We have officially started our first number talks as a class. I will need to update this post as the unit progresses, but here is what we have so far.
Fractions, Decimals and Percents: Unit Expectations
Here are the expectations we will cover in this unit, which is based on the Curriculum and Connections [file unavailable] resource. There are four pillars to what we going to be covering: (1) Number Talks, (2) Strategy Walls and Math Journals, (3) 3-Act Math Problems and (4) Exit Tickets.
(1) Number Talks
We have done our first few number talks for this unit. The idea for Number Talks is simple: I present a math question, students take a moment to solve it individually, and then we discuss strategies. In my classroom, this sort of replaces "drill work" (usually taught through worksheets or a series of problems which become slowly more difficult). Instead of giving the students a bunch of questions to work on at once, we take the time to study one good question together.
(2) Strategy Walls and Math Journals
"In order to learn from experience, in order to have fresh possibilities come to mind when appropriate, it is necessary to sensitize yourself to notice opportunities to respond to situations rather than to react, to choose to act rather than to be caught up in and driven by old habits. Thus, by offering tasks and follow-up prompts it is possible to promote awareness of the use of people's natural powers. As they become more sensitized to and aware of their own use of these powers, those powers develop in flexibility and usefulness." - Thinking Mathematically, Mason & Burton, p. xv
I believe that student learning is what happens in a student's head. The learning process is, in a sense, the action of a student organizing her or his thinking. With that objective in mind, the objective of strategy walls (as a group) and math journals (as individuals) is to give students an opportunity to consolidate their learning and communicate their thinking. While I enjoy working on problems with students, and may write comments and questions in their math journals, I will never give a math journal any type of grade.
(3) 3-Act Math / Inquiry Problems
We just did "The Watermelon Problem" (click link for full article), which was long enough to merit its own post.
(4) Exit Tickets
- The Security Camera Problem
Here is a copy of our first exit ticket. The objective here was to get students to start using their problem-solving methods to find the best place to place a camera. I am a big fan of problems that are easy to understand but difficult to solve. As students went through this problem, they began to understand its nuances, which allowed them to push their understanding further.
Download for Word (editable): 2016-09-16-fractions-security-camera-exit-ticket [file unavailable]
Download as PDF (printable): 2016-09-16-fractions-security-camera-exit-ticket [file unavailable]
- The Square Mural Problem
This was our second exit ticket for this unit. I based it on my first attempt at a 3-act math problem last year, The Square Mural Problem [file unavailable]. I showed students the video from that problem, but I didn't let them ask questions as a group, since I expected them to attack the problem independently.
The purpose of this problem is ultimately to bring students to an understanding of Least Common Multiples and Greatest Common Factors, even though neither of those concepts are immediately apparent in the problem. The extension for this problem was for students to find an efficient way to create the smallest square mural that could be made from any tile. For example, how would you find the smallest square mural made of tiles with a height of 180 mm and a width of 378 mm?
Download for Word (editable): 2016-10-17-square-mural-exit-ticket [file unavailable]
Download as PDF (printable): 2016-10-17-square-mural-exit-ticket [file unavailable]
As students struggled with this problem, they started to realize that they didn't have enough information based on the video. As those students came up and asked about the extra dimensions, I gave them either (or both) of these additional resources.
Download for Word (editable): 2016-10-17-square-mural-resources [file unavailable]
Download as PDF (printable):2016-10-17-square-mural-resources [file unavailable]