In our Math department meeting yesterday we talked about what how warm-ups are a great opportunity to introduce common-core thinking and the eight standards for mathematical practice.
In our school, students must begin working as soon as they enter the class – whether the bell has rung or not. Ideally, a good warm-up should have three qualities:
1) All students can do it. This means it needs to be review, to some extent, or otherwise accessible.
2) Content related. In my class that means my warm up needs to involve math, although it doesn’t necessarily have to be about what we’re studying now.
3) Open ended. Since students come in the room at different times, preferably it should be something that everyone can have a response on after a short time, but also can be explored more fully.
The biggest challenge is making sure our warm-ups open ended. For comparison:
Closed question: “Graph the equation 𝑦=(2/3)𝑥+3 on a coordinate plane.”
Open question: “Write down everything you know about 𝑦=(2/3)𝑥+3 and be prepared to compare your thinking with a partner.”
With the first question, a student who is behind might simply say, “I don’t know how to do that,” and give up, while an accelerated student would be done in under a minute.
But with the second question, even a student who lacks confidence in math could say something like, “2/3 is in front of the x. We are adding a 3. There are two letters.” And an accelerated student would have many, many things to say.
“Write everything you know about (blank)” is a great open ended structure. Others are error analysis (spot the error and correct it), compare reasoning (give an example and ask students to explain how we got there), or a really fun one, give the answer and have the students come up with the questions.
Right now, my warm-ups are focused on getting the students prepared for their CAHSEE, so I probably won’t get a chance to incorporate these open-ended warm-ups into my class until mid-March. I’ll use the time until then coming up with a “bank” of open ended questions.