Help Session on Standard NMHT.4.c

Alex, Alexis, Jordan and Whitney were in attendance.  We started out by reviewing the precision reporting rule for adding and subtracting:

add/subtract rules

add/subtract rules

 

The people who were there wanted an example right away, so I used 12.5 + 3.26, which adds to 15.76.  Since 12.5 is only known to the precision of the nearest 0.01, we have to round our answer to the nearest 0.01, as well.  This means we should actually report an answer of 15.8.

adding examples

adding examples

Next, I gave examples of adding and subtracting:

subtracting examples

subtracting examples

In the first adding example, we round to the nearest 0.01, because that is the precision of both the measurements being added.  In the second example, we round to the nearest 10, because that is the precision of the least precise of the two measurements, 30, which is written without a decimal point.  The only adequate way to report this precision is with scientific notation, so it is written as 3.0 x 10².

In the first subtraction example, the answer is rounded to the nearest 0.1, because the least precise measurement, 1.2, is only known to the nearest 0.1.  In the second subtraction example, the answer is rounded to the nearest 1, because that is the precision of 2, which is the least precise of the measurements.

Next, we reviewed the precision reporting rule for multiplication and division:

multiply/divide rules

multiply/divide rules

Right after that, I showed examples for multiplication and division:

multiplication examples

multiplication examples

In the first multiplication example, the answer is rounded to 2 sig. figs. because the least precise measurement, 3.0, shows only 2 sig. figs. In the second multiplication example, the answer is rounded to 1 sig. fig. because the least precise measurement, 4, shows only 1 sig. fig.

division examples

division examples

In the first division example, the answer is rounded to 2 sig. figs. because the least precise of the two measurements, 4.0, is shown to only 2 sig. figs. In the second division example, the answer is rounded to 3 sig. figs. because both measurements have 3 sig. figs.

Practice Problems

Practice Problems

Last, I posted 4 practice problems:

Try them yourself.  See if you get the right answer by checking here.

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Help Session on Standard NMHT.4.a

Today, during B Lunch, we had a help session on Standard NMHT.4.a, which is, “I am able to differentiate between accuracy and precision in data sets.”  Whitney, Alexis and Alex showed up for the session.

I started out by showing two targets.  The first target had shots from two accurate rifles:

accurate rifles

accurate rifles

Accuracy means “centered on the target” for a rifle, so both these rifles are accurate, even though 4 of the 5 circled bullet holes are barely on the target.  The second had shots from two precise rifles:

precise rifles

precise rifles

 

 

The rifle that is off to the upper right is precise, because precise for a rifle means “close shot grouping.”

Then we talked about what it means for measurements to be precise and accurate.  Precise measurements agree closely with each other.  In other words, the range of values in a group of measurements is small.  Accurate measurements agree with a true or accepted value.  In other words, the average of a group of measurements that is accurate agrees with a true or accepted value for the quantity that is being measured.

Next, we looked at 4 sets of seven measurements and worked out a description for each, in terms of accuracy and precision:

accurate and precise

accurate and precise

 

These measurements are accurate, because the average of their values is the same as the true value of 10.  They are also precise, because the range, 0.2 is small, compared to the average (about 2%).

 

 

accurate, not precise

accurate, not precise

These measurements are accurate, because their average agrees with the true value, but they are not precise, because the range, 8, is large, compared to the average (about 80%).

 

 

 

precise, not accurate

precise, not accurate

These measurements are not accurate, because the average does not agree with the true value, but they are precise, because the range is small, compared with the average.

 

 

 

not accurate, not precise

not accurate, not precise

These measurements are neither accurate nor precise, because the range is large and the average does not agree with the true value.

After this, the students were invited to take a short assessment to demonstrate proficiency on Standard NMHT.4.a