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I would like to construct a good worksheet for my students.

I am thinking of creating an instruction that will cover all problems related to identity equations.

Here is how I initially constructed the worksheet:

Determine the values of a, b, c, and d that will make the following equation an identity.

  1. "equation 1" - the variables that they need to solve is a and b only

  2. "equation 2" - the variables that they need to solve is a, b, and c only

  3. "equation 3" - they need to solve the variables a, b, c, and d.

Notice that for no. 1 and 2, not all the variables a, b, c, and d are asked to find.

Is it still okay to use this instruction or should I write each number separately like this?

Solve the following:

  1. Given that "equation 1" is an algebraic identity in x, what are the values of a and b?

  2. Given that "equation 2" is an algebraic identity in x, what are the values of a, b, and c?

  3. Given that "equation 3" is an algebraic identity in x, what are the values of a, b, c, and d?

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    $\begingroup$ Can you give a concrete example? $\endgroup$ – Andrew Chin Jun 9 '20 at 16:11
  • $\begingroup$ There are no good worksheets. Just ask your students to write the formula for a particular identity, then to provide an example with specific numbers. $\endgroup$ – Rusty Core Jun 9 '20 at 16:31
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    $\begingroup$ @RustyCore Can you elaborate? That's a strong statement. $\endgroup$ – Mark Fantini Jun 9 '20 at 17:53
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    $\begingroup$ @RustyCore Worksheets are just collections of problems. Can you really claim that there is no good collection of problems? Have you ever read "A linear algebra problem book" by Halmos? $\endgroup$ – Steven Gubkin Jun 9 '20 at 18:45
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    $\begingroup$ @MarkFantini Worksheets are evil. Steven, worksheets are not collection of problems. Problem books are collection of problems. Worksheets are fill-in-the-blanks forms, good for providing SSN and VIN, but stifling for anything remotely creative, often having limited space for a solution and often liming the choices, not to mention they are environmentally irresponsible. Blank paper is all one needs. And a problem book, of course. $\endgroup$ – Rusty Core Jun 9 '20 at 18:49

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