Density is an important physical property of all the objects around us. It tells us how closely packed the molecules of something is. Have you ever picked something up and you were surprised at how heavy it was or how light it was? You experienced the concept of density! The heavier than expected objects had a high density. The lighter objects had a much lower than expected density. Mass is a measure of how many molecules an object is made up of. Volume is a measure of how much space something takes up. Density is a measure of the mass of an object divided by its volume. In this series of lessons and worksheets we will learn how density applies to our real world. We will explore well beyond just calculating simple measures of density.
Aligned Standard: High School Geometry - HSG-MG.A.2
- Concert Attendance Step-by-step Lesson - See if you can guess the number of people that came to SuperKron's concert.
- Guided Lesson - We might go a bit overboard on the size and number of packages in this problem.
- Guided Lesson Explanation - This is one of the first word problems you are faced with that has multidimensional requirements.
- Practice Worksheet - Some of these problems took forever to think up and write.
- Matching Worksheet - Match the word problems and their answers.
- Answer Keys - These are for all the unlocked materials above.
I tried to make these super fun. See if I hit my mark.
- Homework 1 - A big stadium has 1.5 million square feet of room. Last year a group surveyed the stadium to make sure there wasn't overcrowding.
- Homework 2 - They found the population density to be 0.017 people per square foot. This included all people in the building. How many total people attended the stadium on that day?
- Homework 3 - Dolly wants to buy a light weight mobile phone to give to her friend. She has two options for mobile phones, but she doesn't know that which one is lighter.
Who doesn't want a light weight mobile phone. I'm still rocking a flip phone. Yes, they still make them!
- Practice 1 - Katy writes down the density of her bag, but she didn't write the mass of her bag. The dimensions of her bag are height 30 cm, length 20 cm, width 40 cm and density of bag is 0.0020 kg/cm3.
- Practice 2 - Her friend wants a very light mobile phone. Which mobile phone is lighter?
- Practice 3 - Mass Requirement of first mobile: Mass = Volume x Density
Math Skill Quizzes
I tried to make sure that I used metric units here, but I did slip on a few problems.
- Quiz 1 - Karl is a ring maker. He received an order to make attractive and light weight gold rings. He has two options.
- Quiz 2 - Roni is Paul's younger brother. His mother told him to buy a light weight lunch box from the store.
- Quiz 3 - A room is 2,500 square feet. The population density of the room is 0.0040 people per square foot. This included all people in the room. How many total people can occupy this room?
What Can Density Tell Us About an Object?
You may be familiar with a company called Nerf. They make a bunch of fun sporty products that allow us to throw balls further and not get hurt when we do. They allow us to shoot darts in our homes and not cause any damage. Why do their products take the real actions of hard balls and darts, but cause no pain or damage. The concept is known as "Density."
What is density? Let's look at it! Density is a word that describes how much space an object or substance takes up- the volume in relation to the amount of matter in that object- the mass. In other words, the amount of mass per unit volume is known as density. This means how tightly packed together the molecules of an object are together. If an object is heavy and compact, it is known to have high density. But if an object is light and takes more space, it has low density. The equation to determine density is based on the relationship between an object’s mass (how many molecules it contains) and volume (how much space those molecules take up). It forms the formula density = mass ÷ volume.
When you go to a visit to your local lake you can easily see this. Throw a tree branch in the water and it will float because dry wood is much less dense than water. If you look at the bottom of the lake you will see a ton of rocks because they are all much denser than the water. Gold is one very dense substance. To illustrate this think about a gallon of water. We see them on the water aisle of every grocery store we go to. A gallon of water is just over 8 pounds, 8.34 pounds to be exact. Gold on the other hand, is much denser than water. A gallon of gold would weigh 160 pounds, that almost 20 gallons of water.