Difference between revisions of "Template:Subst;square roots"
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== Concept Map == | == Concept Map == | ||
<mm>[[SQUARE ROOTS .mm|Flash]]</mm> | <mm>[[SQUARE ROOTS .mm|Flash]]</mm> | ||
| + | |||
== '''square root''' == | == '''square root''' == | ||
| − | Suppose N is a natural number such that N=<math> | + | Suppose N is a natural number such that N=<math>m^2</math> . The number m is called square root of N |
| − | we have <math>m^2</math>=mxm or | + | we have <math>m^2</math>=mxm or <math>(m)^2</math>=-mx-m. Thus <math>m^2</math> has 2 square roots, m and -m. Example 9=<math>3^2</math> or <math>(-3)^2</math>.Thus both 3 and -3 are <math>\sqrt9</math> |
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= Textbook = | = Textbook = | ||
| Line 58: | Line 47: | ||
''''''perfect square-numbers'''''' | ''''''perfect square-numbers'''''' | ||
===Learning objectives=== | ===Learning objectives=== | ||
| − | + | # The students should understand that a perfect square number is the product obtained by multiplying same number with same sign twice.<br> | |
| − | + | # Recognising perfect square-numbers in a given group of numbers<br> | |
| − | + | # perfect square-number patterns<br> | |
| − | + | # differentiating between perfect square-numbers & other numbers.<br> | |
| − | |||
| − | |||
===Notes for teachers=== | ===Notes for teachers=== | ||
| Line 80: | Line 67: | ||
*Process/ Developmental Questions<br> 1) the side of a square is 15 cm .what is area of square ?<br> 2) 121 balls are arranged in square pattern .How many balls in each row? | *Process/ Developmental Questions<br> 1) the side of a square is 15 cm .what is area of square ?<br> 2) 121 balls are arranged in square pattern .How many balls in each row? | ||
*Evaluation <br> 1) squqre of 15 =........<br>2)144 =........... writte in the form n2 | *Evaluation <br> 1) squqre of 15 =........<br>2)144 =........... writte in the form n2 | ||
| + | *Question Corner | ||
| + | |||
| + | ===Activity No 2 === | ||
| + | {| style="height:10px; float:right; align:center;" | ||
| + | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
| + | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
| + | |} | ||
| + | *Materials/ Resources needed :- | ||
| + | *Prerequisites/Instructions, | ||
| + | *Multimedia resources | ||
| + | *Website interactives/ links/ simulations | ||
| + | *Process/ Developmental Questions<br> | ||
| + | *Evaluation <br> | ||
| + | *Question Corner | ||
| + | ===Activity No 3 === | ||
| + | {| style="height:10px; float:right; align:center;" | ||
| + | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
| + | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
| + | |} | ||
| + | *Materials/ Resources needed :- | ||
| + | *Prerequisites/Instructions, | ||
| + | *Multimedia resources | ||
| + | *Website interactives/ links/ simulations | ||
| + | *Process/ Developmental Questions<br> | ||
| + | *Evaluation <br> | ||
| + | *Question Corner | ||
| + | |||
| + | ==Concept #2== | ||
| + | SQUARE ROOT OF A NUMBER | ||
| + | |||
| + | ===Learning objectives=== | ||
| + | # Understanding the geometric meaning of square root. | ||
| + | # Finding square root of a perfect square number by prime factorisation.> | ||
| + | # Finding square root of a number by division method. | ||
| + | # Finding square root of a decimal number. | ||
| + | |||
| + | ===Notes for teachers=== | ||
| + | |||
| + | ===Activity No 1 Activity on square and square roots by exploring the relationship between area of a square and its side length === | ||
| + | {| style="height:10px; float:right; align:center;" | ||
| + | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
| + | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
| + | |} | ||
| + | *Estimated Time : | ||
| + | 40 minutes. | ||
| + | *Materials/ Resources needed :Laptop, geogebra file, projector and a pointer. | ||
| + | *Prerequisites/Instructions: | ||
| + | # The students should know tables and multiplication . | ||
| + | # They should know that the product obtained by multiplying the same number twice is called a perfect square number and the number itself is called its square root. | ||
| + | # They should know a square , its side length and finding area of a square. | ||
| + | *Multimedia resources : Laptop | ||
| + | *Website interactives/ links/ simulations | ||
| + | *Process: | ||
| + | # Initially the teacher can discuss about a square, its sides and area of a square. | ||
