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Math,

Exploring New Realities

Check out how new technology is influencing the way we see reality

By Jessica McKenna-Ratjen
From the December 2022 / January 2023 Issue

Learning Objective: Students will multiply multidigit numbers related to augmented and virtual reality using the standard algorithm.

Lexile: 1080L; 790L
Focus Area: Numbers and Operations,
Standards
  • MATHEMATICAL PRACTICES: MP4, MP5, MP6 COMMON CORE: 5.NBT.B.5 TEKS: 5.3B

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Lexile® measure

  • 1080L
  • 790L

Virtual Reality (VR)
Creates an entirely new, three-dimensional digital world the user experiences using a special wireless headset and controllers

Augmented Reality (AR)

Layers text, images, videos, and sound onto a real image or video, which the user typically views with a smartphone or tablet

Virtual Reality (VR)
Creates an entirely new, three-dimensional digital world the user experiences using a special wireless headset and controllers

Augmented Reality (AR)

Layers text, images, videos, and sound onto a real image or video, which the user typically views with a smartphone or tablet

Courtesy of SAOLA STUDIO/MUSÉUM NATIONAL D’HISTOIRE NATURELLE (AR Glasses, Magical Museum)

Magical Museums

Courtesy of SAOLA STUDIO/MUSÉUM NATIONAL D’HISTOIRE NATURELLE (AR Glasses, Magical Museum)

With AR glasses, a museum in Paris comes to life!

While wandering past animal skeletons in a museum, you might wonder what the creatures looked like when they were alive. Now several museums have developed AR apps to show you! The Smithsonian’s Skin and Bones app allows visitors to the Washington, D.C., museum to see creatures from the collection come to life. For example, visitors can watch a vampire bat take flight after they use their phones to scan its bones.

Using AR glasses, visitors to the National Museum of Natural History in Paris can see extinct animals moving about the galleries. The exhibit is called REVIVRE, which means “to live again” in French.

When you visit a museum, you may see animal skeletons. You might wonder what the creatures looked like when they were alive. Now several museums have developed AR apps to show you! The Smithsonian’s Skin and Bones app allows visitors to the Washington, D.C., museum to see creatures from the collection come to life. For example, visitors can use their phones to scan a vampire bat’s bones. Then they can watch the bat take flight.

The National Museum of Natural History in Paris gives visitors AR glasses. Through the glasses, they can see extinct animals moving around the galleries. The exhibit is called REVIVRE. It means “to live again” in French.

Burak Cingi/Redferns/Getty Images 

With a VR headset, you can watch concerts from your couch!

Cool Concerts

You stand in front of a giant stage. The crowd is packed shoulder to shoulder. Bright lights flash above you as Billie Eilish appears. To experience a concert like this, you’d normally have to buy a ticket. But this past March, anyone with an Oculus Quest VR headset was able to attend virtually!

As part of Women’s History Month, the company MetaQuest uploaded virtual versions of events with female leaders and creators. Eilish’s performance at the 2021 Governors Ball is one example. The company also regularly schedules concerts and other events that users can join from the comfort of their couch.

You stand in front of a giant stage. The crowd is packed shoulder to shoulder. Bright lights flash above you. Then Billie Eilish appears! To experience a concert like this, you’d normally have to buy a ticket. But this past March, anyone with an Oculus Quest VR headset was able to attend virtually!

March is Women’s History Month. So the company MetaQuest uploaded virtual versions of events with female leaders and creators. Eilish’s performance at the 2021 Governors Ball is one example. The company also regularly schedules concerts and other events that users can join from their couch.

Courtesy of True Course Simulations

A VR headset can help you learn to fly!

Perfect Piloting

It often takes years of training to learn how to fly a plane, and that training can be dangerous. That’s why some flight schools are turning to VR! True Course Simulations (TCS) has created virtual copies of a few popular training planes, such as the Cessna 172. Its digital training course includes 73 VR missions. Students experience the plane’s controls and movement as if they were in a real cockpit, without ever leaving the ground.

