Friday, December 8, 2017

Week of December 8

December 8, 2017

Sam’s 4-6th Math Class

Etienne and Ishan work on Sierpinski Carpet fractal.
Counting boxes to make the fractals.
This week we continued to look at fractals. The class spent a significant amount of time working on a fifth iteration Sierpinski Carpet, which is now on display in the MS across from the elevator. It was a technically challenging experience for many of the students that required following an iterative process with a high degree of attention to details. If even one square was miscounted the whole image looked wrong. (If you get a chance to see the finished product, you can see a few places where someone had to correct an error.
Algebra and Pre-Algebra

Nick and Niko explore the relation between batteries (voltage),
 resistance (lightbulbs) and current (brightness of bulbs)
Math this week largely was combined with science activities. As we are working with the Arduinos, we’ve begun to learn some of the basic concepts surrounding electricity and currents. Tuesday’s batteries and lightbulbs investigations emphasized proportional reasoning and we formalized that connection with the introduction of Ohm’s Law on Wednesday.

The d=rt and V=IR graphic organizer pyramids visualize
the proportional relationship of those quantities.
In more formal math classes, the Completing Algebra group has been working on graphing parabolas; especially investigating establishing a relationship between changes in the coefficients of the terms and the appearance of the graph. The Beginning Algebra group continued to work with linear equations and the Pre-Algebra group is going into more depth on single variable equations and inequalities.

Friday, December 1, 2017

Week of December 1

December 1, 2017

Sam’s 4-6th Math Class

This week we dug into concepts related to ratios and fractals. We watched the thought provoking Nova episode: Fractals the Hidden Dimension and then talked about what it means to be “self-similar” and how an object can have a finite area but an infinite perimeter.
It was also very interesting that in their Morning Meeting presentation about Wildlife in Michigan, they mentioned the length of the coastline, which led us to another discussion about fractals and measurement related to “How Long is the Coastline of Britain.”
Algebra and Pre-Algebra

The 7th and 8th graders have mostly been completing assessments this week. All of the groups also had some new material introduced. The pre-algebra group started a unit on factors, fractions and exponents; the beginning algebra group is learning how to write the equations of lines from points or graphs and the completing Algebra group has started working with square roots and quadratic equations.

Friday, November 17, 2017

Week of November 17

November 17, 2017
The highlight of this week was the AMC 8 contest on Tuesday. All of the students in my math classes participated. We spent Monday looking at sample problems and talking about test taking strategies, especially that the goal is to get as many correct as possible in a short time frame and NOT to do every problem correctly and in order. We also talked about identifying which problems might be solvable, but would require such a large investment of time as to not actually be worth completing.

Sam’s 4-6th Math Class

In addition to the AMC contest and the usual work in Singapore math we also started to look at some basic problems in combinatorics, including a lengthy discussion about strategies to stay organized while counting and enumerating possibilities. Specifically, the students worked on these two problems:
  • You have 3 pairs of jeans (we called them X,Y and Z), 7 T-shirts, (called one, two, three, four and five) and 5 pairs of socks (A, B, C, D, and E). Make a list of all of the possible outfits you can wear.
  • What are all the possible outcomes when three normal six-sided dice are rolled, and how likely are each of the possible sums of the three dice.
Algebra and Pre-Algebra

All of the students in these classes are working on finishing up the chapters we’ve been working on with a goal of being done by Thanksgiving break. Some of the students got to the assessments on Thursday or Friday but most will be studying this weekend and working on the assessment on Monday and Tuesday.

Week of November 10

November 10, 2017

Sam’s 4-6th Math Class

On Wednesday we began a new recurring exercise--the timed quiz. This first timed quiz was 3 minutes to complete 60 single-digit multiplication problems. We were practicing quick factual recall; everyone in the class can do these problems, speed, dealing with anxiety and the educational concept of automaticity, were the focus of the discussion post-quiz. On Thursday and Friday the class worked on their Singapore assignments while meeting with Wendy’s class,
Algebra and Pre-Algebra

Because of the aforementioned short week and absences (mine and the students) the pre-algebra group didn’t meet with me this week. They should all be continuing work independently in chapter 3 of the text. The Beginning Algebra group did have a lesson on Wednesday going over the concept of slope--using the “staircase” analogy and as a ratio. The Completing Algebra group also met formally on Wednesday to begin our discussion of exponents and exponential functions, though so far we are only looking at the properties of exponents and vocabulary.

