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:
The students in Mrs. Garcia’s class get a star each time they give a book talk to their class.
In September, Juanita earned 4 stars. Matt earned 2 more stars than Juanita.
Maria received 4 more stars than Matt. Brian got half as many stars as Maria.
Today at my virtual talk at the Scholar Search Education Forum at Northwestern, a student asked me about the hardest math problem I’ve solved. I thought of the hardest problem I haven’t solved. I love it because it came from a real situation!
Say there are 36 people at a workshop. They get in groups of 6 and work for a while. Then, they regroup into new groups, so no one is in a group with anyone they’ve been with before. How many times can they regroup before someone has to be in a group with someone they’ve worked with before?
I also wonder, how could you extend this problem? If you’ve answered the specific problem, what else does it make you wonder?
Here’s a special mid-week edition of our Free Scenarios. We’ll be handing out this scenario at the NCTM Regional Meeting in Atlantic City on Thursday and Friday of this week. Join the conversation, either in person or virtually! What do you notice in the story below? What are you wondering about? Leave a comment to tell us your thoughts!
The pictures below came from an idea a friend of mine had…. Looking at a grid of squares, imagine drawing diagonal lines across the squares. If the line hits a wall, bounce off at a 45º angle. If it hits a corner, stop drawing the line.
You can play around with the game on the NCTM Illuminations site.
Here are some of the patterns we drew. What do you notice about them? What do you wonder? Leave a comment to tell us!
