# Habits Of Mind Case Study

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Timmatha Gagner, McKenna Townsend, Rebecca Hamilton Math 302- Habits of Mind 1 For Habits of Mind Problem 1, we were given the ratios of carnations to daisies, roses to peonies, and peonies to carnations. We were asked to find the remaining ratios of flowers, which would be peonies to daisies, carnations to roses, and roses to daisies. Madison also wants to give her teacher a bouquet using appropriate ratios and whole flowers. So, for this question we were asked how many of each type of flower should be put in the bouquet. The ratios we were already given are represented in tables 1.1, 1.2 and 1.3 Table 1.1 Carnations 14 28 42 56 70 Daisies 7 14 21 28 35 Note that 14:7 simplifies to 2:1 Table 1.2 Roses 3 6 9 12 15 Peonies 5 10 15 20 25…show more content…
Following the same steps, we found that we had ratios comparing roses and daisies to carnations. We remembered when comparing carnations to daisies our ratio of 14:7 simplified to 2:1. Knowing this, we went to our table of carnations to roses (table 1.6) and went to the first even number, since odd numbers in a 2:1 ratio would make a half of a flower. Our first even ratio of carnations to roses was 50:12. Since our ratio of carnations to daisies is 2:1, an equivalent ratio to that would be 50:25. This would mean for every 50 carnations, we would have 12 roses and 25 daisies. With this information we were able to conclude our rose to daisy ratio is 12:25. Again, we are not able to simplify this ratio because the only common factor between 12 and 25 is 1. Below is table 1.7 showing more equivalent rose to daisy…show more content…
To start this problem, we began to look through each ratio chart to try to find a common number. After looking through each of the charts we noticed that each flower is compared to roses, and the even number 12 comes up many times for roses. After we found a common number, we could then find the correct ratio of flowers to be placed into the bouquet. We noticed for every 12 roses, we have 25 daisies, 50 carnations, and 20 peonies. When looking at these four numbers, we didn’t have the option to simplify because 25 only has the factor of 1 in common with each number. In order to check our answers we looked at various tables. We started with table 1.5 and saw when there is 25 daisies there are 20 peonies. Next, we looked at table 1.4, which is an additional version to table 1.1. Since our simplified ratio of carnations to daisies is 2:1, we should have double the amount of carnations to daisies in our bouquet, which we do with a 50:25 ratio. After comparing all of our ratio tables, we concluded the bouquet using appropriate ratios and only whole flowers should be 12 roses, 25 daisies, 50 carnations, and 20