Friday, November 3, 2017

November 3, 2017 -- Coordinate Graphs

November 3, 2017

Sam's 4-6th Math Class

This week we focused on the coordinate plane. Many students were familiar with number lines; introducing the full coordinate plane requires introducing negative numbers (which most students had not worked with formally before) and moving from one-dimensional to two-dimensional thinking. This can be a rather dry conversation, so instead of lecturing on the topic, we talked about the basic ideas and then transitioned right into an activity: making a picture from a set of points--basically an advanced form of connect the dots, but the students had to put the dots in the correct place. After they finished the initial exercise, everyone made a coordinate picture of their own by reversing the process used to make the kitty cat--first make the drawing, locate the important points (places where the line changed direction--vertices), and then right out the list of points as line 1, line 2, etc, so that someone else could recreate their picture. IMG-2990.JPG

Here is one a child made in class if you want to try it at home.

Algebra and Pre-Algebra

We have also been doing quite a bit of graphing on the coordinate plane in the ⅞ math classes. The Completing Algebra group worked on some basic exercises in linear programming as an application and review of graphing systems of inequalities. The Beginning Algebra group is just starting to work with linear equations in two variables and this week talked about graphing lines from an equation by finding points and a little bit about intercepts and horizontal and vertical lines. They also had a brief “pop” quiz, which will be a recurring feature of the class. [One of my professional concerns about timed assessments is that the goal of any timed assessment is to get as many points as possible, not to answer the all questions correctly, our students need practice switching their mindset before being asked to take many timed assessments in high school.] The Pre-algebra group continued their work with linear equations in one-variable.

Friday, October 27, 2017

Melons to Market, Reviewing with Khan Academy

Sam's 4th-6th Grade Math

This week in addition to the usual work in the texts we spent quite a bit of time investigating this situation:

A boy has 45 watermelons in the desert. He needs to get them across to the Oasis fair, 15 miles away. He can only carry 15 watermelons at a time, and he eats one watermelon every mile he walks, including walking back to where he started from. He can also leave watermelons at any mile he has walked, but no fractions of a mile. How many watermelons can he possibly take to the fair? How did you arrive at your conclusion?

The class spent a good amount of time, in groups of 2 or 3, working out how to even begin to approach this problem. Much of the class initially believed it to be impossible. By the end of the first day, everyone agreed that it was possible to get at least 2 melons to the market; the task for day two was how to determine the maximum number. Investigating this problem required much more than straightforward arithmetic; it's more of a logic puzzle and while working through it our class ended up discussing ideas like resupply/refuel depots for Antarctic exploration, note-taking/tracking techniques (how do you keep track of where all the melons are, and how many are left) and the important strategies of using manipulatives, working backwards, and looking at simpler cases.

Evie, Jacob and Ben used a number
line and manipulatives (beads) to help
them think about the problem.
Ishan and Juliana also used beads
to represent the melons. 

Algebra and Pre-Algebra

The seventh and eighth graders had a lot going on this week--two days with field trips and an extended OWL class that cut into our math time. Almost all the students completed an assessment this week and are either working on reviewing concepts using Khan Academy or are moving on to the next major unit of study: solving single-variable linear equations for the Pre-algebra group; linear equations in two-variables for the Beginning Algebra group; a detour into linear programming for the Completing Algebra Group.

Thursday, October 19, 2017

10/16 - 10/20 -- A Math Classic

Sam's 4-6th Math Class

This week in addition to our usual work in the texts, we looked at a classic math puzzle from antiquity. The common phrasing of the puzzle comes to us (translated from Latin) through the author Metrodorus:

'Here lies Diophantus,' the wonder behold.
Through art algebraic, the stone tells how old:
'God gave him his boyhood one-sixth of his life,
One twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage,
After attaining half the measure of his father's life chill fate took him.
After consoling his fate by the science of numbers for four years, he ended his life.

