## Around the Corner

The steel girders being used to construct a building are 27 feet long. One of the corridors the girders are to be carried down has a 90° turn at the end. The width of the hall before the turn is 8 feet.

The steel girders being used to construct a building are 27 feet long. One of the corridors the girders are to be carried down has a 90° turn at the end. The width of the hall before the turn is 8 feet.

A plane traveling 400 mph is rising at an angle of 30 degrees. A second plane, traveling 300 mph, is rising at an angle of 40 degrees.

Today I started to plan my garden. The rectangular garden where I am going to plant is three feet longer than it is wide.

One third of the garden area will be sunflowers.

Another quarter will be planted with brow-eyed susans.

Only a fifth of my garden will contain columbine.

A sixth of my garden will be filled with trillium.

The rest will be foxgloves.

Samantha purchased subway tokens from a machine. The instructions said that, for any amount of money you insert, you would receive the maximum number of tokens your money can purchase, along with your change.

Samantha put a $20 bill into the machine. She received 12 tokens and $2.60 in change.

There are eight teams in the Northern New Jersey High School Soccer League. Here are the recent results:

- Eastside beat Clifton, Montclair, Nutley, and Kennedy High Schools.
- Montclair beat Nutley.
- Bloomfield beat Don Bosco, Clifton, Eastside, Nutley, Kennedy, and Montclair.
- Hackensack beat Bloomfield, Don Bosco, Eastside, Clifton, Montclair, and Kennedy.
- Nutley beat Hackensack.
- Don Bosco beat Eastside, Nutley, Clifton, Kennedy, and Montclair.
- Clifton beat Kennedy, Nutley, and Montclair.

We talk a lot about the problem-solving process here at the Math Forum and try to develop resources that will help teachers help their students get better at problem solving. We discuss how to encourage students to share their thinking (such as through Noticing and Wondering) and how to cultivate classrooms that value those thoughts and ideas as much as answers. But if we take a look at our own “problem solving” product, the Problems of the Week, we have to acknowledge that there isn’t so much support for process, starting with the “Compose Answer” button that appears at the bottom of each problem. Oops!

We have considered a number of possibilities, including an option (chosen by the teacher) to show just the scenario for a problem and then have fields in which students can submit their Noticings and Wonderings. That sort of thing would require some significant programming time, so while we are working on putting it in place (I’ll blog about it more before we get too far), we are first going to support the PoW process through some wording changes in the submission process. We’ve come up with some possibilities and wonder if anyone has alternative ideas.

On a problem page, it says, “Compose Answer”, which of course implies you have “an answer”. We’re thinking of changing that to “Submit Ideas”, which seems a bit more welcoming to submissions that might not actually contain an answer yet (or ever).

Once you get to the “submission” page, there are four spots we’re suggesting alternative wording:

**Original:**Credit for this problem will be given to ….**New:**Credit for these ideas will be given to ….

**Original:**Summarize your answer in a sentence or two**New:**Summarize your ideas in a sentence or two.

**Original:**Explain how you solved the problem. Include your math.**New:**Explain your ideas and how you figured them out.

**Original:**If you’ve created an image as part of your solution, you may upload it here.**New:**If you’ve created an image that illustrates some of your ideas, you may upload it here.

What do you think? Would these sorts of changes convey “process” to your students? Do you have any other suggestions?

© The Math Forum at NCTM 2017. All Rights Reserved