Welcome Back to School

CLASSROOM GUIDELINES

Mrs. McDermott                 Ontario Middle School

Welcome!  In order to guarantee all the students in my classroom the excellent learning climate they deserve, I will tolerate no student stopping another from learning or stopping me from teaching.  I have developed the following set of expectations to help assure this learning environment.

CLASS EXPECTATIONS

1.       Follow all directions the first time they are given.

2.       Come prepared for class each day ready to learn.  Bring:

a.       Paper and pencil/pen

b.       Composition notebook math journal

c.        Your homework assignment

d.       Scientific calculator

e.       Assignment book

f.         Please leave coats and book bags in your locker.

3.       Use common courtesy.  Treat others with consideration and respect.

4.       Be on time for class.  This means being in your seat with materials ready when the bell rings.

THE ONTARIO WAY:

All students at Ontario Middle School are expected to live by three simple, school-wide expectations.  You will find that all the classroom expectations listed above fall under one of these all-encompassing guidelines.  Here are the three guidelines that should guide all of your choices concerning your behavior and actions here at school:

·         BE SAFE

·         BE RESPONSIBLE

·         BE RESPECTFUL

SOME OTHER VERY IMPORTANT ITEMS

                Here are some other policies and routines you will find it helpful to know.

·         Late work is accepted but there is a fine and a deduction of the score. It is critically important that you turn in every assignment each six weeks. Set this as a personal goal for yourself. The option to “redo” is available. 

·         Assignments for my classes will be in my daily assignment book on the counter by our classroom door.  When assignments are given I will write on the homework board what the assignment is and when it is due.  If you are absent, this board should be the first thing you check upon your return to school.  Write down all the assignments you missed in your assignment book and make sure you get copies of any handouts you need.  Extra copies of all handouts will be placed in the bin on the counter by the door. Help yourself to these extra copies as needed, but please don’t make a mess.

·         All of your teachers here at Ontario Middle School will expect you to keep your assignment book up-to-date at all times. 

REQUIRED MATERIALS

·         Three-ring binder with subject pockets or dividers (general use for all your classes.)

·         Notebook paper, white with 3 holes. (for general use)

·         Pencils and pens

·         A scientific calculator (A must for survival in middle school algebra and geometry instruction!)

GRADING POLICY

Mrs. McDermott                            Ontario Middle School

In an effort to provide immediate and meaningful feedback to both you as a student as to myself as a teacher, I have developed the following grading policies. 

The work for this course will consist of a variety of text assignments, in-class activities, problem solving and applied math projects.  Homework will be minimal for this class. I am available every Tuesday-Thursday after-school until 3:15 to help students with their homework for their main math class.

PROBLEM SOLVING ASSIGNMENTS

Learning the fundamental procedures and facts of math is meaningless unless you can apply those skills to solve meaningful problems.  Problem solving will be a major focus of our year together.  I will help you organize some basic problem solving strategies into a framework you can apply to any problem you encounter. 
 

Problem solving assignments will generally take more time than text assignments and will be worth 25 points each.  Scores will be given based on the 5-part scoring guide developed by the Oregon Department of Education.  It will measure conceptual understanding, processes and strategies, verification, communication and accuracy.  You will become very familiar with this scoring guide and it will become an integral part of your problem solving repertoire.

YOUR FINAL GRADE: Compliance with House Bill 2220 requires a change in grading procedures at Ontario Middle School.  A student’s grade will be comprised of ONLY THE ASSESSED PROFICIENCY OF THE ACQUIRED KNOWLEDGE OF THE ACADEMIC CONTENT STANDARDS.  This means only the marks for assessments will be factored into a student’s grade – not practice work, extra credit, participation, etc.  There will be a separate “student responsibility” grade that will reflect their performance in the areas of practice, participation, timeliness, etc.  At this time, the assessment portion of the grade will be weighted 100% and the “student responsibility” portion will be weighted at 0%.  However, this new law is still being interpreted and it is possible there may be some variation in the weights later in the year.  OMS will alert parents of any changes. 