At one major flight school, practicing in VR helped students complete their first solo flight mission more than 30 percent faster than the average first solo flight time!

It often takes years of training to learn how to fly a plane. Plus, that training can be dangerous! That’s why some flight schools are turning to VR. True Course Simulations (TCS) has created virtual copies of a few popular training planes. One example is the Cessna 172. TCS has also designed a digital training course. The course includes 73 VR missions. Students experience the plane’s controls and movement as if they were in a real cockpit. But they never leave the ground!

TCS sold its program to a major flight school. Students there practiced in VR. They completed their first flight mission on their own more than 30 percent faster than most students do!

Courtesy of DribbleUp

This AR app can improve your dribbling skills!

Better Basketball

Want to improve your basketball skills? With Dribbleup, your tablet becomes the trainer! This AR app comes with a smart basketball that pairs wirelessly with your device. As you dribble, the basketball records information about its speed and location. Virtual targets appear on the screen while you train, showing you how to move the ball for the best technique.

Want to improve your basketball skills? With Dribbleup, your tablet becomes the trainer! This AR app comes with a smart basketball. It pairs wirelessly with your device. As you dribble, the basketball records information about its speed and location. Virtual targets appear on the screen while you train. They show you how to move the ball for the best technique.

Multidigit Multiplication

What to Do

When you multiply multidigit numbers, the standard algorithm can help you multiply in parts using partial products.

Example

119 × 23 = ?

Arrange the problem so that the greater number is above the lesser number and the digits are lined up by place value.

Multiply the ones place of the smaller number by each digit of the greater number, working from right to left. Write each product below the line. If a product is greater than or equal to 10, regroup.

Start another partial product by writing a 0 in the next row. Then multiply the tens digit of the smaller number by each digit of the greater number. Write your product below the first partial product. Regroup if needed

Finally, add your partial products to find the total product. Regroup if needed.

So 119 × 23 = 2,737

Multidigit Multiplication

What to Do

When you multiply multidigit numbers, the standard algorithm can help you multiply in parts using partial products.

Example

119 × 23 = ?

Arrange the problem so that the greater number is above the lesser number and the digits are lined up by place value.

Multiply the ones place of the smaller number by each digit of the greater number, working from right to left. Write each product below the line. If a product is greater than or equal to 10, regroup.

Start another partial product by writing a 0 in the next row. Then multiply the tens digit of the smaller number by each digit of the greater number. Write your product below the first partial product. Regroup if needed

Finally, add your partial products to find the total product. Regroup if needed.

So 119 × 23 = 2,737

Now You Try It

It costs about $13 for one ticket to view REVIVRE. If 106 people were to buy tickets in one day, how much money would the museum make from those sales?

It costs about $13 for one ticket to view REVIVRE. If 106 people were to buy tickets in one day, how much money would the museum make from those sales?

An Oculus Quest 2 headset costs $399. If 15 Billie Eilish fans bought headsets to experience Billie Eilish’s performance virtually in March, how much money would they have spent all together?

An Oculus Quest 2 headset costs $399. If 15 Billie Eilish fans bought headsets to experience Billie Eilish’s performance virtually in March, how much money would they have spent all together?

The training course for TCS costs $495. If TCS sold its training course to 24 clients, how much money would the company make?

The training course for TCS costs $495. If TCS sold its training course to 24 clients, how much money would the company make?

It costs $115 to buy a Dribbleup smart basketball and a 1-month subscription to online training sessions. If you and 10 friends each wanted to purchase Dribbleup, how much would you spend all together in 1 month?

It costs $115 to buy a Dribbleup smart basketball and a 1-month subscription to online training sessions. If you and 10 friends each wanted to purchase Dribbleup, how much would you spend all together in 1 month?

