Along with warm ups from Estimation 180 and number talks, I have started using questions from Would You Rather? to start my grade 10 applied math class. This site was started by John Stevens and is a treasure trove of interesting conundrums.
The premise is simple: students have to make a choice between two options and support their choice with mathematics. I randomly place my students into groups of 2 or 3 and each group works on a large whiteboard. Here is the first one we did:
One of the reasons I love these is that it makes students think about what they need to know in order to choose the better option. I don't tell them anything except that they are allowed to use their smart phones if they need to look up information. So they have to figure out what they don't know and find it before they can start calculating. In this case they looked up (or asked Siri) the mass of a new nickel and of a new dime. Some worked with the mass of American coins, others with Canadian coins. It didn't matter. (Interestingly, the ratio turned out the same.) They worked at it and, because they were in groups, they could help each other through any misconceptions. These are also short enough that no one complains about who they are working with and they can stay focused through to a decision.
Today we did this one:
Most groups did well with this one and all chose the same option, with some mathematics to back it up. I then asked them how long a work day is, to which the unanimous reply was 8 hours. I asked what if they weren't paid for their 30 minute lunch - would they still chose the same option? They worked it out and this led to a quick discussion about asking good questions versus making assumptions.
There are many Would You Rather? questions that involve converting units which is part of the measurement curriculum expectation. I love that there is a context for converting and that I can incorporate it 5 minutes at a time. I hope that, at least once, my students will talk about the interesting question they did in math today to a friend or family member. I hope that this helps them connect to math and helps build their questioning and reasoning skills.