Classwork/Homework - Last Week (2/9-2/13)

Hello everyone! I just wanted to tell you what a great experience I had teaching all of you. Although some of you struggled with some of the concepts we are working on, it was great to see you persevere and find success through deconstructing problems and practicing some advanced algebra.  

I hope you continue to work hard and be successful the remainder of the school year. I know you will have a great teacher for the rest of it. Welcome back Mr. Mejia!

In case any of you are looking at Veracross for work you may owe from our last week together it's all listed below. This list includes related blogs with video lessons for certain problems as well as links to worksheets that are not in the textbook.

Classwork/Homework - Last Week (2/9-2/13)

Monday (2/9)

Homework Due - none

Blog - 7.6 Word Problems w Systems of Linear Equations involving Rates

Classwork - 7.6 Rate Problems 1 - #2 & #3 are on the blog

Homework - pg 416 #s 18, 19, 22

Tuesday (2/10)

Homework Due - pg 416 #s 18, 19, 22

Blog - 7.6 More Rate Problems

Classwork - 7.6 Rate Problems 2 (includes #s 18, 19, 22 from HW)

kayak problem (back page) is done on the blog

Homework - pg 415-17 #s 17, 21, 24

Wednesday (2/11)

Homework Due - pg 415-17 #s 17, 21, 24

Blog - 7.6 More Rate Problems Practice & Start of Mixtures (7.7)

Classwork - 7.6 Rate Problems 3 -  #1 done on the blog

Homework - 7.6 Rate Problems 4 AND pg 421 #s 25 & 26

- #1, #2 & #3 are done on the blog

Thursday (2/12)

Homework Due - 7.6 Rate Problems 4 AND pg 421 #s 25 & 26

Blog - 7.7 Mixtures 1

Classwork - 7.7 Mixture Problems 1 - #1, #3 & #5 are done on the blog

Homework - 7.7 Mixture Problems 2

- #1 is solved two ways, one the Teaching Channel & the other on the blog

Friday (2/13)

Homework Due- 7.7 Mixture Problems 2

Blog - none

Classwork - 7.7 Mixture Problems 3 - WP - Homeroom 8Demetrus

7.7 Mixture Problems 3 - WP - Homeroom 8Atkinson

Homework - none

7.7 Mixtures 1

Hello Everyone,

My apologies for being out today.  I have a sick kid at home to take care of.  I hope the Patriotic Assembly went well.

I am not sure who will be with you in Algebra Concepts today so I will put all your work on the blog including links to the worksheets.

First start for classwork:

7.7 Word Problem Worksheet - Mixtures 1

This worksheet is a review of some of what you started last night for homework.  If you need any help please see the video solutions below:  

• 7.7 - Mixtures 1 - #1
• 7.7 - Mixtures 1 - #3 (w error)  then #3 (caught the error)
• 7.7 - Mixtures 1 - #5

You might also want to attempt the problems and then watch me solving them to correct your answers.

Next do for homework:

7.7 Word Problem Worksheet - Mixtures 2

Watch the video about mixtures at the Teaching Channel.  Use the teacher's example to write notes for the first saline solution problem.

Then watch the video of me solving the same problem.  Copy down what I did for notes.  Write a response on the back of your worksheet explaining which method works better for you and why.

Complete the second saline solution problem using either method.

7.6 More Rate Problems Practice & Start of Mixtures (7.7)

As you come in today, please start with your classwork:

CW: 7.6 Word Problem Practice - Rates 3

Please attempt the rate problems on this worksheet.  Hopefully you are getting more familiar with setting up rate problems.  If not, please watch this video of me solving #1.

 Once you have finished the classwork, you can start on your homework:

HW: 7.6 Word Problem Practice - Rates 4b and pg 421 #s 25 & 26

Please attempt #1 and #2 on your own.  Both have to do with rates of speed affected by waves or wind.  These are similar to your homework from last night.  However #2 has an interesting twist which will require you to go back to the work we did with:

DISTANCE = RATE x TIME

Please watch these videos of me solving #1 and #2 if you need help.

