Equations of the form ax + b = c involve both multiplication and addition. Solving this would require division and subtraction. Please write an equation involving multiplication and addition that has a solution of x = 4. ]]>

I am guessing that you are familiar with http://www.graphingstories.com This might be a bit of a way to make inroads to that gulf between words/meanings and graphs/symbolic manipulations ]]>

I wish I could think of a way to write it more clearly. The current form will have to do until I (or someone else, maybe you?) can think of a way to tweak the wording to make it more clear (without giving too much away).

Maybe this:

“The equation 2x+1=7 has a solution of x=3 and involves multiplication and addition.

Please write an equation involving division and subtraction with a solution of x=4.”

What do you think? Improvement, or a step backwards?

]]>I really like question 3 but I wonder how many students clearly read those instructions. Have these been field-tested yet? I love the open-ended nature of that question in particular. I also always like the ‘find the error’ questions although I am not very good at writing them. ]]>