Algebra SYSTEM WORD PROBLEM – Let’s solve it step-by-step...

TabletClass Math
13 Jan 202223:43
EducationalLearning
32 Likes 10 Comments

TLDRIn this engaging video, John, the founder of TabletClass Math and a seasoned middle high school math teacher, addresses the common struggle students face with algebra word problems. He empathizes with the initial apprehension but emphasizes the importance of strengthening general math skills to excel in these problem-solving exercises. John introduces a systematic approach to tackling word problems, particularly focusing on systems of linear equations. He guides viewers through setting up a system of equations using a given word problem involving the sale of wood stain cans. By demonstrating the process of reading the problem carefully, creating a model, assigning variables, setting up equations, and solving them, John simplifies a typically daunting task. He also highlights the significance of taking good math notes and offers resources for further learning, including comprehensive math courses and detailed notes on various subjects. The video is a testament to John's passion for making math accessible and enjoyable, encouraging students to embrace the challenge and transform their understanding of algebra word problems.

Takeaways
  • 📚 **Importance of Math Skills**: Strengthening general math skills is crucial for improving at algebra word problems.
  • 🧩 **Understanding Word Problems**: Word problems are applications of the math skills you're learning, requiring practice and understanding of the basics.
  • 🤔 **Overcoming Initial Challenges**: Students often find word problems difficult because they haven't built up their math skills yet.
  • 📈 **Progression in Learning**: As you get better at algebra, you'll naturally improve at algebra word problems, which are an extension of algebra skills.
  • 👨‍🏫 **John's Introduction**: John, the founder of TabletClass Math and a middle high school math teacher, has created comprehensive online math courses.
  • 📈 **Course Offerings**: John offers over 100 math courses, including pre-algebra, algebra, geometry, and specialized courses for test preparation.
  • 🏆 **Success in Math**: Taking great math notes is a key factor in achieving good grades, as noted from John's decades of teaching experience.
  • 📒 **Note-Taking Advice**: Good note-taking is emphasized as a skill that requires work and helps keep students focused.
  • 🔍 **Reading Word Prompts**: To solve word problems, one must read the problem carefully multiple times to extract all necessary information.
  • 📊 **Creating a Model**: Organizing information from the word problem into a table or model helps in setting up equations to solve the problem.
  • ✅ **System of Equations**: Solving word problems often involves creating a system of equations based on the information provided in the problem.
  • 🔢 **Substitution Method**: The substitution method is a common technique used to solve systems of equations by eliminating one variable.
  • 🎓 **Self-Practice**: It's encouraged to attempt solving the problem on your own after watching the video to ensure understanding and retention of the material.
  • 📘 **Additional Resources**: John suggests additional videos and courses for further help, particularly if you're struggling with solving systems of equations.
Q & A
  • What is the general perception of algebra word problems among students?

    -Many students find algebra word problems difficult and confusing, often preferring to work with pure mathematical problems instead.

  • Why do students struggle with word problems?

    -Students struggle with word problems because they often haven't built up their math skills, particularly the basics and fundamentals, which are essential for understanding and solving these types of problems.

  • What is the relationship between a student's general math skills and their ability to solve algebra word problems?

    -The stronger a student is in general math skills, the better they will perform in solving algebra word problems, as these problems are an application of the skills learned in math.

  • What advice does John, the founder of tabletclassmath, give for improving at algebra word problems?

    -John advises students to first strengthen their general math skills if they are struggling, and then return to word problems. He also emphasizes the importance of taking great math notes.

  • What types of courses does John offer on his platform?

    -John offers over 100 different math courses, including pre-algebra, algebra one, geometry, algebra two, and test preparation courses for exams like the GED, SAT, ACT, GRE, GMAT, and more.

  • How does John describe his math courses?

    -John describes his math courses as comprehensive and of high quality. They are not short tutorials but in-depth, full courses that cover the subject matter thoroughly.

  • What is the first step in solving a word problem, according to the script?

    -The first step in solving a word problem is to read the problem carefully, possibly multiple times, to extract all the necessary information.

