Courtesy of Waymo

New Ways to Zoom

Flying cars: How old-fashioned! The future of transportation holds so much more. And it's already here! From self-driving cars to battery-powered unicycles, these vehicles take movement to the next level.

By Jeanette Ferrara

From the September 2022 Issue

Learning Objective: Students will round decimal numbers to estimate sums and differences related to new forms of transportation.

Lexile: 910L; 720L

Focus Area: Fractions and Decimals,

Electric Unicycles

Zip around town on an electric unicycle—no pedaling required! The V5F is 70 centimeters wide and weighs only as much as a baby stroller. Its thin and foldable design makes it easy to store and carry. The battery-powered unicycle can travel almost 40 kilometers on a single charge.

Building a Surfing Motorcycle

Watch a video about a motorcycle that can surf on water.

Self-Driving Cars

With the Waymo One ride service, the only humans in the car are passengers! The company has been testing its driverless car service since 2018 in Phoenix, Arizona. It serves an area of almost 260 square kilometers. Waymo aims to make travel via car easier and safer. Riders can even request multiple stops per trip.

The cars use cameras and radar to detect other vehicles and objects and avoid hitting them. Waymo recently began testing a new self-driving service in San Francisco, California.

Jet Packs

Richard Browning zooms through the air thanks to a special suit that he invented. Called the Gravity Jet Suit, it looks like a high-tech backpack with jet engine sleeves! The suit includes five engines that allow Browning to zoom up to 90 kilometers per hour.

Browning intends to use his invention for entertainment, not travel. He and his team are organizing a jet suit racing league. Pilots fly through an obstacle course floating on water.

High-speed Pods

An ultrafast system of pods pushed through tubes might sound like science fiction, but it’s real! A hyperloop is a high-speed transit system that runs underground. It can move people and things from place to place faster than a plane.

The Virgin Hyperloop successfully transported passengers in a 2020 test run. However, it is not fully complete yet. The Virgin Hyperloop only runs in a straight line and cannot turn corners. For now, it transports only cargo, not human passengers. But if this form of high-speed travel can be perfected, people will zoom over land 10 times faster than a typical commuter train.

All About Rounding

Watch a math helper video about rounding numbers with real-world examples.

Math Talk

What are some limitations to using rounding and estimates? When might they not be an appropriate tool?

Estimating With Decimals

What to Do

Estimation can make complex calculations quicker and easier. Estimations use friendly, rounded numbers to make calculations close to the actual value. A place value chart shows the value of each digit in a number based on its position. It can help you round decimals to more friendly numbers. This makes decimal numbers easier to work with when you don’t have to be exact.

Remember, when finding an estimate,round before performing an operation.

Example

A 9.6-hour trip by plane takes only 6.183 hours by a high-speed transportation system called a hyperloop. Estimate the time saved traveling by hyperloop.

Round both numbers to friendlier numbers. In this example, both numbers would be easier to work with if we rounded to the nearest one.

Since we’re rounding to the ones place, we need to look
at the tenths place to determine if we’re rounding up or down.

6 tenths is closer to 1 than to 0, so 9.6 rounds up to 10
1 tenth is closer to 0 than to 1, so 6.183 rounds down to 6

Perform the operation (+, −, ×, ÷) with the rounded numbers. Since we’re looking for the time saved, or the difference in time, we subtract.

10 hours – 6 hours = 4 hours

So traveling by hyperloop on this trip saves about 4 hours.

Estimating With Decimals

What to Do

Remember, when finding an estimate,round before performing an operation.

Example

A 9.6-hour trip by plane takes only 6.183 hours by a high-speed transportation system called a hyperloop. Estimate the time saved traveling by hyperloop.

Round both numbers to friendlier numbers. In this example, both numbers would be easier to work with if we rounded to the nearest one.

Since we’re rounding to the ones place, we need to look
at the tenths place to determine if we’re rounding up or down.

