# Lesson Plan: Percents and Measurement Conversion

## Lesson Objectives

- Understand percents as ratios
- Solve problems involving percents
- Use ratio reasoning to convert measurement units
- Apply percent and measurement concepts to real-world scenarios in science, art, and business

## Common Core Standards

6.RP.A.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

## Prerequisite Skills

- Understanding of ratios and unit rates
- Basic fraction and decimal knowledge

## Key Vocabulary

- Percent
- Percentage
- Unit Conversion

## Warm-up Activity (5 minutes)

Here is a slide show that can be used to show percent visualizations:

__https://www.media4math.com/library/slideshow/visualizing-percents__

You can follow-up with this activity:

Display a large 10x10 grid on the board or using a digital projector. Each square represents 1% of the total area. Present the following percentages: 25%, 50%, 75%, 80%, and 120%.

For each percentage:

- Ask students to visualize and describe how many squares would be filled in the 10x10 grid.
- Fill in the squares on the grid to represent the percentage.
- Have students express the percentage as a fraction out of 100.

For 120%, extend the grid by adding two more columns, emphasizing that percentages can exceed 100%.

Discuss how the grid visually represents percentages and reinforces the concept of "per hundred."

## Teach (25 minutes)

### Definitions

- Percent: A ratio that compares a number to 100
- Percentage: The conversion of fractions and decimals to percents.
- Unit conversion: The process of changing a measurement from one unit to another

You can also review these definitions and others with this slide show:

__https://www.media4math.com/library/slideshow/percent-definitions__

### Instruction

**Percents**. Use this slideshow to provide an overview of percents:

__https://www.media4math.com/library/slideshow/overview-percents__

Demonstrate how to solve percent problems:

**Finding a percent of a number.**Use this video to develop this concept. This video includes three detailed examples:__https://www.media4math.com/library/1807/asset-preview__**Finding what percent one number is of another.**Use this video, which also includes three detailed examples:__https://www.media4math.com/library/1810/asset-preview__**Finding the whole when given a part and percent.**Use this video:__https://www.media4math.com/library/1808/asset-preview__

**Real-world applications in science.** Here are real-world applications of percent problems.

- Concentration in solutions: If a saline solution is 0.9% salt, how many grams of salt are in 500 mL of solution?
- Genetic inheritance: If a trait has a 75% chance of being passed on, what's the probability of it appearing in 200 offspring?
- Color mixing: If an artist needs to lighten a color by 20%, how much white paint should be added to 100 mL of the original color?
- Scaling artwork: If a 24-inch painting needs to be reduced to 75% of its original size, what will the new dimensions be?

If time allows, introduce these applications:

Discount Calculation:

A store is offering a 25% discount on a $80 jacket. Calculate the discount amount and the final price of the jacket.

Solution:

- Discount amount: 25% of $80 = 0.25 × $80 = $20
- Final price: $80 - $20 = $60

Simple Interest:

If you invest $1000 at a 6% annual interest rate, how much interest will you earn after 2 years?

Solution:

- Interest formula: I = P × r × t (where I = interest, P = principal, r = rate, t = time in years)
- I = $1000 × 0.06 × 2 = $120

Discuss how percentages are crucial in business and finance for calculating discounts, interest rates, profit margins, and tax rates.

**Measurement**. Show how to use ratio reasoning for measurement unit conversion. This slide show provides a dozen examples of converting measurements using rates:

__https://www.media4math.com/library/slideshow/math-examples-measurement-conversion__

## Review (10 minutes)

Review this video to see visual models of percents:

__https://www.media4math.com/library/1811/asset-preview__

Review properties of percents using this slide show:

__https://www.media4math.com/library/slideshow/fractions-decimals-and-percents__

Use this slide show to demonstrate various conversion formulas for converting units:

__https://www.media4math.com/library/slideshow/conversion-formulas__

## Assess (10 minutes)

Administer a 12-question quiz on percents and measurement conversion, including science, art, and business applications.

## Quiz Questions

- What is 40% of 80?

- 24 is what percent of 60?

- 18 is 75% of what number?

- Convert 3.5 meters to centimeters.

- In a 2-liter solution, 5% is alcohol. How many milliliters of alcohol are present?

- If 30% of a number is 21, what is the number?

- An artist wants to increase the size of a 15-inch sculpture by 120%. What will be the new height?

- What percent of 200 is 150?

- If a gene has a 60% chance of expression, how many individuals in a population of 500 would be expected to show the trait?

- A paint mixture requires 3 parts red to 5 parts blue. What percentage of the mixture is red?

- A store is offering a 15% discount on a $120 item. What is the final price after the discount?

- If you invest $2000 at an annual interest rate of 4.5%, how much interest will you earn after 1 year?

## Answers:

- 32
- 40%
- 24
- 350 cm
- 100 mL
- 70
- 33 inches
- 75%
- 300 individuals
- 37.5%
- $102
- $90

Purchase the lesson plan bundle. __Click here.__