Measuring+a+side+is+different

​ Read the responses below and see if we are all thinking __**appropriately**__ about differences between measuring sides and measuring angles. Hit return after any response and type in your comments/edits in a different color regarding the response immediately above. Are we ready to help children make sense of the differences between these measures rather than just tell them "it is so"?

1.Because angles involve two sides that come together. They are measured by different means... sides inches or sentimeters and angles are measured by degrees**.** - I think this person is correct when saying that sides can be measured in inches or centimeters and angles are measured by degrees. I think there needs to be more explanation on what an angle is and how a side is different from an angle, such as what is being measured. An angle is measuring the space between the two sides that come together, and the side is just measuring a length. -I agree with the person above. Really don't have anything to add.

2. Measuring an angle of a shape is different from measuring a side of a shape because when you measure the side of the shape you are only worrying about one side of the shape, but when you measure the angle of a shape you have to keep into consideration two different sides and how they are compared to one another. -They have the right idea, but if all the sides of the triangle are not the same, then you have to measure all of them, not just the one side. -Some times you do have to worry about more then one of the sides when mesuring the side of the shape.

3. Measuring an angle of a shape is different from measuring a side of a shape because:the side of a shape is measured with a ruler or its length, while angles are two sides that come together so they are measured in degrees, with a protractor. - They are on the right track, but instead of saying "come together" they could have some either line segment/ ray; anything can come together. Also, you can use a protractor or a angle ruler. -She could have added something in there about the fact that angles are measuring the distance that one line goes out from another.

4. Measuring an angle of a shape is different from measuring a side of a shape because the sides of the shape, also known as line segments or rays, come together at a point, or vertex, which makes the angle. -This person is correct when they refer to the sides of the shape as "line segments" or "rays". And it is also good that they know that the line segments/rays come together at a spot called the vertex. They are also using one of our definitions for angles; that an angle is formed when two line segments/rays come together at a vertex. However, I might go into more detail about how you would go about measuring that angle. This statement mostly just talks about what an angle is, it doesn't really explain anything about measurement.

- The person is correct in identifying the difference in the definition between a side and an angle, and how they are both involved in a shape, but not the same thing or measured in the same way. However, they didn't go into detail about how measuring both the side and the angle are different. Yes, they are different things, but how do we go about measuring them differently? Tools, methods, etc? They don't show great knowledge in that area, and therefore, do not fully answer the question put before them.

5. Measuring an angle of a shape is different from measuring a side of a shape because when you measure and an angle you use different units than measuring a side of a shape. Angles are measured in degree and side are measured in length.
 * -I think that this sentence sounds pretty good. They know that you have to use a different unit of measurement when you measure an angle compared to when you measure a side of a shape. It is true that angles are measured in degrees while sides are measured in length. I think they need to add a little more about what they know about an angle and a side to compare their differences.**

6. Measuring an angle of a shape is different from measuring the side of a shape because you are measuring different things with different units. When you measure the side you a measuring a distance. When you are measuring the angle of the shape you are measuring degrees. -This comparison is correct by saying that different units are used when measuring these two different things. More details are needed explaining what an angle is compared to a side, however.

7. Measuring an angle of a shape is different from measuring a side of a shape because when measuring the angle of a shape you measure the distance around a circle the two meeting sides have, while measuring the side of a shape you only find the length of that one side.


 * I think that the understanding is there. This response could say that the when measuring the angle they are measuring the circle around the vertex not the two meeting sides have. When reading that it sounds as if you were attaching a pencil to the end of the sides and as it turns you were tracing the end to make a circle. The response is not clear in saying that the distance being measured around the circle is WHERE the sides meet just that the sides meet.

8. Measuring an angle of a shape is different from measuring a side of a shape because.... measuring the side is measuring the length of a shape's linear side where as measuring an angle is trying to find the area between the two linear sides that meet at a common point. 9. Measuring an angle of a shape is different from measuring a side of a shape because an angle is made up of two sides and is measured in degrees and a side is measured by a ruler.
 * Where as measuring an angle you use degrees to find the area between two linear sides. The units are different one is measuring the length (sides of shapes) and degrees is measuring the turn of an angle or how much area is between the two linear sides that meet at the vertex.
 * I think this was a good definition it just needed to speak about degrees, because I think that is important when talking about measuring angles.
 * I think this person is correct when explaining the differences, but a side can be measured more than just by a ruler. Also, I think this person should have described it in more detail when talking about the angle; maybe by talking about its vertex. Overall though, this person has the the right idea.

10. Measuring an angle of a shape is different from measuring a side of a shape because when you measure an angle you use degrees, and when you measure a side of a shape, you use length; such as inches, feet, meters, etc. - This explanatio describes the differences in the actions taken to measure the different features of a shape but it doesn't explain why different action have to be taken. Yes when measuring an angle you use degrees and when measuring length you use a linear measurement. One would need to do that because an angle is the area between two sides or line segments (like one of our definitions from class) and a side is one of the line segments that makes up the shape.

11. Measuring an angle of shape is different from measuring a side of a shape because the angle of a shape is the degree of how much the angle is opened. The measurement of a side is the length of the shape. - I think the person is correct when saying that the angle of the shape is how much the angle is open. They understand that it isn't area it is a distance measurement in degrees. They could have mentioned that the measure of degree is how much turn there is. The measurment of the side is less clear because they said the length of the shape, but it would be the measurement of the length of one side of the shape. 

12. Measuring an angle of a shape is different from measuring a side of a shape because...when measuring the angle of shape you have to keep in mind the vertex and you are measuring the space inbetween the two line segments of a shape. While measuring the side of a shape you are measuring the "side" of a shape which is the ONE piece (which is a line segment) of a shape. This response is very good! I think it hits all the important parts of what measuring an angle and side involves. It is also important to mention and know that angles involve degrees, being measured by a protractor, while a side could be any type of length like a ruler or any "unit" of measurement as long as it showed how many of the units the certain length was.

13. Measuring an angle of a shape is different from measuring a side of a shape because an angle is the distance around a circle and a side is a line segment. - This person is on the right path but instead of the distance around a circle it should say the turn represented by two rays or line segments.

14. Measuring an angle of a shpe is different from measuring a side of a shape because you can't measure a side. The only way to measure a side is with a ruler, therefore you would get inches, centimeters, yards, etc. When you measure an angle, you are getting a degree at which TWO sides meet at a point called the vertex. -This person has hit the nail on head with this comment. They mentioned that you measure angles with degrees at which two lines meet, which is neccessary to find an angle. The person was also right that you cant measure a side like an angle. They did mention that you can only measure a side by using a ruler but you can use whatever you want, just as long as you know the unit of measure.

15. Measuring an angle of a shape is different from measuring a side of a shape because measuring an angle is in units of degrees and measuring a side of a shape can not be measured in degrees, but can be measured, for example, using the metric system. -This person has the right idea when they mention that you can not measure a side by degrees. Degrees are used is finding the angle, which they do a good job of mentioning. They mention that a side can be measured by the metric system, which is ok because you can use any type of measurement to find the length of a side. All it requires is a specific tool to make your measurements.