Difference between revisions of "Linear Equations in one and two variables"
Jump to navigation
Jump to search
KOER admin (talk | contribs) m (Text replacement - "</mm>" to "") |
Neeta Jose (talk | contribs) m (added Category:Linear Equations using HotCat) |
||
| (30 intermediate revisions by 5 users not shown) | |||
| Line 5: | Line 5: | ||
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" | {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" | ||
|- | |- | ||
| − | |style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] | ||
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics] | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics] |
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] | ||
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | ||
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] | ||
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks] | ||
| − | |style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "| | + | | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | |
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank] | [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank] | ||
|} | |} | ||
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. | While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. | ||
| − | = Concept Map = | + | == Concept Map == |
__FORCETOC__ | __FORCETOC__ | ||
[[File:Linear equations in one variable.mm|Flash]] | [[File:Linear equations in one variable.mm|Flash]] | ||
| − | = Textbook = | + | == Textbook == |
| − | + | Karnataka State textbook- [http://ktbs.kar.nic.in/new/website%20textbooks/class8/8th-english-maths-1.pdf Chapter 9: Linear Equations in one variable] | |
| − | |||
| − | =Additional Information= | + | ==Additional Information== |
| − | + | === Resources === | |
| − | ==Useful websites== | + | |
| − | # | + | ==== Resource Title ==== |
| − | # | + | # [https://phet.colorado.edu/en/simulation/graphing-lines Graphing Lines] |
| + | # [http://www.mathopenref.com/linearexplorermxb.html Linear Function Explorer] | ||
| + | |||
| + | ===Useful websites=== | ||
| + | # Videos related to linear equation in one varable. [https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-intro-equations/v/variables-expressions-and-equations click here] | ||
| + | # More information about linear equation.[http://www.math.utah.edu/~giessing/notes/Ch3.3.pdf click here] | ||
| + | # Help students in understanding equations by making links with graphical representations of algebraic equations and expressions, and by juxtaposing differences and sameness. Encourage creation of concept and mind maps to help further with students’ understanding of mathematical concepts. [http://www.tess-india.edu.in/sites/default/files/imported/57353/SM07_AIE_Final.pdf Click here] | ||
| + | # This unit [https://education.ky.gov/educational/diff/Documents/SolvingLinearEquationsinonevariable.pdf 'Solving linear equations in one variable'] aims to encourage discussion on some common misconceptions about algebra and to assess students on how well they are able to solve linear equations in one variable with rational number coefficients. | ||
==Reference Books== | ==Reference Books== | ||
| + | NCERT textbook for class 8- [http://ncert.nic.in/textbook/textbook.htm?hemh1=2-16 Chapter 2: Linear Equations in One Variable] | ||
= Teaching Outlines = | = Teaching Outlines = | ||
| − | ==Concept | + | ==Concept 1 - Linear equation in one variable== |
===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| Line 47: | Line 54: | ||
===Activity No # === | ===Activity No # === | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
===Activity No # === | ===Activity No # === | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | + | ==Concept 2 - Linear equation in two variables== | |
| − | ==Concept | ||
===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| − | '' | + | Providing sets of 'x' and 'y' values in a spreadsheet helps students to explore a variety of linear equations in two variables. |
| + | |||
| + | Some sets can represent points not on a line. | ||
| + | |||
| + | ===Activity No 2 - [[Linear Equations in one and two variables Activity No 2-Plot linear equation in two variables using Geogebra]] === | ||
| + | ===Activity No 3 - [[Simultaneous linear equation activity|Simultaneous linear equation]] === | ||
| − | === | + | == Concept 3 - Understanding What is a slope == |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| + | === Activity No 1- [['understanding What is a slope?- Activity No1]] === | ||
| − | ===Activity No | + | === Activity No 2- [[Activities on Slope of a line]] === |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
= Hints for difficult problems = | = Hints for difficult problems = | ||
| Line 118: | Line 77: | ||
= Math Fun = | = Math Fun = | ||
| + | '''Constructing linear equations from real-world applications:''' | ||
| + | |||
| + | This activity will have students construct and solve linear equations that they derive from their everyday experiences. Students could work in pairs or groups of 3-4. | ||
| + | |||
| + | 1. Construct a linear equation in which the solution is the number of apps that you have on your smart-phone. (If you do not have a smart-phone then your solution should be a= 0). The equation should involve at least three arithmetic operations. | ||
