The Nuts and Bolts
By Timon Piccini, posted December 4, 2017 —
When I think of my professional development, I struggle with how to
balance my desire to know the theory and framework a person puts behind his or
her craft and the day-to-day resources that bring that framework to life. In my
previous two posts, I have built the whys and the hows that I ask when looking
at a new topic. If that is all I shared, you wouldn’t be able to start next
week. If I am in a workshop on Friday, I want to know that I can do something
new on Monday. Here are a few “Monday” resources that I have developed or used;
what I hope to unveil is how I reframed the question in each of these examples.
They have for the most part been mentioned in previous posts.
Army Men Integers
The Link: http://mrpiccmath.weebly.com/blog/my-battle-with-the-integers
The Math Question: How do you add and subtract positive and negative
The Translated Question: When the red army and the blue army fights,
The Elaboration: This was my first attempt at making (and remaking)
a conceptually based lesson. It needed to have instant buy-in, and it needed to
have play; most important, it needed to give a clear answerable question that
put the basics of integer addition and subtraction to the forefront. This
lesson makes the concept of zero pairs so understandable that it is almost too
Subtraction is still hard and seems like a magic trick, but let’s be
real: I still didn’t know why to a negative x negative = positive until I took
modern algebra in my third year of university.
Balancing Scale Equations
The link: http://mrpiccmath.weebly.com/blog/what-the-x-how-i-teach-basic-linear-equations
The Math Question: How do you solve all linear equations of the form
ax + b = c?
The Translated Question: How many pennies are in the cup?
The Elaboration: This was mentioned in the last post, but I can
elaborate further. I have had teachers use this activity to help with
inequalities (what values would make the scales tip?), negatives, distributive
property, and variables on both sides of the equation. It is so versatile,
especially when you realize that once you have students sold on the metaphor of
balance, you don’t need to worry about how many pictures you have, you can just
start drawing them.
The Broken Calculator (and James
Tanton’s Exploding Dots)
The Link: http://mrpiccmath.weebly.com/blog/3-acts-broken-calculator
The Math Question: How do you represent numbers in different bases?
The Translated Question: What is up with that calculator?
The Elaboration: This is my baby; I use it at the beginning of the
year mainly to teach kids perseverance in problem solving and experimentation
in math. My seventh graders have never heard of different bases, and messing
with this calculator that does operations in base five messes with them. Some
years they pick up what is happening with the calculator faster than others,
but even if they don’t understand it in the slightest, I have James Tanton’s
exploding dots! He does another conceptual translation by turning groups of
numbers into dots that “explode” when they reach their base’s limit. It is
awesome, and my kids love learning it.
There’s Always More
I am not the first person to come up with this way of thinking. I
know that I have stood on the shoulders of giants up to this point. The reason
I can even think of half of this stuff is because I have been connected with so
many great math teachers over the years. If you are not out there on Twitter
and in blogs looking for this stuff, then get out there.
Timon Piccini is an
elementary school teacher who has a strong love of getting students to see that
mathematics is more than just numbers. His favorite sound is
when an entire grade 7 class cheers because they are starting to understand a
base five number system (a true story). Piccini considers himself a jack of all
trades, and when he is not teaching, he can be seen running, hiking, playing
guitar, playing video games, and attending concerts, and pursuing just about
anything to do with good food. He especially loves doing all this alongside his
better half, Kelli.
I love how you made these mathematical questions into questions that are easier to understand, and draw in the students. With the way you worded these questions, the students are doing math, without knowing they are doing math, which is genius! I also like how you incorporated hands-on activities, and manipulanda into each of these lessons!