Help with a couple math problems and help with explaining

[camrynsmom07]

I need help with the following math problems. These are from my 5th grader. Can someone explain in the easiest way how to do these please?
1) Mya has 3 kinds of candy-skittles, m&m's, and gummy worms. She has 48 pieces of candy in all. She has 5 times as many skittles as gummy worms and 2 times as many m&ms as gummy worms. How many pieces does she have of each candy?

2)Compare the number of planes that flew from the airport today.
This morning, 12 planes flew out of the airport.
This afternoon, 4 planes flew ou of the airport.
There were __________ as many planes that flew out this morning than this afternoon.

There were _________ as many planes that flew out this afternoon as this morning.

Thanks in advance.

 

[JeffM]

I need help with the following math problems. These are from my 5th grader. Can someone explain in the easiest way how to do these please?
1) Mya has 3 kinds of candy-skittles, m&m's, and gummy worms. She has 48 pieces of candy in all. She has 5 times as many skittles as gummy worms and 2 times as many m&ms as gummy worms. How many pieces does she have of each candy?

2)Compare the number of planes that flew from the airport today.
This morning, 12 planes flew out of the airport.
This afternoon, 4 planes flew ou of the airport.
There were __________ as many planes that flew out this morning than this afternoon.

There were _________ as many planes that flew out this afternoon as this morning.

Thanks in advance.

The first problem is most easily solved by algebra, but presumably your child does not know algebra.

Here is one way to think about it. Imagine that Mya has candy bags to hold her candy. She puts the same number of pieces of candy in each bag. What is the smallest number of bags she must use? Well obviously, she could put ALL the gummy worms in one bag. But because she has twice as many m&ms, she would need how many bags (given that she puts the same number of candies in each bag). See if your child can figure out on his or her own that twice as many candies will require twice as many bags. Then it should be easy for the child to figure out how many bags will be needed for skittles. Now count how many bags are needed. Each bag contains the same number of candies, and the total number of candies is 48 so how many candies are in each bag? Does this make sense? (I must admit this method requires a little ingenuity.)

Here is a different way to think about it called guess and check. Guess 1 gummy worm, then there are are 2 m&ms and 5 skittles, making 8 candies. WAY too small. Guess 10 gummy worms. Then there are 20 m&ms and 50 skittles, or 80 candies in all. WAY too big. Let's go halfway between and try 5 gummy worms, which means 10 m&ms and 25 skittles, or 40 candies in all. Just a little too small. What would be a good next guess?

 

[HallsofIvy]

JeffM, that is very clever!

For the second problem:

2)Compare the number of planes that flew from the airport today.
This morning, 12 planes flew out of the airport.
This afternoon, 4 planes flew ou of the airport.
There were __________ as many planes that flew out this morning than this afternoon.

12 planes in the morning, 4 in the after noon. 12 is "what number" times 4?

There were _________ as many planes that flew out this afternoon as this morning.

This just the 'opposite' isn't it? And the answer is a fraction.

 

[camrynsmom07]

Ok....this helps but they are already doing pre algebra. How would set up the candy question in an equation? That is what I need help showing my child. Thanks

 

[JeffM]

Ok....this helps but they are already doing pre algebra. How would set up the candy question in an equation? That is what I need help showing my child. Thanks

In that case, start by assigning a letter to what is to be found.

g =number of gummy worms

m = number of m&ms

s = number of skittles

But m = 2g

And s = 5g

So g + 2g + 5g = 48 or 8g = 48 or g = 6.

gummies = 6

m&ms = 2 * 6 = 12

skittles = 5 * 6 = 30

Let's check 6 + 12 + 30 = 18 + 30 = 48.

By the way, it probably works best to have the child ask directly.