Finding good sources for assessment questions can be tricky. If you're like us, you've probably spent hours on internet deep dives searching for interesting problems. What you find instead are hundreds of questions that assess basic facts and procedures. Where do we go for deeper, more thoughtful questions? Maybe you already have an online resource that you love, but we're here to propose that writing your own questions may be easier than you think.

Here are our favorite strategies for writing good questions in an intentional but efficient way:

**Focus on underlying structure, not just specific examples:**

Replace some numbers with parameters so students can't just perform a standard algorithm to get an answer. While students may be able to apply a learned procedure to a specific example and get an answer, they often don’t understand why that method works in general. By stripping away some of the numbers, we ask students to consider how changing the part affects the whole.

In the equation 𝑓(𝑥)=𝑎𝑠𝑖𝑛(𝑏𝑥−𝑐)+𝑑

*f*(*x*)=*asin*(*bx*−*c*)+*d*, changing which parameter(s) would affect the range of the function?Find the value of k such that the linear system has no solution.

**Ask the question backward:**

Consider turning a standard question on its head.

Standard: What is the horizontal asymptote of 𝑦=3𝑥^2−5𝑥^2+2𝑥2

*y*=2+2*x*23*x*2−5*x*?Backward: Write an equation of a rational function that has a horizontal asymptote of y=3/2.

**Incorporate multiple representations:**

Have students reason using graphs and tables, not just equations. For example, instead of always providing an equation (analytical approach), have students evaluate functions using selected values on a table (numerical approach) or by finding ordered pairs on a graph (graphical approach). Students should be able to demonstrate the deeper understanding that “evaluate” doesn’t just mean "plug in", but finding a corresponding output for a particular input.

**Use question stems:**

We use some versions of these questions in almost every test we write. You don’t have to reinvent the wheel!

Which of the following is false? (Provide four statements that have to do with the current unit)

Find the value of k such that…

Determine if the statement is always, sometimes, or never true.

Give a possible (value, equation, graph) such that…

Interpret the ______ in the context of this problem.

Which of the following is/is NOT equivalent to _____?

Error analysis: In which step did the student make his first mistake? (Label the steps of a sample solution. Make sure one of the answer choices is “there is no mistake.”)

As always, the more you do this, the more efficient you will become. We encourage you to do this work alongside your colleagues and share the workload!

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