5 Adapting questions from textbooks

The last activity in this unit shows how you can help students to tackle some harder questions and to identify the different places in their mathematics course where they have to use HCF and LCM, and, hence, get equivalent numbers before they can add or subtract. They will also be asked to notice what is the same and what is different in these questions, so they can become aware of which methods and processes to use in which situation. Asking students to engage in this way with textbook questions encourages them to think about the mathematical thinking processes involved.

Activity 5: Adapting questions from textbooks

Tell your students to look at the following problems:

negative three divided by 10 plus five divided by six
cap c times o times s times cap a divided by one minus cap s times i times n times cap a plus one plus cap s times i times n times cap a divided by cap c times o times s times cap a
24 divided by 18 minus x plus 24 divided by 18 plus x equals one
five divided by open x plus one close times open x minus two close plus two divided by open x minus two close times open x plus three close
  • Are there any similarities in the above questions? What ‘mathematical differences’ can you see?
  • How would you solve these problems?
  • Is there any one correct or incorrect way of doing this?
  • Look at exercises in the NCERT textbook for different topics and see if you can identify the exercises where you have encountered such questions.
  • What is same and what is different in these questions?

When most of your students have found some more exercises, stop their discussions and ask them to share their ideas with the whole class. Again, your role is as a facilitator, challenging their thinking and encouraging them to ask each other for clarification.

Pause for thought

  • What responses from students were unexpected? Why?
  • How did you evaluate your students understanding? Did this exercise help to improve their learning?
  • Did you modify the task in any way? If so, what was your reasoning for this?

Again, you can use this exercise for different topics to help your students to build mathematical connections. This will develop their confidence with mathematics and in particular when they are asked to solve an unfamiliar problem.

4 Learning from the work of fictitious students