Difference between revisions of "Simultaneous Linear Equations"
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= Concept Map = | = Concept Map = | ||
| − | + | [[File:Simultaneous_Linear_Equations.mm|Flash]] | |
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__FORCETOC__ | __FORCETOC__ | ||
= Textbook = | = Textbook = | ||
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==Concept #1 - Where do I use simultaenous equations == | ==Concept #1 - Where do I use simultaenous equations == | ||
===Learning objectives=== | ===Learning objectives=== | ||
| − | = | + | |
| + | #There are two quantities/ parameters that are used together to describe something. | ||
| + | #This is of the forms ax+by = c | ||
| + | #You need two sets of equations to find the solutions. | ||
| + | #Extend this understanding for different sets of variables. | ||
| − | + | ===Notes for teachers=== | |
===Activity No # === | ===Activity No # === | ||
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| − | ''[http:// | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
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*Estimated Time | *Estimated Time | ||
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*Question Corner | *Question Corner | ||
| − | ==Concept #== | + | ==Concept #2 - Graphical Method of Simultaneous Equations== |
===Learning objectives=== | ===Learning objectives=== | ||
| + | #State a given problem in algebraic terms | ||
| + | #Identifying the variables | ||
| + | #Interpret a linear equation as a line | ||
| + | #Understand that the solution is a point on both the lines, they intersect | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| − | ===Activity No | + | It is better to use the graphical method before the algebraic manipulation.<br> |
| + | {{#widget:YouTube|id=MRAIgJmRmag}} | ||
| + | |||
| + | ===Activity No 1: [[Simultaneous linear equation activity|Simultaneous linear equation]] === | ||
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===Activity No # === | ===Activity No # === | ||
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*Estimated Time | *Estimated Time | ||
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*Evaluation | *Evaluation | ||
*Question Corner | *Question Corner | ||
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= Hints for difficult problems = | = Hints for difficult problems = | ||
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== Applications of Simultaneous Linear Equations - Exercise 3.5.5 == | == Applications of Simultaneous Linear Equations - Exercise 3.5.5 == | ||
| − | ===Problem #5=== | + | ===Problem #5, Exercise 3.5.5, Page 213 === |
| − | + | The measure of the sides (in cms) of a triangle are :<br> | |
| − | + | <math>\frac{5}{3}x+y+\frac{1}{2}</math><br> | |
| − | + | <math>2x+\frac{1}{2}y</math><br> | |
| + | <math>\frac{2}{3}x+2y+\frac{5}{2}</math> | ||
| + | When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle? | ||
| + | '''How to solve''' | ||
| + | #These are measurements of the sides of the triangle | ||
| + | #Equate the three | ||
| + | #Substitute and solve for x and y. | ||
| − | + | '''Competencies''' | |
| + | #Equilateral triangle must have all sides equal | ||
| + | #The sides of a triangle are line (segments) and can be expressed as a linear equation. Though this is not used for solving this problem | ||
| + | #Infer that if the sides are same, the expressions must be the same numerical value | ||
| + | #If that is true, I can use combine the expressions to express one in terms of the other | ||
| + | #Rearranging terms and combining expressions to form equations | ||
| + | #Solve | ||
= Project Ideas = | = Project Ideas = | ||
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template | Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template | ||
| + | |||
| + | [[Category:Simultaneous Linear Equations]] | ||
Latest revision as of 20:09, 19 December 2020
| Philosophy of Mathematics |
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Concept Map
Textbook
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Additional Information
Useful websites
Reference Books
Teaching Outlines
Concept #1 - Where do I use simultaenous equations
Learning objectives
- There are two quantities/ parameters that are used together to describe something.
- This is of the forms ax+by = c
- You need two sets of equations to find the solutions.
- Extend this understanding for different sets of variables.
Notes for teachers
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept #2 - Graphical Method of Simultaneous Equations
Learning objectives
- State a given problem in algebraic terms
- Identifying the variables
- Interpret a linear equation as a line
- Understand that the solution is a point on both the lines, they intersect
Notes for teachers
It is better to use the graphical method before the algebraic manipulation.
Activity No 1: Simultaneous linear equation
Activity No #
- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner
Hints for difficult problems
Applications of Simultaneous Linear Equations - Exercise 3.5.5
Problem #5, Exercise 3.5.5, Page 213
The measure of the sides (in cms) of a triangle are :
When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle?
How to solve
- These are measurements of the sides of the triangle
- Equate the three
- Substitute and solve for x and y.
Competencies
- Equilateral triangle must have all sides equal
- The sides of a triangle are line (segments) and can be expressed as a linear equation. Though this is not used for solving this problem
- Infer that if the sides are same, the expressions must be the same numerical value
- If that is true, I can use combine the expressions to express one in terms of the other
- Rearranging terms and combining expressions to form equations
- Solve
Project Ideas
Math Fun
Usage
Create a new page and type {{subst:Math-Content}} to use this template