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Please complete the worksheets provide with the lessons if you have missed a day within my class with the material. You can get the answer key from me in class.

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Please complete the worksheets provide with the lessons if you have missed a day within my class with the material. You can get the answer key from me in class.

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Unit 5 material - During this unit you will be learning how to solve for systems of equations using one of 3 ways: Graphing, substitution, & elimination. You will need to understand that we will be solving these systems with linear equations. You will need to know slope intercept form and standard form when dealing with these problems.

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Solving Systems of Equations By Graphing

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Solving Systems of Equations By Elimination & Substitution With 2 Variables

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Day 2 - Systems of Equations - System of Equations (Graphing and Substitution) Worksheet.docx

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Day 3 - Systems of Equations - System of Equations (Elimination Method) Worksheet.docx

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Systems of Equations - Solutions Of Linear Equations

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Probably the most important method of solution of a system of equations is the elimination method because it can be used for higher order systems. The method of elimination by addition involves replacing systems of equations with simpler equations, called equivalent systems. Consider the system with the following equations; equation 1: x - y = 1; and equation 2: x + y = 5.

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This summer, the political scientist Andrew Hacker's New York Times Op-Ed essay "Is Algebra Necessary?" set off a national debate on mathematics education. Here is how the essay begins:

A typical American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I've found myself moving toward the strong view that we shouldn't.

The debate inspired us to suggest several algebraic opportunities right here in the pages of The Times. After considering them, and reading Mr. Hacker's essay in full, we invite you to tell us what you think. Is algebra necessary?
1. Mathematically Modeling Mortgages
Use algebra to evaluate the housing market. Find some homes for sale in your area (for example in Atlanta), research current interest rates for mortgages and apply this formula to determine the required monthly mortgage payment.

Experiment with different home prices, different interest rates and different mortgage lengths to explore the impact of each variable on the resulting monthly mortgage payment. Use the Real Estate section's built-in mortgage calculator to check your work.

For a given house, explore questions like "How much would you end up paying over the entire term of the mortgage, and how does this compare to the value of the house?" and "How big is the difference in monthly payments between a 15-year mortgage and a 30-year mortgage?"

Do you think it is more cost effective to rent an apartment or buy a house? Read this article and play around with this Times Interactive to explore the answer.
2. Evaluating Colleges
Check out how algebra is used to rank colleges. Read this article about the history of the Academic Index and then check out this informational graphic detailing the formulas that are used to create college rankings.

Calculate and compare the Academic Index of colleges like SUNY Binghamton and the University of Southern California by finding the appropriate data here. Are your results consistent with those of the U.S. News & World Report rankings, or those of The Princeton Review?

Use other available data - like tuition, acceptance rates and faculty information - to create your own algebraic formula for evaluating colleges. Can you create a ranking system that puts SUNY Binghamton ahead of U.S.C.? Can you create a different ranking that puts U.S.C. ahead of SUNY Binghamton? Can you create a ranking that puts your favorite college at the top of the list?
3. Calculating Car Costs
Use data from The Times's Automobiles section to create a model for how quickly cars lose their value.

Use the Used Car Search to collect price information on specific makes and models of cars. Select your automobile, get your list of prices (for example, there are nearly 20,000 Ford Explorers for sale nationwide), and create a scatter plot with "year" on the horizontal access and "price" on the vertical access.

Use the graph and your data to explore questions like "How much value does a used car lose per year?" and "When does an automobile depreciate fastest?" Use technology like a graphing calculator or a computer spreadsheet to generate a possible function that models this data. Use the model to project the value of a new car two, three or 10 years from now. Set up equations to solve questions like "After how long will the car be worth 50 percent of its original value?"

Ratchet up the reality and complexity by compensating for the differences in new car prices and inflation. Go deeper by exploring questions like "Do SUVs lose value faster than sedans?" and "Which cars are the best long-term investments?"
4. Algebra of the Election
To win the presidency, a candidate must secure more than half of the 538 electoral votes. Take a look at the current breakdown of electoral votes by state, and find combinations of states that add up to 270 (or more) electoral votes. Each solution to this equation (or inequality) represents a potential path to the presidency.