  • What is the significance of understanding the term 'revenue' in the context of the word problem presented?

    -Revenue refers to the total sales made, which is a key piece of information needed to set up equations and solve for the number of cans sold in the word problem.

  • How many equations are needed to solve a system of linear equations involving two variables?

    -Two equations are needed to solve a system of linear equations involving two variables.

  • What method does John use to solve the system of equations in the word problem?

    -John uses the substitution method to solve the system of equations, where he replaces one variable with its equivalent expression in terms of the other variable.

  • What is the final step in solving a word problem after solving the system of equations?

    -The final step is to interpret the solution to the system of equations in the context of the word problem to answer the question asked.

  • Why is it important to take good math notes according to the script?

    -Taking good math notes is crucial as it helps students stay focused, retain information, and have a reference to study from, which is essential for improving math skills and understanding.

Outlines
00:00
😀 Algebra Word Problems: Overcoming Challenges

The speaker begins by acknowledging the common apprehension towards algebra word problems, suggesting that many students find them difficult and confusing. He empathizes with this sentiment, recalling his own experiences as a student in the 80s. The key advice given is to strengthen general math skills as a foundation for tackling word problems more effectively. The speaker introduces himself as John, the founder of TabletClass Math and a middle-high school math teacher, and promotes his comprehensive online math courses and programs for various tests and independent learners, emphasizing the importance of taking good math notes.

05:01
📚 Approaching Algebra Word Problems

The paragraph outlines a structured approach to solving algebra word problems, emphasizing the importance of reading the problem multiple times to extract all necessary information. It suggests creating a model, such as a geometric model, chart, or table, to organize the information before assigning variables and setting up equations. The speaker also provides a general framework for solving word problems and encourages viewers to pause the video and attempt the problem before proceeding to the solution. The paragraph concludes with the introduction of a specific word problem involving a store selling two sizes of wood stain, with a hint towards using systems of equations for the solution.

10:03
🧮 Setting Up a System of Equations

This section delves into the specifics of setting up a system of equations to solve the word problem. It explains the need for as many equations as there are variables, which in this case are the number of small and large cans sold. The speaker advises on how to use the information given in the problem to create these equations, such as the price of each can size, the total revenue, and the fact that twice as many large cans were sold as small cans. The paragraph also provides a table to organize this information and hints at the process of solving the system of equations, suggesting resources for further learning if needed.

15:03
🔍 Solving the System: Substitution Method

The speaker demonstrates the process of solving the system of equations using the substitution method. He shows how to replace one variable with an expression involving the other variable to create a single equation that can be solved. By substituting y with 2x (from the equation y = 2x) into the revenue equation, he simplifies the system to a single equation with one variable, x. After solving for x, which represents the number of small cans sold, he then solves for y to find the number of large cans sold. The paragraph concludes with the solution to the problem, stating that 17 small cans and 34 large cans were sold.

20:04
🎓 Embracing Mathematics and Seeking Further Help

In the final paragraph, the speaker encourages a positive attitude towards learning mathematics and emphasizes the importance of effort and hard work. He advises students to take their own notes and to seek extra help when needed, offering his own math program as a resource. The speaker also suggests that students try to solve the word problem independently to reinforce their understanding. He concludes by inviting viewers to subscribe to his channel and like the video, and to check out his algebra courses for further assistance with systems of equations and other mathematical topics.

