Page 1 of 15 MCC@WCCUSD 06/04/14
Grade&Level/Course:&&&
!"#$%&'$(()*+)#,-./%0%
Lesson/Unit&Plan&Name:&%%
1./2$%345/.,%.((6%/78%'5-,%.((6%957'6"(73:%
Rationale/Lesson&Abstract:&
;(%53,%6$,%2/.,76%#./2$%(9%345/.,%.((6%/78%'5-,%.((6%957'6"(73%/78%6(%578,.36/78%6$,%
3"<")/."6",3%/78%8"99,.,7',3%-,6=,,7%6$,%6=(%#./2$3:%;(%=."6,%,45/6"(73%8,2,78"7#%(7%6$,%
>,.6"'/)%/78%$(."?(76/)%3$"963@%/3%=,))%/3@%'(<2.,33,8%/78%36.,6'$,8%#./2$3:%A"7/))B@%6(%#./2$%
345/.,%.((6%/78%'5-,%.((6%,45/6"(73:%
Timeframe:&
0CD%8/B%),33(7%E%F,2,78"7#%(7%'(<9(.6%),>,)%="6$%2/.,76%#./2$3%/78%3$"963:%
Common&Core&Standard(s):&
A:GA:H-%E%1./2$%345/.,%.((6%/78%'5-,%.((6%957'6"(73:% %
Instructional&Resources/Materials:&
I."76%(56%),33(7%/78%$/78(56%(9%7(6,3:%%
%
Activity/Lesson:&
J/.<%K2L%
M/6'$%6$,%9())(="7#%,45/6"(73%="6$%6$,".%#./2$3%/78%=."6,%/7%,45/6"(7%9(.%6$,%(6$,.3:%
/:
2
2xy =
%
-:
( )
3
1−= xy
%
':
%
8:%
( )
11
2
+−= xy
%
0:%D&
%
D:%
1
2
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%
%
N:%C&
%
O:%B&
%
P:%A&
%
Q:%
3
xy −=
%
%
%
%
Page 2 of 15 MCC@WCCUSD 06/04/14
R(<2),6,%6$,%#">,7%'$/.6L%
x
%
xxx ⋅=
2
%%%%%%%%%%%%%%%%%%%%%
xxxx ⋅⋅=
3
%
3−
%
( ) ( )( )
9333
2
=−−=−
%
( ) ( )( )( )
273333
3
−=−−−=−
%
2−
%
( ) ( )( )
4222
2
=−−=−
%
( ) ( )( )( )
82222
3
−=−−−=−
%
1−
%
( ) ( )( )
1111
2
=−−=−
%
( ) ( )( )( )
11111
3
−=−−−=−
%
0
%
( ) ( )( )
0000
2
==
%
( ) ( )( )( )
00000
3
==
%
1
%
( ) ( )( )
1111
2
==
%
( ) ( )( )( )
11111
3
==
%
2
%
( ) ( )( )
4222
2
==
%
( ) ( )( )( )
82222
3
==
%
3
%
( ) ( )( )
9333
2
==
%
( ) ( )( )( )
273333
3
==
%
F,3'."-,%6$,%3"<")/."6",3%/7 8%8"99, .,7 ',3%- ,6= ,, 7%34 5/ .,8%/78%'5-, 8%75< -,.3:%+)3(@%,S2)/"7%/7B6$"7#%B(5%7(6"',:%
The$square$numbers$are$positive$while$the$cube$numbers$have$negatives.$$
The$square$numbers$m atch$up$aroun d$0,$while$the$cube$numb ers$are$opposites$around$0. $
A"))%"7%6$,%6/-),3%-,)(=%53"7#%%B(5.%(-3,.>/6"(7%%/-(>,%6(%'$((3,%/22.(2."/6,%>/)5,3%9(.%xL%
x
%
xy =
%
y
%
( )
yx,
%
%
x
%
3
xy =
%
y
%
( )
yx,
%
0
%
0=y
%
0
%
( )
0,0
%
%
8−
%
3
8−=y
%
2−
%
( )
2,8 −−
%
1
%
1=y
%
1
%
( )
1,1
%
%
1−
%
3
1−=y
%
1−
%
( )
1,1 −−
%
4
%
4=y
%
2
%
( )
2,4
%
%
0
%
3
0=y
%
0
%
( )
0,0
%
9
%
9=y
%
3
%
( )
3,9
%
%
1
%
3
1=y
%
1
%
( )
1,1
%
16
%
16=y
%
4
%
( )
4,16
%
%
8
%
3
8=y
%
2
%
( )
2,8
%
1./2$%6$,%9())(="7#%957'6"(73%53"7#%B(5.%6/-),3%/-(>,:%
( )
xxf =
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3
xxf =
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G8,76"9B%6 $ ,%# . /2 $ 3 %T, B %9, /6 5 ., 3%"7 %6 $ , %3$ / 2 , %/7 8%6$,%2/. 6"' 5 )/. %2 ( "763%/.(57 8 %6$,%( ."#"7:%J."6,%8(=7%6$,%3"<")/."6",3%/78%
8"99,.,7',3%-,6=,,7%345/.,%.((6%/78%'5-,%.((6%#./2$3:%%
Quadrant$1$of$the$graphs$have$the$same$curved$shape,$but$different$values.$The$cube$root$function$ha s$ne ga tive $and $
positive$values$for$x$and$y,$while$the $sq u a re $ro o t$fu n ct io n$o n ly $h a s$p o sit ive $v alu e s $fo r$x and$y.$$
