DETAILED LESSON PLAN IN GRADE IX I
Spec pecific fic Obj Objeectiv tives
At the end of 60 minute period at least 75% of the students should be able to: • • •
Identify the equation that expresses a direct variation Determine the table of values and the raph that expresses a direct variation !olve !olve the iven problem problem usin usin y=kx as y=kx as the mathematical equation of direct variation" #here k is is a constant of variation
II Su Subj bjec ectt Mat Matte terr
A Topic: Topic: Direct $ariation B Reference: athematics Reference: athematics &earner's aterial for (rade )" pp* +),-.0/ http:###*purplemath*commodulesvariatn*htm
http:###*freemathhelp*comdirect-variation*html
C Materials: + &aptop 1 for encodin lesson plan + 2artolina 1 for visual aid .3entel pen 4lac and ed8 1 for visual aid + !cotch tape 1 for visual aid D Concepts: 9ssential 2oncept: Direct $ariation • !ub-2oncepts: Identify the equation that expresses a direct variation • Determine the table of values and raph that expresses a direct variation • !olve the iven problem usin y=kx usin y=kx as as the mathematical equation of direct • variation" #here k is is a constant of variation Teaching Teaching Strategies: Demonstration&ecture ethod" Discovery and 3rocess Approach" 3roblem ethod" oard #or III Proc Procedu edure re Teachers Activit!
Stude"ts Activit!
A# Acti Activi vit! t! $# Pre% Pre%ac acti tivi vit! t! 3rayer • 2hecin of Attendance • (reetins • &# I"tr I"trod oduc uctor tor! ! Activit ctivit! ! 3lease see at the last pae of this lesson
In the name of the ather;* Amen* Amen* (ood mornin" ma'am<
plan* '# Lesso" Proper =he activity you've done is connected to the topic for today #hich is >Direct $ariation?* Direct Variation 1 #hen a situation produces pairs of numbers in #hich their ratio is constant* =he mathematical formula of Direct $ariation" y@x" #here x - independent variable y 1 dependent variable 1 constant of variation can be translated in mathematical statements >y varies directly as x? >y is directly proportional to x? >y is proportional to x? or . quantities" x and y" an increase in x causes an increase in y as #ell* !imilarly" a decrease in x causes a decrease in y* !uppose #e have the equations" its table of values and raphs: !()*
x y
-. -B
-+ -,
0 0
+ ,
. B
-.
-+
0
+
.
!(%&*
x
y
,
.
0
-.
,
-. -+
-+ +
0 /
+ 5
. 7
!(&*+'
x y
y@,x and
[email protected]" because it's in the form rom the / equations #hich do you thin of y@x" #hile
[email protected]/ is not an example isare the examples of a direct variationC of direct variation* hyC 2orrect< =his is in the form of slopeintercept form y@mxEb" #here m is the slope and b is the y-intercept* Fo# about y@,x and
[email protected]" is it in a form of slope-intercept formC hyC 2orrect< =herefore" direct variation is simply in a slope-intercept form #hen byintercept is Gero* !o" in y@,x and
[email protected]"
Hes* It is in the form of y@mxEb" but its yinterceptb is Gero*
their y@intercepts are Gero and their slope are , and -." similarly the slope determines the constant of variation* Do you et itC rom the iven / raphs" ho# do you determine if it expresses a direct variationC 2orrect<
rom the iven / table of values" ho# do you determine if it expresses a direct variationC 2orrect< ut #hen the value of x is Gero the value of y #ill al#ays be Gero and its ratio #ill al#ays be Gero* If you tae a loo in its raph" the raph of y@, and y@-. crosses the oriin 40"08*
Hes< =he raph should have the same slope and al#ays crosses the oriin 40"08 (raph of y@,x: 9xpresses Direct $ariation (raph of y@-.: 9xpresses Direct $ariation (raph of
[email protected]/: Do not expresses Direct $ariation (et the ratio of y and x in each column* If it is the sameequal then there is a constant of variation and the table of values express a direct variation*
!()*
x -. -+ 0 y -B -, 0 , , 0 (et the ratio of y and x in each table of 9xpresses Direct $ariation values to determine if it expresses a direct !(%&* variation* x -. -+ 0 y , . 0 As you can see the ratio is equal to the -. -. 0 constant of variation* 9xpresses Direct $ariation
+ , ,
. B ,
+ -. -.
. , -.
x -. -+ 0 + y -+ + / 5 -+. -+ J 5 Do not expresses direct variation
. 7 7.
