Angles: Learning in Degrees

Teaching angle measurement?* Although it's tempting to put a protractor straight into the hands of students, with a little creativity, pattern blocks, and some simple movements you can build a foundation for the concept of angle measurement. This week, we've been challenged by a fun, free set of lessons by The Math Learning Center, C3 Circles & Angles.

Our first challenge, in Activity 1, was to measure all angles in a set of pattern blocks using nothing more than this:

My normally brilliant student looked at me like I had lost my mind. How in the world could you measure the angles of a pattern block with that??? We first talked about what we knew:

1. Straight line = 180 degrees
2. Perpendicular line = 90 degrees
3. Orange square pattern block has to have 90 degree angles because it's a square. It also fits in the corner of the drawing above.

But what about all the rest of the shapes? How could you figure their angles?

After a time, we discovered that pattern blocks could be combined to form a straight angle of 180 degrees. In the example below, we could see that 3 triangles (or in the illustration, 1 triangle + 1 rhombus) formed a straight angle. Therefore, 180/3 = 60 degrees...or 1 green triangle has angles of 60 degrees each since it's an equilateral triangle. In a similar fashion, we made combinations of pattern blocks until we knew the angles of all the pattern blocks. Pattern blocks now became a tool for additional measurement opportunities.

In Activity 2, we measured "Human Angles," first considering real-world connections: a sister who had to have physical therapy for a knee injury, a brother whose extreme joint mobility allows him to do circus-like feats of movement,...even a non-human connection--an owl--and it's circular head movement. But at first it wasn't easy for us to see human movement in degrees.

We added a number of visual tools: still photos, craft sticks, and moveable paper models. The following video captures some of our thoughts as we explored angles...one step degree at a time.

You can grab a free set of the angle lessons by looking for C3 Circles & Angles. What do you do to bring angle measurement to life?

This lesson includes CCSS Standards:
CCSS 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement
CCSS 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Credit: Drawings from The Math Learning Center. Used by permission.

Dividing with Fractions: Great Videos!

A math friend recently sent me a link to some wonderful videos that walk through visual models on dividing with fractions. If you are an adult who memorized the rule for dividing fractions--invert and multiply--but had absolutely no idea of the reason behind the rule -OR- if you are a teacher (homeschool or public!) and are trying to help your kiddos understand this concept, you'll love these videos.

What Children Need to Thrive

Are you familiar with the work of Dr. Bruce Perry? He's an incredible resource on so many topics...the human brain and development in children, childhood trauma, the way children develop relationships. This time he discusses "the disconnect between what our children need to thrive and what the modern world has to offer, emphasizing the importance of human connections at early stages in life. He also offers tools for parents to help their children develop healthy minds, nurture friendships, overcome traumatic experiences, and feel cherished. Drawing from his own experience as a parent, Dr. Perry further informs us how parents can evaluate themselves as friends, spouses, workers, etc. to become better role models for their children Living Smart by emphasizing the importance of human connections." WWW.HOUSTONPBS.ORG



A sample quote..."It's probably not good AT ALL for children under the age of 3 to watch television. Anything you think they can benefit on television, they could probably learn better in a relationship." Perry talks a lot about the importance of relationship for children.

Fabulous Math Website

I accidentally found Links Learning when I was searching for a math site. It's phenomenal. The "Illustrated Lessons" are short movies that explain math concepts and then allow students to follow-up with interactive quizzes. From the site:

In this section, you will find some fun ways to learn about math. You can start out with Estimation of Length, Place Value, Weight and Capacity. If you want something more challenging, take a look at Line Symmetry, Patterns and Tangrams. Try some of these at home with your family!

On the Tangram movie, it gives you step by step instructions on making your own tangram. You push the button when you're ready for the next step. The lessons are great for introducing or reinforcing a concept.