Show Big Numbers

Est. Class Sessions: 2–3

Developing the Lesson

Part 3. Represent Larger Numbers Using the Number Line

Direct students to the Population Lines page in the Student Activity Book. Students use skip counting by large numbers to complete the number lines in Questions 1–4. To complete these questions, students place large numbers within a range on the number line and refer to the number line in order to round large numbers. Display the Population Lines page and guide students to complete the first number line in Question 1 on their pages as the first number line on the display is completed. See Figure 5.

After completing the first number line, invite students to come to the display and point out the answers to these or similar discussion prompts.

Ask:

Where is 50,000 on this number line? (The student should point directly at the 50,000 mark that is shown on the number line.)
Where is 25,000? (25,000 is located in the middle between 20,000 and 30,000 on the number line.)
Where would you place 88,000? (88,000 would be between the 80,000 and 90,000 marks. It would be just to the left of 90,000.)
How did you decide where to place 88,000? (Possible response: Since 88,000 is only 2000 away from 90,000, it is only slightly less than 90,000, so it would be very close to 90,000 on the number line.)
Where would you place 12,000 on the number line? (12,000 will be just past 10,000 because it is slightly bigger than 10,000.)
Where would you place 37,000 on the number line? (37,000 will be between 30,000 and 40,000, but it will be closer to 40,000.)
If you were going to round 37,000 to the nearest 10,000, what would it round to and why? (It will round to 40,000 since it is closer to 40,000 than 30,000.)

Complete the number line for Question 2 on the display as students complete the same number line on the Student Activity Book page. Guide students to find and name interim points on this number line. Ask different students to come to the display and show where the following numbers would be placed on this number line:

217,000
588,000
902,000

For each of these numbers ask students to identify the nearest 100,000.

Complete the number lines in Questions 3–4 on the display as students complete them in their book.

Once students have completed the number lines in Questions 1–4, they can use this page to complete Questions 15–18 on the Represent Large Numbers Using Number Lines section of the Student Guide.

Question 15 challenges students to write the state population and state name for each state listed in the 2012 State Populations Table 1 on the appropriate number line. Encourage students to first identify which line would be best to represent each state and then to identify the two benchmark numbers that the population is between. Students then decide where to place the state within that range.

As students begin work on this question, these and other similar prompts can be used to help students clarify their thinking:

Why is the population for Alaska closer to 700,000 than it is to 800,000? (731,000 is between 700,000 and 800,000 but it is closer to 700,000 than it is to 800,000.)
Can the population of Arizona be placed on the same number line as the population of Alaska? (no) How did you decide? (The number line with Alaska's population only goes up to 1 million. The population of Arizona is greater than 1 million but it is less than 10 million, so it will go on the number line in Question 3.)
Which number line will you use for the population of Delaware? (the number line in Question 2) How did you decide? (The population of Delaware is larger than 100,000 but smaller than 1 million, and this number line goes from 100,000 to 1 million.)
Will any state's population be placed on the first number line? (no) How do you know? (No state has a population that is less than 100,000, and the first number line only goes to 100,000.)

Students are asked to identify and use benchmark numbers to round numbers in Questions 16–18.

To help guide them as they work, these or similar prompts can be used.

The population of Arizona is between which two millions? (between 6 million and 7 million)
Which million is it closest to? (7 million)
So what is 6,553,255 rounded to the nearest million? (7 million)

Students are asked to round the population of Colorado to the nearest million in Question 17A. For this question they can use the number line on the Population Lines page in the Student Activity Book. However, in Question 17B, they are asked to round the population of Colorado to the nearest hundred thousand. For this problem the number lines will not be helpful. Encourage students to write the population of Colorado on the Place Value Chart page from their Student Activity Book.

Have students look at the thousands period for 5,187,582 and ask:

Is the population of Colorado closer to 5,100,000 or 5,200,000? (5,200,000) How did you decide? (Possible response: The number on the thousands period is 187 thousand. 187 thousand is closer to 200,000 than it is to 100,000. So, I knew 5,187,582 will be closer to 5,200,000.)

Student Guide: 127

Answers