6 tenths is closer to 1 than to 0, so 9.6 rounds up to 10
1 tenth is closer to 0 than to 1, so 6.183 rounds down to 6

Perform the operation (+, −, ×, ÷) with the rounded numbers. Since we’re looking for the time saved, or the difference in time, we subtract.

10 hours – 6 hours = 4 hours

So traveling by hyperloop on this trip saves about 4 hours.

Now You Try It

The V5F electric unicycle takes 3.5 hours to charge.

A. To make 3.5 a friendly number, what place value should we round to?

B. What is 3.5 rounded to the place value you chose above?

Grid showing the ones and tenths places of a number

A rider takes a Waymo car 5.62 kilometers to the library. Then he travels another 3.12 km to a store.

A. Round each distance to the nearest whole number.

B. Use the rounded distances to estimate the total distance traveled.

Grid showing ones, tenths, and hundreths position of a number for distance to the library and store

The combined weight of the jet suit and fuel is 35 kilograms. A pilot who weighs 88.7 kilograms puts on the suit.

A. Round each weight to the nearest ten.

B. Use the rounded weights to estimate the combined weight of the pilot and suit.

C. The pilot calculated a combined weight of 92.2 kg. Compare your estimate with the pilot’s calculation. Is his calculation reasonable?

If built, a hyperloop journey from Houston, Texas, to New York City would take 2.626 hours. The same journey would take 3.53 hours by plane.

A. Round these times to the nearest tenth.

B. Estimate the time difference using your rounded times.

C. Determine the actual difference in time. How does your estimate compare to the actual difference in time?

Continue Your Learning

Rewatch the video “Building a Surfing Motorcycle” (above). Then create your own amazing vehicle! Draw a diagram of your new way to zoom and write a small paragraph beneath it that explains how it would work. Include at least 3 number facts in your paragraph or diagram.
Find two coins and label a set of cards with the numbers 1-9. Shuffle them and select 3 cards. Lay them out on a table to make a decimal number, using one coin to represent the decimal point. Shuffle again and select 3 more cards, using the second coin as a decimal point. Then estimate the sum and the difference between the two decimal numbers you created.

Multimedia

video (1)

All About Rounding

Watch a math helper video about rounding numbers with real-world examples.

1. SPARK ENGAGEMENT.

Play the video "Building a Surfing Motorcycle." Then, before or after reading the article, spark a discussion based on the following questions.

What is your favorite way to travel? Explain why.

What factors and/or design elements can make a vehicle move faster or slower?

2. INTRODUCE THE MATH CONCEPT AND VOCABULARY.

Display the following list: Hotel-$684.13; Food-$329.50; Shopping-$158.67. This list shows the expenses for a trip. Using only mental math, how much did this trip cost in total? ($1,172.30) Was this problem difficult to answer? Explain. (Answers will vary.)

Display a second list: Hotel-$700; Food-$300; Shopping-$200. Using mental math, how much did this trip cost in total? ($1,200) How did finding this answer compare to your calculation in the first problem? (Answers will vary.)

The second list shows numbers that have been rounded. The total represents an estimate, which uses rounding as a faster way to come close to an answer without doing an exact calculation.

Allow students to calculate the actual cost of the trip. Then display the total costs beneath each list. How could we have made a closer estimate to the actual cost? (rounded the values to the nearest ten instead of hundred)

Today we will use place value charts to help us round decimals to different place values.

Play the math video, "All About Rounding" and/or review the skills slide deck "Rounding Strategies."

3. WORK THROUGH THE "WHAT TO DO" BOX.

What place value were the numbers rounded to? (ones place)

How do you determine if you round up or round down? (If the place value to the right of the place value you are rounding to is 5 or more, you will round up. If it is less than 5, you will round down.)

Should you round before or after you perform the operation? Explain. (before; answers will vary)

4. REINFORCE WITH MATH PRACTICE.

Have students complete questions 1 through 4 on pages 17-19.

Class Discussion:

The article shared several innovative ways to travel. Hold a class discussion about the meaning of innovation (a new idea, method, or device). Encourage students to think of ways a classroom could be innovative. Then create a class poster of students' ideas.