The Nuts and Bolts

• # 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 Math Question: How do you add and subtract positive and negative numbers?

The Translated Question: When the red army and the blue army fights, who wins?

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 easy.

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 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 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.