*Mathematics Calendar 2018*, Theoni Pappas writes:

Find the area of this triangle to the nearest whole number.

[The side lengths are given as 6", 8", 12".]

This is a job for a hero -- as in Heron's Formula. The semiperimeter is (6 + 8 + 12)/2 = 13.

*A*= sqrt(

*s*(

*s*-

*a*)(

*s*-

*b*)(

*s*-

*c*))

*A*= sqrt(13(13 - 6)(13 - 8)(13 - 12))

*A*= sqrt(13(7)5)

*A*= sqrt(455)

*A*= 21.3

And rounded off to the nearest whole number, the area is 21 square inches -- and of course, today's date is the 21st. Heron's Formula isn't emphasized in most Geometry courses -- in the U of Chicago text, it's squeezed into Lesson 10-6 on Remembering Formulas, since this is indeed a formula that some people may remember.

Today I subbed in a seventh grade science class. I wish to focus more on classroom management in middle school classrooms, and so I'll do a "Day in the Life" today, with management as the focus resolution (first resolution).

**8:15**--- The school day begins with homeroom and morning announcements.

**8:25**-- The middle school rotation starts with fourth period today. The students are working on a group project -- they are to create an infomercial to describe one way that man impacts the ecosystem. They must watch a video, write a reflection, and then decide as a group what topic to do the project on, as well as whether the project should be completed on Google Docs or poster paper.

**9:20**-- Fourth period ends and fifth period begins. While most of fourth period has worked hard on the reflections, many students in fifth period are talkative. They keep playing the video over and over (or watching non-academic videos such as Yanny/Laurel) and never begin the reflection.

**10:15**-- Sixth period is the teacher's conference period. It gives me the perfect time to adjust my management so that the noisy fifth period experience isn't repeated during first through third periods.

**11:10**-- First period arrives, and I project my warning onto the screen. I go to each group to make sure that they are doing their work. A few students are summoned to make up their SBAC tests, implying that the seventh graders have already completed testing (even though eighth graders are taking the infamous NGSS Science Test). This is great, since I don't want to be in charge of administering the SBAC.

I prepare the following note to place under the document camera:

* Any individual who doesn't have at least half a page of video reflection will be placed on the detention list.

* If you can't come up with half a page of reflection, then discuss it more with your group members only.

* Every group must have one person say the following sentence at the end of class: "Our group is doing a (Google doc/poster) on (topic from video)." For any group that can't say this, the whole group gets detention.

* You have a lot of work to do today and barely enough time to do it. You have no time to talk to other groups or watch any video other than "Man."

The regular teacher requests that I leave her a good list, bad list (or more to the point, a detention list) and the best behaved class of the day. This note explains what criteria I'm using to determine who gets placed on each list.

**12:05**-- First period leaves for lunch. This is the second best class of the day (with the best class being fourth period).

**12:50**-- Second period arrives. At this middle school, the class right after lunch (no matter which period rotates into this spot) has silent reading.

Only one student fails to take notes, and so I write her name on the detention list. First and second periods are both considered to be Honors classes, and so the real test is coming up next.

**2:00**-- Second period leaves and third period arrives. One student does throw a water bottle for no reason, and a whopping seven students fail to follow the instructions that I project onto the screen, and so I write down all of their names for detention.

**2:55**-- Third period ends -- but as so often happens at middle schools, the regular teacher is assigned after school yard duty, which I must do for her.

**3:05**-- My day finally ends.

Question 11 of the SBAC Practice Exam is on statistics:

Click above the numbers to create a line plot for the given percent chances of rain in different cities.

65, 65, 70, 70, 80, 80, 80, 80, 85, 95, 95, 95, 100

This is a statistics question -- and as I mentioned in my last post, stats, it's to be taught in Algebra I at all, is covered in the second semester. So I won't have to deal with this question at all in my summer Algebra I class.

As with many Common Core Statistics questions, this is the first time that I've ever seen a "line plot." Apparently, it's similar to a bar graph. There should be two X's above 65, two X's above 70, no X above 75, four X's above 80, one X above 85, no X above 90, three X's above 95, and one X above 100.

Question 12 of the SBAC Practice Exam is on dimensional analysis:

The formula for the rate at which water flows is R = V/t, where

* R is the rate,

* V is the volume of water measured in gallons (g), and

* t is the amount of time, in seconds (s), for which the water was measured.

Select an appropriate measurement unit for the rate.

A) gs

B) g/s

C) s/g

D) 1/sg

This question on units could appear in the first half of an Algebra I text, since this is a linear equation (provided t is given or a constant). This problem basically solves itself -- the rate is V/t, and V is in g while t is in s. Thus V/t is in g/s, or gallons per second. The correct answer is B).

**SBAC Practice Exam Question 11**

Common Core Standard:

Represent data with plots on the real number line (dot plots, histograms, and box plots).

**SBAC Practice Exam Question 12**

Common Core Standard:

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

**Commentary: In the U of Chicago Algebra I text, there is a little stats in the last chapter, but not line plots specifically (even though other plots do appear). Meanwhile, in Chapter 5, the division chapter, there is a lesson on rates. Units are briefly mentioned, but not in detail. Still, this question should be easy enough for our students to answer.**

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