Multiplying & Dividing Integers

The rules for multiplying and dividing integers are the same because multiplication and division are inverse operations.  The rules are fairly straightforward and are a bit easier than the rules for adding and subtracting integers.

When multiplying or dividing integers of the same sign, the answer is always positive.

When multiplying or dividing integers of different signs, the answer is always negative.


Even though the rules are mentioned above it is important to understand why those rules work.  In class you took some notes and saw a presentation on this using a chip model.  This boys in the video below do a nice job of showing you why the rules work.  They're a little loud, but they get the point across. LOL

This video show you how the rules work by looking for patterns.  What do you notice when he is finished?  Do the results look similar to the coordinate graph to you?

Adding & Subtracting Integers

In class we looked at various models to understand what happens when we add and subtract integers.  Some of us prefer to use a number line while others understand better using chips and zero pairs.

Remember:  Memorizing a rule will only get you so far.  You want to be able to understand why the rule works and came into existence. Understanding helps you develop the reasoning skills to solve novel problems.


This video demonstrates adding integers.  When you are adding integers of the same sign the sum has the sign of the two addends. For example, (-3) + (-7) = (-10)  When adding integers of different signs, take the absolute value of both numbers and subtract.  The sign of the sum is the sign of the larger absolute value.  Another way to think about it is to think about whether you had more negatives or positives in your problem.  For example, 5 + (-17) = (-12).  I have subtracted 5 from 17 (using absolute value).  I notice that there are 17 negatives and only 5 positives so the sum must be negative.




Here's a nice video to help you understand why it is necessary to add the opposite integer when you see subtraction problems.

Transformations on the Coordinate Grid

We have discussed three basic transformations on the coordinate grid.

• Translation - (slide) every point moves the same distance in the same direction.  To translate points of a figure simply add the number of spaces moved horizontally to the x value and the number of spaces moved vertically to the y value.
• Reflection - (flip) figures can be flipped horizontally or vertically at any point or can be flipped across an axis.  If you reflect figure across the x axis, change the y values in each point to their opposite to create reflected points.
• Rotation - (turn) the figure is turned around a single point.  You describe the rotation in degrees either counter-clockwise or clockwise

Use this site to develop your understanding of transformations.  Their are different levels you can choose as you get more comfortable with the concepts.

Key Transformations on the Coordinate Graph

Online Plotting Practice and Games

Use the following sites to practice your plotting.

http://www.mathsisfun.com/data/cartesian-coordinates-interactive.html

Find the Aliens

http://www.mathplayground.com/locate_aliens.html

Looking for the Top Quark (similar to Battleship)

http://education.jlab.org/topquarkgame/index.html

The Coordinate Graph

Vocabulary to know:

• Ordered Pair or Coordinate - this is a point on the coordinate graph designated by a value of  x (horizontal) and a value of y (vertical).  They are always ordered alphabetically (x,y)
• Quadrant - one of four sections on the coordinate plane created by the intersection of the x and y axis.  Quadrant I is the section where both the x and y are positive.  We go counter clockwise to name the remaining three quadrants.
• Origin - (0,0) on the coordinate graph.  This is the point where the x axis crosses the y axis.
• x-axis - horizontal number line
• y- axis - vertical number line

image from www.math.com

New Jobs Are Here! (Period 1& 2)

Job List Marking Period 2 Period 1_2 2011-2012

New Jobs Are Here! (Period 5& 6)

Job List Marking Period 2 Period 5_6 2011-2012

New Jobs Are Here! (Period 8& 9)

Job List Marking Period 2 Period 8_9 2011-2012

Finding Percentages for Data on a Table

Here is a question that is similar to one you will see on future assessments.  The key to these types of questions is determining the whole.  You need to determine the total to find the percentage of the part.  For example, to complete number 1 below, you need to add the number of boys (85) and the number of girls (65) to determine the total number of people who prefer tacos.  To find the percentage of boys who like tacos create the fraction 85/150, then convert to a decimal to easily convert to a percent.  I would recommending reducing the fraction first to 17/30 to make the division easier when converting the fraction to a decimal.

Benchmarks

Remember in class I mentioned that it is really helpful to have a few fractions and decimal equivalents memorized.  Having a handful of these memorized will help you with your fluency to convert among the various forms of a number.

Take a look at the following tables.  Look for patterns.  You might notice that you don't have to memorize the whole table but only one fraction for a given denominator.  For example, if you know that every eighth is equal to 0.125, you can determine 3/8 by adding 0.125 to itself three times.

Notice that the ninths are missing from both tables.  Just remember that the numerator is the decimal repeated.  So 4/9 is equal to .4444...

Halloween Service Activity

Hi Ladies & Ghouls!

Don't forgot to bring your donations for our Halloween treat bags for the Homefront organization.  We're putting these bags together on Halloween morning before our field trip.  The goodie bags will be delivered to Homefront for families who have been left homeless. Thanks in advance for your generosity and remembering those that are less fortunate than us.

Happy Halloween!

Study Guide

Hi Everyone,
This week we should be taking our unit test for Prime Time.  Periods 1,2,8,9 will be testing Wednesday, October 5th and Period 5,6 will most likely be testing Friday, October 7th.  Below are a list of problems from ACE pages, Additional Practice Sheets, and Skills sheets that you can find in Prime Time on the math website.  These problems are hand picked to target specific skills and types of problems you'll encounter on the test.

• ACE Investigation 1 Problems #32, 34
• ACE Investigation 2 Problems #16, 23, 33
• ACE Investigation 3 Problems #1-9, 14, 27, 30, 36, 37
• ACE Investigation 4 Problems #4-12, 14, 19-26, 31
• Additional Practice Investigation 3 #1, 3
• Skills Investigation 3 #7
• Skills Investigation 4 - All

You may not want to limit yourself to only these problems.  It may be helpful to practice the other problems not mentioned to deepen your understanding.  Remember the answers are also supplied on the site to check your work.

A LCM Challenge...LCM of more than two numbers.

Finding the LCM for three or more numbers is a bit more complicated.  Still, find the GCF first.

Now look at the image below. 

Previously, we just multiplied the GCF by the rest of the prime factors listed.  However, in this case I only multiplied by 5 one time even though the prime 5 is list more than once (see first image).  Can you guess why this is?  Reply to this post!

Remember These Guest Stars?

Review

Here's some important review.  You'll see problems like these on quizzes and tests.

U-Turn

Hi Guys, Remember this from class?  We talked about why this method is useful and how it keeps us organized, but one of the great things about this method is that if you are stuck or can't think of a factor pair quickly, you can skip it and come back later using the other factors you found as clues.

Here's the screencast.

Prime Time Vocabulary

Hi Guys!  I've noticed some of us are still having trouble remembering the difference between factors and multiples.  I made a screencast of key vocabulary words in the unit.  It is no longer than five minutes.  I hope it helps.

Inaugural Blog Post!

Hi Everyone,

Welcome to the first blog post for the 2011-2012 school year.  I will attempt to post at least once a week to with all the items we have discussed in class.  Please comment on any and all posts.  You may ask questions, respond to your classmates questions, or simply add to the discussion.  When commenting be mindful of your tone, often sarcasm does not translate through our writing.  It is also important that we be as professional as possible even though we are in a digital format.  It is my expectation that you will make an effort to proofread, edit, and use correct grammar before you publish your post.  Also, be sure not to add any identifying comments to your posts including your full name, address, email address, or photos.  I'm looking forward to hearing from you!  More to come.  In the meantime, enjoy one of my favorite panels of my favorite comic strip.