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.

My vague criteria for the activity:

- Relatively easy to explain, and doesn’t require constant attention from knowledgeable helpers (I’ll have three or four volunteer helpers, who don’t have to know any math)
- Could have some examples or diagrams available for the more self-directed
- Doesn’t take a wicked long time to accomplish something, but could go on for a while (low floor, high ceiling, that sort of thing)
- Is fun and art-y
- Involves some math, even if it’s not obvious to everyone
- Could be something they take with them, or leave to display in our area, maybe hanging on a fence

Here’s what I’m thinking about so far.

One idea was a double Tumbling Blocks quilt pattern. It’s not that exciting, since it’s basically coloring by numbers – you pick a light, medium, and dark color, and color the chunks numbered 1, 2, and 3 respectively. The pattern would be half of an 8.5 x 11 sheet of paper. See below, plus the “finished” product if we put a bunch of them together.

Another option is the Rail Fence quilt pattern. Again, not very exciting to color, but fun to see how it looks as a “quilt” depending on how you put them together. I’d provide two different half-sheet templates with six to 10 squares on them – one that is arranged in the zigzag, and the other in the pinwheel.

But the more I think about this, the more I’m thinking I might do frieze patterns. I’ve done an activity with them before, where we learned about them, then acted them out physically, and then made them using The Geometer’s Sketchpad software (read about the time we did it with the Drexel Math Contest, and even download the instructions). We could for sure have groups of people acting them out with guidance – we have plenty of room. But I haven’t done the arty-y part with paper and markers before. I wonder how that would work? I sketched out a couple of possible templates – one of triangles, one just squares, both on about a 2″ strip. There are four examples in this picture, then a picture (with a link to a PDF) of all seven types of frieze patterns with their John Conway-given names.

That’s where I’m at right now, and am looking forward to getting some ideas from y’all. I know, especially, that I’ve missed something with the quilt blocks and coloring/symmetry, and am wondering if anyone else has done a frieze pattern coloring activity. Thanks in advance for your contributions!

]]>One fourth of the vehicles at Danielle’s Cycle Shop are tricycles. The rest are bicycles. Danielle counted a total of 45 wheels in her shop.

**Problem #1**: Getting your problem-solving year off to a good start!

* At Least a Mile* [16003]

This problem aligns to 4th, 5th, and 6th grade CCSStandards and provides opportunities to revisit the idea of **Notice and Wonder®** or introduce it to students who have not yet been exposed to the idea. If it’s new for you, check this page for ideas: http://mathforum.org/pow/noticewonder/

**Problems #2, #3, #4, #5**: Proportional Reasoning / Distance = Rate • Time

* Cork Costs *[3524]

* Buying Cola *[1982]

* Downloading Duel *[4724]

* Apple Picking *[4544]

**Problems #6, #7**: The success that students can feel using a non-threatening strategy can build their confidence to use these strategies along with an algebraic approach.

* Pumpkin Carving for Charity* [3560]

* Peeling Potatoes *[5264]

**Problems #8, #9, #10, #11**: Using a single variable to find unknown amounts

* A Cranberry Craving *[3284]

* Eight Squares on a Table* [17049]

* A Snowy Driveway *[3308]

* Which Coupon Is Better *[3656]

**Problems #12, #13, #14**: Extending patterns and finding rules or shortcuts

* Anjelica’s Very Odd Magic Sweater *[4052]

* Gearing Up *[1898]

* Shortcut Savings *[16984]

**Problems #15, #16, #17**: Using variables to solve situations with multiple unknowns

* Boxes of Stationery *[2078]

* Ostrich Llama Count *[5156]

* Kaytee’s Contest *[16004]

**Problems #18, #19, #20**: Algebraic proof and justification

* Accounting for Age *[3056]

* Divisible by a Dozen *[2960]

* Suli’s Sense *[5300]

**NOTES:**

Access to these 20 PoWs (and the other 20 in each of the other 5 services on the Calendar for the Current Problems) costs just **$25 **(or just **$20** if you are an NCTM member!). Read the details of a Current PoW subscription here: http://mathforum.org/pow/productinfo.html

Try Annie’s Phone in the Pocket idea. Read: http://mathforum.org/blogs/suzanne/2014/08/10/listening-to-yourself/

Help your students add to their problem-solving toolbox. Read: “Examining Solution Methods” activity. Just use the Teacher Packet [pdf] that we provide for each PoW and you can create a similar activity for any of the PoWs you’re using with your students.

Are you wondering how to give feedback to all of your students. Read:

Feedback for 140+ http://mathforum.org/blogs/suzanne/2014/08/09/feedback-for-140/

Tips on encouraging student discussions. Read:

Keeping Quiet: http://mathforum.org/blogs/suzanne/2015/02/25/keeping-quiet/

Unsilence Students’ Voices: http://mathforum.org/articles/communicator.article.sep.2012.pdf

**If you have questions, please ask and I’ll be happy to respond. Have stories to share? Please do!
Sincerely,
Suzanne**

Raquel and Esperanza were asked to count Dr. Dolittle’s ostrichs and pushimi-pullyus. Raquel counted 67 heads, while Esperana counted 134 legs.

]]>A voussoir is a trapezoidal piece of stone often used to build arches.

It’s your ten-year high school reunion and committees have been formed to help plan the celebration. Each committee will meet in person once before the reunion.

**Food:** Rachel, Angie, Aubrey, Dan, Sean, Ryan

**Invitations:** Katie, Gavin, Dan, Jason, Ryan

**Entertainment:** Eric, Kyle, Tosin, Rachel, Julie, Sean

**Lodging:** Jennifer, Amber, Travis, Tosin, Anne

**Decorations:** Robert, Travis, Jason, Gavin, Matt

**Alumni Directory:** April, Zach, Robert, Eric, Matt