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.

Annie Fetter, The Math Forum @ Drexel University, Philadelphia, PA

Session 12 Handout [pdf]

**How This All Started – Formative Assessment
**

- Constructing Quadrilaterals Activity (see handout)
- Making Movies Using Jing – Instructions [PDF]
- Kathy’s Movie
- Danielle’s Movie

**Where it Went from There – Summative Assessment
**

- Red Shirt’s Movie
- Christina’s Rubric (see handout)

**Then Debbie Got Involved**

Annie is the Problem of the Week Coordinator and Professional Development Specialist at the Math Forum. She also teaches three courses in Drexel’s Math Learning and Teaching Masters program,

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

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

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.

The corner deli sells roses in bunches of 6. If Dylan buys 3 bunches of roses, how many roses does he have?

A. 3

B. 9

C. 18

D. 24

Almost half the third graders (46%) in a group of schools I was supporting chose B. The correct answer, C, was chosen by 31% of the students. I don’t recall being all that surprised, but as I have thought about it over the years, I’ve come to see it as one more piece of evidence that many students do not do “sense-making” when they’re doing math. They look for numbers and guess what operation they’re supposed to do (addition is very popular). I have a theory that if you had asked those same third graders to draw a picture of the story, many more of them would get the problem correct. So the problem above becomes this task:

The corner deli sells roses in bunches of 6. Dylan buys 3 bunches. Draw a picture of the story.

To informally test this theory, I invite anyone with access to students in grades 2-5 (or older kids if you think they might be good subjects) to run a small experiment for me. I’ve written two sets of questions, one math and one drawing. Each has three questions. The math questions are taken directly from some Grade 3 benchmark tests, but I can see them being used in grades 2-5 for the purposes of this experiment (though you are welcome to use them with whomever you want – it’s an experiment, after all, not hard scientific research).

Since I am interested in how students solve problems when they think they’re supposed to “do math” versus when they might not realize they’re engaging in mathematical thinking, I’d ask that the math questions be given during math instructional time and the drawing questions be given during literacy instructional time, or, barring that, any time that isn’t math, and that the two sets of questions be given a couple of weeks apart.

The attached PDF contains 26 copies of each set of tasks (labled Student A through Student Z), instructions, and a roster sheet so that you can keep track of which student corresponds to which letter. (If you have more than 26 students, be creative.) You can report results through an online survey or send me copies of the completed task sheets (as a scanned PDF, or toss them in an envelope) or both.

Download the files: Fetter Sense-Making Experiment v1 [PDF]

So, wanna play? I hope so!

]]>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.

]]>One year, on December 31, Curtis, who doesn’t trust banks, put $1000 in a can and buried it in his back yard. He plans to continue adding $1000 to the can on the last day of each year until he’s ready to retire.

On the same day, Bill invested $1000 in a bank account that will pay 10% interest annually on the last day of the year. Unlike Curtis, he does not plan to continue investing more money each year.