## Lesson Plan #23 - Adding and subtracting like factors

1. (5 min) Mental Math
• What is the probability of flipping a coin 3 times
and getting a 'heads' all 3 times? [1/8]
• Start with 2400, divide by 100, then divide by 3 [8]
• What is the probability of drawing a red 6
out of a deck of 52 cards? [1/26]
• What is 20% of 80? [16]
• Multiply 1/4 by 4/5 and reduce [1/5]

2. (5 min) Review of homework #22 (<= 3 problems)

3. (10 min) Discuss adding and subtracting like factors:

1. Use this example to introduce adding X's:

X + 2X = 27

Point out that 2X means that there are 2 X's there. So

X + 2X = 3X, so

3X = 27,

Therefore X = 9, because 3 X 9 = 27.
2. Key point: So 3X means 2 things:
1. 3 X's
2. 3 times X
Point out that these mean the same thing.
3. Use a subtraction example:

4X - 2X = 18
4. Applications in geometry:
1. Draw a rectangle twice as wide as it is high and label 2 of the sides "X" and "2X". Construct the equation for the perimeter:
X + 2X + X + 2X = 24 inches.
What is the length of the short side?
6X = 24
X = 4.
2. Draw a tall isosceles triangle with angles X, 2X, and 2X.
Construct an equation for the sum of the angles:
X + 2X + 2X = 180
What is the smallest angle?
5X = 180
X = 36 degrees!
4. (Remainder of class) In-class Exercise.

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

Note: Biggest student problem with this lesson:
Understanding that for the equation:
2X + X = 9,
when you ask "How many X's are there? that the answer is not 2. This means understanding that 2X really means that there are 2 X's here.