- Proportional reasoning in the deliberate use of multiplicative relationships to compare quantities and to predict the value of one quantity based of the values of others
- Ratios, rates, and percents, just like fractions and decimals, are comparisons of quantities. A rate compares quantities with different units, for example, distance to time, or price to number of items. A percent always compares a quantity to 100.
- Solving rate, ratio, or percent problems generally involves representing the rate or ratio in a different form
Here are some ideas our class had on what we know about ratios:
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| Chamberlain, 2015 (C) |
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| Chamberlain, 2015 (C) |
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| Chamberlain, 2015 (C) |
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Our Learning Activity presenter Mathieu got our minds by relating some ratios to real life, which seems to be the essential goal for teaching math. An interesting point he made was that ratios are not introduced until grade 6, but they are introduced in informal ways earlier on. He gave the example of how Kindergarten teachers will say there are 2 eyes for every person. So they are using the ratio 2:1.
When we relate math to real life, students have a better understanding of how math shapes their world, and concepts are well remembered when they can be associated with what they already know to be true.
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| An example of ratios in salad dressing. A good dressing is typically 2 parts oil and 1 part vinegar, the ratio would be 2:1 (Image URL: http://www.tv411.org/sites/default/files/Math16_0.jpg ) |
I thought the activity that Mathieu had picked out was really great. Students started to find their own algorithms within the activity. For myself, I found the points where the lines would hit an intersection on the grid, and from there you can extend and double your lines to basically connect the dots. Some students complained that it was too hard, but when you focus too much on perfecting the drawing it takes away from the actual meaning of the activity, which is to double the proportions. I thought it was unfair that he was put on the spot and justified his choice of imagery. I think that in order to avoid this type of situation in our classrooms where students are complaining about the difficulty, we as teachers would probably have to do some modelling and do an example together as a class before they did it on their own. Or like some people said to start off with a simple square and then change the shape to something more abstract. I didn't really see the shape difficulty being a factor, I thought it was a really fun way to tie a holiday like halloween into math. But again this shows that as teachers we can never expect what may come up.
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| Chamberlain, 2015 (C) |
I liked how afterwards we talked about how we could extend this activity, or how we could present it with different ways. Mathieu's hand-out also suggested two different ways he would present the activity, for grade 4s: to enlarge the pictures so it is twice as high and twice as wide, and for grade 6s: ask questions such as, "What is the ratio of the pumpkin's eyes." I thought that this was a great addition to the activity because now we are able to start thinking about reusing activities for different grades and meeting different expectations just by asking our students different types of questions.
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| Don't you hate when someone has changed the aspect ratio on your TV? (Image URL: http://imgs.xkcd.com/comics/aspect_ratio.png ) |
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