The students new to Algebra finished reviewing chapter one and then took a longer look at function notation, and the concepts of functions, relations and mappings. The Geometry class showed the couple of students returning to Algebra the basics of formal proofs using solving single variable equations and the properties of arithmetic as their givens and reasons.

# Middle School Math @ Summers Knoll

Workings, doings, viewings and talk from Sam Hirschman's middle school math classes.

## Friday, October 5, 2018

### September 28, 2018 -- Coordinate Planes, Functions and Proofs

This week the Pre-Algebra group focused on vocabulary and concepts relating to the (XY) Coordinate Plane. We made and labelled a set of axes and then physically moved around the plane to reinforce the difference between x and y and horizontal and vertical.

The students new to Algebra finished reviewing chapter one and then took a longer look at function notation, and the concepts of functions, relations and mappings. The Geometry class showed the couple of students returning to Algebra the basics of formal proofs using solving single variable equations and the properties of arithmetic as their givens and reasons.

The students new to Algebra finished reviewing chapter one and then took a longer look at function notation, and the concepts of functions, relations and mappings. The Geometry class showed the couple of students returning to Algebra the basics of formal proofs using solving single variable equations and the properties of arithmetic as their givens and reasons.

### October 5, 2018 -- Chapter Tests, Properties,

This week most of the Pre-Algebra students began (and many completed) the chapter one assessment from the textbook. While the chapter assessments in form look like a traditional test--they are literally photocopies from the “tests” manual that comes with the teacher material for the text--we do a lot in class to make the experience more useful and less anxiety provoking than some find the traditional model. After completing the assessment at their own pace, students meet with me individually to review, not correct and wrong answers (though I do make note of those), but rather to discuss what major concepts might need further review and how that is going to be achieved. From this assessment I determined that the whole class needed to go back and look more closely at vocabulary and concepts of mean, median and mode, which we will work on next week.

In the Algebra group the students are working with expressions and equations in some form or another; the students starting algebra are working on basic arithmetic properties--particularly the distributive property; while the returning students are working on solving linear equations in one variable including with fractions and decimals which is new this year.

The Geometry class is doing elementary exercises in formal logic; making truth tables, discussing Boolean operators, tautologies, and proofs using formal symbolic logic.

## Thursday, September 20, 2018

### September 21, 2018 -- Integers and Words to Symbols

This week the Pre-Algebra/ Singapore class continued their work with integers, using the Algebra Tiles to model addition, subtraction, multiplication, and a little bit of division. Manipulatives are more commonly employed with younger students however, in this case, the tangibility of the algebra tiles allows for more concrete representations of opposites, reflections, and commutativity (our unofficial word of the week).

The Algebra class worked on making connections between words, verbal models, and algebraic representations--first words like sum, difference then onto more complex statements like “the sum of three consecutive even integers”.

The Geometry Group looked over the basic notation used to describe points, lines, angles and planes and began to dig more deeply into formal proofs.

The Algebra class worked on making connections between words, verbal models, and algebraic representations--first words like sum, difference then onto more complex statements like “the sum of three consecutive even integers”.

The Geometry Group looked over the basic notation used to describe points, lines, angles and planes and began to dig more deeply into formal proofs.

### Getting into the Swing of Things

September 14, 2018

Math is now in full swing for all of the students. Most students received a textbook this week.

The book is theirs to keep, and I encourage, and in fact have already required, them to write

in their books. (A few of the sixth graders are still finishing up Singapore books from last year;

they will move on to Pre-Algebra when they finish.)

The book is theirs to keep, and I encourage, and in fact have already required, them to write

in their books. (A few of the sixth graders are still finishing up Singapore books from last year;

they will move on to Pre-Algebra when they finish.)

For the Algebra, Pre-Algebra and Geometry Students a list of suggested assignments homework

assignments (by section in the books) has been shared with them and will be with parents after

curriculum night next week. For all of the students, math will be increasingly (eventually wholly)

self paced; for the first chapter with the Pre-Algebra class, I will lead them in a more traditional

framework as they get used to working in the new book and on new concepts.

assignments (by section in the books) has been shared with them and will be with parents after

curriculum night next week. For all of the students, math will be increasingly (eventually wholly)

self paced; for the first chapter with the Pre-Algebra class, I will lead them in a more traditional

framework as they get used to working in the new book and on new concepts.

In non-book math, the Algebra class has spent much of the time looking at Taxicab Geometry specifically,

if you know that you are a specified distance from an unknown point, how many guesses

will it take to determine the point. What is the best strategy for making the guesses and

what is the maximum number of guesses required to locate the point.

if you know that you are a specified distance from an unknown point, how many guesses

will it take to determine the point. What is the best strategy for making the guesses and

what is the maximum number of guesses required to locate the point.

The Pre-Algebra class has been learning about arithmetic with negative integers on the number line.

Addition is modelled as motion to the right, subtraction motion to the left, and a negative sign as a

U turn.

With this approach students can visually see the “two negatives cancel out” rule and begin to develop

a better understanding of the mathematical idea of inverses. Multiplication is modelled as scaling and

duplicating rather than motion.

Addition is modelled as motion to the right, subtraction motion to the left, and a negative sign as a

U turn.

With this approach students can visually see the “two negatives cancel out” rule and begin to develop

a better understanding of the mathematical idea of inverses. Multiplication is modelled as scaling and

duplicating rather than motion.

## Thursday, September 6, 2018

### Welcome to the 2018-2019 School Year

Welcome!

You'll find weekly updates about middle school math classes here.