The$square$root$function$has$key$points$at$
( )
0,0
@
( )
1,1
@%and%
( )
2,4
:%The$cube$root$function$has$key$poin ts$
at
( )
1,1 −−
@
( )
0,0
@%and$
( )
1,1
:%%
You$only$plug$in$0$and$positive$values$for$x$in$the$squa re$root$function ,$bu t$neg a tive,$0$$an d$po sitive $valu es $in$the$ cube$
root$function.$It’s$best$to$p lu g $in $n u m b e rs $th a t$a r e$s q u a re d $an d $c u b ed $t o$g e t$in t eger$values.$$
Page 3 of 15 MCC@WCCUSD 06/04/14
K3"7#%6$,%2/.,76%#./2$%(9%/%345/.,%.((6%957'6"(7@%7/<,%6$,%'(736/76@%'(,99"'",76%/78%/.#5<,76%/78%8,3'."-,%$(=%"6%="))%
/99,'6%6$,%#./2$%(9%6$,%,45/6"(7%-,)(=L%%
;$,%/.#5<,76%"3%6$,%,S2.,33"(7%"73"8,%6$,%./8"'/):%G7%6$ ,%# "> ,7 %957'6"(7 @%
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xxf =
@%U
x
V%"3%6$,%/.#5<,76:%
( )
358 −+= xxf
%
&2,'"9"'/))BL%
G7%1,7, . /)L%
Constant$=$
3−
@%%shifts$down$3$$
Constant:$Vertical$shift,$Up$if$+,$Down$if$J$
Coefficient$=$8,$vertical$stretch,$values$are$8$times$bigger$$
Coefficient:$Stretch,$vertical$if$greater$than$1,$horizontal$if$
between$0$and$1.%
Argument$=$
5+x
@%shifts$to$the$left$5,$since$
055 =+−
$
Argument:$Horizontal$shift,$right$if$a$value$is$subtracting$
from$x,$le ft $if $a$v a lu e$is $a d d ed $t o x. This happens$because$
we$are$looking$for$when$the argument$is$0.$
%
K3,%6$,%9())(="7#%,45/6"(73%6(%</6'$%6(%6$,%#">,7%#./2$3%-,)(=%/78%=."6,%/7%,45/6"(7%9(.%6$,%(6$,.3:%F,3'."-,%$(=%6$,%
#./2$%'$/7#,3%9.(<%6$,%2/.,76%#./2$%/78%$(=%6$/6%,99,'63%6$,%,45/6"(73%'(736/76@%'(,99"'",76%(.%/.#5<,76:%A"7/))B@%9"78%
P%>/)5,3%6$/6%B(5%=(5)8%256%"7%B(5.%6C6/-),:%
%
/:%
3
2−= xy
%
-:%
1+= xy
%%
':%
3
2 xy =
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8:%
xy
2
1
=
%
%
0:%%%
%
%
D:%
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%
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%
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F,3'."26"(7L%%&45/.,%.((6%
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&$/2,%"3%6$,%3/<,:%
Y45/6"(7L%
1+= xy
%%
%
F,3'."26"(7L%&45/.,%.((6%
+6%(."#"7@%7(%>,.6"'/)%(.%$(."?(76/)%
3$"96:%%%
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⎟
⎠
⎞
⎜
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2
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F,3'."26"(7L%&45/.,%.((6%
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6$,%'(736/76:%! (."?( 76/ )%3$"96%
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32 −+= xy
%
%
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F,3'."26"(7L%R5-,%.((6%
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3
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F,3'."26"(7L%R5-,%.((6%
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2,1
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2 xy =
%
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x values: 0, 1, 4, 9, 16, ….
