This Warm up asks students to write as many ratios in as many ways for two given scenarios. The first is a black & white tile design and the second is a textual scenario. I expect students to work together and help each other. As always, if there is disagreement or misunderstanding I expect students to explain their reasoning and use evidence to show what they mean.
I circulate to scaffold where needed Warm up whats being counted notes. The two main mistakes I expect are not simplifying the ratios and writing them backwards. I am looking to make sure students define what is being compared in each ratio, so they develop the vocabulary they need to use ratios as evidence and support an argument.
Students are given three figures showing black and white tile floor designs. They are asked to write as many ratios (part:part and part:whole) as they can and use the ratios to decide which is blackest. I circulate and scaffold where needed. comparing ratios activity notes I specifically listen for someone to mention how messy their work looks or how it would help if there was some way to organize their work, etc. This is a good segue into using a table, which I may make with them or just give them.
Then they are asked which floor is the "blackest". It's obvious just by looking which floor is the blackest and I ask them how they can tell. I expect someone might say that out of 9 total squares the last one has the most black. This may help them understand the next questions, which asks them which ratios are easiest to compare. I might have to rephrase the question and ask if the part:part or the part:whole ratios show better which is the blackest. Or I may need to ask which one would they use in order to explain to someone else which floor is blackest. I expect most students will say that the part:whole ratios are better at this, especially after taking time to explain at the beginning why one of them "looks" blackest.
Lastly, I want students to look just at the numbers in the part:whole ratios we just identified and decide what it is about the numbers that makes this set of ratios easier to compare here. (All the denominators are the same or the totals are all the same)
Hopefully students will have a couple of minutes to start looking at their homework homework comparing ratios.docx . They are being asked to do the same thing they just did but with floor designs of different sizes.