Lesson 2 — GCF, PEMDAS & Variable Isolation

Curriculum / Mathematics / Level GGCF & Variables
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Lesson 2 — GCF, PEMDAS & Variable Isolation

Show all steps clearly. What you do to one side, you must do to the other!

Page 1 space:12/12 row slots (100% H) · 100% fit ✓
25% V × 100% H
1
Find the Greatest Common Factor (GCF) of:
a)
18 and 24
b)
30 and 45
c)
36 and 60
25% V × 100% H
2
Calculate:
a)
14 + 6 · 3
b)
(14 + 6) · 3
c)
5 + 2 · 32
d)
364 · 3 - 23
25% V × 100% H
3
Simplify the fraction:
a)
x3x
b)
8x32x
c)
12x318x2
25% V × 100% H
Visual Concept: The Balance Scale Method
Equations are like a balanced scale. Whatever operation you perform on one side, you MUST do to the other side to keep it equal!
Vector Hop Math — Cosmic Problem Solving — US Letter (8.5" × 11")
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Lesson 2 — GCF, PEMDAS & Variable Isolation (Continued)Vector Hop
Page 2 space:6/12 row slots (50% H) · 6 row slots free
25% V × 100% H
4
Solve for x:
a)
x + 14 = 31
b)
6x = 42
c)
Solve the two − step equation: 3x + 7 = 22
25% V × 100% H
5
Three crabs want to reach a shiny seashell on a high rock. The Red Crab is 15 cm tall. The Blue Crab is twice as tall as the Red Crab, and the Green Crab is three times as tall as the Blue Crab. If they stand on top of each other, what is their total height?
Vector Hop Math — Cosmic Problem Solving — US Letter (8.5" × 11")
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Answer Key & Misconception Rubric

KEY-L2
#1a
Find the Greatest Common Factor (GCF) of:18 and 24
6
3 is a common factor, but is it the GREATEST common factor? Check if 6 divides into both
#1b
Find the Greatest Common Factor (GCF) of:30 and 45
15
5 is a factor, but they also both share 3. 3 · 5 = 15 is larger
#1c
Find the Greatest Common Factor (GCF) of:36 and 60
12
6 divides both, but 12 is even greater!
#2a
Calculate:14 + 6 · 3
32
You added 14 + 6 first to get 20, then multiplied by 3. Remember: multiply before adding!
#2b
Calculate:(14 + 6) · 3
60
#2c
Calculate:5 + 2 · 32
23
Did you do (2 · 3)2 = 62 = 36? The exponent 2 belongs only to the 3. 32 = 9, so 2 · 9 = 18
#2d
Calculate:364 · 3 - 23
9
#3a
Simplify the fraction:x3x
x2
Remember that dividing by x cancels out one factor of x
#3b
Simplify the fraction:8x32x
4x2
You divided 8 by 2 to get 4, but did you cancel an x from the bottom?
#3c
Simplify the fraction:12x318x2
2x3
#4a
Solve for x:x + 14 = 31
17
You added 14 to 31. To undo addition, you must SUBTRACT 14 from both sides
#4b
Solve for x:6x = 42
7
6x is 6 TIMES x, not x + 6. To undo multiplication, DIVIDE both sides by 6
#4c
Solve for x:Solve the two − step equation: 3x + 7 = 22
5
Check your steps:subtract 7 first, then divide by 3
#5
Three crabs want to reach a shiny seashell on a high rock. The Red Crab is 15 cm tall. The Blue Crab is twice as tall as the Red Crab, and the Green Crab is three times as tall as the Blue Crab. If they stand on top of each other, what is their total height?
135
The Blue Crab is 30 cm tall, and the Green Crab is three times the Blue Crab: 90 cm
EzSteps Parent Guide — Teacher KeyPage 3 of 3
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