Math and Science Update...

Dear Families,

Well, our first week back is almost done and I wanted to update you about what we have been up to.

MATH

On Monday we started investigating ratios. Students learned that ratios are just comparisons of things. There are two kinds of ratios that we see commonly in 6th grade:

1. Comparing parts of groups to the whole group.
   Students know these more commonly as fractions. For example, if I have a group of seven marbles and three of them are red, but four of them are blue, the ratio of red marbles to the total number of marbles is 3:7 (pronounced "three to seven"). This can also be expressed as the fraction 3/7.
2. Comparing parts of groups to the other parts of the group.
   This was the new way of thinking about it. If I have the same set of seven marbles (three red and four blue), then I can compare the red marbles to the blue marbles using a ratio. The ratio of red to blue marbles is 3:4, and the ratio of blue marbles to red marbles is 4:3. Notice, the order of the parts is important. 

• You might be thinking to yourself, "so... if a ratio is a part:whole ratio, it's clear why it's a fraction. But why can we use fractions for part:part ratios? Sure, the ratio of red:blue is 3:4... but why can it also be 3/4 when there are more than four marbles?"
  
  
• Well, that comes down to the comparison of one part to another part. If we ask "what fraction of the number of blue marbles is the number of red marbles?" then we are comparing the number of red marbles to the number of blue ones. Since there are four blue marbles and only three red ones, we can say that the red marbles are 3/4 of the number of blue marbles. So the use of a fraction there works just fine as long as we remember that we are describing the size of one part of the collection relative to the other part of the collection.
  

SCIENCE

• Just before break we began investigating these fan cars as a way of looking at forces, motion and energy. The big question we are asking is "what causes what?" Does energy cause motion? Or does force cause motion? Or does motion cause force?
  
• This week we have been learning to use two tools to help us investigate this:
• Force Diagrams: These simple diagrams represent forces acting on an object as an arrow. If two forces are acting on the same object, we draw the greater force with a longer arrow. 
• Average Speed: This one was fun. Through a reading, students were introduced to the idea that speed is the change in position over a change in time. When I then asked a student to come up and change my position, in both classes someone turned me sideways! *laughing* They were reading the word position as pose. But for scientists, position means location. So we described that instead as the change in position divided by the change in time and we recorded the formula like this:
  
  speed= dx/dt
  
  where dx means the change in position and dt means the change in time (d is an abbreviation for difference). 
  
  
•  The two HUGE understandings in these experiments are:
  

1. I know that motion is the result of an unequal application of forces.
2. I know that a constant application of force results in increasing speeds (until "terminal velocity" is reached -- Shane pointed that out for us!).  

 Warm regards,

Brian MacNevin