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| == Concept Map == | | == Concept Map == |
| <mm>[[SQUARE ROOTS .mm|Flash]]</mm> | | <mm>[[SQUARE ROOTS .mm|Flash]]</mm> |
| + | |
| + | == '''square root''' == |
| + | 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 <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 = |
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| ==Reference Books== | | ==Reference Books== |
| + | This text book contains activities for students to understand square and square root |
| + | [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=6-16 NCERT 8th std maths text book of chapter 6 ] |
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| = Teaching Outlines = | | = Teaching Outlines = |
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− | ==Concept #== | + | ==Concept #1== |
| + | ''''''perfect square-numbers'''''' |
| ===Learning objectives=== | | ===Learning objectives=== |
− | '''1. Finding perfect square-numbers'''<br>
| + | # The students should understand that a perfect square number is the product obtained by multiplying same number with same sign twice.<br> |
− | '''2. Recognising perfect square-numbers in a given group of numbers'''<br>
| + | # Recognising perfect square-numbers in a given group of numbers<br> |
− | '''3. perfect square-number patterns'''<br>
| + | # perfect square-number patterns<br> |
− | '''4. differentiating between perfect square-numbers & other numbers.'''<br>
| + | # differentiating between perfect square-numbers & other numbers.<br> |
− | '''5. Finding square root of a perfect square number by prime facterisation and division method'''<br>
| |
− | '''6. Finding square root of a decimal number'''
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| ===Notes for teachers=== | | ===Notes for teachers=== |
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| |} | | |} |
| *Materials/ Resources needed :- One white paper with 3 columns likeN , NxN &product.Pen or pencil to every student | | *Materials/ Resources needed :- One white paper with 3 columns likeN , NxN &product.Pen or pencil to every student |
− | *Prerequisites/Instructions, if any | + | *Prerequisites/Instructions, STUDENTS SHOULD PERFECTLY KNOW ABOUT MULTIPLICATION OF NUMBERS |
− | *Multimedia resources | + | *Multimedia resources INTERNET , |
− | *Website interactives/ links/ simulations | + | *Website interactives/ links/ simulations [http://www.miniwebtool.com/square-numbers-list/?to=1000 Inthis web site you can play with perfect square number s from 1 to 1000 & play games with numbers.] |
− | *Process/ Developmental Questions | + | *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 | + | *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 |
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