# Patchwork Tile Patterns

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## Objective

SWBAT write recursive and explicit rules to describe linear and non-linear patterns.

#### Big Idea

What happens to the patchwork pieces needed to create these designs as the size of the designs increases? Students jump right into problem-solving with the Practice standards on their first day!

30 minutes

## Investigation and New Learning

30 minutes

I started this investigation by telling students some of the key questions of the first unit:

*How can we describe a pattern?

*What kinds of patterns are there?

I ask them to get started answering these questions by working on the patchwork questions. I distribute extra graph paper and square dot paper. The big idea while circulating at first is to make sure that all students have a way to get started--which might be counting the squares and triangles in each of the figures provided or attempting to draw the next figure. If students get stuck, I suggest a data table, but only if they seem to have locked up.

Students take about 10 or 15 minutes to attempt to answer these questions for figure 6 and figure 10. After this amount of time, I randomly assign them a new partner (I give a number to each student randomly, and they find the other student with the same number.) I ask them to solidify their answers to these 4 questions.

It is essential that you not tell students whether their answers are right or wrong. I send this message from day 1, and I know I will need to repeat myself many times. Students are used to having the teacher tell them the right answer, or at least tell them whether or not they have the correct answer. When they complain, I take the time to thoroughly explain my reasoning to them: