## Splitting a Square

What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!

A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1.

What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!

A square is drawn on a coordinate plane. The square is in the first quadrant and the sides of the square are parallel to the axis.

A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1.

What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!

A circus clown has 16 balloons. One half of the balloons are red. Half of the remaining balloons are blue. The rest are yellow.

Every Friday night, Drew’s family makes pizza for dinner. This week, Drew wants pepperoni and his sister wants extra cheese. His parents both want mushrooms as a topping.

Since they couldn’t agree, they decided to divide the pizza into four equal parts so everyone could have the topping of their choice.

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?

During the February 26th MoMath Masters Tournament, @MoMath1 tweeted, “No googling – how many sides on an enneagon?” We thought, “Hey! We know enneagons!” If you don’t, maybe this scenario from a problem we first used in 1998 will give you some hints (as well as some ideas for something you could do with one).

Extend the sides AB and ED of the regular enneagon ABCDEFGHI until they intersect.

## Baseball Cards

Third grade students at Hanover Street School made this awesome video as a Free Scenario based on the Math Forum problem called “Baseball Cards.” We are so excited to share their video!

The students’ video is based on the Math Forum Baseball Cards Scenario [PDF]

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