Unit 5

Solve inequalities

Graph inequalities on a number line

Slope-intercept form

• Identify slope and y intercept
• Graph an equation written in this form
• Find the x intercept by filling in 0 for y

Graph equations

Find intercepts

Writing the equation of a line from 2 points

• Use the slope formula to find the slope of two points
• Fill in the slope and one point to find b
• Write the equation of the line in slope-intercept form

Decide if a graph is a function or not

Unit 6

Percent of a number

Probability

Fill out a baseball Player Analysis Sheet

Notes

Okay guys, honest confession.  I taught this lesson all wrong…which is why you were so confused.  If you look at this, please still try to do your homework but because I messed up I won’t be putting probability of dependent events on the final.  Remember when, at the beginning of the year, I told you it was okay to make mistakes and that I would make plenty of them this year, this is one of those times.  I’m sorry I confused you.

To find probability of dependent events you will multiply fractions/ratios similar to how you did with probability of independent events.  The difference is that you assume the first event happens.  Like I told you in class the denominator of the fraction will go down because there is one less item.  The thing that I told you wrong is that if you are picking two of the same thing in a row then that number will go down two.  You assume the first event happens so there is one less of the event as well as one less of the total possible events.

For example:  You have 3 pennies, 5 nickles, 8 quarters and 4 dimes.

(like what I taught you)  Find P(penny and then a nickel)   3/20 * 5/19

(unlike what I taught you) Find P(2 pennies)  3/20 * 2/19  The only thing that is different about this is that no only the 20 went down to 19 but the 3 went down to 2 because we assume that one penny is missing.

Other Examples

From Learning Wave

From Online Math Learning – lots of examples

Video Explanation

Homework

HW4 – Probability of Dependent Events

Notes

Probability – the chance of an event occurring.

Probability problems are written P(…)  The P stands for probability and inside the parentheses is what you a looking for.

Probability is written as a fraction.

Theoretical Probability is what you expect to happen.  Experimental Probability is what actually happens in an experiment.

For example…  If you have a normal deck of cards – hearts/clubs/spades/clovers – ace through 10, jack, queen and king in each suit – what is the probability that you will choose:

P(heart) = 13/52 = 1/4

P(9) = 4/52 = 1/13            There is a 9 in each suit so there are 4 in all.

P(face card) = 12/52 = 3/13            There are 3 face cards in each suit, 12 in all.

P(not even number) = 32/52 = 8/13            There are 8 cards in each suit that are NOT even, 32 in all.

Probability of 2 Independent Events also known as Mutually Exclusive Events

this is for when you are finding the probability of 2 or more events occuring and the outcome of the first event does NOT influence the outcome of the second event

P(A and B) = P(A) * P(B)

All you do is multiply the probabilities of each independent event

Using the above example, if a card is drawn at random, REPLACED, and then another card is drawn – what is the probability you will choose:  (we will learn in lesson 4 what happens if you do not replace the card)

P(heart and diamond) =

P(heart) = 1/4 and P(diamond) = 1/4

1/4 * 1/4 = 1/16

P(9 and face card) =

P(9) = 1/13 and P(face card) = 3/13

1/13 * 3/13 = 3/169

Other Explanations

Pre Algebra book – Single events, page 310 and Mutually Exclusive Events, page 650

From MathGoodies.com, explanation and practice problems – http://www.mathgoodies.com/lessons/vol6/independent_events.html

Homework

HW3 – Probability

Baseball Grading Rubric (you will be given this in class)

For Monday

Bring everything you have been given that has to do with baseball.  Bring anything you printed or wrote down about your players.  Bring it all.  Do not forget it.  Do not lose it.

If you signed up to bring food please remember to do so.

If you want to dress up in baseball clothing you may.  This is not required but it is fun.  You may wear a jersey from another team if it is the only one you have.  If you team is the angles and you want to dress up like an angel that is also okay.  This is NOT a chance to wear your favorite shirt just because you feel like it.  All special clothing may only be worn during math class.

MAKE SURE YOUR PLAYER CIRCLES ARE COMPLETED!  If you come to class without this it is like you don’t have a team.  You cannot play baseball without a team.  If you do not have this you will get a 0 out of 20 for the tournament and will spend the day doing work out of the math book.

Let me know if you have any problems completing these over the weekend.

Baseball Day 3

Check Player Analysis Chart – If you add the degrees for each player they should equal between 355 and 365.  The reason they might not add up to exactly 360 is because of rounding.

Begin making Player Circles

• 1 piece of paper with 5 circles per side
• label each piece of the circle with: 1B, 2B, 3B, HR, SO, BB or Other Outs
• Label each circle with the player’s name and their batting order (1-9 and alternate)
• Your team name needs to be somewhere on your paper.

If you want to decorate this or cut out the circles you can but YOU DO NOT HAVE TO.  Whatever you do, make sure that you can still use the circles for the game.

Baseball Day 2

Fill out Player Analysis Chart

Cum AB = AB + BB

1B = H – (2B + 3B + HR)

Other Outs = Cum AB – (H + BB + SO)

Ratio = #/Cum AB

Decimal Equivalent = Divide the ratio.  Round to the nearest hundredth or thousandth.

Degrees = multiply the decimal equivalent by 360.  Round to the nearest whole number.

Homework:  Finish player analysis chart.

Baseball Day 1

Review Chipper and Evan stats

Draft – Each students picks a team

Practice using a scorecard by looking at game statistics.

