How to Write a Number Trick

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Objective

SWBAT use algebraic representations and the strategy of working backwards to develop their own number tricks.

Big Idea

One of the hardest things about writing a number trick is that you have to be willing to abandon an idea that doesn't work in favor of one that does.

Opener: Patterns Once Again

10 minutes

For the third consecutive day, the opener (Opener Sept6 Patterns.pdf) is about number patterns.  I should note that these are all arithmetic sequences, but for the students, I haven't even framed the conversation with those words.  Consider what we're doing this week a little bit of pre-season training: as I get to know my students and they get to know how this class works, we spend a little time talking about patterns.  We will formalize things later, and these pattern problems will be a reference point in the coming weeks.

Today's opener looks a little different from the previous two.  This time, for two of the problems, students are given the pattern rule and asked to find some of the terms.

Today is a Friday, and I tell students that they'll have their first quiz on Tuesday.  I explain that in this class, quizzes will always be open-notebook.  I make the distinction that it won't be the same for tests, but I repeat that "For quizzes, I will always let you use your notes."  The quiz will be about pattern problems, and problems will be presented in a few different ways, and I'm using today's opener to show everyone some examples of what to look for.  

As I circulate among students, I remind them individually that they'll be able to use their notes on Tuesday's quiz.  I ask what they think should be written in their notes.  I want to cultivate the habit of taking great notes.

I ask for volunteers to share their solutions to these problems.  In some classes, this goes off with little help from me, while in others I may need to step in and clarify a few ideas.  Most often, students are answering the questions correctly, but I need to take a moment to show them how to neatly present those answers on paper and/or on the board.

The Number Trick Project, Part 2

10 minutes

On the second part of the Number Trick Project, students will write three number tricks of their own.  I do not distribute a handout for this part of the project.  Instead, I post the instructions on the screen: NTP Part 2.

I take this approach because I want to encourage students to play, to be wrong, and to try multiple messy drafts.  If I use a handout to give them the same instructions, they think they'll have to start over each time they try these tasks, and I'll burn through twice as many copies as I have students.  If they're working in their notebooks and on their own paper, they'll have the space to set things up how they want and to try what they can.  

On the other hand, some students have the impression that if there's no handout from the teacher, it's not to be taken as seriously.  I emphasize the instructions here, making a big deal of writing a perfect heading, like students saw yesterday, when I showed them how to do homework.  

Then I say that this is the second part of a three-part project.  The entire project is due next week, on Wednesday.  That gives everyone the weekend to complete Part 2 (they'll get help on that today), then to complete Part 3 early next week.  I briefly preview Part 3 by saying that it will the chance to beautifully present one of these three number tricks.  "For now, I'm not worried about how nice your paper looks," I say.  "I'm more interested in giving you the time to figure out how to write a number trick."

With that said, I give everyone 10 minutes to struggle and to play with the task of writing a trick on their own.  A few have already been successful on the task of writing a trick of their choice, which was the last of the four tasks on Part 1.  Many need help.  After 10 minutes of grappling, I draw their attention to today's mini-lesson.

How to Write a Number Trick: Work Backwards

20 minutes