!(&*+'
o#" ho# do you solve the iven #ord
problem #hich expresses a direct variation E*a,p-e .$ If y varies directly as x and y@., #hen x@6" find the variation constant and the equation of variation* Solution: 9xpress > y varies directly as x” as y@x !olve for k by substitutin the iven values in the equation* y @ x ., @ 6 @ , 1 constant of variation
!ubstitutin , to in y@x" y @ ,x 1 equation of variation E*a,p-e .& =he table belo# sho#s that the distance varies directly as the time t * ind the constant of variation and the equation #hich describes the relation*
=ime 4hr*8 + . / , 5 Distance + . / , 5 4m8 0 0 0 0 0 Solution: !ince the distance varies directly as the time t " then d@t* Ksin one of the pairs of values" 4." .08" from the table" substitute the values of and t in d@t and solve for * d @ t .0 @ . @ +0 1 constant of variation y @ t y @ +0t 1 equation of the variation E*a,p-e .'
If x varies directly as y and x@/5 #hen y@7" #hat is the value of y #hen
[email protected] Solution: x @ y /5 @ 7
@ 5 1 constant of variation x @ y .5 @ 5y y@5 Lther solution by proportion" !ince xy is a constant" #e #rite @xy" from here #e can x 1
obtain a proportion
y 1
=
x 2 y 2
*
x+ @ /5 y+ @ 7 x. @ .5 y. @ C x 1 y 1
35 7
=
x 2
=
@ -5
y 2
y @ .,
25
@+5"
[email protected] @," x@B
y 2
/5y. @ +75 y. @ 5 #e obtain the same ans#er* E*a,p-e .) /Dri--01oard 2or34 I* In each of the follo#in" y varies directly as x* ind the values as indicated* + ind the constant of a direct variation #hen x @ 6 and y @ -/0* . If the constant variation is -," then #hat is the value of y #hen x @ -6C / If y@/ #hen x@+5" find x #hen y @ 5* , If y @ -B #hen x @ -." find x #hen y @ /.* II* =he distance traveled varies directly #ith the time of travel* If the distance traveled is .50 meters in .5 seconds" find the distance traveled in 60 seconds*
d @ t .50 @ .5 @ +0 d @ t d @ +0y d @ +04608 d @ 600 meters
1# Abstractio" Fo# do you identify expresses direct variationC
equation
that
5# A"a-!sis
Fo# do you determine the table of values that expresses a direct variationC Fo# do you determine the raph that expresses a direct variationC Fo# do you solve the iven #ord problem usin y@x as the mathematical equation of direct variation" #here k is a constant of variation D# App-icatio" ella uses .0 liters of asoline to travel .00 m* Fo# many liters of asoline #ill be use on a trip of 700 mC
I6 Eva-uatio" 0 Assess,e"t A* ind the constant of variation and #rite an equation #here y varies directly as x* + y @ .B #hen x @ 7 . y @ /0 #hen x @ B * In each of the follo#in" y varies directly as x* ind the value as indicated* / If y @ /6" #hen x @ ," find y #hen x @ 7 , If y @ +0" #hen x @ ." find y #hen x @ / 2* =he distance you travel varies directly #ith time* If you travel +,7 miles in / hours" ho# lon #ith it tae to travel .,5 milesC 6 Assi7",e"t Activity 6" pp* .00-.0." 4+-/" 7-B8 and D4+-58* A* Determine if the table and raphs belo# express a direct variation bet#een the variables* If they do" find the constant of variation and an equation that defines the relation* + x + . / , y -/ -6 -) -+. . x + . / , y / 6 -) -+. / x + . / , y -/ . -, 5 , 5*
* In each of the follo#in" y varies directly as x* ind the values as indicated* + If y @ +. #hen x @ ," find y #hen x @ +. . If y @ -+B #hen x @ )" find y #hen x @ 7 / If y @ -/ #hen x @ -," find x #hen y @ . , If y @ / #hen x @ +0" find x #hen y @ +*. 5 If y @ .*5 #hen x @ *.5" find y #hen x @ *75 Group Activit! /$8 7roups9 7ood for $8 ,i"utes4
I* Direction: 2omplete the table of values usin the formula of the perimeter of the square 43@,s8 then raph the points from the table of values you've completed* P()s
!ide of the square 4cm8 3erimeter of the square
+
.
/
,
5
6
7
Direction: ase table of values and raph you've completed" ans#er the ff* questions* +* hat equation describes the raphC .* hat happened to the perimeter #hen the side is .C /C " /* hat happened to the perimeter of the square as the side of the square increasesC
from
,* ind the ratio of the perimeter of the square and the side of the square* !ide of the square 4cm8 3erimeter of the square
+
.
/
,
5
6
7
P
( ) atio S 5* hat have you observed about the ratios of perimeter of the square and the side of the squareC
