Favorite Plants
(page 153)

(January 2011) Here are several solutions from a group of fifth-grade students at Hale Kula Elementary, Wahiawa, Hawaii. When you look at these, see if you can tell whether the solutions are basically the same, or did the groups take different approaches?

The answer is 24 and I know that because I used a step by step process to find it out. First, I looked at the question and first clue and the saw that four people preferred the Split-leaf Philodendren so I wrote down 4 in that section. The next clue said that one-third of everyone surveyed preferred the most popular plant, the Venus Fly-trap. Next, I saw that clue number 3 only half as many preferred the Split-leaf Philodendren as preferred the Venus Fly-trap. Then, clue #4 said the number of people who preferred the African Violet was the same as the number that preferred the Boston Fern. So, I wrote AV=BF. There were only four choices; each person had to choose only one of the four.

I figured this problem out by first, knowing that the Split-leaf Philodendron was the favorite of four people, and it's also half of the Venus Fly Trap. Which means that it's eight people's favorite. Also, sense that it's one-third of people's favorite multiply it by three which gives you twenty-four and that's the total! Because the total is twenty-four, and the African Violet and Boston Fern are one-fourth of the total, they're both four. Last-minute checking: (4+6+6+8=24)

In this problem, i figured out the awnser by first finding out that only 4 people liked the Split-Leaf Philodendron, which is have of the Venus Fly Trap (8). Then i did 8+4=12, and the other two plats had to be half of the 12, so the Boston Fern and the African Violet were 6 each. 6+6=12, 12+12=24. 24 poeple took the survey.

I figured the guestion out by folowing the directions step by step and having the group talk. I used clue number #5 to triple the number because, of clue #3. Then I used all of the other clues to see who voted for what. 24 people voted in all.

  • Boston Fern-6 people
  • Venus Fly Trap-8 people
  • Split Leaf Philopendron-4 people
  • African Violet-6 people

That is my method to figuring that out and the answer and how many people voted.

I know that the answer is 24 because the split leaf philodendron has 4 people who like it, and clue 3 says that Only half as many preferred the Split-leaf philodendron as preferred the Venus Fly-trap, so 4+4=8, next I saw clue 2. One-third of everyone surveyed preferred the most popular plant, the Venus Fly-trap, so I multiplied 8x3=24, and got 24.

Here's a solution from a group in Westminster, Maryland:

Dear Tim,

Here is how we got our answer to the Favorite Plants problem.

We know that the same number of people preferred Boston Fern and African Violet. Then, one card said that the Boston Fern was voted by 1/4 of the people, so we know that both Boston Fern and African Violet have 1/4 of the vote. Another card said that the Venue Fly Trap was voted by 1/3 of the people. When you add 1/4 for the Boston Fern, 1/4 for the African Violet, and 1/3 for the Venus Fly Trap you get 5/6. You know that 6/6-5/6=1/6, so the other flower, the Split Leaf Philodendron must have 1/6 of the votes. Another card said that 4 people voted for the Split Leaf Philodendron, so 1/6 of the people equal 4. If 1/6 of the people equal 4, then you know that 6/6 of the people equal 24 because when you multiply 1/6 times 6/1 to get 6/6. Then, you have to multiply 4/1 times 6/1 you get 24/1. This mean 24 people voted.

West Middle School,
Westminster, Maryland
Jen, Gilbert, Scott, and Leah
Mrs. Airing (Teacher)

(March 2003)

eeps comments:

Hooray! The first solution for this problem! Thank you VERY much for explaining all the steps you used. What a lot of fractions! I wonder if some other group can come up with a different strategy for solving this problem....

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