x values: 0, 1, 4, 9, 16, ….
x values: -2, -1, 2, 7, 14, …. Subtract 2
x values: -27, -8, -1, 0, 1, 8, 27, ….
x values: -27, -8, -1, 0, 1, 8, 27, ….
x values: -25, -6, -3, 2, 3, 10, 29, …. Add 2
Page 4 of 15 MCC@WCCUSD 06/04/14
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53 += xy
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>,.6"'/)%3$"963%52%P:%
x
53 += xy
y
( )
yx,
0
( )
503
503
+=
+=y
5
( )
5,0
1
( )
513
513
+=
+=y
8
( )
8,1
4
( )
523
543
+=
+=y
11
( )
11,4
9
( )
533
593
+=
+=y
14
( )
14,9
%
%
YOU&Try:&
%
D:
2−= xy
%
%
I/.,76%1./2$L%
%
&45/.,%.((6%
%
+.#5<,76%"3%x. Z(%
$(."?(76/)%3$"96@%3(%
345/.,8%>/)5,3%
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>,.6"'/)%3$"963%8(=7%
D:%
x
2−= xy
y
( )
yx,
0
20
20
−=
−=y
-2
( )
2,0 −
1
21
21
−=
−=y
-1
( )
1,1 −
4
22
24
−=
−=y
0
( )
0,4
9
23
29
−=
−=y
1
( )
1,9
%
%
N:
4−−= xy
%
%
I/.,76%1./2$L%
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R(,99"'",76%"3%C0@%%
3(%(22(3"6,%>/)5,3%
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$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%
%
x
4−−= xy
y
( )
yx,
4
0
44
−=
−−=y
0
( )
0,4
5
1
45
−=
−−=y
-1
( )
1,5 −
8
4
48
−=
−−=y
-2
( )
2,8 −
13
9
413
−=
−−=y
-3
( )
3,13 −
%
%
YOU&Try:&
%
O:%
2+= xy
%
%
I/.,76%1./2$L%
%
&45/.,%.((6%
%
+.#5<,76%"3%x+2,%
3$"963%),96%D@%3 ( %
35-6./'6%D%6(%
345/.,8%75<-,.3:%
[\@%0@%O@%]@%0Q@%^_$%
%
%
x
2+= xy
y
( )
yx,
-2
0
22
=
+−=y
0
( )
0,2−
-1
1
21
=
+−=y
1
( )
1,1−
2
4
22
=
+=y
2
( )
2,2
7
9
27
=
+=y
3
( )
3,7
%
%
%
Page 5 of 15 MCC@WCCUSD 06/04/14
A"))%"7%6$,%'$/.6%-,)(=%6(%#./2$%6$,%#">,7%,45/6"(73L%
Y45/6"(7L%
F,3'."26"(7L%%
;C6/-), L%
1./2$L%
P:%
3
3+= xy
%
%
I/.,76%1./2$L%
%
R5-,%.((6%
%
+.#5<,76%"3%x+3,
3$"963%),96%N@%3(%
35-6./'6%N%6(%'5-,8%
75<-,.3:%%
[^@%CDH@%C`@%C0@%\@%0@%
`@%DH@%^_$%
%
x
3
3+= xy
y
( )
yx,
-4
3
3
1
34
−=
+−=y
-1
-3
3
3
0
33
=
+−=y
0
( )
0,3−
-2
3
3
1
32
=
+−=y
1
( )
1,2−
5
3
3
8
35
=
+=y
2
( )
2,5
%
%
YOU&Try:&
%
Q:
3
1+−= xy
%
%
I/.,76%1./2$L%
%
R5-,%.((6%
%
+.#5<,76%"3%x+1,
3$"963%),96%0@%3(%
35-6./'6%0%6(%'5- ,8 %
75<-,.3:%%
[^@%CDH@%C`@%C0@%\@%0@%
`@%DH@%^_$%
%
R(,99"'",76%"3%C0@%%
3(%(22(3"6,%>/)5,3%
9(.%y%
x
3
1+−= xy
y
( )
yx,
-2
3
3
1
12
−−=
+−−=y
1
( )
1,2−
-1
3
3
0
11
−=
+−−=y
0
( )
0,1−
0
3
3
1
10
−=
+−=y
-1
( )
1,0 −
7
3
3
8
17
−=
+−=y
-2
( )
2,7 −
%
%
H:
12
3
−+= xy
%
%
I/.,76%1./2$L%
%
R5-,%.((6%
%
+.#5<,76%"3%x+2,
3$"963%),96%D@%3(%
35-6./'6%D%6(%'5-,8%
75<-,.3:%%
[^@%CDH@%C`@%C0@%\@%0@%
`@%DH@%^_$%
%
R(736/76%"3%C0@%
>,.6"'/)%3$"96%8(=7%
0:%
x
12
3
−+= xy
y
( )
yx,
-3
11
123
3
3
−−=
−+−=y
-2
( )
2,3 −−
-2
10
122
3
3
−=
−+−=y
-1
-1
11
121
3
3
−=
−+−=y
0
( )
0,1−
6
18
126
3
3
−=
−+=y
1
( )
1,6
%
%
YOU&Try:&
%
`:%