Then your points will be compared to the following scale:

            90% = A

            80% = B

            70% = C

            60% = D

            59% and below = F

CHECKING YOUR GRADE

You are expected to check regularly on your progress in this class.  I will keep grades current on SchoolMaster and they can be checked from home via the HomeAccess system.  You will be provided with a username and password at the beginning of the year. DO NOT LOSE IT!  It is YOUR RESPONSIBILITY to know how you are doing in your classes. This is a critical skill for success in high school. Additionally, your assignments will be posted on e-school daily. We have a class blogspot where we can ask/ answer questions:   mcdermottmath.blogspot.com

Your text book and other resources are on-line at www.corefocusonmath.com .

Username: ontario

Password: ontario1995

The Art of Gift Wrapping: Solving Equations by Danica McKellar

I wonder if the holidays leave dogs rather perplexed. They watch us do things like hide painted eggs in the yard in the springtime, watch fireworks in July, stick candles in food only to light them and blow them out, dress up in costumes in October, and bring a tree inside to decorate. (They totally get Thanksgiving though).

As if this weren't confusing enough, Sparky watches us bring presents home and wrap them up, only to unwrap them again, save some of the silky ribbons and sparkly bows, and do it all over again at the next event. What's with the wrapping and unwrapping? I'm guessing he'd just as soon get the toy and be done with it.

If you're like me, shiny wrapping paper and bows are one of the best parts of holidays. What is another benefit of wrapping and unwrapping presents? It makes understanding inverse operations so much easier.

What's It Called?
Inverse Operations

Inverse operations are operations that undo each other. For example: opening a box and closing a box are inverse operations. They undo each other. Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.

Below is a list of operations and the operations that undo them; in other words, their inverse operations!

Operation How to Undo It (its inverse operation)
Addition   .....  Subtraction
Subtraction ....  Addition
Multiplication  ......  Division
Division ......  Multiplication
Squaring ....... Taking the Square Root
Taking the Square Root........Squaring

So if we start with the plain ol' x and we add 2, we get x+2. Undoing that action would mean subtract 2, right? That looks like this: x+2 -2 = x. We end up where we started, because we undid adding of 2.

How about if we start with x and multiply it by 3? So we'd do x--> 3x. To undo that action and get back to where we started, we'd divide by 3, right? So, 3x --> 3x = x. Obviously, this
                                                                                                                            3
works for numbers too. If we start with 5 and multiply it by 3, we get 5(3)=15. Then, to undo what we've just done, we divide 15 by 3, and we're right back to where we started.
15 = 5.
3

Gift Wrapping 101

We've talked about undoing single operations so far; it's just a one-step "undoing" process. The process of undoing more than one step (like in sovling equations) is just like unwrapping a gift.....or taking off boots!

Let's say you put on some ankle socks and then some cute boots. To undo this, you'd have to first take off the boots and then take of your ankle socks, obviously. So if you did A and then did B, to UNDO what you've done, first you'd undo B and then you'd undo A. Makes sense, right? Now let's see how it works when there are three steps.

If you wanted to wrap a beautiful pink sweater for your sister, first you'd put it in a box. Then you'd wrap the box in wrapping paper, and then you'd stick a sparkly bow on it. When your sister unwraps it, she would do the inverse of each action you did, in the reverse order.

Wrapping: Unwrapping:

1. put in box 1. unstick sparkly bow

2. wrap with paper 2. unwrap paper

3. stick on sparkly bow 3. take out of box

See how the first thing she does to unwrap the gift undoes the last thing you did when you wrapped it? And how the last she did to unwrap it undoes the first thing you did to wrap it?

And believe it or not, when we isolate x by undoing a series of operations, it works just the same way!

Isolating X

Let's take a look at this: 2(x + 3) - 8. How did this come to be?

Once upon a time, x was all by himself. Then someone wrapped him up! Here's what happened to him: First, 3 was added to him: x +3. Then the whole thing was multiplied by 2, and here's how he looked at that point: 2(x +3). THEN, 8 was subtracted from this whole thing, so this is how he looks now: 2(x +3) - 8.