| + | # Tell the students that each small inner square measures 1 unit . | ||
| + | # Formula to find area of square is side X side. | ||
| + | # Each inner square's area is 1 sq unit. | ||
| + | # Start with a outer big square of side length 3, which gives an area of 9. Then after doing side lengths of 3-5, put up a square and say the area is 64, so what must the side lengths be? The students will know it must be 8. Do this a few times and then introduce the new notation saying that the side length for the square with area 64 is the sqrt(64) = 8, and that is along the side of the square. Similarly repeat for area 144 and write it as square root of 144 =12 on the side length. Tell them that a square root is the inverse of squaring a number. | ||
| + | # Introduce the symbols forsquare and square root. | ||
| + | Extending the analogy to the area of a square and its side length helps students visualize the geometric meanings of square and square roots. | ||
| + | [Note : Disadvantage of this activity: here we can consider only positive numbers as square roots. Hence in further classes the concept of square root should be extended to negative numbers as well.] | ||
| + | *Developmental Questions: | ||
| + | # What is the figure called ? | ||
| + | # How do you know its a square ? | ||
| + | # Why is the figure called a perfect square ? | ||
| + | # What are the dimensions of each inner smaller square ? | ||
| + | # What is the area of each small inner square ? | ||
| + | # What is the area of two such small squares ? | ||
| + | # What is the area of 9 such small squares ? | ||
| + | # If the small squares are of 1 unit dimension, and area of each such square is one sqcm, can we say that the whole area is equal to the total number of smaller squares. | ||
| + | # (The number of cells/small squares in each row) x (number of rows) gives us ________. | ||
| + | # If the number of cells in each row and number of rows is same then we multiply the _________ number twice. | ||
| + | # Conversely if area is known, then its ___________ can be found out. | ||
| + | # For ex : If the area of a square is 81, then what would be its side length? | ||
| + | |||
| + | *Evaluation : | ||
| + | # Did students make the connection between the area of a square and square numbers? How do you know? | ||
| + | # What evidence helped you assess students' understanding of the geometric meaning of square root? | ||
| + | *Question Corner: | ||
| + | # If you know the side length of a square, how can you determine its area? | ||
| + | # If you know the area of a square, how can you determine its side length? | ||
| + | |||
| + | ===Activity No 2 === | ||
| + | {| style="height:10px; float:right; align:center;" | ||
| + | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | ||
| + | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | ||
| + | |} | ||
| + | *Materials/ Resources needed :- | ||
| + | *Prerequisites/Instructions, | ||
| + | *Multimedia resources | ||
| + | *Website interactives/ links/ simulations | ||
| + | *Process/ Developmental Questions<br> | ||
| + | *Evaluation <br> | ||
*Question Corner | *Question Corner | ||
Latest revision as of 13:37, 2 November 2013
| Philosophy of Science |
While creating a resource page, please click here for a resource creation checklist
Concept Map
Error: Mind Map file SQUARE ROOTS .mm not found
square root
Suppose N is a natural number such that N= . The number m is called square root of N we have =mxm or =-mx-m. Thus has 2 square roots, m and -m. Example 9= or .Thus both 3 and -3 are
Textbook
8 and 9 maths text books of Karnataka state
To add textbook links, please follow these instructions to:
(Click to create the subpage)
Additional information
Useful websites
you can play with perfect square numbers from 1 to 1000 & play games with numbers please click here
To estimate the square root of a number click here
To play quiz on square root of a number click here
Reference Books
This text book contains activities for students to understand square and square root NCERT 8th std maths text book of chapter 6
Teaching Outlines
Concept #1
'perfect square-numbers'
Learning objectives
- The students should understand that a perfect square number is the product obtained by multiplying same number with same sign twice.
- Recognising perfect square-numbers in a given group of numbers
- perfect square-number patterns
- differentiating between perfect square-numbers & other numbers.
