Lesson 5

News Number Line

Est. Class Sessions: 2

Developing the Lesson

Part 2. Use the Number Line Benchmarks

Place Large Numbers on the Number Line. When the number line has been completed, model placing numbers on it. See Sample Dialog 2.

  1. Read the number.
  2. Determine and state the 100,000 interval. Name the two benchmarks you will use.
  3. Determine the 10,000 interval. Name the two benchmarks you will use.
  4. Explain why you are placing the number in that spot.

Ask student pairs to place one number from the Newswire display on the number line, following the same procedure. Use only numbers less than one million. Have students place additional numbers on the number line, as time allows.

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Use this sample dialog to place large numbers on the News Number Line.

Teacher: Let's place 214,788 on our number line. Which benchmark numbers should we begin with?

Tanya: I would begin with 200,000 and 300,000.

Teacher: Why did you select those numbers as benchmarks?

Tanya: 214,788 is greater than 200,000, but less than 300,000.

Teacher: How do you know that, Tanya?

Tanya: Well, I know it is 200,000 because that's what the 2 is.

Teacher: What do you mean? Can you tell me using place value terms?

Tanya: The 2 has all those number places after it.

Teacher: What number places does it have after the 2?

Tanya: It has ones, tens, hundreds, thousands, and ten thousands all after it. So the 2 means two hundred thousand.

Teacher: Good explanation. Is the number 214,788 just about two hundred thousand? Greater than two hundred thousand? Or a little less than two hundred thousand?

Tanya: It is bigger, because of the other numbers. It is 14,788 past two hundred thousand.

Teacher: Is it up to 300,000?

Tanya: No. If it were, it would have a 3 in this place [pointing to the 2 in the number].

Teacher: Good thinking! What is the next thing we should consider when placing our number?

Luis: Now, we should look for benchmark numbers using the 10,000 marks.

Teacher: Explain what you mean.

Luis: I look at the next numbers after the 2. The next number is 1.

Teacher: What place is the “one” in?

Luis: I think it means ten thousand.

Maya: But the 4 means it is fourteen thousand, because the 4 is in the thousand place. It makes it fourteen thousand.

Luis: Yes, and 14 thousand is less than twenty thousand. [Pointing to the 10,000 and 20,000 markers.] So the number goes here, right between these two.

Teacher: Luis, your explanation was very clear. How many think they could use Luis's strategy to place the rest of our numbers on the number line?

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  • Ask students to write a number sentence that shows the partitions of the number they are placing on the number line. Encourage students to use the 10,000 and 100,000 benchmarks they have used as benchmarks on the number line, e.g., 214,788 = 200,000 + 10,000 + 4000 + 700 + 80 + 8.
  • Ask student pairs to draw a picture showing their number using the Big Base-Ten Pieces.

Explore Numbers Greater than One Million. Discuss extending the number line to place numbers greater than 1 million. To continue the proportional model, 10 metersticks would be needed to represent each additional million. Ask the following questions to help students develop a clearer sense of the relative sizes of numbers.

Ask:

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  • Where would 18 million be? (down the hall, out the door, etc.)
  • Where would small numbers less than 1000 be on our number line (e.g., number of students or students in our class, in our school, numbers of days in a week)? (At the beginning of the number line.)
  • Would this be the most meaningful number line to use for this data? (This number line is not good for numbers less than 1000.)

Count to One Million. Ask students to turn to the News Number Line pages in the Student Guide. Questions 1–2 ask students to skip count by 10,000s and 100,000s to 1 million using a calculator. See the TIMS Tip.

Question 3 asks students to use a calculator to find the number of pencils each student would get if they divided 1 million pencils equally among all the students in the school. They will need to know the number of students in the school to answer the question.

In Unit 3, students used their calculators to determine if a number is a factor of another number by checking to see if it would divide evenly into the number; that is, if the answer is a whole number. Depending on the number of students in your school, a million pencils may not be divided evenly. In interpreting their answers, remind students that numbers to the right of the decimal point mean that the number will not come out evenly and there will be some pencils left over.

Question 4 provides additional opportunities for students to demonstrate using benchmark numbers to locate numbers on the number line.

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Rounding. In this activity, students estimate with a technique that uses benchmarks such as the nearest 10,000 or 100,000 to order numbers. Having experience using the number line helps prepare students for more formal study of rounding and estimation presented in Lesson 6 of this unit.

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Pressing on many four-function calculators will continuously add 10,000. You may need to test the calculators used in your classroom before presenting this to students. If it does not work, consult the manual that came with your particular model of calculator to find the correct sequence of keystrokes to use a constant. Many scientific calculators have a constant, , function.

Student Guide: 232
Answers
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