Reflect on your day today. Think about all the times you considered how much space something took up to help make a choice. List as many examples from the past 24 hours as you can recall. Which of those did you quantify (measure) before acting? In which cases might you have saved yourself some resources if you would have used what you are learning this week to quantify the situation?

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

What are the measures of ∠a, ∠b, ∠c and ∠d? explain how to find each of the angle measure.

Write two subtraction equations that are equivalent to 5 + 12 = 17.