Home School Life Journal

Home School Life Journal ........... painting by Katie Bergenholtz
"Let us strive to make each moment beautiful."
Saint Francis DeSales

Unstandardized Measurement (3-6)

I like to start out teaching measurement by helping them understand the kinds of problems that historically led to the development of standardized systems of measurement. Civilization felt the need for standard units of measurement because to be without such units was a constant source of frustration. Exposing them to these frustrations helps them to see the need for such standardized units of measure which can be satisfied later with problem solving.
People
I familiarize the boys with taking measurements by using lengths of string or yarn. This introduces them to the idea that some displays of measurements are more useful in answering questions that others. By letting them take control of how the measurements are displayed they learn some valuable concepts on their own, such as making sure they label and place them on a page.  I then let them come up with questions that this data might answer. They came up with:

  • who has the largest or smallest of a particular measurement
  • which measurements are larger than others, such as the neck was always larger than the wrist
  • which measurements were the same?
I then ask them how they could display the data they collected to see the answers to these questions more easily.


Now that I am not always well enough to give assignments orally, I am writing them more in their journals for them to follow. Using only one body measurement; in this case, the wrist, I got him to get measurements from everyone in the family. This exercise showed James very quickly that it is hard to make sure that the measurements were consistent.  He developed a way of making sure that the wrist on each person was in the same place by placing the string between the wrist bone and the hand. It was the beginning of thinking of all the factors that must be considered if two people are to measure an object and get the same results.

"Students may find they know less about measuring at the end of this lesson than they thought they did at the start. The confusion they face now, however will eventually lead them to a fuller understanding of measurement."- Mathematics, A Way of Thinking 

Next, I had him take his own wrist measurement and measure his neck, his arm and his first finger. The purpose of this exercise is for him to find ratios of length that exist between the various parts of the body.  Most human bodies have similar proportions. Not every neck will be exactly two wrists around, but most do. James and Quentin will find the the ratios between their own body parts will be similar.

Objects

The next task is for him to use the body as a measuring tool to measure some object in the room.  The purpose of the assignment is to force him to examine the imprecise nature of their measuring devices.

"This exposes him to the kinds of problems that have historically lead to the development of standardized systems of measurement"- Mathematics, A Way of Thinking 


Using Unifix cubes to measure the string or yarn makes a nice transition before introducing standardized measurement.Use the Unifix cubes to measure your family's hand-spans, which then can be used for comparison and averaging.
What they have learned about unstandardized measurement will help them to more easily understand standardized measurement and the reasoning behind its development.

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4 comments:

  1. I read once that one of the bridges in Boston was measured years ago by a bunch of undergrads by using another undergrad by the name of Smoot. They calculated how many Smoots end to end were needed to build the bridge.

    I love how you introduced non-standard measurement and made it relatable for the varied ages in your house.

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  2. I remember when I taught 2nd grade there was a great book about measuring by feet. The king wanted a bed for the queen and said she was 8 feet tall. Well the carpenter measured out his apprentice's feet and the bed was way too small, so he tried his own and it was way too big. It was hilarious.

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  3. Look how happy they are to measure!

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  4. I love that you have such great hands on and visual lessons. You have wonderful ideas!

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