Tuesday, September 8, 2020

CCSS.MATH.CONTENT.7.G.B.4: Circumference and Paper Towel Rolls

This article describes a math activity for learning about circumference.

CCSS.MATH.CONTENT.7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Circles have several properties, including diameter, radius, area, and circumference. The diameter, radius and area are often described in expressions and equations that are related to π ("pi"). 

The radius is the segment from the center to the perimeter of the circle. The diameter is twice the the length of the radius. The diameter is the width of the circle, through its center, which makes it a very useful measurement. The area is often calculated in terms of the radius or diameter. 

However, the circumference is almost never discussed with as much detail. This activity provides an opportunity for the student to become more familiar with the practical application of circumference and how it relates to pi.

A paper towel roll is helpful in a kitchen. This prior knowledge can help students build new ideas about geometry topics related objects with round surfaces. Daily interactions with common household objects, such as paper towel rolls, can strengthen the relevance of math in everyday life.

From observation, we see that a circumference is the perimeter around a circle. If you walk around the entire perimeter of a circle, we find that the total distance around the circle is equal to the length of a segment that has been "un-rolled" from a round arc into a straight line.

Let us take a cardboard paper towel roll. The cross section is a circle.

If we make a single cut along its longest side, we can "un-roll" the paper towel roll into a flat sheet of cardboard. (The straightness of the cut does not need to be perfect.)

We know that a circumference is the length around a circle. We also know that the length remains unchanged. Also, the surface area of the paper towel roll along its longest length is also unchanged. The only change was the path of the length, which was transformed from a round arc into a straight line. This activity demonstrates the powerful the idea of π ("pi"). 

Pi is an important math tool that allows us to relate the diameter of an object to its circumference without the need for tedious physical measurement or destructive modification. 

We also see in this activity that circumference is simply the arc length that travels completely around a circle.

How to Make Simple Bar Chart in Google Sheets


Bar charts are allow readers to understand item counts at a glance. In micro school math instruction, you may want to use bar charts as a learning objects, which can be created as part of the constructivist learning process.

Using Google Sheets to create a bar chart is simple.

We will use a bag of candy (Milk Chocolate M&M's) as an example data set. The bag of candy contains chocolate lentils. Each lentil is one of six colors.
  • Red
  • Green
  • Blue
  • Brown
  • Yellow
  • Orange
For our bar chart, we will use a single-letter symbol to represent each of the six candy colors. Assigning symbols to each color can be very helpful for analysis of sets or combinations.


Collectively, we refer to this set of colors as RGBWYN (pronounced as "rugby win" as heard on Google Translate).  

We count the number of lentils in the bag of candy, and we find the following quantities:


We can switch the columns and remove the headers in Google Sheets like so:

This is the data set we can now use to generate a bar chart.

From the Insert menu, select the Chart item, and Google Sheets will automatically (or automagically) create a bar chart with your data set.

Here is a video example of how to make a bar chart in Google Sheets.

This is only a simple bar chart that represents the frequency of colors in a bag of chocolate candy. However, bar charts can describe the frequency of anything, which makes these charts a wonderful tool for exploring statistics.

HTML Merged Tables for GitHub Markdown

GitHub Flavored Markdown does not support merged tables. However, GitHub does support a special subset of HTML (GitHub HTML?) that allows you to build complex, tables with merged cells. 

Here is a demo on GitHub.

Add caption

The table was exported using Box Table Baker for Google Sheets, which allows you to export selections of a spreadsheet as HTML tables. 

Google Sheets does not allow export of selected spreadsheet ranges. Its built-in HTML export feature only downloads all the sheets within the spreadsheet as a “web page” to a zip file. 

Box Table Baker adds several features that improve productivity. The most important feature for this post is the export of formatted merged tables, which are supported by GitHub HTML.

Bold, italic, and strikethrough font styles for each spreadsheet cell are exported to “GitHub HTML” tags (e.g., <b>, <i>, and <del>, respectively). Also, monospace fonts are detected and exported within <code> tags.

CCSS.MATH.CONTENT.7.G.B.4: Circumference and Paper Towel Rolls

This article describes a math activity for learning about circumference. CCSS.MATH.CONTENT.7.G.B.4:  Know the formulas for the area and circ...