### Rumors!

Rumors is another great lesson from Mathline! This lesson allows students to explore exponential growth, in the context of spreading a rumor. In addition to the focus on math concepts, this lesson can also help students to understand how quickly rumors can actually spread....an important idea for middle schoolers to consider.

To begin the lesson, students are presented with the following scenario:

"Two students who were both born on December 21st, the date of the winter solstice, decide that it would be great not to have to attend school on that day. Therefore, they start a rumor that schools will be closed to celebrate the winter solstice. So, on December 1st, one of the students told two of her friends that school would be closed. On the next day, each of these students tells 2 students and on consecutive days, each of the new students tells 2 more students and so on. If there are 8,000 students in the school district, the question arises as to whether the rumor was started early enough for everyone to have heard it?"

Students can act out this scenario by having students form a human triangle, with Student A first, then the two students she told (students B and C), then four students representing the two that Student B told and the two that Student C told, etc (as far as possible, depending on how many students in the class). This will help students visualize the problem and understand how this rumor is being spread. The triangle also help students to understand the growth pattern.

The human triangle will only go so far,  so students will then need to use their calculators or paper and pencil to find how many days it will take for the rumor to reach 8,000 people. I would recommend providing the students with a blank chart to give some structure to the students' work after they try the human triangle.

The chart below includes the first several days (the numbers for the entire chart can be found in the lesson).

In addition to understanding exponential growth, students can be asked to determine the algebraic expression to describe the number of new people to hear the rumor each day (2n), as well as the  expression for the total number of people  (2n+1-1).

To read the full lesson and the possible extensions, check out the lesson here.

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Tara
The Math Maniac

### Differentiation and the Brain - Introduction

It's summer-time and time to get some reading done! Myself and my Tools for Teaching Teens collaborators are going to read and review Differentiation and the Brain, How Neuroscience Supports the Learner-Friendly Classroom , by David A. Sousa and Carol Ann Tomlinson.We will each be reviewing different chapters, and those blog posts will be linked together as we go. If you're interested in learning more about this book, check back and follow the links to the different chapters:) I'm going to give a quick review of the book introduction here, and then later today I'll be reviewing Chapter 1. According to the authors, differentiation is brain-friendly and brain-compatible! They describe the rise, fall, and rise of differentiation, starting with the one-room schoolhouses, where teachers taught all subjects to all students, of all ages, and HAD to differentiate - there was no other way! As the country's population grew, public schools grew, and students were separat

### Love to Doodle (and a freedbie)

Exponents Color by Number For most of my school life as a student (and even as an adult, during PD), I have really liked doodling! During lectures, discussions...it would help me focus, but also give me something to make me look busy, so I wouldn't get called on in class! I always hated being called on and almost never participated voluntarily:) I liked to draw cubes, rectangles, squiggly lines, etc, and color in different parts of the doodles. Download this freebie:-) I really wanted to make some color by number activities. Since I am not good at creating actual pictures, I decided to make my color by numbers similar to my random drawing/doodling. My Exponent Color by Number is most similar to my past doodles, but I thought it was a little too random, so I started using actual shapes. The Integer Operations Color by Number (freebie), as well as most of my other color by numbers are more structured, but so much fun for me to make! Computerized doodling! Anyone else