He can hardly recognize himself. Let's get him out of there! In order to unwrap x, first we'd need to add 8, and we'd get 2(x +3). Then we could divide the whole thing by 2 and get x +3. And then, subtractiong 3, we'd finally get x back to his normal self again, totally unwrapped. NICE.

See how isolating x has more to do with the holidays than you might have thought?

Watch OUT!

Notice how I keep saying "the whole thing was multiplied by 2" or "then we subtract 8 from the whole thing." When we're wrapping x or unwrapping x, it's important that we always "do" things to the entire expression, not just one part of the expression. So if we had 2x +1 and we wanted to wrap it up more by dividing by 2, we could NOT just divide the 2x by 2; we'd have to divide the whole thing by 2:


2x + 1.

    2

This is because soon we'll be using these techniques to solve for x, and when you do things to both sides of the equation, you need to do things to each entire side of the equation in order to keep the scales balanced.

Quick Note: I keep saying x, but of course this works for any variable you want to isolate: a, b, c, n, w, x, y, z, :) , etc.

Doing the Math
I'll describe the steps that were used to build an expression, starting with x (or some other variable). Your job is to actually build it! Remember at each step to do "things" to the entire expression. Then, list the unwrapping steps. I'll do the first one for you.


1. Start with y. Divide by 8, then subtract 4, and then multiply by 3.


Working out the solution: Okay, we start with y, and we divide by 8. That can be written like this y, right?
                               8   
Next, we're supposed to subtract 4. Remember this would be wrong
y-4 .
8


We have to subtract 4 from the whole thing, so we would have to write: y/8 - 4 .



So far, so good? BTW, you would build y-4 by first subtracting 4 from y and then dividing by 8.                                                   8


Do you see the difference?


Now we're ready for the next instruction: "Multiply by 3." We know we must multiply the whole thing by 3, so that means 3(y/8 -4). Okay, we're done with that part! The unwrapping steps would be the inverse of the instructions we got, just like unwrapping a gift: divide by 3, add 4, and multiply by 8. Done!


Answer: 3(y/8 -4). And to unwrap it, we'd first divide by 3, then add 4, and then multiply by 8.


2. Start with x. Add 3, and then multiply by 4.


3. Start with y. Multiply by 4, and then add 3.


4. Start with z. Add 3, and then divide by 4.


5. Start with w. Divide by 3, then subtract 1, and then multiply by 5.


6. Start with n. Multiply by 6, then subtract 5, and then divide by 7.


Answers coming soon.


Solving for x
Now let's apply our unwrapping knowledge to solving for x. Before we do, let's review what it means to solve equations. Remember, when you get an equation to solve like 5(2x+1)-6=29, you're being asked to find out what number x has to be in order for the equation to indeed be a true statement. That's our job-to discover x's value! Sure, we could just stick a bunch of values in until one of them works, but x is often a fraction. Are you really going to guess every fraction you can think of too? There's got to be a better way to find out x's value, and there is!

After-school math programs

Mrs. McDermott is available after-school to help with math. She plans to make this worth your time (tiger tickets and extra credit).

Rational (sensible) Numbers: let's be rational about this!

Estimating Rational Numbers' Sums and Differences:

Remember to round to the nearest whole number (or integer) when working with estimates of rational numbers UNLESS the numbers are between -1 and 1. Then, estimate to nearest -1, -1/2, 0, 1/2, or 1. It is worth the effort to form an estimate when working with rational number operations so that the answer can be checked for reasonableness.

Reminder: before and after school tutoring

Our classroom doors are open from 7am- 430 pm. There may be days I have meetings before or after school. Regardless, students are welcome to stay during these meetings and I will assist as much as possible.

Equivalent Fractions, Improper Fractions, and Mixed Numbers

Worksheets (lessons one and two) examining equivalent and improper fractions and mixed numbers are assigned for homework if not finished in class.

The mental math multiplication exercise on the back of lesson two is extra credit. The best way to learn is to teach. Try to find someone at home to teach the commutative property of multiplication (move the factors around to find the product). See if you both would 'take the same commute.'

See you after school for open house tonight.