Lesson 5.2: Identifying and Writing Proportions was introduced, modeled, and practiced. Students were asked to generate proportions from word problems. Proportions were explained as being two ratios that were equivalent using cross-multiplication a:b = c:d, where a times d = b times c.
P.O.N. 11.25.14
Marc earned $230 for 40 hours of work. Marko earned $192 for 32 hours of work. Are these pay rates proportional? Explain your reasoning.
Answer to P.O.N. 11.24.14: The answer is 90 km. There are a few different algorithms to use to solve this proportion. 2 cm : 10 km reduces to 1 cm : 5 km. That shows me that 18 cm x 5 would give me the 90 km. We can also do cross products and divide. 10 x 18 = 180 divided by 2 equals 90 km.
Answer to P.O.N. 11.24.14: The answer is 90 km. There are a few different algorithms to use to solve this proportion. 2 cm : 10 km reduces to 1 cm : 5 km. That shows me that 18 cm x 5 would give me the 90 km. We can also do cross products and divide. 10 x 18 = 180 divided by 2 equals 90 km.
- understand the concept of a ratio.
- use ratio language to describe a ratio relationship between two quantities.
For Evening Practice, the student is expected to...
- complete Khan Skill: Ratio Word Problems.
The answer is they are not proportional. I got my answer by knowing that to find out if things are proportional that you can either simplify or do cross product. First it say that you get paid $230 for 40h. Then it says that you get paid $192 for 32h. Next, I am going to make both of these into fractions ( you don't always have to put them into fractions. For example you could make them like $192:32h or $192 to 32h.) Now when doing cross product you multiply across. So in this case you have to multiply $230 and 32h. When you multiply those two you get $4360. After that you have to multiply $192 and 40h together. When you multiply them you would get $7280. Now, I know that these aren't proportional because at the end the numbers are supposed to be the same and both of these numbers aren't. Another way that you can answer this question is by simplifying $230:40h and $192:32h. If you simplify $230 to 40h you should get $23/4h and if you simplify $192 to 32h you should get $6 per hour. When I simplified $230 to 40h first divided it by 2 and that turned $230 dollars into $115 and it turned 40h into 20h. Then I divided it by 5 and that turned $115 into $23, and turned 20h into 4h. I got my first answer by doing what I just did. When I simplified $192 to 32h I first divided them both by 2 and that turned $192 into $96,and it turned 32h into 16h. After that I divided it again by 2 and that turned $92 into $48, and it turned 16h into 8h. Last I divided them both by 8 and that turned $48 into $6 and 8h into 1h.
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