## 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 axes.

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.

Richard went apple picking at a pick-your-own orchard. One of the growers gave him a basket, and in talking with her, he learned:

- a full basket of apples weighs about 20 pounds
- ten pounds of apples or less costs $0.99 a pound
- more than ten pounds of apples costs $0.85 a pound
- 80 average-sized apples weigh about 40 pounds

At Richard’s local market, apples cost $0.39 each.

Start your day with some math about a favorite breakfast food. What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!

We all know that Harry can be a clever guy! What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!

I want to bake blackberry cobbler. The recipe calls for a 9″ pie pan. All I have are rectangular ones.

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?

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