G8

Copyright © Swun Math Grade 8 Unit 2 Lesson 5 C TE

Input/Model

(Teacher Presents)

Directions: Write the expanded and standard form.

1.

Power Expanded Standard

24

23

22

21

20

Solution:

• Begin by recording the expanded form and standard
  form for the powers of 2^4 , 2^3 , 2^2 , and 2^1 (not 2^0 ).


• Discuss the decreasing pattern in the standard form
  column. Each value decreases by a factor of 2, which is
  equivalent to dividing by two.


• Have students predict what the value of 2^0 is equivalent
  to.


• Using the pattern established, determine that since
  21 = 2, 2 will be divided by the base to yield the value of
  20.


• 2 ÷ 2 = 1; Therefore, 2^0 = 1

Power Expanded Standard

(^24 2) ⋅ 2 ⋅ 2 ⋅ 2 16
23 2 ⋅ 2 ⋅ 2 8
22 2 ⋅ (^2 4)
(^21 2 2)
(^20 1 1)
2.
Power Expanded Standard
23 2 ⋅^2 ⋅^2 8
22 2 ⋅ 2 4
21 2 2
20
2 −1 (^)
2 −2
2 −3
Solution:

• Continue to build the base 2 chart.


• Review the pattern found in input 1. Remind students
  that each value is divided by the “base,” in this case 2.


• Note the chart is partially filled in; continue building
  the chart beginning with 2^0 (to reinforce that 2^0 = 1).


• Using the established pattern, determine that since
  20 = 1, 1 will be divided by the base 2 to yield the value of
  2 -1.


• 12 ÷=^12. Therefore, 2 −^1 =^12


• Continue the pattern to find 2 −2 and 2 −3.


• 
  

(^112)
24
÷=. Therefore 22 1
4
−=

(^112)
48
÷=. Therefore 23 1
8
−=

• Note: students may need to be reminded how to divide
  fractions by a whole number.
  Power Expanded Standard
  23 2 ⋅^2 ⋅^2 8
  22 2 ⋅^2 4
  21 2 2
  20 1 1

2 −^1 1

2

1

2

2 −^2 1

2 ⋅

1

2

1

4

2 −^3 1

2

⋅

1

2

⋅

1

2

1

8

1

4 ÷ 2^

1

2 ÷ 2^

(^1) ÷ 2