Continue Your Learning

  • Rewatch the video “Flight Simulator” (above). Then think about how you could practice your favorite sport or hobby using a virtual reality (VR) simulator. Create a poster of your VR invention including how VR would be beneficial for this sport or hobby, which skills your simulator would allow a user to practice, and the proposed cost of your program. Make sure to include at least 3 number facts in your poster.
  • Go on a number scavenger hunt with a partner! Find and record at least three 3-digit numbers around your home. Nutrition labels and book pages are a good place to look. Meanwhile, ask a friend or family member to search for at least three 2-digit numbers. When you’ve each completed your lists, choose a number from each list. Then practice multiplying the 3-digit number by the 2-digit number. Repeat with the rest of the numbers on your lists.

Continue Your Learning

  • Rewatch the video “Flight Simulator” (above). Then think about how you could practice your favorite sport or hobby using a virtual reality (VR) simulator. Create a poster of your VR invention including how VR would be beneficial for this sport or hobby, which skills your simulator would allow a user to practice, and the proposed cost of your program. Make sure to include at least 3 number facts in your poster.
  • Go on a number scavenger hunt with a partner! Find and record at least three 3-digit numbers around your home. Nutrition labels and book pages are a good place to look. Meanwhile, ask a friend or family member to search for at least three 2-digit numbers. When you’ve each completed your lists, choose a number from each list. Then practice multiplying the 3-digit number by the 2-digit number. Repeat with the rest of the numbers on your lists.
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Activities (8)
Question & Answer Sheets
Reference
Skills Activities
Answer Key (1)
video (1)
Activities (8)
Question & Answer Sheets
Reference
Skills Activities
Answer Key (1)
Step-by-Step Lesson Plan
Download the Lesson Plan

1. SPARK ENGAGEMENT.

Play the video "Flight Simulator." Then, before or after reading the article, spark a discussion based on the following questions.

  • Have you ever played a game or used an app that made the world look different than it is in real life?
  • What does virtual reality mean to you?
  • What are some strategies you can use to multiply numbers?

2. INTRODUCE THE MATH CONCEPT AND VOCABULARY.

  • Display the following equations vertically on the board, as if using the standard algorithm: 12 x 4 = 48 and 12 x 4 = 84. Which of these is correct? How do you know? (12 x 4 = 48; Answers will vary)
  • When we multiply a 2-digit number by a 1-digit number using the standard algorithm, we start by multiplying the factors in the ones place. Since 4 x 2 = 8, we write that number first. Then we move to the left to multiply the 1 in the tens place by 4. Our product is 40. The sum of our partial products, 40 and 8, is 48.
  • Display the equation 120 x 4 vertically on the board. What two factors should we multiply first? Explain. (The 4 and 0 because they are in the ones place.) What do we multiply next? (The 4 in the ones place and the 2 in the tens place of 120.) Continue working through the problem as a class to solve the equation. (120 x 4 = 480)
  • Today we will multiply multidigit numbers using the standard algorithm.

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

  • Why was there a 2 written above the tens place in the second step? (It respresented the 2 tens regrouped from the product of 9 and 3, 27.)
  • Why do you think you should write a 0 before starting your second partial product? (Answers will vary. Possible answer: You are working with the tens place of the bottom factor now.)
  • Why was the 2 crossed out in step 3? (It was not needed to calculate the second partial product.)

4. REINFORCE WITH MATH PRACTICE.

Have students complete probelms 1 through 4 on pages 11-13.

EDITOR'S TIP:

Have students use grid paper to align their equations when using the standard algorithm to help them organize the ones, tens, and hundreds columns as they solve—Jessica McKenna-Ratjen, Associate Editor

EDITOR'S TIP:

Have students use grid paper to align their equations when using the standard algorithm to help them organize the ones, tens, and hundreds columns as they solve—Jessica McKenna-Ratjen, Associate Editor

Class Debate

With so much new technology, daily screen time is increasing for most people. Have a class debate on whether it is more important as a society to decrease screen time and experience more of the real world or to buil and explore the capabilities of new digital worlds.

 

Class Debate

With so much new technology, daily screen time is increasing for most people. Have a class debate on whether it is more important as a society to decrease screen time and experience more of the real world or to buil and explore the capabilities of new digital worlds.

 

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