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Evaluating Statements about Length and Area
Before the
  • Assessment Task: Shape Statements (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, Shape Statements, and some plain paper.
        • Spend 15 minutes working individually, answering these questions on the plain paper provided.

      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 engage in a similar task, which should help them.

      Explain to students that by the end of the next lesson, they should expect to be able to answer questions such as these confidently. This is their goal.

  • Assessing Students' Responses
    • Collect students' written work and read through their responses. Make some informal notes on what their work reveals about their current levels of understanding and their different problem-solving approaches.

      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 attention on aspects of their work. Some suggestions for these are given on the next page. These have been drawn from common difficulties observed in trials of this unit.

      We suggest that you write your own lists of questions, based on your own students' work, using the ideas that follow. You may choose to write questions on each student's work, or, if you do not have time for this, select a few questions that will help the majority of students. These can then be written on the board at the end of the lesson.

      Common Issues: Suggested Questions and Prompts

      Student makes incorrect assumptions.

      • For example: The student assumes that the shape with the greater area has the greater perimeter. (Q1.)
      • Or: The student assumes that only congruent shapes have equal areas. (Q2.)
      • Do shapes with greater perimeters have to have greater areas? How could you check?
      • Do shapes need to be congruent to have equal areas?

      Student fails to consider specific example.

      • For example: The student does not create shapes with different dimensions to support or disprove a statement.
      • Think of a shape. Think of some dimensions for this shape. Is the statement true for this shape?
      • Can you think of another shape for which the statement is not true?

      Student fails to consider a wide range of examples.

      • For example: The student assumes that a specific example is sufficient to prove a conjecture.
      • Or: The student does not consider extreme cases. (Q1., Q2., and Q3.)
      • Try drawing some other examples to test the statement.
      • How do you know your answer is correct for all shapes?
      • Does the statement work for obtuse angles? (Q3.)

      Student fails to draw construction lines

      • (Q2. and Q3.).
      • Can you split the shape into smaller shapes to help test the statement?
      • Can you add lines to the shape to help test the statement?

      Student fails to apply algebraic reasoning.

      • For example: The student cannot see the relevance of the formula for the area of a trapezoid or triangle. (Q2. and Q3.)
      • Can you use an area formula to support your answer?
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