Once you have completed these you can attempt #3, a mixture problem.  For support you can choose to watch a video of me solving #3 or look in your textbook on pg 418.

7.6 More Rate Problems

Today we will review last night's homework problems.  As you can see the level of difficulty is ratcheting up but you are ready for it (even if you don't believe that yet).  I've listed how things are getting more challenging and the tools you have to meet the challenge:

• the problems require more translating from English into algebraic terms
1. use grids to break down the word problems
2. list information
3. rewrite tasks or questions
4. use the info and question to determine what answer you are seeking
5. label the answer with variables
6. go back and use the information to do the work and create linear equations that will help you solve for the variables

• the calculations are starting to involve more decimals or fractions. This is all the pre-algebra rational number work that can get tricky:
• with fractions you can multiply through BOTH sides of the equations to change fractions to whole numbers
• maintain your number sense while you do your fraction or decimal work 
• i.e. 1.9 X 1.2 approximates to 2 X 1 
• so when you get the answer of 228 you should know that you can place the decimal between the 2s
• the answer would be 2.28
• use a calculator to check your answers

After we are finished reviewing, you can start the next concept related to rates which focuses more on currents.  Please watch me solving the first part of the Rate w. Currents problem on the back of your classwork page.  Be sure you take notes and turn it in for full credit.

Then you can begin your homework:

HW: pg 415-17 #s 17, 21, 24

7.6 Word Problems w Systems of Linear Equations involving Rates

We've done some practice of translating word problems from the English language into Algebra language over the past few weeks.  Recently I challenged you to translate the guacamole and salsa word problem from pg 403 in our textbook.  Working on translating will help you as we move into word problems with rates.

Please watch the video of me solving #2 of your classwork page.  Watch it a second time and take notes on your classwork page.  Then write equations for #1 and solve using elimination, substitution or graphing.  

IF YOU NEED HELP WITH ANY OF THE CLASSWORK AND THE VIDEO IS NOT WORKING FOR YOU PLEASE LET ME KNOW.

After that please watch me solving #3(a) of your classwork.  Watch it a second time and take notes.  Then solve 3b on your own.  

Once you have completed the classwork page (including copying notes), please bring it to me and you can start your homework for tonight:

HW pg 416 #s 18, 19, 22 (show grids, equations & solve for all including 18)

7.2 to 7.4 Quiz Tomorrow

Just reminding you that we have a quiz tomorrow.  You will need to show that you can solve problems algebraically in the following ways:

1. graphing the equations for the common solution
2. using substitution to solve the system of equations
3. using elimination (starting by multiplying) to solve the system of equations

Please be sure to do the Practice Quiz - Homework.  I am attaching videos below of the solutions for those problems.  My suggestion would be to watch the video after you attempt the homework, similarly to how we reviewed the Practice Quiz - Classwork in class today.

HW: 7.2, 7.3, 7.4 Quiz - Practice Quiz Homework

Videos of Solutions to Practice Quiz - Homework

1. solving systems of equations by graphing
2. solving systems of equations by substitution
3. solving systems of equations by elimination

If you still have questions, please feel free to email me:

jadams@a-cs.org

See you tomorrow!

7.4 Solve Word Problems with Systems of Linear Equations by Multiplying & Eliminating

Since most people do not get paid simply for solving systems of linear equations, we will now practice the algebraic work we have done multiplying and eliminating with word problems.

Accordingly we will use grids to help us disaggregate the data we find in the word problems, translate the words into algebraic equations and then solve using appropriate steps to eliminate variables.

Start by practicing elimination with multiplication:

HW: pg 402 #s 20, 21, 22

Then, follow my lead by taking notes while you watch me solve #33 of your HW.

HW: pg 402-3 #s 33*, 34, 35, 39** (grid, equations & solve by elimination) 

**For number 39, be sure to graph your answer as well.

7.4 Solving Systems of Equations by Multiplying and Eliminating

Just like it says in the title, we are moving into solving systems of equations by multiplying and eliminating.  Sounds difficult, but you already know most of the steps to do this.

