Phew! I have loved working on the If the World Were a Village projects, but I am so not a project- lovin’ gal! By the end of the unit, Iwas so ready to get back to a regular activity with a little more structure. I will take pictures of the final produts and tell you how we finished up the projects as soon as I grade them.

So today, I did an activity where students had to match up equivalent ratios, then write some of their own ratios.

After my first class, I thought it was pretty successful, but then my second class had absolutely no clue where to even start. I directed them to the ratio 1/2 since most students are most familiar with that number as a fraction and can easily give answers. The problem is that they were so stuck on making the 1 into a 2, so when I asked why something like 3/6 was equivalent, they would just say “3 is half of 6” instead of recognizing the relationship between the 1/2 and the 3/6. So then when they saw something like 2/5, and they couldn’t make 2 into 5 by multiplying by a whole number, they had no idea where to start to find an equivalent ratio. I stopped the activity and did some whole class explanation, but I am going to need to go back and make a new plan for tomorrow.

Equivalent Ratios

On another note, I got an iPad for my room this week! I am so excited to jump in and see what can be done with it. If you have any awesome ideas for proportions, I need some ideas!

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Maybe you could have students look for different relationships between the numbers in two equivalent ratios? Have you seen equivalent ratios written in a 2 by 2 square? This is going to be hard to show without being able to draw the square, but I’ll try. You’ll just have to imagine squares drawn around each of the numbers below, with the 4 squares creating one larger square:

2 8

5

I’m not sure why that posted as I was typing!

2 8

5 20

So if your original ratio was 2 to 5 and you’re trying to figure out whether 8 to 40 is equivalent (and you don’t realize that 2 x 2.5 = 5 and 8 x 2.5 = 20) then you may notice that 2 x 4 = 8 and 5 x 4 = 20. Or maybe 8 ÷ 4 = 2 and 20 ÷ 4 = 5. I spent some time with my 6th graders having them come up with as many relationships between the numbers as possible. Along the way some of them came up with the idea of cross multiplication on their own, when after many examples they realized that connection! Cross products aren’t part of the CCSS curriculum, but I was proud of them for noticing the pattern! 🙂

I will try that- thanks for the suggestion!