Makeover Monday: Introduction

2013 Jun 26. See every edition of Makeover Monday.

Here is a “high-leverage teaching practice,” according to Deborah Ball:

Teachers appraise and modify curriculum materials to determine their appropriateness for helping particular students work towards specific learning goals. This involves considering students’ needs and assessing what questions and ideas particular materials will raise and the ways in which they are likely to challenge students. Teachers choose and modify materials accordingly, sometimes deciding to use parts of a text or activity and not others, for example, or to combine material from more than one source.

So every Monday this summer, I’ll post a problem from a textbook and start a conversation about how we could modify it. The details of that makeover may take the form of a loose sketch or something more formal. In either case, I’m going to be explicit about the goal of the makeover.

Fawn Nguyen, who’s been on an absolute tear lately, illustrated this process recently. She took this task:


And then she showed how she implemented it with her students. Her goal wasn’t something formless along the lines of, “Well this sucks and I want to make it more engaging.” In the title of her post, she says explicitly she wanted students to have some personal, creative input on the constraints of the problem. So she had her students start by drawing their own golf course. She set a high bar for the rest of us.

You should play along. You can feel free to e-mail me a textbook task you’d like us to consider. Include the name of the textbook it came from. Or, if you have a blog, post your own makeover and send me a link. I’ll feature it in my own weekly installment. I’m at

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. If you have the students try out their answers you get into some fun but sometimes scary parts of math‚Ķ when it doesn’t work. The conversations from that can be pretty powerful. We close off math so much sometimes and simplify that they really don’t know that math is actually more complex in most situations. It’s just a lot of fun to think about these opportunities and the kinds of discussions they can spark.

  2. Santosh Zachariah

    June 11, 2013 - 4:41 am -


    when you introduce the textbook problem, it would help to know what age-level or which standard-course it targets.

  3. Bill Bradley

    June 11, 2013 - 7:54 am -

    You can do similar lessons/demonstrations with lasers and mirrors. Have them set up mirrors and a laser to try to hit a target. The other surprising thing would be to draw a line to the image of an object in a mirror, and then the reflected line from the mirror to the object, which would also give the similar triangles. The fact that the reflected line seems to continue the first line that they drew always surprises my students.

  4. This looks like a project that I have used during my first unit in Geometry.

    I would have the students play Mini-Putt3 for a few minutes:
    (My school has 1-1 laptops, but if you don’t and you have a projector, you could have students come up and play the game.)

    As they are playing talk about the angles that are formed before the ball hits the wall and after the ball hits the wall. You can also have them start thinking about how hard you have to hit the ball (or the distance that the ball travels).

    Then give them a print out of the problem with the measurements, but without the path drawn out and a protractor. Have them find a hole-in-one path.

    I think the distance aspect of this problem is forced. But if you want to go there, you could ask the students about how hard you would have to hit the ball (the distance it would travel). The students would simply measure their distance and you would miss the Algebra, but I think the Algebra is forced and messy.

  5. This OT, but what does “dy/dan” mean? “The change in y with respect to an”??? An what?? The particle “an”?? An aardvark?? An Lushan, the general who almost brought down the Tang Dynasty in medieval China?

  6. @noah. Good point but sometimes it’s ok to turn off the critical thinking and just enjoy.

  7. Dan, love the idea of Makeover Monday. And I’m glad you featured Fawn’s work — I’m following her blog now, too!