Homework:  Pick 10 players from your team.  Find the following stats for each player- AB, H, 2B, 3B, HR, BB, SO – remember to use 2008 statistics, not current ones

The best way to find player stats is to follow this link too MLB.com.  There are 4 search criteria you need to fill in. 1.  Major League  2.  Select Team – choose your team 3.  Stat – Hitting – Entire Season  4.  Timeframe – Season Stats – 2008

Once you have the results I suggest sorting your team by AVG.  Do not choose players that have less than 100 AB.

Here are links to individual team sites.

Baltimore OrIoles

Boston Red Sox

Chicago White Sox

Cleveland Indians

Detroit Tigers

Kansas City Royals

Los Angeles Angels

Minnesota Twins

New York Yankees

Oakland Athletics

Seattle Mariners (the best team ever)

Tampa Bay Rays

Texas Rangers

Toronto Blue Jays

Arizona Diamondbacks

Atlanta Braves

Chicago Cubs

Cincinnati Reds

Colorado Rockies

Houston Astros

Los Angeles Dodgers

Milwaukee Brewers

New York Mets

Philadelphia Phillies

Pittsburgh Pirates

San Diego Padres

Florida Marlins

San Francisco Giants

St. Louis Cardinals

Washington Nationals

Baseball Intro

Handout – what each abbreviation means

Handout – find statistcs for Chipper Jones and Evan Longoria.  This is practice for when you get your team.

Homework:  finish Chipper and Evan stats – find ratio, decimal equivalent and degrees

Notes

To find percent of a number there are two options:  proportions and equations.

Proportions:    part/whole = percent/100   (in this program I can’t do the division line so I am using / and you should know it represents a big division line).

What is 24% of 250?

x/250 = 24/100

What percent of 20 is 30?

30/20 = x/100

Equations:    The word “of” means multiply and the word “is” means equals.  Whenever you see the word “what” that is where the variable goes.  To put a percent in an equation you have to turn it to a decimal by diving by 100 or moving the decimal 2 spots to the left, NOT just to the front of the number.  Write the equation exactly the way the words are written.

What is 24% of 250?

x = .24 * 250

What percent of 20 is 30?

x * 20 = 30

Other Explanations

Proportion

Pre Algebra Book Page 288

Online Examples

Equation

Pre Algebra Book Page 298

Online Examples

Maybe the best video ever put on YouTube!

Homework

HW2 – Percents

I just posted grades to Edline.  They include everything from Unit 5 but your Inequalities Books.  I’m still working on those.

Here are the answers to what we did in class.

Day 2 Review Answers

The test will have 2 parts. Next to each topic I’m including the lesson we learned it and the page in the textbook where the explanation begins.

INEQUALITIES

Be able to:

• Write inequalities from words (lesson 1, page 340)
• Graph inequalities (lesson 1, page 340)
• Solve 1 step inequalities with addition and subtraction (lesson 2, page 345)
• Solve 1 step inequalities with multiplication and division (lesson 3, page 350)
• Solve 2 step inequalities (Lesson 4 and 5, page 355)

LINEAR EQUATIONS

Be able to:

• Determine if a table/graph is a function or not (lesson 6, page 369)
• Graph linear equations in slope-intercept form (lesson 7 and 8, page 398)
  • be able to identify the slope and y intercepts as well as graph the line
• Find x and y intercepts of lines (lesson 9, page 381)
• Chart solutions of linear equations (lesson 10, page 375)
• Find slope – for equations in slope intercept form, standard form and when given 2 points (lesson 11, 387)
• Write linear equations when given 2 points (lesson 12, page 404)

VOCABULARY

linear equation

slope intercept form

standard form

coefficient

slope

y intercept

x intercept

constant

function

domain

range

greater than

less than

greater than or equal to

less than or equal to

open circle

closed circle

inequality

infinite (solutions)

reciprocal

Notes

From Word Problems

Slope (m) – This is the value that changes based on what you choose/do.  The slope will always be written as the coefficient of x.

Y Intercept (b) – This is the value that stays the same (in the equation) no matter what.  It may be your starting point.  The y intercept will alway be written as a constant (by itself).

When you are given a word problem you should identify m and b.  Then fill them into the y=mx+b format.

From Graphs

1. Identify the y intercept.  This will be b.
2. Find two points on the line that have whole number coordinates (points where the line hits both the x and y lines at the same time).  Count the slope between these two points – remember rise/run.  This will be m.
3. Write your equation filling in b and m for y=mx+b.

Try this HERE.

Homework

HW13 – Writing Equations from Word Problems

Notes

Writing Linear Equation from 2 points

• Find the slope of the line.  Use (y-y)/(x-x).   REMEMBER THAT THE Y VALUES GO ON TOP – THEY ARE THE RISE
• Using y=mx+b fill in the slope and x and y from one of the points.  Solve for b.
• Write your equation.  Fill in m (from step 1) and b (from step 2).  Leave x and y as x and y.

These notes are not very detailed because it is impossible to write equations in this program.  See the explanations section for more help.

Extra Explanations

Pre Algebra book, pages 404-408.  Look at Example 4.  Problems 23-28.

I love this tutorial – it’s in color with pretty pictures and good examples.

Exactly the same as what we did in class – but this one has the equations included.   Practice problems with answers.  See if you get the same answer they did.  Writing y=mx+b from 2 points

Homework

HW12 – Writing equations of lines