Mindmap
Keywords
💡Algebra word problems
Algebra word problems are a type of mathematical problem that require the solver to translate a verbal description into an algebraic equation or set of equations. In the video, the speaker discusses the common struggle students face with these problems and offers strategies to improve understanding and skills. An example from the script is the problem involving the sale of wood stain in two different sizes, which is used to demonstrate how to approach and solve a word problem.
💡Systems of equations
A system of equations refers to a set of two or more equations that contain the same variables. Solving a system involves finding the values of the variables that satisfy all equations simultaneously. The video focuses on systems of linear equations, which are algebraic equations involving two or more variables but only to the first power. The wood stain problem presented in the video is an example of a system of equations where two variables, x and y, represent the number of small and large cans sold, respectively.
💡Substitution method
The substitution method is a technique used to solve systems of equations by expressing one variable in terms of another and then substituting this expression into the other equation to solve for the remaining variable. In the context of the video, the substitution method is applied by replacing 'y' with '2x' in the second equation, given that 'y equals 2x' from the first equation, to find the value of 'x'.
💡Math skills
Math skills encompass the various abilities and knowledge required to understand and solve mathematical problems. The video emphasizes the importance of building strong math skills, particularly in algebra, as a foundation for effectively tackling algebra word problems. The development of these skills is portrayed as essential to becoming proficient in mathematics.
💡Variables
In algebra, variables are symbols, often letters like x, y, or z, that represent unknown quantities. The video script discusses assigning variables to unknown values in a word problem as a preliminary step to setting up equations. For instance, in the wood stain problem, 'x' is assigned to the number of small cans, and 'y' to the number of large cans sold.
💡Revenue
Revenue in the context of the video refers to the total income generated from sales, which is a key piece of information used to set up an equation in the word problem. The speaker clarifies that revenue is the gross sales figure, not considering costs. The total revenue from the sale of wood stain is given as $694.45, which is used to form one of the equations in the system.
💡Note-taking
Note-taking is the act of recording information during a lecture or while studying. The video stresses the importance of taking great math notes as a critical skill for success in mathematics. It is suggested that students who take organized and comprehensive notes tend to perform better in math, whereas those who neglect this practice often struggle.
💡Test preparation
Test preparation involves activities and strategies designed to ready students for upcoming exams. The speaker mentions offering specialized courses for various tests, such as the GED, SAT, ACT, GRE, GMAT, and others, indicating the significance of math skills across different educational and professional assessments.
💡Homeschool learning system
A homeschool learning system refers to an educational framework designed for students who are educated at home rather than in a traditional school setting. The video mentions that the speaker's program caters to independent learners, including homeschoolers, offering a structured approach to learning math outside of a formal classroom environment.
💡Comprehensive math courses
Comprehensive math courses are detailed and thorough educational programs that cover all aspects of a particular area of mathematics. The speaker describes his math courses as comprehensive, indicating that they are not short tutorials but in-depth and complete, covering a wide range of topics from pre-algebra to pre-calculus.
💡Mathematical model
A mathematical model is a representation of a real-world situation using mathematical concepts and language. In the video, the speaker suggests creating a model, such as a table or chart, to organize information from the word problem in a structured way before setting up equations. This helps in visualizing the relationships between different elements of the problem.
Highlights

Algebra word problems are an application of general math skills, and improving in math will naturally lead to better performance in word problems.

The importance of strengthening basic math skills before tackling word problems is emphasized.

Introduction of John, the founder of tabletclassmath and a middle high school math teacher, who has created comprehensive online math courses.

John offers over 100 math courses covering a wide range of topics, from pre-algebra to upcoming pre-calculus.

Specialized courses for test preparation like the GED, SAT, ACT, GRE, GMAT, and more are available.

The significance of taking great math notes as a key to academic success in math is discussed.

John provides detailed math notes for various levels, including pre-algebra, algebra 1, geometry, algebra 2, and trigonometry.

The steps to solve a word problem include reading the problem, creating a model, assigning variables, setting up equations, solving the equations, and answering the question.

The transcript walks through a specific word problem involving a store selling two sizes of wood stain, using a system of equations.

The problem-solving approach uses a table to organize information about the price, number of cans sold, and total revenue for small and large cans.

Two equations are formed based on the information given: one stating that large cans sold were twice the number of small cans, and another based on the total revenue.

The substitution method is used to solve the system of equations, resulting in finding the number of small and large cans sold.

The solution to the word problem is obtained by substituting the value of x (number of small cans) into the equation for y (number of large cans).

The importance of practicing the problem-solving process independently after watching a tutorial is stressed.

John encourages students to seek extra help if they are struggling, and to utilize his math program and additional video resources for further assistance.

The transcript concludes with an emphasis on the joy of learning mathematics and the availability of John's algebra courses for different levels of study.

Transcripts
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