## Foundations

**Exploring some big ideas. How do we use maths? Why does mathematics matter?**

Many times, students view mathematics as simply another school subject. It is a class with a teacher and some content and maybe a worksheet. They either like it or they don't. They're either good at it or they're not. But I want to do a couple things at the very beginning of the school year.

One is building positive relationships with students I only see for about an hour a day, helping them see that our classroom is a safe place for taking risks, celebrating the fact that we can learn from our mistakes and "failures." (See this article from Jenn Gonzalez for more on academic risk taking.)

The other thing I want to accomplish is helping these 5th graders see that mathematics is everywhere around us. It is useful to us. Our opportunity this year is to better understand how the world works. Sure, there may be some folks who don't like math class--but I've rarely met a person who truly dislikes

*mathematics*.

Numbers In The News

- Students are asked to bring in a clipping from a newspaper--or magazine, advertisement, etc.--that demonstrates ways we communicate using mathematics. Even when we are not using mathematical operations (adding, subtracting, multiplying, and dividing) we are constantly using numbers to communicate.

- Imagine a world in which mathematics did not exist. There are no numbers, decimals, fractions, percentages. You cannot count. Geometry has disappeared. How would your life be different?

- This documentary covers topics ranging from Pi and the Fibonacci Sequence to the Mars Rover and the Large Hadron Collider. Students learn about Pythagoras, Galileo, Aristotle, Marconi, lemurs, and a lovely jazz bassist named Esperanza Spalding. I think it is beautiful. Best of all, it sets students up to write about this question: "Is mathematics something that humans invented, or did it already exist and we merely discovered it?"

- What patterns can you find in a 100s chart--even when you can't see the numbers? Are you brave enough to take some risks? Do you approach your mathematics learning with a
*growth mindset,*viewing y____our mistakes as opportunities to learn?

- What if you didn't only have 100 options, as with the game above? What if you had 360? This activity challenges students to locate points on a circle to the nearest degree. (And we find that 6 degrees pass with each tick of the second hand on an analog clock. Degrees are small!) The goal is not so much to learn about degrees and circles--it is to stretch one's abilities and take risks.

- This activity introduces students to a number system with which they have limited knowledge: the binary system. How does this system work? What patterns can you observe? How is it similar to our own base 10 system? How is it different? If we can become increasingly proficient with a brand new system, that will help us as we begin to explore base 10 in Unit One. (This activity is also a bridge to a series of logic games my students always enjoy.)

- The final activity in our introduction pertains to rules and patterns to be found within this multiplication chart. Rather than viewing this as a set of 144 discrete facts, we can observe a few powerful principles that leave us with only 37 things to memorize. (And here are the "Essential 37".)