Quick review:

They need two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. They went on 4 rides altogether.  

First,

Two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. can be translated into algebra:

Where
     x = # of rides on the bumper cars and 
     y = # of rides on the ferris wheel

     2x + 3y = 10 

Now the first part of our word problem is represented as a linear function. If we wanted, we could graph this function with the help of a table.  The line would represent all the solutions that work.

Next,

They went on 4 rides altogether.  Assuming the same variables x and y, we can place this equation underneath our original.

     2x +  3y = 10 
       x +   y = 4

These two formulas represent to linear functions that together make a system of equations.

Then, we can solve by any number of options:

• by graphing and identifying the point where the two lines cross

• by substituting
• x + y = 4 can be changed into x = y - 4
• we can then substitute the x in the first equation
• 2 (y - 4) + 3y = 10 and
• solve for y, then use our solution for y to help solve for x

• by multiplying and eliminating
• we can multiply the second equation by -3
• -3 (x + y = 4) becomes -3x + -3y = -12
• we can use that to eliminate the y in the first equation and
• solve for y, then use our solution for y to help solve for x

On Friday, we will have a quiz practicing these three options for solving.  I will find systems of equations, give you the answers to them and then ask you to show your understanding of all three of these processes for solving them.

Today we will practice the last two methods.

Please start with practicing substituting.  Watch the video of me solving #18 if  you need any help.

HW: pg 386 #18*, 19, 20

Then watch the videos of me solving #3 on page 401 and #17 on 402.  Take notes and then solve the remaining two by multiplying and eliminating.

HW: pg 401-2 #3*, 4, 5 and #17*, 18, 19

7.2 Substitution Review & 7.3 Elimination

Hope you all had a good weekend!

I corrected your quizzes and saw some consistent errors with regard to substitution.  One was that a number of people solved for variables in both equations and the other was a tendency to solve for y only rather than x.

It's important to note two things:

1. You can solve for either variable in either equation.  Generally, the best thing to do is to identify the variable that will be easiest to isolate.  
2. You only need to solve for one variable (of the four options) and substitute that into the other equation.  No matter which variable you choose, you will get the same answer.

For your classwork/homework please watch the videos below, take notes and then replicate the process of solving for all four variables for #2 (see HW below).

Substitution - pg 386 #15 - solve for first variable, first equation
Substitution - pg 386 #15 - solve for second variable, first equation
Substitution - pg 386 #15 - solve for first & second variables, second equation


HW: pg 386 #2 (solve for each variable in each equation, 4 times, same equation)

1. isolate x in 2x - 3y = 24, then substitute
2. isolate y in 2x - 3y = 24, then substitute
3. isolate x in 2x + y = 8, then substitute
4. isolate y in 2x + y = 8, then substitute

The answer for all of these should be x = 6 and y = -4

Then, for additional homework please:

1. make grids
2. translate the word problem into equations & 
3. solve by elimination

the following problems:

HW: pg 396 #43 & 45 (show grid, equations and solution by elimination)

7.3 Solving by Elimination

Hope you all worked hard on your quiz today.  My apologies for not being there.

As we move into solving systems of linear equations through elimination, it's important you track the signs of our terms.  Mistakes with negatives will make solving by elimination difficult.  If you need any additional practice (extra credit) with integer work, please let me know.

Please start by watching an overview of what solving linear equations through elimination is:

Solving Linear Equations by Elimination - Overview

Then, watch the videos for each section and do the related problems (#* done in video):

Solving Linear Equations by Elimination - Addition #4

HW: pg 394 #s 3, 4*, 5

Solving Linear Equations by Elimination - Subtraction #12

HW: pg 394 #s 12*, 13, 14

Solving Linear Equations by Elimination - Arrange & Add/Subtract #22

HW: pg 394 #s 22*, 23, 24

7.1 & 7.2 Quiz Tomorrow

Just reminding you that I have moved our quiz from Thursday to tomorrow.  It will not include "elimination" as a method for solving systems of linear equations.

