KutaSoftware: Algebra 1- System Of Equations Substitution Part 1
KutaSoftware: Algebra 1- System Of Equations Substitution Part 1

For all of my life, I’ve been a self-proclaimed math nerd. Math has always come easy to me and I actually ENJOY solving equations. Crazy, right?

For me, systems of equations are simple to solve. It just makes sense to me. But for MANY people, many of your students included, it doesn’t make sense. It isn’t simple. I always used to say that a teacher should actually teach skills they are NOT super confident with because it would require them to find new ways to teach that would help their students understand. When you teach something you are comfortable with, you often lose sight of the potential struggles. It is so clear to you that you are unable to actually understand the mistakes that can be made. In this blog post I’ll share with you some teaching strategies for systems that can help you provide the best instruction possible!

The Tips!

First – Let them figure it out on their own. I always suggest introducing systems with a real world situation. For example, “Two types of tickets are sold to a play. Floor seats cost \$45 each and balcony seats cost \$25 each. A play sells 107 tickets and makes a total of \$3,375. How many of each type of ticket are sold?” Allow students to work in groups of 2-3 to figure out the problem. Have each pair/group share how they found their answer. The point of this type of exploration is to allow students to see that there are multiple ways to arrive at the same answer. This will be a great intro into sharing the multiple ways a single system can be solved.

Second – Break it down. Systems have a lot of moving parts. For many students, too many moving parts. Allow students to focus on one piece of the puzzle at a time, one equation at a time. Stop many times along the way to have them share their steps, ideas, thoughts. The more discussion involved, the better.

Third – Allow exploration with technology. Don’t let students be limited to just solving systems by hand. While yes, it is incredibly important for students to understand how to solve systems using substitution and elimination, it is also important for students to understand what systems look like when graphed – how it is possible for two equations that look different (when written in standard or other forms) to actually represent the same line. They can explore using graphing calculators, but desmos is the most amazing resource to let students see a system.

Fourth – Bring out the pencils. Once your students understand HOW and WHY systems are what they are, they need to understand that solving systems by either elimination or substitution involves nothing more than basic arithmetic. Guided practice is essential with guided notes, teacher-assisted practice and lots of trial and error. Click here to head to my YouTube channel, where I share videos on how to solve systems (among other things) with all three methods! There are many different ways to practice systems on paper (and digitally) available that are engaging and far beyond typical drill and practice.

Fifth – Don’t use a matrix. This might go against what some of your districts tell you do to, and by all means, if it is required of you – please teach it. Otherwise, systems with matrices are confusing, difficult and out of all four possible ways to solve, come in dead last.
The text is a blog post about teaching strategies for solving systems of equations, including an example problem and tips for instruction.
single_question_with_answer

the text contains a single mathematical question: "two types of tickets are sold to a play. floor seats cost \$45 each and balcony seats cost \$25 each. a play sells 107 tickets and makes a total of \$3,375. how many of each type of ticket are sold?" the answer is not explicitly provided, but the text suggests that students should work in groups to figure out the problem and share their answers.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
KutaSoftware: Algebra 1- System Of Equations Substitution Part 1
KutaSoftware: Algebra 1- System Of Equations Substitution Part 1

For all of my life, I’ve been a self-proclaimed math nerd. Math has always come easy to me and I actually ENJOY solving equations. Crazy, right?

For me, systems of equations are simple to solve. It just makes sense to me. But for MANY people, many of your students included, it doesn’t make sense. It isn’t simple. I always used to say that a teacher should actually teach skills they are NOT super confident with because it would require them to find new ways to teach that would help their students understand. When you teach something you are comfortable with, you often lose sight of the potential struggles. It is so clear to you that you are unable to actually understand the mistakes that can be made. In this blog post I’ll share with you some teaching strategies for systems that can help you provide the best instruction possible!

The Tips!

First – Let them figure it out on their own. I always suggest introducing systems with a real world situation. For example, “Two types of tickets are sold to a play. Floor seats cost \$45 each and balcony seats cost \$25 each. A play sells 107 tickets and makes a total of \$3,375. How many of each type of ticket are sold?” Allow students to work in groups of 2-3 to figure out the problem. Have each pair/group share how they found their answer. The point of this type of exploration is to allow students to see that there are multiple ways to arrive at the same answer. This will be a great intro into sharing the multiple ways a single system can be solved.

Second – Break it down. Systems have a lot of moving parts. For many students, too many moving parts. Allow students to focus on one piece of the puzzle at a time, one equation at a time. Stop many times along the way to have them share their steps, ideas, thoughts. The more discussion involved, the better.

Third – Allow exploration with technology. Don’t let students be limited to just solving systems by hand. While yes, it is incredibly important for students to understand how to solve systems using substitution and elimination, it is also important for students to understand what systems look like when graphed – how it is possible for two equations that look different (when written in standard or other forms) to actually represent the same line. They can explore using graphing calculators, but desmos is the most amazing resource to let students see a system.

Fourth – Bring out the pencils. Once your students understand HOW and WHY systems are what they are, they need to understand that solving systems by either elimination or substitution involves nothing more than basic arithmetic. Guided practice is essential with guided notes, teacher-assisted practice and lots of trial and error. Click here to head to my YouTube channel, where I share videos on how to solve systems (among other things) with all three methods! There are many different ways to practice systems on paper (and digitally) available that are engaging and far beyond typical drill and practice.

Fifth – Don’t use a matrix. This might go against what some of your districts tell you do to, and by all means, if it is required of you – please teach it. Otherwise, systems with matrices are confusing, difficult and out of all four possible ways to solve, come in dead last.
user
The text is a blog post about teaching strategies for solving systems of equations, including an example problem and tips for instruction.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The text contains a single mathematical question: "Two types of tickets are sold to a play. Floor seats cost \$45 each and balcony seats cost \$25 each. A play sells 107 tickets and makes a total of \$3,375. How many of each type of ticket are sold?" The answer is not explicitly provided, but the text suggests that students should work in groups to figure out the problem and share their answers.