## Year 2 Lesson Plan 20 - Working with Percents

1. (5 min) Mental Math
1. 38% of \$1 is how much? [38 cents]
2. 100% of \$1 is how much? [All of it = \$1]
3. 138% of \$1 is how much? [\$1.38]
4. 138% of \$10 is how much? [\$13.80]
5. Find 30% of 40, then add 25 [37]

2. (5 min) Review of selected problems from previous lesson (no more than 3 problems)

3. Hand out the Fractions, Decimals, and Percents reference sheet. Review how to convert decimals to percents and back by moving the decimal point.

4. Setting up and solving Percent problems When you have to solve a problem involving percents:
1. Write down this equation: D x N = A
D is the percent, changed into a decimal
N is the amount you are working on
A is the answer. It can be larger than N if D is larger than 1 (100%)
2. If you are given a percent, change it to a decimal (D)
3. Figure out whether you are missing D, N or A
4. Put the other two that you have into the equation
5. Solve for the missing number
6. Convert D back to a percent if that was what you are asked for
7. REMEMBER: of means multiply and is means "="

• EXAMPLE 1--Find the answer: What is 8% of 752?
Well, D = .08 and N = 752 and A is the missing number, so
.08 x 752 = A
A = 60.16

• EXAMPLE 2--Find the percent: 64 is what percent of 512?
Here you are given the answer and must find the percent:
D is the missing number, N = 512 and A = 64
D x 512 = 64
D = 64/512 = .125 or 12.5%

• EXAMPLE 3--Find the "mystery" number: 125% of what number is 15?
D = 1.25, N is the missing number, and A = 15
1.25 x N = 15 N = 15/1.25 = 12
Does this seem reasonable? Yes! We are told 15 is more than 100% of the number, so the number must be smaller than 15.

5. Extending the concept
• Discount means you subtract a percent from the original amount.
• If a \$100 bicycle is discounted 25%, how much do you pay? [\$75]
• If Lamont's has a 30% off sale, how much do you pay for \$30 shoes? [\$21] Not 20, that would be 1/3 off.
• Tax or interest means you add a precent to the original amount. You pay tax after you take any discounts.
• If you buy a \$100 bicycle with 8.2% tax, how much do you pay? [\$108.20]
• If you borrow \$100 at 5% interest, how much do you have to pay back? [\$105] This is called simple interest.
• Interest is charged over time. If you borrow \$100 for 2 years at 5% interest per year, how much do you have to pay back? Well, the first year you owe \$105. The second year you owe \$105 + 5% of 105, or \$5.25. So after 2 years you owe\$110.25. This is called compound interest. This mounts up after a long time with big loans. If your parents borrowed \$100,000 for a house at 5% interest for 30 years, they would have to pay back \$193,255 in all!

6. (Remainder of class) In-class exercise

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