. Score Wyatt’s classroom assignment below by marking each incorrect digit.
4. Review Wyatt’s scored assignment sheet.
a. Describe Wyatt’s error pattern.
b. Discuss any exceptions to this error pattern. What might these indicate?
5. Based on Wyatt’s error pattern, which of the two strategies described in the Addressing Error
Patterns STAR Sheet would you recommend that Mr. Goldberg use to remediate this error?Explain your response.

1. What is Wyatt’s error pattern in multiplying fractions?,

2. Are there any exceptions to his error pattern, and what might they indicate?,

3. What incorrect digits appear in Wyatt’s assignment?,

4. Which remediation strategy from the STAR Sheets is most appropriate?,

5. Why is this strategy effective for Wyatt’s needs?

6. Step 1: Analyze Wyatt’s Assignment

   (Assuming typical student errors in fraction multiplication as the assignment sheet is not provided.)

   Examples of Wyatt’s work:

   • 2/3 × 4/5 → Wyatt’s answer: 6/8
     – Incorrectly added denominators (3+5) and numerators (2+4)

   • 5/6 × 1/2 → Wyatt’s answer: 6/12
     – Added both parts: (5+1)/(6+2)

   • 3/4 × 2/3 → Wyatt’s answer: 5/7
     – Same mistake again: (3+2)/(4+3)

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   Step 2: Error Pattern Description

   Wyatt’s consistent error:
   He is using addition rules when solving multiplication problems with fractions—adding numerators and denominators instead of multiplying them.

   This shows a procedural misunderstanding and a possible overgeneralization of recently learned addition skills.

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   Step 3: Exceptions to the Error Pattern

   If Wyatt has a few correct answers among mostly incorrect ones, these might be due to:

   • Guessing

   • Accidental success

   • Partial conceptual understanding on simpler problems

   These exceptions suggest he may not fully understand when or why to use a certain operation.

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   Step 4: Recommended Strategy

   Best strategy: Concrete–Representational–Abstract (CRA)

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   Step 5: Explanation for Strategy

   CRA helps students:

   • Concrete: Use manipulatives (like fraction tiles or grids)

   • Representational: Draw visual models to show fraction multiplication

   • Abstract: Solve with numbers only once the concept is clear

   This is ideal for Wyatt because it rebuilds conceptual understanding rather than relying on memorized steps. He needs to see what it means to take a part of a part, not just manipulate numbers.