Large-scale Measuring with Younger Students
The wonderful units of measurement that young children invent can extend into large-scale work in several ways. We often use clothes- line or similar rope, knotted at fixed intervals (yards, meters, or your class’s own unit). The rope becomes a great tool for measuring to ten or twenty units, continuing and repeating to one hundred. It is just as important to give younger children a chance to explore num- bers outdoors as it is for older students to work carefully and gather specific data. Younger kids might compute how many paces from the door to the swings? Does everyone get the same results and what does that tell us? For us as teachers, the problem is not that oppor- tunities are unavailable. It is, instead, that we have to find ways to seize opportunities as they present themselves.
Up in the Air Even without fancy equipment it is possible to measure tall things
safely and accurately, such as the height of a tree, or a building near your school. Once again, Pythagoras can help us. We need a right angle made by the tree trunk and the ground, or a wall and the ground. Then a stick or broom handle with sighting tube (a large straw or piece of rigid plastic tubing) mounted at 45°. The “eye- piece” end of the sighting tube should be at the right height for your students. Move the stick closer or farther away from the object you are measuring. When you
can see the top of the object through the sight, measure from your stick to the base of the object. With that nice 45° angle of the sight, the distance from the sight to the base will be the same as the height of the object you are measuring. Students building and using these devices, known as clinometers, quickly notice that
the 45° angle is only true if the stick is vertical. After this discovery by students we usu- ally attach a small builder’s level to the stick. When it shows that the stick is vertical, then the angle is accurate. In this photo we show a level that has a 45º angle built into it, so that when the bubble is centered, the angle is correct. There are other variables: for example if you are measuring on a slope, the data will differ. And there is the question of the height of the stick, or where exactly is that great big triangle that you are working with, most of which you have to imagine? But that is an excellent question for your students to consider. A next step could be to invite a forester or civil engineer to visit your class. You could
see digital devices that make tree height or distances very easy to compute. The forester needs them, as does the engineer for other purposes, but digital tools often hide the basic mathematical ideas that can help students to see both the why and the how.
Brains at Work
For both real-world engagement and motivation, it is important that math be more than paper and pencil in the classroom. Students who may be confused by a problem in a text- book can see it in a different way in a new setting. Working on a larger scale also gets them physically engaged in an activity, causing their memory of the whole experience to be different, including the mathematics. Concepts that are hard to grasp in the paper- pencil-computer world of the classroom can be understood in new ways through field-based work that then comes back to the classroom, providing a resource for further work. !
Casey Murrow is the Director of Synergy Learning. Check our home page to find more about the work of Synergy Learning, publishers of Connect.
©synergy learning • 800-769-6199 • May/June 2011 Connect • Page 25
Using a homemade clinometer to measure tall things
Students quickly
notice that the 45° angle is only true if the stick is vertical.
casey murrow
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28