Word problem question

An interesting math teaching related question again from someone.

Hi Maria,

I have purchased some e-books from you and they are very helpful. My daughter is in 4th grade and I felt that she is weak in understanding the following problems. Would you please suggest which e-book we need to buy from you to help improve her basics.

Problems are as below:

1) Marge spent $4 for a magazine. She spent half of her remaining money on T-shirt. Then she spent $2 on a snack. Marge had $14 remaining. How much money did Marge begin with?

2) Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall, in feet and inches, is each boy?

I have not written an ebook that would concentrate on those kind of problems. I do have some similar ones included in the 6th grade worksheets collection.

However, I wouldn't worry so much about those problems at 4th grade, especially the first one, because it requires quite many steps. She's still young.

You might be interested in Singapore math's word problem books; they might be helpful. They often employ diagrams that enable children to solve these kind of problems without the use of algebra.

But let's try to find the easiest way to solve these.


1) Marge spent $4 for a magazine. She spent half of her remaining money on T-shirt. Then she spent $2 on a snack. Marge had $14 remaining. How much money did Marge begin with?

|-- $4 --|----- half -----|----- half -----|
                          | $2 |----$14 ---|

From the above you can see that $16 was the 'half of what was remaining'. Total is $32 + $4 = $36.


2) Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall, in feet and inches, is each boy?

|-------Dan ---------|----------- Mike -----------|

This one is easiest to solve with this reasoning:
If the two boys were of equal height, they'd both be 4 feet 4 inches. The DIFFERENCE in their heights is 4 inches, so just add half of that-or 2 inches- to the "midpoint" 4 ft 4 in to find the taller boy's height, and subtract that same 2 inches to find the shorter boy's height.

So Dan is 4 ft 6 in and Mike is 4 ft 2 in.