PATTERNING �AND ALGEBRA
TERM 1
MRSTAV
PATTERNING AND ALGEBRA
Represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic expressions.
MRSTAV
CURRICULUM
PATTERNING AND ALGEBRA
Determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation.
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CURRICULUM
DO IT NOW
# Solving Algebraic Equations PA
Solving Algebraic Equations
PA
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LAST WEEK
v=2n+3
WE KNEW WHAT n WAS
AND FOUND OUT �WHAT v WAS
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THIS WEEK
v=2n+3
WE’LL KNOW WHAT v IS
AND HAVE TO FIND OUT�WHAT n IS
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TO DO THIS:
V = n
WE NEED TO GET n ALONE
2
+3
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00110011
INVERSE
RECIPROCAL
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ALGEBRA DEFINITION
INVERSE
OPERATIONS
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ALGEBRA DEFINITION
RECIPROCAL
OPERATIONS
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INVERSE OPERATIONS
+
-
x
÷
x2
√
The opposite of
The opposite of
The opposite of
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INVERSE OPERATIONS
0 + 4 = 4
4 - 4 = 0
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INVERSE OPERATIONS
6
6 ÷ 2 = 3
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INVERSE OPERATIONS
3 x 2 = 6
6 ÷ 2 = 3
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TO DO THIS:
13 = n
WE NEED TO GET n ALONE
2
+3
-3
÷2
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BUT WAIT!
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MRSTAV
ALGEBRA RULE #1
WHAT YOU DO TO 1 SIDE YOU MUST DO TO THE OTHER!
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WHAT �YOU DO FOR ONE CHILD…
…YOU MUST �DO FOR �THE OTHER
#MRSTAVSSISTER
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TO DO THIS:
= n
WE NEED TO GET n ALONE
2
+3
-3
-3
13
10
MRSTAV
TO DO THIS:
= n
WE NEED TO GET n ALONE
2
÷2
÷2
10
5
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LET�THEN�CHECK
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THEN:
LINE IT UP (Line up your equal signs)
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HOW DOES THAT LOOK IN MY BOOK?
13 =
2n + 3
13 - 3 =
2n + 3
- 3
10 =
2n
10 ÷ 2 =
2n
÷ 2
5 = n
ALL “=” SIGNS ARE ALL LINED UP
THEN: v =
2n + 3
LET:
v =13
MRSTAV
TRY ANOTHER
= n
WE NEED TO GET n ALONE
9
-7
+7
+7
20
27
MRSTAV
TRY ANOTHER
= n
WE NEED TO GET n ALONE
9
÷9
÷9
27
3
MRSTAV
HOW DOES THAT LOOK IN MY BOOK?
20 =
9n - 7
20 + 7 =
9n - 7
+ 7
27 =
9n
27 ÷ 9 =
9n
÷ 9
3 = n
ALL “=” SIGNS ARE ALL LINED UP
THEN: v =
9n – 7
LET:
v =13
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30 = 2n + 4
n
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699 = 51n + 87
n
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TRY IT
Solve the equation if v = 59
1) v = 5n + 19
2) v = 2n – 78 007
LET v = 59
THEN
V = 2n – 78 007
59 = 2n – 78 007
59 + 78 007 = 2n – 78 007 + 78 007
78 066 ÷2 = 2n ÷2
39 033 = n
LET v = 59
THEN
v = 5n + 19
59 = 5n + 19
59 – 19 = 5n + 19 – 19
40 = 5n
59 ÷ 5 = 5n ÷ 5
8 = n
MRSTAV
TRY IT
Solve the equation if v = 59
1) v = 5n + 19
LET v = 59
THEN
v = 5n + 19
59 = 5n + 19
59 – 19 = 5n + 19 – 19
40 = 5n
59 ÷ 5 = 5n ÷ 5
8 = n
CHECK:
LET: v = 59, n = 8
THEN:
v = 5n + 19
59 = 5(8) + 19
LS = RS
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Kayla R |
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Cole |
Kayla E |
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GUIDED
WITH STAV
1 2 3 4 5
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WORK
MATH
JOURNAL
MATH GAME
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TECH
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CENTRES
GUIDED
WITH STAV
1 2 3 4 5
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ROTATION 6
WITH STAV
GUIDED
1 2 3 4 5 6
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WORK
MATH
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|
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NUMBER TALK
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WORK
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Kylie |
Matthew |
|
Brendan |
Cameron |
Cole |
Javon |
Kaden |
Phoenix |
Austin |
Areej |
Avril |
Eleesha |
Tamera |
Satanna |
Alexander |
Anwar |
Gavin |
Keegan |
Zohaib |
Anthony F |
Class Code: 0D2D90
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Brooklyn |
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Carly |
Jaylen |
Lexi |
Nathan |
Andre |
Damien |
Kimberlee |
Linden |
Shaazil |
Anthony |
Class Code: 0D2D90
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CENTRES
GUIDED
WITH STAV
1 2 3 4 5
-42 +(s2)2 + s – a + stav + y – v = sat + [(2t) ÷ a2]2 + at - a2v – 30 – (stav)2 + 32
GROUP 5 GUIDED
-42 +(s2)2 + s – a + stav + y – v = sat + [(2t) ÷ a2]2 + at - a2v – 30 – (stav)2 + 32
-42 +(52)2 + 5 – 2 + 5· 32· 2· 1 + y – 1 = 5· 2· 32 + [(2· 32) ÷ 22]2 + 2· 32 - 22· 1 – 30 – (5· 32· 2· 1)2 + 32
16 + (25)2 + 5 – 2 + 320 + y – 1 = 320 + [(64) ÷ 4]2 + 2· 32 - 4· 1 – 30 – (320)2 + 9
16 + 625 + 5 – 2 + 320 + y – 1 = 320 + [16]2 + 64 – 4 – 30 – 102400 + 9
16 + 625 + 5 – 2 + 320 + y – 1 = 320 + 256 + 64 – 4 – 30 – 102400 + 9
964 -964 + y – 1 = -101 785 -964
y – 1 +1 = -102 749 +1
y = -102 748
GROUP 5 GUIDED
ALGEBRAIC �EXPRESSION
5, 7, 9, 11, ?...
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1
2
3
5
7
9
n
v
4
11
100
?
1
2
3
4
100
2
2
2
FIRST
DIFFERENCE
V=
FIRST�DIF
n
+or- #
5 =
2
(1)
+or-?
5 =
2 +or- ?
7-5=
9-7=
11-9=
5 =
2 + 3
5 =
5
v = 2n + 3
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