Find x.
(Here is the given info from the diagram: a right triangle with legs 4.5 and x and hypotenuse 20.5.)
This is an obvious Pythagorean Theorem problem:
a^2 + b^2 = c^2
4.5^2 + x^2 = 20.5^2
20.25 + x^2 = 420.25
x^2 = 400
x = 20
The desired leg length is 20 -- and of course, today's date is the twentieth. The Pythagorean Theorem will be taught in Lesson 8-7 of the U of Chicago text.
This is what I wrote last year about today's lesson:
Lesson 0.4 of Michael Serra's Discovering Geometry is called "Op Art." Serra explains what this is:
"Op art (optical art) is a form of abstract art that uses straight lines or geometric patterns to create a special visual effect."
Optical art is closely related to the concept of optical illusions. I don't even want to attempt to draw some of the more complex optical illusions by hand, so I just use a Google search instead. On the other hand, the impossible objects page comes directly from this site:
http://brainden.com/impossible-objects.htm
Unfortunately, only the Penrose triangle printed properly. It is named for Sir Roger Penrose, whom Serra describes as a British mathematician and avid puzzle enthusiast. He is in fact still alive -- he just turned 89 this month.
So I actually had to draw in one of the impossible drawings -- "Three prongs from two?" (called "the devil's fork" by Brainden). Well, I suppose if I can draw it, then so can our students.
Here is the Blaugust prompt for today:
How do you handle Parent Communication? What has been successful for you?
That's one thing I don't write about much on this blog -- parent communication. During the one year I worked at a charter middle school, I wrote about parent communication during the first week of school:
9:55 -- The previous day we discussed the classroom rules. Today I pass out Behavior Contracts for all of the students. Each student writes down the rules we agreed to, and then the students take them home for the parents to sign. In this way, each student is to be made accountable for his or her own behavior throughout the year -- and if a parent requests a conference, I can just take out the contract and let the parents know that their child has violated that contract.
I also wrote once about my main form of home communication -- Parent Conferences Week. Let me cut and paste some of what I wrote that day:
7:50 -- Our first parent arrives -- yes, parents can choose to come before school if they desire. It's the mother of one of our sixth graders. The mother and her daughter arrive at the history room, where all three middle school teachers -- the history teacher, the English teacher, and me -- are sitting. We've agreed that it's easiest to do it this way, so parents can speak to all three of us together.
As it turns out, this girl is earning straight A's and is one of the quietest students our classes. So naturally, all of us have only positive things to tell her mother. We three teachers wish that all of our students were like this girl.
1:30 -- Our first afternoon conference begins. It's the father of one of our most troublesome seventh graders -- he just barely scraped through my class with a C, but he failed history and English, and even received a C in music -- a class in which almost everyone gets an A. I tell his father that he can do much better, but he hangs out with the wrong crowd. Just yesterday he or one of his friends pulled a classic prank -- putting a tack in my chair.
2:55 -- After a lull without any parents, the mother of a sixth grader arrives. The girl is getting B's in both my class and history, yet is failing English. The mother is a Spanish speaker, so our history teacher must translate for the English teacher, who explains that the girl has trouble writing. My colleague tells her mother about an time last month where I had the whole class write standards when they were too loud (during IXL time, of course), and the poor girl cried as she was unable to finish.
3:00 -- In the middle of the English teacher's exposition, the mother of an eighth grader arrives. I go over to talk to this mother as the English teacher is still talking to the sixth grader's mom. The eighth grade girl is earning C's in all three classes -- mine, history, and English. I tell the mother that even though her daughter passed some of her tests, she failed some others. Still, I let the mother know that the girl is very well-behaved and likes to help us out after school, especially the English teacher.
3:40 -- The parents of a sixth grader arrive -- but they are in a hurry due to a family emergency, so they just pick up their son's report card (I gave him a C) and leave.
3:55 -- No more parents show up. The history teacher counts out the remaining reports and figures that about two-thirds of the parents showed up this week.
But six months before the first day of school that year, I wrote the following statement on my blog:
I know that I can be a better teacher by showing common courtesy to students, parents, and staff members.
So this is the guiding principle when it comes to communication with anyone, including parents. I'm not quite sure whether I adhered to this principle fully -- was I completely courteous to parents?
There is one form of parent communication that I used that year -- yet I never wrote about it in any blog entry. At our school, I was required to file all completed assignments in folders -- the students had nothing to take home. Some kids wanted to show something to their parents, and so one day, I decided to type up notes to parents of students who earned A's on tests. This way, parents can receive positive information about their children, not just negative info. Unfortunately, I also had to make many phone calls to the parents of misbehaving students.
Let's link to some other Blaugust participants. Yesterday I mentioned one Sara, and so now it's time to get back to the other Sarah -- Carter, that is. And the topic is the same -- so many of her readers want to do Sarah's activities, but adapted for the coronavirus era:
https://mathequalslove.blogspot.com/2020/08/digital-activities-repository.html
I've been blogging for over nine years now. And, those nine years have been full of resource sharing. Now, it feels like the tables have turned with the pandemic. Instead of me sharing resources with you guys, I keep getting all these emails, DMs, tweets, etc full of links to virtual/digital versions of the activities I've blogged about over the years. This has been amazing, but I haven't done a very good job of organizing all these links. I especially haven't done a good job of sharing them. As a result, many of you are recreating the same activities over and over. So, I've decided to dedicate this blog post to sharing links to these digital versions of activities that have been shared with me. Hopefully this will save you some time and prevent someone from reinventing the wheel over and over again.
Ah, so it's her readers who are creating the distance learning versions, not Carter herself. Anyway, here's a link to one of these activities, called "Question Stacks":
Farica Erwin has created a page on her blog that is chock full of digital question stacks. Thank you so much for sharing! Can we just bask in her amazing organization skills as well?!?
So this Farica Erwin is a math teacher-blogger as well. But she's not a Blaugust participant, though -- her post linked to above is dated July 28th, and she hasn't posted since.
Here's a link to an actual Blaugust participant -- Denise Gaskins:
https://denisegaskins.com/2020/08/20/language-and-math/
Her post is about the academic language used in math classes:
Of course, several of these are words (or at least concepts) students will have learned before. But a large part of prealgebra is consolidating previous ideas and mastering their names (sum, quotient, factor, multiple, etc.) before moving on to apply them in algebra class.
And of course, this was what my Shapelore project was all about, except I take it one step further and try to replace the words students find tough with easier words (such as adding for sum, dividing for quotient, and so on).
Here are today's worksheets:
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