Unit 7, Lesson 10
Applications of Arithmetic with Powers of 10
Accelerated 7
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Arrange students in groups of 2. Tell students that the Burj Khalifa is the tallest building in the world and is located in the city of Dubai. Then give students 1 minute of quiet think time, followed by 1 minute to share their responses with a partner. Follow with a whole-class discussion.
What information would you need to answer these questions?
The goal of this discussion is for students to share their list of information needed to answer the questions. Invite students to share their responses for each question. Record and display the responses for all to see.
Consider asking questions like these to encourage students to reason further about each question:
If time allows, ask students to make predictions for each of the questions in the Task Statement. Record and display their responses for all to see.
Optional
None
This optional activity further illustrates the utility of using powers of 10 to work with and interpret very large quantities. Students practice modeling skills, such as identifying essential features of a problem and gathering the required information (MP4).
Ask a student to read the first problem in the Task Statement out loud. Invite students to ask for the information they need. Provide students with only the information they request. Display the information for students to see throughout the activity. If students find that they need more information later, provide it to the whole class then.
Here is information students might ask for in order to solve the problems:
Arrange students in groups of 2–4, and give 15 minutes of work time followed by a whole-class discussion.
Answer the question “How many meter sticks does it take to equal the mass of the Moon?” and explain or show your reasoning.
Label the number line and plot your answer for the number of meter sticks.
One light year is approximately
The goal of this discussion is for students to see how powers of 10 can be a useful strategy when dealing with problems that involve very large numbers. Begin by inviting students to share how they used the information to answer the question. Here are some questions for discussion:
It might be illuminating to put 35 million light years into some context. It is over a thousand trillion times as far as the distance to the Moon, or about the size of a supercluster of galaxies. The Sun is less than
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In 2010, the Burj Khalifa became the tallest building in the world. It was very expensive to build.
Decide what power of 10 to use to label the rightmost tick mark of the number line so that both the height of the stack of money and the height of the Burj Khalifa can be plotted on the same number line. Label the tick marks, and plot and label both values.
Answer the question “Which has more mass, the Burj Khalifa or the mass of the pennies it cost to build the Burj Khalifa?” and explain or show your reasoning.
Decide what power of 10 to use to label the rightmost tick mark of the number line so that both the mass of the Burj Khalifa and the mass of the pennies it cost to build the Burj Khalifa can be plotted on the same number line. Label the tick marks and plot and label both values.