Additional Materials

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(Times are approximate and will depend on the needs of the students.)

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Forming Quadratics
Before the
Lesson
  • Assessment Task: Quadratic Functions (15 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 difficultiesstudents 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 Quadratic Functions.
      • Briefly introduce the task and help the class to understand the problem and its context.
        • Read through the task, and try to answer it as carefully as you can.
        • Show all your work so that I can understand your reasoning.

      It is important that as far as possible, students 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' responses to the task. Make some notes on what their work reveals about their current levels of understanding, and their different problem solving approaches.

      We suggest that you do not score students' work. The research shows that this will be counterproductive as it will encourage students to compare their scores, and will 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 series of questions. 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 a list of your own questions, based on your 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, select a few questions that will be of help to the majority of students. These can be written on the board at the end of the lesson.

      Common Issues: Suggested Questions and Prompts:

      Q1. Student has difficulty getting started.

      • You are given two pieces of information. Which form of a quadratic equation can you match this information to?

      Q2. Student makes incorrect assumptions about what the different forms of the equation reveal about the properties of its parabola.

      • What does an equation in standard form tell you about the graph? Explain.
      • What does an equation in completed square form tell you about the graph? Explain.

      Q2. Student uses an inefficient method.

      • For example: For each quadratic function, the student figures out the coordinates of several points by substituting x-values into the equation.
      • Your method is quite difficult work. Think about the information each equation tells you about its graph. Think about the information each graph tells you about its equation.

      Student makes a technical error.

      • For example: The student makes an error when manipulating an equation.
      • Check your answer.

      Student correctly answers all the questions.

      • The student needs an extension task.
      • Q2. Can you think of any more coordinates for the key features of the Graphs 1, 2, 3, and 4? Explain your answers.
      • Another quadratic has the same coordinates for the minimum, but the y-intercept is (0,14). What is the equation of this curve? [ y = 2x2 −12x + 14 ]
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