Please be sure to do the Practice Quiz - Homework.  I am attaching videos below of the solutions for those problems.  My suggestion would be to watch the video after you attempt the homework similar to how we did the Practice Quiz - Classwork in class today.

Videos of Solutions to Practice Quiz - Homework

1. translating into algebra
2. solving systems of equations by graphing
3. solving systems of equations by substitution

If you still have questions, please feel free to email me:

jadams@a-cs.org

Good luck tomorrow!

7.2 Solving Linear Equations Word Problems through Substitution

Hope you all had a good weekend.  Your homework was to watch the video in the last post.  I know we're not supposed to give homework on weekends but this seemed pretty important;)

Anyway, I'm hoping you are feeling confident with solving linear equations by graphing.  It's a lot of work but the goal was to see how all the tools: grids, equations, tables & graphs interrelate.  

As we've begun work on solving systems of linear equations I've gotten a resounding, "Wow, this is so much quicker!"  True, but we still want to maintain a conceptual understanding of the conceptual process of finding a shared solution point.

Accordingly, your homework will include translation tasks (words to algebra) and two word problems.

Please watch this video of me solving #16 on your homework and then complete the following:

HW: pg 386 #s 8, 14, 15, 16

Then answer:

HW: pg 387 #s 25 & 26 (pay close attention to "The value of x is 4 times the value of y"
                                     as you might write this as 4x = y which is incorrect.)

Watch the second video of me solving #29 starting with a grid and then using substitution (instead of tables & graphs) once I have the equations set up.  Write down the notes from my work on # 29 and then solve your own word problem #30 using a grid to make your equations and then substitution.

HW: pg 387 #s 29 & 30

Kid Snippets: "Math Class" (Imagined by Kids)

7.2 Systems of Equations & Start of Solving by Substitution

We will wrap up some practice constructing systems of linear equations from word problems.  A hard part can be learning to translate English into Algebra and vice-versa. 

An example would be:

     Small cards cost $3 each and large cards cost $5 each.  The total amount from the
     sale of the cards is $95. 

     We can choose to make:
     x = the number of small cards sold and 
     y = the number of large cards sold.

     In this scenario 3x + 5y = 95 means $3 per small card plus $5 per large card adds up to

     a total of $95 dollars.  

     There are multiple ways of solving this first equation.  It's only when we say the total
     number of cards is 25, translated to x + y = 25 that we have a systems of equations
     with one common answer.

     In this scenario x + y = 25 translates to "the number of small cards plus the number of
     large cards is 25 cards.  Note that cost is not associated with this function.

HW: pgs 380-81 #s 31, 32, *36 (*do a grid/table/equation/graph for 36)

Today, we will also begin solving linear systems by substitution.  Please watch the following videos of me solving #3 & #4 from your HW, copy the work and answers down, and do the remaining HW problems:

AND HW: pg 386 #s 3-7

7.2 Solving Linear Systems by Substitution - Page 386, #3 - part 1

7.2 Solving Linear Systems by Substitution - Page 386, #3 - part 2
7.2 Solving Linear Systems by Substitution - Page 386, #4

7.1 Suggestions for Long-Term Success in Math

I was one of those students that had it pretty easy in math until about the time of algebra.  I could tune out the teacher most of the time and "figure out" the math I was required to do.  On some level I even passed through Algebra pretty well.

Unfortunately, instead of developing the tools I needed to succeed long-term in math I continued to look for quicker, easier ways of doing math.  By the time I got into Calculus my ability to just "figure out" math was not longer working.  I had not developed the problem-solving and reasoning I needed to continue into advanced mathematics.

Here are some simple (but time-consuming) suggestions:

• watch the videos at least once (jump ahead if it seems slow, review if you're uncertain)
• show all your work (done in columns so you can more easily track errors with negatives)
• check your answers (especially if the instructions ask you to)
• use our tools of algebra to help you:
• a grid for word problems
• a function table (x,y) with labels
• a graph with labels
• the function written as a linear equation (y=mx+b)

I'll quiz you tomorrow on these as an extra credit you can apply later.