Compare your possibilities to those demonstrated in this Electoral Map informational graphic. Take a look at some possible situations and interact with the mathematics by moving states around and exploring other solutions to this equation. If you were running for president, where would you focus your campaign resources?
5. Do the MetroCard Math
Is it better to buy a card that gives you unlimited access to public transit, or should you just pay ride by ride? Check out this article on the mathematics of New York City MetroCards. Currently, a seven-day unlimited MetroCard costs $29 and a 30-day unlimited MetroCard costs $104. If a single ride costs $2.25, under what circumstances would you be better off buying the weekly unlimited? The monthly unlimited? Set up simple linear equations and inequalities to answer these questions. Who should buy the 30-day unlimited?

Transfer over to some harder problems by factoring in the 7 percent bonus you get when you prepay for a pay-per-ride card. How does this discount affect the above calculations? And for even more real-world complexity, consider the effect that pretax commuter benefits can have on the equation. Check your numbers against the Metropolitan Transportation Authority.'s own comparisons here, and research the commuter cards in your area to find your best local options.
6. Olympic Algebra
Use mathematics to explore the wealth of Olympic data The Times has to offer. Take a look at the world records set this year in London, and check out the history of world records for events in track, field, swimming and more at the bottom of the page. Use simple formulas like Distance = Rate * Time to compare and contrast the average speeds of athletes over time, across events and even by gender. How much faster is the fastest sprinter now than 50 years ago? How much faster is the fastest sprinter than the fastest long-distance runner? How do swimmers, runners and cyclists compare in speed?

Pick an event, like the 100-meter freestyle swim, and take a look at the history of the world-record times. Create a scatter plot of the data with the horizontal axis representing the year and the vertical axis representing the world-record time. Experiment with some simple linear equations to find a line that fits the data, and use this equation to project the possible world-record times in 2016, or to hypothesize when the fastest time might drop below 43 seconds. If appropriate, use computing technologies to generate regression equations to compare to your own work.

Be sure to check out how beautifully mathematical results can be visualized and presented by watching this amazing video showing the Jamaican sprinter Usain Bolt running against every other Olympic medalist in history.
7. Redo Those Recipes
Search this Times Topics page for some tasty recipes with your favorite ingredients like chicken with lemon and rosemary or midnight pasta. Suppose you had twice as many people coming for dinner: what would the new recipe look like? Turn your recipe into an algebra problem by converting all amounts into some standard measure (like grams) and creating expressions that tell you exactly how much you need for any number of people. How many grams of chicken will you need if N guests show up for dinner?

Use a calorie counter to determine the number of calories per serving of your dishes. Using this United States Department of Agriculture guide, plan out meals for breakfast, lunch and dinner that keep you in the healthy range for caloric intake. Or list the 10 foods you most like to eat and find out how many calories are in each of them. Set up inequalities to figure out how many you should, or shouldn't, consume to keep within your healthy range.
8. Solve for Stocks
Choose some of your favorite companies and use Times resources to collect historical stock price information: for example, check out Ford Motor Company, Apple or Amazon.com. Look at the prices over some fixed period of time, say the past two years, and determine the growth of the value of the stock over that period. If you had invested $1,000 at the beginning of that time period, how much would you have at the end?

Using the formula for compound interest, A = P(1+(r/n)) nt, run the numbers on some hypothetical investments of the same principle investment over the same time period, and compare the results to the performance of the stock. Did the stock do better than a 5 percent annual rate of return? How about 8 percent? Set A equal to the final value of the stock, and solve for the rate, r, to figure out the exact rate of growth of your chosen stock.

Find the rates of return for several stocks, and put together a hypothetical investment portfolio for the school year. Watch your stocks through the year and compare their performance to your calculations. Does past performance guarantee future returns?
9. Population Growth, Football, the Economy and More
Use existing Learning Network resources to apply algebraic tools to rank sports teams, chart population growth analyze economic measures or even succeed in fantasy football.
10. Is Algebra Necessary?
Read Mr. Hacker's original essay and decide for yourself. Do you use internal equations to help plan out your schedule? Or inequalities when you're spending your money? Or graphs when you are plotting your performance? Or maybe you use algebra to figure out if that frequent shopper program is worth sticking to.

Find the algebra that's around you and write a response to Professor Hacker. Maybe algebra isn't necessary, but it sure can be useful.

This lesson addresses the following Common Core domains, standards and practices under Algebra:

Domains
Create equations that describe numbers or relationships.
Solve equations or inequalities in one variable.
Represent and solve equations graphically.
Interpret the structure of expressions.
Standards
Seeing Structure in Expressions
1. Interpret expressions that represent a quantity in terms of its context.
4. Derive the formula for the sum of a finite geometric series and use the formula to solve problems. For example, calculate mortgage payments.

