# Battle of the Homework

Discussion in 'Teacher Time Out' started by GoehringTeaches, Sep 1, 2009.

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Sep 1, 2009

Ok, so I have been in a battle with my stepson over his homework. He is not understanding venn diagrams and we are both in tears. Maybe I am the one not understanding but seriously I need help! What is this answer???

A group of friends went to an amusement park. Ten of them rode the Ferris Wheel, 15 rode the carousel, and 11 rode the roller coaster. Seven of them rode both the Ferris Wheel and roller coaster, 4 rode both the Ferris wheel and carousel, 5 rode both the carousel and roller coaster, and 3 rode all three rides. How many friends went to the amusement park?

Ugh! I wish I could explain it to him without all of us getting frustrated!

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4. ### 3SonsEnthusiast

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Sep 1, 2009

I get 23 friends. I hope I'm right. It's not really the easiest question in the world, but it is just a process.

1) Draw the overlapping circles. Schools aren't likely to give you more than three.

2) Start with the intersection of all circles, and fill in the number. Here, it's given as 3.

3) Go to the wings of the center. Since the center is part of it, any number they give you needs to take that into account. So, since 4 people did the Ferris wheel and carousel and three did all the rides, one person did the ferris wheel and carousel but not the roller coaster (adding to the given number, 4).

4) Repeat for the rest of the wings, and then work your way to the outside.

It sounds like manipulatives might help if he's not getting the concept.

5. ### TeacherGrl7Devotee

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I worked it out and got 23 friends as well, but could not articulate how to do it!

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Sep 1, 2009

Well crud. I got 55 friends and he came up with 77 friends! UGH!

7. ### LMath85Companion

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Sep 1, 2009

This is exactly how I did it.

I always start with the overlap. In this case there are three overlapping circles that have 3 friends in common. Then look at the overlap between two rides - but remember you must subtract out the friends who also went on all three rides. The same goes for the single rides where you must subtract out the overlap of two rides and three rides.

I always tell my students that the whole circle represents the number given. For example, they tell you that 10 kids went on the Ferris Wheel this includes the kids that only went on the Ferris Wheel and those that went on double rides as well as all three.

Good luck! Hope that helps!

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9. ### TennisPlayerCohort

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That is tricky. I tried using toothpicks - something I have a lot of! and put labels next to each group with the # of toothpicks: FW, RC, and C. I began counting 1 toothpick where it said both but then ran out of a group when I thought I'd have more.

What grade is this problem for and when will you get the answer?

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This is 5th grade, and hopefully tomorrow I will get the answer.

11. ### RainStormPhenom

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Sep 1, 2009

Goehring,
THe answer is 23 as previous posters have said. I have drawn it out in a venn, and will be glad to email it to you if you pm me with your email addy.

12. ### RainStormPhenom

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And as another poster said, start in the middle of the three circles, and put the 3 people there. Then go to the "double sections."

Ferris Wheel and Roller coaster is 7, so 7-3 = 4. Draw four there.

Ferris Wheel and carousel is 4, so 4 - 3 = 1. Draw one there.

Carousel and Roller coaster is 5, so 5 - 3 = 2. Draw two there.

Now figure the middle, plus the double section, to get the total for the single ring.

10 rode on the ferris wheel, but we've already accounted for 8 of them, so only draw 2 more.

15 rode the carousel, but we've already accounted for 6 of them, so draw only 9 more.

11 rode the roller coaster, but we've already accounted for 9, so draw only 2 more.

Count all the figures drawn, and you will have 23.

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