Notes for teachers
Patterns & games of perfect square-number may be given to students
Activity No 1
On a paper make 3 columns like N , NxN & product .give some numbers under column N and students can fill the other 2 columns
- Materials/ Resources needed :- One white paper with 3 columns likeN , NxN &product.Pen or pencil to every student
- Prerequisites/Instructions, STUDENTS SHOULD PERFECTLY KNOW ABOUT MULTIPLICATION OF NUMBERS
- Multimedia resources INTERNET ,
- Website interactives/ links/ simulations Inthis web site you can play with perfect square number s from 1 to 1000 & play games with numbers.
- Process/ Developmental Questions
1) the side of a square is 15 cm .what is area of square ?
2) 121 balls are arranged in square pattern .How many balls in each row? - Evaluation
1) squqre of 15 =........
2)144 =........... writte in the form n2 - Question Corner
Activity No 2
- Materials/ Resources needed :-
- Prerequisites/Instructions,
- Multimedia resources
- Website interactives/ links/ simulations
- Process/ Developmental Questions
- Evaluation
- Question Corner
Activity No 3
- Materials/ Resources needed :-
- Prerequisites/Instructions,
- Multimedia resources
- Website interactives/ links/ simulations
- Process/ Developmental Questions
- Evaluation
- Question Corner
Concept #2
SQUARE ROOT OF A NUMBER
Learning objectives
- Understanding the geometric meaning of square root.
- Finding square root of a perfect square number by prime factorisation.>
- Finding square root of a number by division method.
- Finding square root of a decimal number.
Notes for teachers
Activity No 1 Activity on square and square roots by exploring the relationship between area of a square and its side length
- Estimated Time :
40 minutes.
- Materials/ Resources needed :Laptop, geogebra file, projector and a pointer.
- Prerequisites/Instructions:
- The students should know tables and multiplication .
- They should know that the product obtained by multiplying the same number twice is called a perfect square number and the number itself is called its square root.
- They should know a square , its side length and finding area of a square.
- Multimedia resources : Laptop
- Website interactives/ links/ simulations
- Process:
- Initially the teacher can discuss about a square, its sides and area of a square.
- Tell the students that each small inner square measures 1 unit .
- Formula to find area of square is side X side.
- Each inner square's area is 1 sq unit.
- Start with a outer big square of side length 3, which gives an area of 9. Then after doing side lengths of 3-5, put up a square and say the area is 64, so what must the side lengths be? The students will know it must be 8. Do this a few times and then introduce the new notation saying that the side length for the square with area 64 is the sqrt(64) = 8, and that is along the side of the square. Similarly repeat for area 144 and write it as square root of 144 =12 on the side length. Tell them that a square root is the inverse of squaring a number.
- Introduce the symbols forsquare and square root.
Extending the analogy to the area of a square and its side length helps students visualize the geometric meanings of square and square roots. [Note : Disadvantage of this activity: here we can consider only positive numbers as square roots. Hence in further classes the concept of square root should be extended to negative numbers as well.]
- Developmental Questions:
- What is the figure called ?
- How do you know its a square ?
- Why is the figure called a perfect square ?
- What are the dimensions of each inner smaller square ?
- What is the area of each small inner square ?
- What is the area of two such small squares ?
- What is the area of 9 such small squares ?
- If the small squares are of 1 unit dimension, and area of each such square is one sqcm, can we say that the whole area is equal to the total number of smaller squares.
- (The number of cells/small squares in each row) x (number of rows) gives us ________.
- If the number of cells in each row and number of rows is same then we multiply the _________ number twice.
- Conversely if area is known, then its ___________ can be found out.
- For ex : If the area of a square is 81, then what would be its side length?
- Evaluation :
- Did students make the connection between the area of a square and square numbers? How do you know?
- What evidence helped you assess students' understanding of the geometric meaning of square root?
- Question Corner:
- If you know the side length of a square, how can you determine its area?
- If you know the area of a square, how can you determine its side length?
Activity No 2
- Materials/ Resources needed :-
- Prerequisites/Instructions,
- Multimedia resources
- Website interactives/ links/ simulations
- Process/ Developmental Questions
- Evaluation
- Question Corner