| + | |||
| + | For example: 2(a–17)=50 where ''<nowiki/>'a''' represents the number of apps. Pass your paper to one of the classmates in your group. That classmate will solve the equation and verify that the answer is correct. | ||
| + | |||
| + | 2. Construct another linear equation. The solution to this equation could be the number of ice-creams eaten by you in the last six months. For this equation, have a variable on each side of the equation. | ||
| + | |||
| + | For example: 6x-22=2x+10 where ''<nowiki/>'x''' represent the number of ice-creams. Pass your paper another of your classmate. That classmate will solve the equation and verify that the answer is correct. | ||
| + | |||
| + | 3. Construct another equation in which the solution is the number of holidays you have this semester. The equation could include fractions in the equation. | ||
| + | |||
| + | For example: 8/12 c+15=17 where c represents the number of holidays. Pass your paper to a classmate. That classmate will solve the equation and verify that the answer is correct. | ||
| + | |||
| + | 4. Construct a linear equation whose solution is the current price of one kilogram of rice. | ||
| + | |||
| + | For example: 22p-202=1206 where p represents price of one kilo of of rice. Pass your paper to a classmate. That classmate will solve the equation and verify that the answer is correct. | ||
| − | + | 5. Similarly various groups can create such equations, exchange with each other and try solving them. | |
| − | + | [[Category:Class 8]] | |
| + | [[Category:Class 9]] | ||
| + | [[Category:Linear Equations]] | ||
Latest revision as of 19:15, 23 May 2021
| Philosophy of Mathematics |
While creating a resource page, please click here for a resource creation checklist.
Concept Map
Textbook
Karnataka State textbook- Chapter 9: Linear Equations in one variable
Additional Information
Resources
Resource Title
Useful websites
- Videos related to linear equation in one varable. click here
- More information about linear equation.click here
- Help students in understanding equations by making links with graphical representations of algebraic equations and expressions, and by juxtaposing differences and sameness. Encourage creation of concept and mind maps to help further with students’ understanding of mathematical concepts. Click here
- This unit 'Solving linear equations in one variable' aims to encourage discussion on some common misconceptions about algebra and to assess students on how well they are able to solve linear equations in one variable with rational number coefficients.
Reference Books
NCERT textbook for class 8- Chapter 2: Linear Equations in One Variable
Teaching Outlines
Concept 1 - Linear equation in one variable
Learning objectives
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activity No #
Activity No #
Concept 2 - Linear equation in two variables
Learning objectives
Notes for teachers
Providing sets of 'x' and 'y' values in a spreadsheet helps students to explore a variety of linear equations in two variables.
Some sets can represent points not on a line.
Activity No 2 - Linear Equations in one and two variables Activity No 2-Plot linear equation in two variables using Geogebra
Activity No 3 - Simultaneous linear equation
Concept 3 - Understanding What is a slope
Activity No 1- 'understanding What is a slope?- Activity No1
Activity No 2- Activities on Slope of a line
Hints for difficult problems
Project Ideas
Math Fun
Constructing linear equations from real-world applications:
This activity will have students construct and solve linear equations that they derive from their everyday experiences. Students could work in pairs or groups of 3-4.
1. Construct a linear equation in which the solution is the number of apps that you have on your smart-phone. (If you do not have a smart-phone then your solution should be a= 0). The equation should involve at least three arithmetic operations.
For example: 2(a–17)=50 where 'a' represents the number of apps. Pass your paper to one of the classmates in your group. That classmate will solve the equation and verify that the answer is correct.
2. Construct another linear equation. The solution to this equation could be the number of ice-creams eaten by you in the last six months. For this equation, have a variable on each side of the equation.
For example: 6x-22=2x+10 where 'x' represent the number of ice-creams. Pass your paper another of your classmate. That classmate will solve the equation and verify that the answer is correct.
3. Construct another equation in which the solution is the number of holidays you have this semester. The equation could include fractions in the equation.
For example: 8/12 c+15=17 where c represents the number of holidays. Pass your paper to a classmate. That classmate will solve the equation and verify that the answer is correct.
4. Construct a linear equation whose solution is the current price of one kilogram of rice.
For example: 22p-202=1206 where p represents price of one kilo of of rice. Pass your paper to a classmate. That classmate will solve the equation and verify that the answer is correct.
5. Similarly various groups can create such equations, exchange with each other and try solving them.