Today, please watch the video of me solving question #3 on your homework.

HW: Practice Sheet 7.1, #s 1-4 
(For question #4, feel free to substitute non-blooming annuals cost $1.60 and the total for 24 plants is $48.)

7.1 Nice job! Now going deeper into systems of equations with word problems.

Well done on your quizzes last week!  I observed that a number of you took the time to use all three tools (function, table & graph) to solve the word problems on quiz.  Your process is getting stronger as you make mistakes, catch them and continue to work hard on your conceptual understanding of what you are doing.

You may be starting to realize that algebra is getting rather time-consuming.  This week there will be even more steps to solve our assigned tasks. As it gets more complicated it is important you understand what you are doing and why so you can remember the process for solving systems of equations.

Chapter 7 - Section 1
Basically we are combining the questions you answered on your quiz.  You will be solving word problems that have 2 linear equations instead of just one linear equation.

If this seems totally new to you, please review the videos from last week:

page 378 - Example 3
grid
function/equation
graph/table/solution

If you feel you're ready to try a more difficult problem, go to these videos:

page 380 - #34
grid
table/graph
function/solution

HW: pg 379-81 #s 18, 20, 30, 37 (show function/table/graph)  

6.5, 6.1 & 7.1 Pre-Quiz, Quiz Practice HW, Quiz

Hi, 

Don't freak out:)  We will do a pre-quiz today in class and will review it together.  You will have our pre-quiz from today to help you with tonight's practice quiz for homework.

Our quiz is tomorrow.  The format will look exactly like the pre-quiz and practice quiz. Like the pre-quiz it will have 4 questions:

1. graphing a perpendicular line through a given coordinate (chap/section 6.5)
2. graphing a linear equation on a regular graph from a word-problem (6.1)
3. graphing a linear equation on a "skewed" graph from a word-problem (6.1)
4. finding the solution to a system of linear equations (two lines) by graphing them (7.1)

If you have any areas that your are feeling uncertain review the online videos linked below and email me any specific questions:

• graphing a perpendicular line through a given coordinate (6.5)
• graphing a linear equation on a regular graph from a word-problem (6.1)
• graphing a linear equation on a "skewed" graph from a word-problem (6.1)
• finding the solution to a system of linear equations (two lines) by graphing them (7.1)

7.1 Word Problems with Graphing Linear Equations - Part Three

Hello!

I'm delighted to announce that I had three of you arguing yesterday about an algebraic solution.  Nothing warms my heart as students arguing, respectfully of course, over math.  Glad you're feeling adamant about your hard work!

As we move further into linear equations we will continue to use our tools: 

• equations like y-mx+b
• function tables (those x/y charts) and
• graphing

to helps us solve word problems.  Although it may seem cumbersome now to use all these tools, they payoff will be worth it when you can understand the concepts behind the procedures to better remember your process & computations.  It's also a great way to catch mistakes as I have frequently modeled for you:)

Please start by reviewing:

Solving Linear Equations by Graphing

and then move on to pg 378, EXAMPLE 3, shown below in the video lessons: 

Solving Word Problems with Linear Equations (make a grid) - optional
Solving Word Problems with Linear Equations (set up equation)
Solving Word Problems with Linear Equations (table, graph & test solution)

HW: pg 379, #s 13,14,16 & pg 380, #35

7.1 Word Problems with Graphing Linear Equations - Part Two

So basically there are three tools that we use in algebra to understand the work we are doing: (oh yeah, hope you had a good weekend and all that good stuff:)

1. formulaic expressions of linear equations (functions) such as our beloved slope-intercept form, y=mx+b, or standard form (used more in Chap. 7)
2. tables of coordinates (x,y) that list answers to the functions and show us patterns that helps us to identify changes like slope
3. graphs of solution sets (coordinates that work) on a cartesian plane or visuals representing the changes of variables on a scaled or skewed graph

As you read this list, it is important you know what these three tools or components are because we are working on adding a forth.  If you are not familiar with these tools please review the following video:

Systems Intro 3 - 3 Tools for Algebra

The forth area we will be working on has the actual real-world word problems that require the use of algebra to solve them, the reason we study algebra.  It's not just about getting ready for the next math class in our sequence, typically Geometry, it's about using algebra in applied settings.

