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Interpreting Algebraic Expressions
Before the
  • Assessment Task: Interpreting Expressions (10 minutes)
    • Have the students do this task in class or for homework a day or more before the formative assessment lesson. This will give you an opportunity to assess the work and to find out the kinds of difficulties students have with it. You will then be able to target your help more effectively in the follow-up lesson.

      • Give each student a copy of Interpreting Expressions.
      • Introduce the task briefly and help students to understand what they are being asked to do.
        • I want you to spend ten minutes working individually on this task.
        • Don't worry too much if you can't understand or do everything. There will be a lesson [tomorrow] with a similar task that will help you improve.

      It is important that, as far as possible, students are allowed to answer the questions without assistance.

      • If students are struggling to get started, ask them questions that help them understand what is required, but do not do the task for them.
  • Assessing Students' Responses
    • Collect students' responses to the task. Make some notes about what their work reveals about their current levels of understanding. The purpose of doing this is to forewarn you of the difficulties students will experience during the lesson itself, so that you may prepare carefully.

      We suggest that you do not score students' papers. The research shows that this will be counterproductive, as it will encourage students to compare their scores and distract their attention from what they can do to improve their mathematics.

      Instead, help students to make further progress by summarizing their difficulties as a list of questions. Some suggestions for these are given on the next page. These have been drawn from common difficulties observed in trials of this lesson unit.

      We suggest that you write your own lists of questions, based on your own students' work, using the ideas in the Common Issues table below. You may choose to write questions on each student's work. If you do not have time to do this, you could write a few questions that will help the majority of students. These can then be displayed on the board at the end of the lesson.

      Common Issues: Suggested Questions and Prompts:

      Student writes expressions left to right, showing little understanding of the order of operations implied by the symbolic representation.

      For example:

      • Q1a Writes n × 5 + 4 (not incorrect).
      • Q1b Writes 4 + n × 5.
      • Q1c Writes 4 + n ÷ 5.
      • Q1d Writes n × n × 3.
      • Can you write answers to the following?

      4 + 1 × 5

      4 + 2 × 5

      4 + 3 × 5

      • Check your answers with your calculator. How is your calculator working these out?
      • So what does 4 + n × 5 mean? Is this the same as Q1b?

      Student does not construct parentheses correctly or expands them incorrectly

      For example:

      • Q1b Writes 4 + n × 5 instead of 5(n + 4).
      • Q1c Writes 4 + n ÷ 5 instead of
        4 + n
      • Q2 2(n + 3) = 2n + 3 is counted as correct.
      • Q2 (5n)2 = 5n2 is counted as correct.
      • Q2 (n + 3)2 = n2 + 32 is counted as correct.
      • Which one of the following is the odd one out and why?
      • Think of a number, add 3, and then multiply your answer by 2.
      • Think of a number, multiply it by 2, and then add 3.
      • Think of a number, multiply it by 2, and then add 6.

      Student identifies errors but does not give explanations.

      • In question 2, there are corrections to the first, third, and fourth statements, but no explanation or diagram is used to explain why they are incorrect.
      • How would you write down expressions for these areas?
      • Can you do this in different ways?
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