I’m attempting to help a teacher friend of mine (Jackie) make over some lessons in her district’s new online curriculum. It’s a frustrating challenge; every lesson simply tells information and shows processes without any exploration or sense-making opportunities for the students. Very Old School, very passive (aka confused) students, very much perpetuating the myth that math is a jumbled bunch of random rules to memorize.

The topic in an upcoming lesson is irrational square roots. For Cathy Yenca’s very helpful online class Seeking Students Who Hide , I made a Socrative “quiz” to generate discussion about the relationship between the area and side lengths of squares, the rational roots of perfect squares, and some perplexity about the root of a “not-perfect” square. If you already have a Socrative account, the import number to share my quiz with you is SOC-30095225*. If you don’t have an account, get one now, I’ll wait. It’s FREE and fairly self-explanatory. Even *I* am figuring it out, and that’s something.

What’s important to note is that Cathy is showing us how this tech tool can be used for giving every student a voice, even an anonymous one. Anonymous is safe. No one gets to hide or opt out or dominate a discussion. So **it’s not a quiz**, its an equity tool, a real-time formative assessment tool. I chose to have my “quiz” (what should this be called instead?) be teacher-controlled and anonymous so questioning, discussion, exploration, and justification can happen in between each prompt,** depending on what students say, ask, and need**. I’m picturing having them draw perfect squares on graph paper (low floor), introducing them to the square root symbol, using area models to make sense of the length/area relationship, and challenging them to make whole number “not-perfect” squares (high ceiling).

The final multiple choice question about an area of 20 square units is meant to be the zinger. Four of the five choices can be justified, IMO, so I purposefully marked every answer “correct” when creating it so that the data we’d see as a class would be about the percent of students who chose each answer, **NOT NOT NOT** about which answer (or who) is “right”. I actually hope for quite a mixed bag, which is the perfect place to start an exploration into irrational roots of “not-perfect” squares.

*I’d **love** feedback from anyone who even just *looks* at this quiz. This is new territory for me and I am not sure I’m going to get to implement it. If you use it, even modified, let me know what happened! Here’s the bare-bones version; keep in mind something should be happening in between each question.

1. What are square numbers?

2. How do you find the area of a square?

3. Describe the relationship between the area of a square and the length of its sides.

4. T/F. √ 49 = 7 5. T/F √18 = 9

6-8 Solve each of these: a + √36 = –5, √121 – x = 7 , –14 = n – √64

9. If y2 = 25, what’s y? **Explain**.

10. If a square has an area of 20 square units, how long is each side?

UPDATE: Jackie and I have decided to go for the gusto and implement this Socrative lesson *tomorrow! * What excites me the most? **Finding out what students say!**