We spent a good portion of the class decoding--discussing the phrasing of the problem and how to parse the words into mathematical notation--a skill critical for real world problem solving. The students rapidly found fractions they could extract from the text and with a little direction were generally able to make some kind of model to represent the situation.

Most of the students choose to treat the problem as they would a word problem from the Singapore texts and drew a model something like this:

But what do the orange regions represent?

The difficulty with this approach was how to think about the extra 5 years between his marriage and the birth of his son and the four years at the end of his life. Eventually, we got to the idea that the orange regions in the above picture must be those 9 (5 +4) years. By figuring out what fraction of his life these 9 years represented, the students could then figure out his age.

One group of students who have some experience with algebra and variables was asked to express and solve the problem algebraically. They, correctly, arrived at:
x/6 + x/12 + x/7 + 5 + x/2 + 4 = x 
which can be solved for the correct answer.

At the end of the lesson we spent some time talking about the similarities between the algebraic and pictorial representations. One of the foundational principles of the Singapore Math program is the idea that student learning should progress from concrete models (physical objects) through pictorial representations (bar models, other drawings) before students are asked to work on fully abstract, algebraic notation. Explicitly showing the students the connection between the bar models and algebra facilitates this transition.

Pre-Algebra and Algebra

The 7/8s had a number of special activities this week that preempted or cut into math, you can read about those in the 7/8 class section. Nevertheless,  all the students were at the end of a unit of study and are independently reviewing or working on a assessment (in this case a chapter test).  

Thursday, October 12, 2017

Counterfeit Coin Puzzles -- What's the Real Value?

There is a great tradition of mathematicians sending each other puzzles with simple guidelines and potentially deep mathematical content. One category of these are the counterfeit coin problems.

The basic phrasing is given N coins, a simple double-pan balance, and the knowledge that one coin is counterfeit, how many weighings is the least that will be required to be guaranteed we can determine the identity of the bogus coin.

We began looking at a few simple cases:
--often in math it is useful to consider a simple cases and then build up to more complex ones, even if the ultimate goal is to solve the more complex problem. (In this problem it is very useful to know how many weighings it will take with 2, 3 and 4 coins if we want to analyze larger numbers because a situation often arises in the middle of solving for a larger number that results in needing to identify the coin from a remaining group of 3, 4 or 5 coins. 

Case of 3 coins -- how many weighings will it take?

This one is pretty straightforward and the kids all figured it out. I'll leave it as an exercise for the reader.

Case of 9 coins, one is heavier. How many?
(If you work through this note how useful it is to already know how to do 3 coins.)

The added restriction makes this problem a little simpler. Again, I will leave it to the reader.

What is the most than can be done in 2 weighings?

This is not a trivial question, though it can be solved exhaustively. 

Throughout these exercises I emphasized the importance of accurate data recording and the value of finding useful ways of displaying the data. For this type of problem we learned about branching (tree) diagrams and how to work back through or data to check the validity of each conclusion.

It is doubly important for the children to see math as not always an open and shut, algorithmic process. While this problem does have an algorithmic solution, developing that algorithm is as much art as an exhaustive search for every possibility. Through these kinds of exercises the students can come to see the value of trying out different tactics because sometimes what doesn't work for one situation actually informs the next step and leads to a process that does work. Interestingly, in class we also tried to figure out the maximum number of coins that could be done in three weighings, given that we didn't know if the bogus coin was lighter or heavier; I hadn't looked at the solution in a while and we tried to re-derive it in class, but failed to arrive at the correct answer. Sometimes, 55 minutes just isn't enough time to try out all the possibilities.

Thursday, October 5, 2017

10/2 - 10/5 -- Fractions, Negative Numbers, Story Problems and Isolating a Variable

Sam's 4-6th Math Class

Another shortened week meant that many of the kids didn't get to finish their sticky note. The kids should still try to have their Singapore assignments completed for Monday 10/9.
Following on last week's discussions about the Bar Model strategy, on Monday and Tuesday we talked about using the bar model strategy to solve problems with fractions. The bar model is particularly useful for fractions and ratios as they are easy to represent pictorially; if Hermione has 3/4 as many Bertie Bott's as Ron, the kids can generally figure out to draw 3 boxes for Hermione and 4 for Ron. It is relatively straightforward, though it does require paying significant attention to the exact wording, for the kids to take this drawing and figure out the answers to a variety of different questions like:
Q: If Ron has 20 more than Hermione, how many do they have all together.
A: Ron has one more box than Hermione, so each box is 20; there are seven boxes, so the kids have 140 candies.