Creating Equations
1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Reasoning With Equations and Inequalities
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
C.C.S.S. Practices
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

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N Ways to Apply Algebra With The New York Times

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This summer, the political scientist Andrew Hacker's New York Times Op-Ed essay "Is Algebra Necessary?" set off a national debate on mathematics education. Here is how the essay begins: A typical American school day finds some six million high school students and two million college freshmen struggling with algebra.

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Over view, what to do with the lesson...

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Over view, what to do with the lesson...

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What other materials can you use to help assess others with Systems of Equations? Add new material below.

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What other materials can you use to help assess others with Systems of Equations? Add new material below.

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Khan Academy also give good feedback with videos and also allows you to find other relevant lessons.

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Systems of equations with graphing: exact & approximate solutions

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Sal solves a system of two linear equations in standard form, and then approximates the solution of a system whose solution isn't clearly visible.

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Other Assessment Activities to show understanding of Systems of equations.

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Systems of equations can be challenging for Algebra 1 students! The first day of my solving systems by substitution lesson, I see so many heads explode. I've developed some favorite ideas and resources over the years that I'd love to share with you!

Here are my favorite tips and resources to help you through your systems of equations unit! (in no particular order)

1 - Emoji Logic Puzzles - These logic puzzles are a fun way to get students solving systems without even realizing it! They would also be fun warmups or as emergency sub plans during this unit.

2 - Solving Systems of Equations by Graphing Pennant - Solving systems by graphing is the best place to start the unit. It helps students visualize solving algebraically and starts in their comfort zone. This pennant is a fun way for students to practice!

3 - Review Literal Equations - Solving systems by substitution is very overwhelming for students at first. However, I have found that if I review solving literal equations as a warmup before the lesson, things go a little bit better that day. :)

4 - Systems of Equations Sum 'Em Activity: Word Problems - You better believe that I'm going to use a sum 'em to help students figure out systems of equations word problems! Sum 'em activities get students working together and discussing math. They are so easy to use, but keep students persistent and engaged the entire class period. Word problems can be so difficult, so I absolutely use this activity to help students master them!

5 - Linear Systems Interactive Notebook Unit - If you want an entire interactive notebook unit for systems of equations, look no further. This complete unit is ready to copy!
6 - Solving Systems of Equations Interactive Notes Activity - This set of notes is ready to go in an interactive notebook. I like that it compares the different methods for solving systems and keeps the information organized in one place.

7 - Systems of Equations INB Pages - These are the interactive notebook pages that I used last year! The notes pages are a FREE download.

8 - Have Students Highlight the Variables - When teaching solving systems by elimination, have students "stack" the like terms and highlight them like the picture below. My students struggle when the variables aren't lined up and this helps them remember to add and subtract the like terms.

9 - Systems of Equations Matching Game and Quiz - This FREE download is a fun matching game to give students practice solving systems. Also, the quiz that's included could be used as an exit ticket or as an additional INB page. So many uses!

10 - How Can You Win Every Prize at Chuck E. Cheese's? - This is a cool 3-act task that keeps students interest while introducing them to the topic. To be successful, students need to be very comfortable graphing equations of lines. Also, this would be a good introduction to systems of equations word problems.

11 - Solving Systems of Equations Puzzle - This hands-on puzzle gets students practicing elimination and substitution. Since this is self-checking, students don't practice incorrectly - they must ask for help if they don't find their answer.

12 - Systems of Two Equations Task Cards - Sometimes you just need a good set of task cards. This set of task cards is perfect for warmups or playing speed dating. You can find some great ideas for using task cards here and here.
13 - Systems of Equations Word Problems Stations Maze - Students need LOTS of practice with word problems! This stations maze gets students out of their seats and moving. It also encourages students to check their work carefully since an incorrect answer will eventually send them back to a problem they have already solved. Successfully completing the stations maze requires students to slow down and check their work.

I hope you have found something useful to use in your classroom this year!

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13 Engaging Ideas for Teaching Systems of Equations

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Systems of equations can be challenging for Algebra 1 students! The first day of my solving systems by substitution lesson, I see so many heads explode. I've developed some favorite ideas and resources over the years that I'd love to share with you!

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Its hard to find other articles that pertain to systems of equations in the real world. I could think of other places where they can use it like business, but I don't see many articles relevant to this tope