## Year 2 Lesson Plan 14 - Solving x + a = b and x - a = b

1. (5 min) Mental Math
1. Take 25% of 200 and add 8 [58]
2. What is one half squared? [1/4]
3. Multiply 45 by 20, multiply by 10, then add 79 [9079]
4. Three consecutive numbers add up to 15. What are they? [4,5,6]
5. What is the average of {3,4,5}? [4]

2. (5 min) Review adding positive and negative numbers
• If signs are the SAME:
Add numbers and use their common sign
(Example: - 3 - 8 = -(8 + 3) = - 11)

• If signs are DIFFERENT:
Subtract the numbers and use the sign of the larger number.
(Example: - 3 + 8 = +(8 - 3) = + 5)
Try these examples:
• - 5 - 6
• - 5 - (- 6)
• - 8 + 4
• - 8 - (+ 4)
• - 4 + 8
• - 4 - (+ 8)
3. (5 Min) Solving x + a = b

GENERAL RULE:
To solve x + a = b, subtract a (add -a) to both sides of the equation and simplify

Examples:

1. ```
Equation: x  + 15 =   25
Subtract 15 from both sides:    - 15   - 15   <--both sides!!
----------------
Simplify: x       = + 10
```
2. Tamara has \$5.27. A solar calculator costs \$14. How much more money does she need to buy a solar calculator? Let x be how much more she needs.
```
Equation: x  + \$5.27 =  \$14.00
Subtract \$5.27 from both sides:    - \$5.27   -\$ 5.27
---------------------
Simplify: x          = +\$ 8.73
```
4. (5 Min) Solving x - a = b

GENERAL RULE:
To solve x - a = b, add a to both sides of the equation and simplify

Examples:

1. ```
Equation: x  - 15 =   25
Add 15 to both sides:    + 15   + 15 <--both sides!!
----------------
Simplify: x       = + 40
```
2. Mount Everest is 29,028 feet above sea level. If it were standing on the ocean floor in the Marianas Trench in the Western Pacific Ocean, its peak would be 7,170 feet below sea level.. How deep is the Marianas Trench? Let x be the depth of the Marianas Trench.
```
Equation: x  - 29028 =    7170
Add 29028 to both sides:    + 29028   + 29028
----------------------
Simplify: x          =   36198
```
3. Student problem:

What do you do with:

x + 40 - 12 = 60 ?

Answer: Two ways to do this:
1. Combine 40 - 12 to get 28 or...
2. Add 12 to both sides then subtract 40 from both sides.
5. (Remainder of class) In-class exercise

6. Hand out homework as students successfully complete the in-class exercise.