Q: If Ron gives Hermione 5 candies, they will have the same amount. How many candies did Hermione start with.
A: Ron has one extra box, to make him and Hermione even he'd need to give her half a box,; so half a box is 5, which means a box is 10, therefore Hermione has 10 x 4 = 40 candies to start.
The algebra to solve these kinds of problems is further removed from tangible objects. For the above problems you start with something like H = (3/4)R, which isn't too bad, but it gets rapidly more complex -- can you figure out how to represent and solve the second example problem?
It's in these years (8-12) that kids start being able to handle increasing levels of abstraction, but the more it connects back to a concrete understanding of the world, the easier time they tend to have.

Pre-Algebra and Algebra

The 7/8s had four full math classes this week and as a group are making good progress on their missions in the textbooks.

This week I introduced a bit more Khan Academy, particularly for the Pre-Algebra group who all benefitted from some reviewing of concepts about negative numbers which hadn't been introduced on the Singapore series.

The Beginning Algebra group continues to work with linear equations; the hot new topic for this week was solving generic equations for a specified variable.

​From my past experience I have found that this is a difficult topic for many children and requires a strong ability to think abstractly.

An example of isolating a variable by "undistributing".

The Completing Algebra Group has been looking at complex story problems in one and two variables and technique using charts for working with specific types of problems, particularly distance-rate-time problems. Feel free to ask them about the train leaving Chicago and the other leaving New York.

Friday, September 29, 2017

9/25-9/29 Problem Solving w/ Bar Models, Integers, Graphs

Sam's 4-6th Math Class

With the 5/6s gone on Thursday and Friday the workload was a little smaller this week. The kids should still try to have their Singapore assignments completed for Monday 10/2. On Tuesday and Wednesday we learned about using the bar model strategy to solve problems with whole numbers, particularly problems involving the idea of consecutive multiples. It is important for the students to develop a way to represent these ideas graphically, as many of them are not developmentally ready to approach these problems abstractly using algebra.

For the problem, "The sum of three consecutive even numbers is 36. Find the greatest," the students would make a drawing akin to this:
We can then talk about the idea of maintaining equality by removing the same amount from the bars as from the total, such that this problem can be reduced to the three boxes being equal to 30, which then allows the student to figure out that one box is 10, and then carefully re-read the problem to figure out how to answer the question asked. 
We will continue to work with this technique for problems with percent, fractions, and ratios in coming weeks. 

If you'd like more background on the technique or the rationale take a look at these websites:

Pre-Algebra and Algebra

The blue and green groups both got some lessons on the need for orthopraxy [our unofficial vocab. word for the week] in the creation of coordinate graphs, which is a fancy way of saying I told them exactly how I want them to make their graphs every time. The key features of a coordinate graph are: clearly labelled origins and axes, consistent and clear numbering of the grid, and in my case I add the requirement that the axes are only labelled with arrowheads in the positive direction, which is a convention I learned to use in physics classes. 

The (Blue) Pre-algebra group completed chapter 1 in the text and had their first formal assessment (that's a traditional test in this case). The major topics covered in chapter 1 were variables, the order of operations, exponents, basic absolute value concepts and the coordinate plane.

Maddy uses the Algebra Tiles to
investigate inconsistent linear equations.
The (Green) completing Algebra group is digging into a chapter on systems of linear equations. We've talked about graphing and estimating solutions, using substitution and the elimination by linear combinations method. 

The (Red) beginning Algebra group is working on linear equations in one-variable which is partially a review from last year, but now we are adding in the additional complication of working with fractions and decimals. We spent most of Thursday talking about problems that are "weird", where the solution is that the problem is always or never true; things like 2x + 4 = 2x - 3.