41
3
+−= xy
%
%
I/.,76%1./2$L%
%
R5-,%.((6%
%
+.#5<,76%"3%xC0,
3$"963%."#$6%0@%3(%
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75<-,.3:%%
[^@%CDH@%C`@%C0@%\@%0@%
`@%DH@%^_$%
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R(736/76%"3%XO@%
>,.6"'/)%3$"96%52%O:%
x
41
3
+−= xy
y
( )
yx,
-7
48
417
3
3
+−=
+−−=y
2
( )
2,7 −−
0
41
410
3
3
+−=
+−=y
3
( )
3,0
1
40
411
3
3
+=
+−=y
4
( )
4,1
2
41
412
3
3
+=
+−=y
5
( )
5,2
%
%
Page 6 of 15 MCC@WCCUSD 06/04/14
Homework&(day&1):%K3,%6$,%9())(="7#%,45/6"(73%6(%</6'$%6(%6$,%#">,7%#./2$3%-,)(=%/78%=."6,%/7%,45/6"(7%9(.%6$,%
(6$,.3:%F,3'."-,%$(=%6$,%#./2$%'$/7#,3%9.(<%6$,%2/.,76%#./2$%/78%$(=%6$/6%,99,'63%6$,%,45/6"(73%'(736/76@%'(,99"'",76%
(.%/.#5<,76:%%A"7/))B@%9"78%P%>/)5,3%6$/6%B(5%=(5)8%256%"7%B(5.%6C6/-),:%
/:%
3
3
+= xy
%
-:%
6+= xy
%%
':%
3
12 += xy
%
8:%
38 −+= xy
%
%
0:%%%
%
%
x C%>/)5,3L%&5-6./'6%0a%C0@%\@%N@%`@%0P%
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F,3'."26"(7L%R5-,%
.((6:%b,96%3$"96%0@%
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&$/2,%$/3%>,.6"'/)%
3$"96@%'(,99"'",76%(9%
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Y45/6"(7L%R%
3
12 += xy
%
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F,3'."26"(7L%&45/.,%
.((6:%%
W,.6"'/)%3$"96@%52%Q:%
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Y45/6"(7L%c%
6+= xy
%
%
F,3'."26"(7L%&45/.,%
.((6:%Z(%3$"963:%
d22(3"6,%>/)5,3%9(.%y:%
R(,99"'",76%"3%C0:%
&$/2,%"3%6$,%3/<,:%
Y45/6"(7L%
xy −=
%
%
F,3'."26"(7L%R5-,%.((6%
W,.6"'/)%3$"96%52%N@%3(%
'(736/76%XN:%
%
&$/2,%"3%6$,%3/<,:%
%
Y45/6"(7L%+%
3
3
+= xy
%
%
F,3'."26"(7L%&45/.,%
.((6:%W,.6"'/)%%3$"96%
8(=7N@%3(%'(736/76%"3%
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Y45/6"(7L%%F%
38 −+= xy
%
%
F,3'."26"(7L%R5-,%.((6%
W,.6"'/)%3$"96%52%0@%
'(736/76%"3%X0:%
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Page 7 of 15 MCC@WCCUSD 06/04/14
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Page 8 of 15 MCC@WCCUSD 06/04/14
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Page 9 of 15 MCC@WCCUSD 06/04/14
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Page 10 of 15 MCC@WCCUSD 06/04/14
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Page 11 of 15 MCC@WCCUSD 06/04/14
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Page 12 of 15 MCC@WCCUSD 06/04/14
1./2$%6$ ,%#">, 7%,4 5 /6"(7 3:%
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Page 13 of 15 MCC@WCCUSD 06/04/14
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Page 14 of 15 MCC@WCCUSD 06/04/14
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Page 15 of 15 MCC@WCCUSD 06/04/14
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