How does problem solving provide access to student understanding?

Problem solving provides opportunities for students to explain their reasoning and their solution paths.


Jade's family is planning to travel to her Aunt Mazie's house to celebrate Aunt Mazie's 102nd birthday. On the first day of the trip they'll drive halfway there and then stop to set up camp for the night. On the second day of the trip they'll drive two-thirds of the remaining distance before stopping for some sightseeing and camping. On the last day they'll have 145 miles left to drive. Question: How far is the trip to Aunt Mazie's house?

Student Solutions

Gia, age 10

Jade's family will travel 362.5 miles to get to Aunt Mazie's house.

To solve Birthday Trip, I followed several steps.

First, I noticed that for the first two days,
fractions were used to describe the distances.
 I added the two fractions together.

                        ( 1/2 + 2/3 )

      My answer came out to three fifths. ( 3/5 )

     Next I realized that the remaning
     number of miles is given to me.

This number is 145. (miles)

     I then figured out that
145 is 2/5 of the final answer.

    To get the remaining
three fifths ( 3/5 ), I divided
145 by 2 and got 72.5.

     I did this because now
 I have 1/5 of the final total.

      I multiplied 72.5 by 5
          and got 362.5.

Rico, age 10

The answer i came to is 48 and 1/3 miles

I times 145 which is the miles they have left times 2/3 and times 1/2
to get the original miles

Aleda, age 9

The trip to Aunt Mazie's is 146 and two-thirds mile.

The answer I got for this problem was 146 and two-thirds mile. The
reason I got this answer was because on the first day of the
family's trip they drove halfway which was 0.5. The next day the
family drove two-thirds which is 0.6 repeating and rounds to 0.7.
The last day they drove the rest of the way which was 145 miles. By
adding all of those numbers the result I got was 146 and two-thirds
mile. The reason I added those numbers together was because you
wanted to find how many miles all together the family's trip was, as
it said in the problem.

Jose, age 12

Aunt mazie's house is 652 and one half miles away.

I got 652 and one half miles because 1 third is 145 miles and three of 145
miles is 435 miles and half of 435 is 217 and one half. And if you add it all
up you get 652 and one half. Thats how I got my answer.

Troy, age 10

The trip was 304.5 miles long.

I took 145 and mutiplied it by .5 and adde 72.5 to 145. and then
multiplied 145 by .6 then added 87 to 217.5 then that equaled 304.5

Ulrika, age 11

211 miles away.

I put 2/3 on my paper then i put that into 100. i got 66%. Then i
wrote down 145 and added 66 and got 211 miles away.