Thursday, September 21, 2017

9/18-9/22 Fractions, Books, Khan Academy and Blackjack

Sam's 4-6th Math Class

This week has mostly focused on fractions. We've been practicing a technique using partially shaded arrays to represent fractions; two arrays (carefully constructed to be the correct sizes) can be overlapped to create a set of boxes, depending on how the shaded boxes are counted, the sum, difference and product of the fractions can be determined. 
Here is an example of a fraction graph that is incorrect. We used this example to check for student understanding of the process. 

How many mistakes can you find in the above problem?

After the discussion about what was wrong with the above grid we started to talk about how this technique often gives you an answer that is an unreduced fraction. We spent Wednesday examining what aspects of the problem determined whether or not this technique would produce a reduced or unreduced fraction, eventually arriving at the idea of whether or not the denominators shared any common factors or were relatively prime.

On Thursday with some faculty and students out for a holiday, our group met with Wendy's math class and played a variety of teacher selected board and card games that have some mathematical or logical component--Tsuro, Castle Panic, Forbidden Island, Poison, and Gimme the Brain!. 

Pre-algebra and Algebra:

This week the Pre-algebra class is working on completing chapter one in the text; they had a lecture covering the general topics--arithmetic with integers on the number line--on Monday, and had time to work and ask questions during the middle of the week. 
The Beginning Algebra Group finished up the activities with the lab gear, including thinking about like terms and some discussion of how to use the Lab Gear to factor polynomials, though that will mostly be covered later on. 
The group of students already in the middle of the Algebra curriculum spent the week reviewing for and then taking a traditional test on inequalities in one and two variable including with absolute value. 
On Friday, Ed Feng returned for his first visit of the year. Ed is continuing to focus on probability & statistics, and Python programming. This week the students have begun investigating the probabilities in Blackjack. More about Ed's experiences at SK can be found on his blog:

Friday, September 15, 2017

Week of 9/11 - 9/15

Sam's 4-6 Math Group:

This week the class was led by guest teachers on Monday and Tuesday. On Monday, Mary Perrin assisted the students in creating a tessellating tile from which the students are making a larger art piece. On Tuesday, Josh got the class started on their Singapore books, though a few students were still finishing assessments this week. On Wednesday, one small group of students had a lesson about using estimation to help with multiplication and division problems when decimals are involved, while the other kids had time to work. On Thursday, we reversed that, except instead of a lesson I met individually with each of the kids who had not had the lesson on Wednesday. Friday the class had time to finish up the tessellations and Singapore assignments, and then got to play math games if they finished.

Working on tessellating art.

Some of the finished Tessellated Art with the original cardboard tile.

7/8 Math:

After being at Tiller's International on Monday and Tuesday, the 7/8s fully split into their small groups for lessons on Wednesday and Thursday. 
The pre-algebra group is still getting used to working in the textbook and some of the introductory ideas and notation used; mostly we are working in chapter 1 in the text. 
The group just starting Algebra this year has been doing an enrichment about algorithms and exercises using the Algebra Tiles to solve single variable equations. They decided they needed negative versions of the blocks and we figured out that we could put black stripes on the side of a block to make it a "negative". They then derived the idea that a black block and a regular block of the same shape eliminated each other. Essentially, they were able to derive the inverse property of addition from working with the blocks. 
The other students have been learning or reviewing linear inequalities in one dimension with absolute value, and at the end of the week linear inequalities in two-variables.

Friday, September 8, 2017

Welcome to the 2017-2018 School Year

Hello Parents, Students, and Friends, 

Welcome back from the summer. For those of you who have followed this blog in past years, you may have noticed a title change. My role at Summers Knoll continues to evolve; this year I will be primarily focusing on teaching math. I will also be working with Rachel in the 7/8 homeroom. This blog will solely report on the activities of my math classes.

Week 1: 

Sam's 4-6th Math Group

This week on Tuesday and Wednesday our math group met with Wendy's group as we did some sorting out (some students are working on an assessment) and getting reacquainted. We began instruction with a number guessing game and then talked about factors and divisibility rules, using factor trees.

