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Line 47: − '''1. Finding perfect square-numbers'''<br>+ − '''2. Recognising perfect square-numbers in a given group of numbers'''<br>+ − '''3. perfect square-number patterns'''<br>+ − '''4. 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''' Line 80:
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Template:Subst;square roots (view source)
Revision as of 08:07, 2 November 2013
, 08:07, 2 November 2013→Activity No 1
== 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> M^2 </math> . The number M is called square root of M
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 (-m)x(-m)=<math>(-m)^2</math> thus <math>m^2</math> has 2 square roots, m;m and m example 9=<math>3^2</math> or <math>(-3)^2</math>.thus both 3 and -3 or <math>\sqrt9</math>
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>
= Textbook =
= Textbook =
''''''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===
*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