Accordingly, please watch the following videos on graphing linear equations with positive and negative slopes.  Please watch them in order as the second video builds on the first and starts with a y-axis of 1970 which also ends up being 0 when we apply the equation.

Graphing Linear Equations (positive slope word problems)
Graphing Linear Equations (negative slope word problems)

Then do the homework questions as practice:

HW: pgs 327-8, #s 42, 43, 44, (write equations, show tables & graphs for each)

Challenge: pg 328, #51 (same three tasks)

7.1 Word Problems with Graphing Linear Equations - Part One

Happy Friday everyone!

Two things:

1)  Please be sure to bring your HW to class today and have it in order so I can check it.  I will be grading for effort, not correct answers.  Effort looks like organized attempts at answers (with work shown) or written questions about what you might not understand in the homework.  I plan to be pretty generous this week.

2)  We will be working on word problems with functions from Chapter 6 and graphing them to build fluency with graphing on scaled cartesian planes (similar to the graphs on the back of last night's worksheet).

classzone.com - 6.1 - example 5 - powerpoint

Our classwork will be graded today.  We will be working on:

Classwork: Practice Sheet 6.1, #s 16 & 17

Have a great weekend!

7.1 (c) Systems of Linear Equations - Solve by Graphing - Post 2

So hopefully you have a pretty good understanding of the meaning of finding the solution of two linear equations.  Tomorrow we will dive into applied real-world word problems that require the use of this type of algebra to solve them.

For today we will practice getting some fluency with finding the intersection of two lines which represents the solution for two different linear equations.  Please start by reviewing our 3 tools for doing algebra:

Systems Intro 3 - 3 Tools for Algebra

Solving Systems of Equations by Graphing 1

HW: Complete worksheet SLE#1

PLEASE MAKE SURE YOU BRING ALL HW FOR THE WEEK TOMORROW SO I CAN ENTER IT IN OUR GRADEBOOK

7.1 (b) Systems of Linear Equations - Solve by Graphing - Post 1

Looking at the Cartesian plane above you will see two distinct linear equations.  The equations are in standard form rather than slope-intercept form.  I've mentioned that we will be using standard form more as we progress through chapter 7.  Doesn't mean we have to like it (I don't) for graphing equations:)

So as you look at these two functions (equations) graphed above, you should notice that the lines represent a solution set (list of answers) for each linear equation.  I can prove this to you by plugging in and solving for one of the points:

• Looking at the blue line (4x-6y=12), I see it crosses the y-axis at (0,-2).  I will put the coordinates (x,7) for this point into the equation to show it is a correct solution to the function:
• 4x   -   6y     = 12
• 4(0) -  6(-2) = 12 (note that -6 times -2 equals +12)
• 0      +  12   = 12 
•             12   = 12  
• You can see that 12 does in fact equal 12 so this is a correct solution for this function.

Go ahead and prove that the coordinate (3,0), where the two lines intersect, is a solution for both linear equations by plugging that into both functions.

7.1 (a) System of Linear Equations (Don't worry you've already created one:)

I have three exciting videos for you today!

First, we will review

Parallel & Perpendicular Lines Review

HW: pg 357-8, #s 1*, 2*, 6 & 9 (* indicate written response questions)

Then, we will review the connect between representing equations (functions) as both lines on a cartesian plane as well as lists of coordinates.  

Systems Intro 1 - Line as set of answers (solutions)

HW: pg 325-6, #s 14, 20, 30*, 38 (* indicate written response questions)

The last video uses perpendicular lines to begin explaining how the point where two lines (equations) cross is a common answer (solution) for the two lines.  This is the definition of a solution of a system of linear equations.

Systems Intro 2 - Common Answer (Solution)