On Thursday we split off from Wendy's group and spent the time getting familiar with our space (upstairs) and some of the tools we will be using this year (rulers and protractors) and then began an investigation of tessellations and tilings that will lead to an art project that should be finished next week.

Oliver, Mark and Manon work to figure out which shapes can gaplessly tile the plane.

7/8 Math

The 7/8s are working on a couple of different things depending on what they were working on last year. The pre-algebra group is working with the order of operations, exponents and variables. The group starting algebra this year is doing an investigation of algorithms with the algebra tiles. The students who were well into, or done with, algebra had some time to get reacquainted and find their place in the textbooks and are now working on reviewing or learning about absolute value equations and inequalities in one variable.

Miel and Niko work through and algorithm with the Algebra Tiles.

Saturday, June 3, 2017

2017 Spring Trip Up North


With an on-time departure of approximately 7:55 AM this morning, Sam's class is off for our adventures Up North!

Mostly, Shan will be driving. I'll be available by email, text and phone. 

Next scheduled stop: The Mystery Spot

Getting introduced to the wonders of the Mystery Spot

Sophie is floating in midair?

What does 'level' mean anyway?

We concluded our day with a boat tour of the Soo Locks, dinner at the fine Pennies diner, and a round of putt putt in Sault Ste. Marie. (Apparently, the more tired I get the fewer photos I take, Shan took many of this part of the trip, I'll link to them once I've got them.)


After a rainy morning our day on Mackinac Island is looking a bit clearer. 

At the public boat dock on Liberty Mackinac Island

We're stopped for lunch midway through our carriage tour after looking at the butterfly house. 

Next stop Arch Rock and then on to Fort Mackinaw:

We returned to the mainland after completing our adventures on Mackinac Island and now, after an hour at the pool, we're getting ready for bed.

Notice the boxes of fudge


We had gorgeous weather all day as we made a loop through the Upper Peninsula.
The kids got to touch Lake Superior and skip rocks at Whitefish Point, before visiting the Great Lakes Shipwreck Museum. 

Whitefish Point

Our next stop was lunch in Paradise, a few kids even had a cheeseburger, but the star of the meal was the authentic pasties. We stopped at the upper and lower Falls in Tahquamenon, and then proceeded to Oswald's Bear Sanctuary. 

The Upper Falls at Tahquamenon

The Lower Falls

Baby bears are exceptionally cute.

We returned to Mackinac for dinner and are now taking a short rest before heading out for stargazing at the Headlands International Dark Sky Park. Stargazing was a big hit with the kids (once the clouds of Mayflies went to bed). We were able to see the four Galilean moons of Jupiter and, had a great view of the half moon of in the telescope Ore brought. It was pretty cold so we didn't stay out too long, but interest level was high so Ore suggested planning a night of stargazing closer to home. 


We've now said our goodbyes to Mackinaw and are headed to Petoskey to look for the eponymous stones on the beach before making out way back down state. Rock hunting in Petoskey was a bit hit, everyone found at least one Petoskey stone. There were also some other interesting finds. 

Is that a Petoskey Stone?

Locals told us that in season this beach is so picked over it's very difficult to find anything. Good thing we were there before the crowds.

After lunch in Grayling at the Bear's Den Pizzeria (the owner made a point of introducing himself and saying how well behaved the kids were) we cruised back home.

Friday, May 19, 2017

Mid-May Photos

Here are a bunch of photos from Late April and May:

Working on a math activity about area vs. volume

Another math activity, this time curious triangles

Showing off the Hubble telescope luminary.

A fish tank luminary at Morning Meeting

Juliana's fashion show, with Lucas as Erik the Red

Weeding and transplanting the milkweed bed

Analyzing rock samples with HCl

Digging out the bed for the Pollinator Garden/Monarch Way Station

Friday, March 24, 2017

Week 26 -- POOT Testimony and Projects

Sam's Homeroom:

This week we went further into the Place Out of Time trial. Looking further at the testimony of Tom Joad, each student wrote a reply to an initial comment made by some other member of the simulation. In this way, the kids are not only responding to testimony but also critiquing and furthering others responses, which requires a different type of thinking.

