Lesson | Loading...

Unit 2, Lesson 2

Scale of the Solar System (Optional)

$Course Icon$

Integrated Math 2

2.1

Warm-up

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Gather

Four-function calculators

Activity Narrative

The context of an eclipse lends itself to diagrams of dilations. Students may or may not have intuition about an eclipse. Some may have observed an eclipse. During the Launch, displaying pictures from a total solar eclipse will support students who are unfamiliar with the context. If the moon were a different size or a different distance away, eclipses would look very different!

Launch

Make sure that students understand the context of an eclipse: that three celestial bodies are in a line, and because of their relative sizes and locations, one (in this case the moon) can cover the body behind it (in this case the sun) in such a way that the body is completely covered, or in such a way that a ring of light is visible around the eclipsing object. Showing images of a solar eclipse might help students understand the question better.

Activity

None

<p>3 spheres. Moon is in the middle, and is the smallest. Sun is the largest. 2 dotted lines extend from Earth at the same point, hit the edges of Moon, and then hit the edges of Sun.</p> — NOT TO SCALE

The diameter of the sun is 1,391,000 km. The diameter of the moon is 3,475 km. The distance from Earth to the sun is 149,600,000 km.

How far would the moon have to be from Earth for the moon to appear the same size as the sun?

Student Response

to access Student Response.

Building on Student Thinking

Activity Synthesis

Invite students to share how they did their calculations.

“The average radius of the moon’s orbit of Earth is 384,400 km. How well does reality match your calculations?” (The moon’s actual orbit is very close to what I calculated. The moon is a little farther away than it would need to be to appear the same size as the sun, which means that you might see a little bit of the sun peeking around the moon during an eclipse.)

2.2

Activity

Optional

Instructional Routines

Aspects of Mathematical Modeling Extend It MLR7: Compare and Connect

Materials

To Gather

Four-function calculators Geometry toolkits (HS)Rulers marked with centimeters String

2.3

Activity

Optional

Instructional Routines

Extend It

Materials

To Gather

Geometry toolkits (HS)Rulers marked with centimeters

Activity Narrative

This activity gives students extra practice with scale drawings and finding unknown values in proportional relationships. It also provides students with another chance to grapple with the size of the solar system and unit conversion. If students struggled to use an efficient method to find unknown values in proportional relationships, encourage students to use a strategy that a classmate demonstrated in the previous activity.

Making spreadsheet technology available gives students an opportunity to choose appropriate tools strategically (MP5).

Launch

Lesson Synthesis

Discuss just how big the solar system is. These images might help students to understand the scale of the solar system. In one image they can see the planets to scale. Note that the sun does not fit in the image and the distances are not to scale. In the other image the planets and orbits are both to scale, but the planets are so small that most are invisible, and some orbits still extend beyond the image. This is hard to imagine. Performing an internet search for “solar system to scale video” and playing a video for all to see can help students get a better sense of the vastness of space.

<p>Image of orbits of our solar system shown to scale.</p>

to access Cool-down.

Student Lesson Summary

To make a scaled copy of this figure so that its new height is 3 cm instead of 8 cm, we could start calculating what the lengths of different parts of the figure would be. One way to calculate the measurements of the scaled copy is to multiply every length in the original figure by the scale factor to find the corresponding length in the scaled copy. For example, the radius of the head is 1.3 cm. Because , the radius of the scaled head is about 0.5 cm.

<p>Stick figure with arms, right arm down and left arm up.</p>

The length of segment is 2.4 cm. How long is segment ? Instead of multiplying by the scale factor we could use equivalent ratios. Because then . So is 0.9 cm.

<p>Large stick figure with left leg segment A B and small stick figure with left leg segment A prime B prime.</p>

Launch

Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 3–4.

Tell students they will be making a scale drawing of the solar system, with accurately scaled sizes and distances from Earth for each planet. Display a circle with a 1-meter diameter, and explain that it will represent the sun. Show students where the class will (attempt to) display the scale drawing of the solar system. Explain that each group will be assigned a planet to draw and to add to the scale drawing, at the appropriate distance.

Ask students what information they need to create the scale model. Listen for students to mention something about the size of the planet (radius, diameter, circumference around the equator, surface area) as well as something about the distance of the planet from the sun (orbit radius, diameter, or distance traveled in a year for the planet).

Assign each group a planet. If there aren't enough groups to do all the planets pick some planets that are smaller than Earth and some that are larger than Earth. It is also fine to have multiple groups work on the same planet.

Select work from students with different strategies, such as those described in the Activity Narrative, to share later.

Engagement: Develop Effort and Persistence. Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy, such as

“First, I _____ because _____.”
“I noticed _____, so I _____.”
“Why did you _____?”

Supports accessibility for: Language, Social-Emotional Functioning

Activity

None

The class is going to make a scale drawing of the planets in the solar system and their distances from Earth. Your teacher will assign you a planet to draw. A circle with a diameter of 1 meter represents the sun.

object	average diameter (km)	average orbit radius (km)
sun	696,340	0
Mercury	4,879	57,900,000
Venus	12,104	108,200,000
Earth	12,756	149,600,000
Mars	6,792	227,900,000
Jupiter	142,984	778,600,000
Saturn	120,536	1,433,500,000
Uranus	51,118	2,872,500,000
Neptune	49,528	4,495,100,000

Draw the scale drawing of your planet on a separate sheet of blank paper. Label it with measurements. When you’re finished, place it the correct distance from the sun on the class’s scale drawing.
You probably weren’t able to place your planet the correct scaled distance from the sun. Why not?

Student Response

to access Student Response.

Building on Student Thinking

Display the table and invite students to predict what size Earth would need to be for the scale drawing of the solar system to fit in the classroom.

planet	average diameter (km)	average orbit radius (km)
Mercury	4,879	57,900,000
Venus	12,104	108,200,000
Earth	12,756	149,600,000
Mars	6,792	227,900,000
Jupiter	142,984	778,600,000
Saturn	120,536	1,433,500,000
Uranus	51,118	2,872,500,000
Neptune	49,528	4,495,100,000

Keep students in the same groups they were in for the previous activity. Tell students to continue using the same planet that they used in the previous activity.

Lesson | Loading...

Settings

Audience

Assessment Access

Lesson 2

Scale of the Solar System (Optional)

Warm-up

Standards Alignment

Building On

7.G.A.1

Addressing

Building Toward

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Instructional Routines

Materials

To Gather

Activity

Instructional Routines

Materials

To Gather

Activity Narrative

Launch

Lesson Synthesis

Student Lesson Summary

Activity Narrative

Launch

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Activity

Student Response

Building on Student Thinking

Activity Synthesis

Standards Alignment

Building On

7.G.A.1

Addressing

HSG-MG.A.3

HSN-Q.A.1

Building Toward

HSG-SRT.A.2

Standards Alignment

Building On

7.G.A.1

Addressing

Building Toward

HSG-SRT.A.2