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Sorting Equations and Identities
Before the
Lesson
  • Assessment Task: Equations and Identities (15 minutes)
    • Set this task, in class or for homework, a few days before the formative assessment lesson. This will give you an opportunity to assess the work, 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 the assessment task Equations and Identities.
        • Read through the questions and try to answer them as carefully as you can.

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

      Students should not worry too much if they cannot understand or do everything, because in the next lesson they will work on a similar task, which should help them. Explain to students that by the end of the next lesson, they should be able to answer questions such as these confidently. This is their goal.

  • Assessing Students' Responses
    • Collect students' responses to the task, and make some notes on 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 write scores on students' work. The research shows that this is counterproductive as it encourages students to compare scores, and distracts their attention from what they are to do to improve their mathematics. Instead, help students to make further progress by asking questions that focus their attention on aspects of their work. Some suggestions for these are given on the table below. These have been drawn from common difficulties observed in trials of this unit.

      We suggest that you write your own list of questions, based on your own students' work, using the ideas that follow. You may choose to write questions on each student's work. If you do not have time to do this, 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 rather than equations.

      • For example: The student writes y + 3 for an equation with an infinite number of solutions.
      • What is the difference between an equation and an expression?
      • How can you change your expression to an equation?

      Student fails to include a variable in their equation.

      • For example: The student has written 5 + 5 = 10 as an example of an equation with one solution.
      • Can you include an unknown number or a variable in the equation so that we can look at all possible values of that unknown?

      Student fails to provide an example of an equation with an infinite number of solutions.

      • What would an equation with an infinite number of solutions look like?

      Student provides a quadratic with non-integer solutions as an example of an equation with no solutions.

      • For example: The student gives x2 + 8x + 13 = 0 as an answer to Q1d. The student has assumed that because it won't factorize there are no solutions.
      • Can a quadratic equation that will not factorize still have solutions/cross the x-axis? How can you check whether or not a quadratic equation has solutions?

      Student assumes that −(x2) is the same as (−x)2.

      • For example: The student classifies x2 + 4 = 0 as true when x = −2.
      • What does (−x)2 mean? What kind of number do we get when we multiply two negative numbers together?
      • Is x2; positive or negative?

      Student correctly answers all the questions.

      • The student needs an extension task.
      • Use algebra to justify one of your answers to Question 2.
      • Draw a diagram to justify one of your answers to Question 2.
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