Separate from, but related to the simulation, each student was asked to brainstorm a few topics for a long-term project that somehow builds on their character's life and times. Each project will lead to the creation of some kind of artefact (that's educational jargon for a tangible, physical or digital product). So far the ideas for the projects run the gamut from designing clothing and putting on a fashion show, to investigating the impact of minor technical tweaks to the performance of an RC-car, to short graphic novel biographies, and more traditional slideshow presentations or formal reports. We will be working on these projects well into May, each week taking time to think about the next steps. 

 Above: Tomoe Gozen taming a horse.
Monday's Warm Up asked the students to draw their
POOT character doing something typical.
Below: Coco Chanel making a dress.

On Tuesday the whole middle school went to see the Ann Arbor Symphony perform several pieces of classical music at Hill Auditorium; the highlight was the loud booming bass drums at the beginning of selections from Stravinsky's Firebird Suite.

The class has been getting so good at completing the Perplexors (grid logic puzzles) that this week we moved on to a different kind of logic puzzle that involved thinking about missing letter combinations in words--a mini-spelling lesson in addition to a logic puzzle.

Sam's 5/6 Math

This week we spent some time reviewing concepts relating to percents, especially calculating discounts and markups with an emphasis on using a 10x10 grid to help us think about what quantity in each problem represented 100% and then figuring out what 1% would be so that other percents could be calculated more easily. (Singapore Math calls this the Unitary Method).
We also took a look at concepts surrounding averages: calculating the total (sum) based on an average, finding the value of one item from the average and information about the other items, recalculating the average of a subset when members of known value are removed from the group.

Friday, March 17, 2017

Week 25 -- Origami, π, the Legal System

Sam's Homeroom:

This week we've been getting into the meat of the Place Out of Time simulation. As the trial phase begins, we spent some time going over various legal terms (plaintiff, defendant, testimony, magistrate, objections, evidence, hearsay, etc.) and looking at and responding to the opening arguments from the plaintiff and defense attorneys. 

On Wednesday the first witness, Tom Joad from the Grapes of Wrath, was called by the defense. We spent a lot of time discussing: the basic legal framework, the content of the opening arguments, and the testimony of Mr. Joad (including a sidetrack into the history of the dustbowl, US labor relations and 1930s era socialism), so that the students were all clear on what was being said, argued, and meant. They were all asked to respond, in character, to open of the opening arguments.  

To further their engagement with the topic, we did our first round of "Take a Stand" this year; an activity where, in or out of character, the students are asked to take a position ranging from strongly agree (standing by the window of the classroom) to strongly disagree (standing by the door) in response to a prompt. This time we did it in character and talked about two prompts about the role of the individual and society in creating and maintaining wealth inequality. Unsurprisingly, Al Capone and Erik the Red had a very different perspective than St. Nicholas of Myra or Pierre Trudeau. I've found this activity a great way to encourage the children to think about how to respond to topics that might show up in their research of their character. 

[As an aside, this week's logic puzzle, has a poorly worded clue that was, to my reading, missing a colon. This lead to a good conversation about the importance of accurate punctuation, and for those who were ready to think about, an introduction into the proper use of a colon for lists.] 

Jarod and Folu argued that video games should be considered a sport.
This weeks Scholastic News asked the children to take a position on whether or not video games should be considered sports (E-sports). Thursday afternoon, we had a lively discussion about their opinions based on what they'd written.

Working on a luminary for the Fool Moon parade.
Sam's Math

This week has us spinning around in circles and folding ourselves up. Monday, we continued to look at Origami, this time working on actually folding cranes, dragon heads or cups -- which was an interesting exercise in following directions. The rest of the week was spent in a celebration of Pi-day, looking at some of the basic concepts about circles: circumference, radius, diameter and area, which required the introduction of the concepts of irrational numbers and square roots. 
On Tuesday, we had a special guest lecturer, our very own sixth grader, Jarod Meakins, who presented the basic formulas and did some examples with the class. On Thursday, we measured real-world circles and talked about the difference between abstract and potentially perfect ideas, versus the inexactitude of measurement in reality.
Friday was the big celebration of Pi-Day, complete with Pie!