For information about 7/8 Homeroom and Projects look at the 7/8 blog I share with Rachel.

General Overview:

You'll find weekly updates about middle school math classes here.

For information about 7/8 Homeroom and Projects look at the 7/8 blog I share with Rachel.

General Overview:

Class Times and Groups:

As in past years, I will be working directly with all of the 7-8 students in math. However, this year, our classes will also include some fifth and sixth grade students who are working on the same material. Every student will have math class for 50 minutes each morning. The students are split up based on on there progress in the pre-algebra/algebra/geometry sequence, with all the students working on pre-algebra content on one group and the remaining students in the other group.

Textbooks and Content:

We will be continuing to use the same books we’ve been using for the last several years, McDougall-Littell’s Pre-Algebra, Algebra: Concepts and Skills, and Jurgensen Geometry.

Homework:

This year, I am asking that students work on their core (textbook) math at home at least three times per week. This is a guideline, not a strict requirement, and the exact amount will vary depending on prior familiarity/comfort of the individual with the specific content and the amount of math content that is part of the current project.

A document called “<Algebra/Pre-algebra/Geometry> Suggested Assignments” will be shared with students and parents. This document has the book/Khan Academy assignments broken down into discrete chunks roughly corresponding to one section in the text. The exact problems to be completed are suggestions; if a topic is truly review, or if something is especially difficult, a student may end up glossing over some of the problems, or choosing/being asked to complete more of a specific type.

**Checking the Answers and Homework Feedback:**

I will not be collecting and correcting book assignments. Students will have an opportunity to ask for assistance about specific concepts or problems during whole group or one-on-one sessions. The majority of the suggested problems have answers in the back of the textbook and students are expected to make an attempt and check their own answers before deciding to move on from a topic or asking for help. Students should endeavor to complete three to five sections (a row in the assignments document) per week, expecting to do one to two in school and two or three at home.

Assessments: (Quizzes, Tests, and Other)

The goal is always comprehension of concepts and mastery of skills. To that end, assessments are not solely summative checklists, but also used throughout the course of study to refine and direct the next steps in the learning process.

End of Unit:

At the end of each unit (usually one chapter in the text), students will complete a formal assessment (test). These end of unit assessments are untimed and may be worked on outside of school. These are meant to identify any areas that need further instruction before moving on to new content. Frequently, after completing an assessment, a student will be asked to review a specific topic in greater depth using any of a variety of handouts, online programs, or direct conversation/instruction from me. The goal, again, is always comprehension of concepts and mastery of skills.

Snapshot/”Pop” Quiz:

Every so often students will be asked to complete a short, timed assessment during class. These assessments are meant as a snapshot of current progress/status and as an opportunity for students to gain familiarity working on traditional assessments in a relatively low stakes setting (with an eye toward high school preparedness).

## Saturday, June 16, 2018

### June and Graduation

Last Week and Graduation

There were no formal math classes the last week of school.

The 7/8s were prepping for graduation and the 4/6s were finishing up projects in homeroom.

My speech for the graduating class is below:

I’ve tried out 9 ways to speak about these nine graduates and continue to have trouble. They are nine individual who make a coherent whole, with interests both wide and overlapping.

What else comes in nines? Analogies are always a great way to write these speeches how about that:

Nine Justices of the Supreme Court, nah, who wouldn’t want to be RBG, but then what; nine planets of the solar system, orbiting the bright center that is SK--the astronomers tanked that one a few years ago; Muses? I simply can’t force Melpomene (tragedy) on any of these delightful children. Baseball players? Naw, all of these kids are way out in left field, but Then it came to me: 9 rings for the kings of men! No, while I had someone in mind for the Witch King, I’m not sure who else is ready for a life of service to Sauron.

When analogies fail it must be because there is something incomparable about the group. So, I decided to trust myself like I trust these children. I’ve been with some of these kids since my first days at SK, and I’ve watched them all grow from brash, timid, and eager children into assertive, confident and excited adolescents.

This class means a lot to me: they are the second (and final) class of Samurai. They have been with me in faery camp, through magic shows and Magic cards, disconcerting bus rides, a trip to Mars, forced marches for cheesesteaks, short circuits (really don’t plug the thermistor in backwards), and all sorts of adventures with fruit. We’ve faced down zombified creepers and told more puns than I can remember (from me and them),

And so, I as I literally have my back turned to you all today; know that it is not because I’m ignoring or forgetting you--that will be impossible, but because I know you’ve got my back.

## Thursday, May 31, 2018

### Week of May 24

**Week of May 24**

__4-6 Math Class__We used this week to finish up assignments and activities that were started during my leave. We spent Tuesday and Wednesday digging more deeply into the abstract algebra and group theory assignments the class worked on during my leave. Specifically, we looked at a more complex group with two cyclical elements with different periods. (The rules were: YYY can be deleted, ZZ can be deleted and Y ⇔ ZYZ; the operation was “multiplication”.) The operation table for that group is in the center of the photo below:

After discussing the idea that sometimes to simplify a statement you needed to make it more complex first (a key step in developing the table for the above problem), we moved on to the simplest finite group I am familiar with using numbers: (-1, 0, 1) on multiplication. The students were able to identify the identity element, the inverse (or lack thereof) for each element and conclude that the situation was a group; they were also able to explain why these numbers would not be a group under addition, division, or subtraction because of a lack of closure. We finished out our look at groups thinking about a few infinite groups: even and odd numbers under multiplication and/or addition. Including discussing why odd numbers was a group under multiplication but not addition.

**(The 7/8s are on their Spring Trip this week.)**

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