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  3. really big numbers - math grade 4 - lesson 2

really big numbers - math grade 4 - lesson 2

 
Lesson Overview
In this lesson, students review place value concepts they learned in Primary 2 and Primary 3 and apply 
that learning to building understanding of place value through the One Milliard place. They play a game to practice creating, reading, and writing large numbers. 

Lesson Essential Question
• How does the value of a digit change as it moves in a whole number?
Learning ObjectivesIn this lesson
• Students will identify all whole number place values through the One Milliard place. 
• Students will explain how the value of a digit changes based on its place in a number.

Grade-Level Standards
4.A.1 Apply and extend understanding of the place value system to multi-digit whole numbers.
4.A.1.b Explain place value using numbers to 1,000,000,000, including the relative sizes of numbers in 
each place.

Exploring Place Value
1. Direct students to Lesson 2 ACCESS Exploring Place Value. Ask students to talk to their Shoulder Partner about what they remember from earlier grades about the place value system and record their notes. 
2. Ask a few volunteers to share their ideas. Students may remember different concepts, so 
answers will vary.
3. Project or draw the Place Value chart that follows. Cover the Millions and Milliard periods. Explain that the chart shows the Ones period and the Thousands period. Each period contains Ones, Tens, and Hundreds places. The names of the periods help us name numbers. Milliards Millions Thousands Ones
4. Ask students to talk to their Shoulder Partner about things that can be represented by numbers in the 
Ones or Thousands periods. (For example, hundreds of students attend the school. Thousands of people live in the community.) 
5. Reveal the next two periods (Millions and Milliards) on the place value chart. 
6. Ask students to brainstorm things that can be represented by numbers in the Millions or Milliards periods. (For example, millions of people live in Cairo. Milliards of people live in the world.) 
7. Display and ask students to read the statement, “For every 1 human on Earth there are about 1,000,000 ants.” Allow students to react to the statement. Explain that they will return to that statement at the end of the mathematics period.

BUILD (40 min)

Reading the Place Value Chart (20 min)

1. Direct students to Lesson 2 BUILD Reading the Place Value Chart. Have students read aloud with you the labels for the place value chart. Begin at the Ones period and move through the One Milliard place (Ones, Tens, Hundreds, One Thousands, Ten Thousands, Hundred Thousands, One Millions, Ten Millions, Hundred Millions, One Milliard).

2. Guide students through practice reading five large numbers and writing them in a place value chart. Write large numbers on the place value chart and help students read them aloud with you. Ask students to record the numbers in their Student Materials. (For example, write 35,891,455 and chorally read “thirty-five million, eight hundred ninety-one thousand, four hundred fifty-five.”) Remind students to say numbers grouped in each period followed by the name of the period (an example is shown below). Continue this practice of reading large numbers until most students respond with accuracy.

3. Ask students to read the first learning target and reflect on how well they can meet the target right now. Use a “Fist to Five,” where “fist” indicates no understanding and “five fingers” indicates a deep understanding of all terms.

Creating Really Big Numbers (20 min)
1. Ask students to Turn and Talk to discuss the following question: Is a 2 always worth 2?
2. Ask volunteers to share their thinking and model examples on the place value chart.
3. Direct students to Lesson 2 BUILD Creating Really Big Numbers. Give students time to cut apart the Digit Cards 0–9. Have them write their names or initials on the backs of their cards.

Ask volunteers to read aloud the directions for the game Creating Really Big Numbers. Decide whether students will play in partners, small groups, or larger groups and divide them accordingly. 
5. Give students 10–15 minutes to play. Then, stop and ask one student to write their greatest numeral on the board. Ask students to walk through each digit.
ASK • What is this digit? 
• What is this digit’s value? 
• What would happen to the value of this digit if it were here (point to another place in the numeral)? 
• Why did the value of the digit change when its location changed?
6. Ask students to share how they determined who had the greatest numeral. 
ASK • What strategies did you use to create the greatest numeral? 
• If you could play this game again, what would you do differently?

CONNECT (7 min)

Writing About Math 
1. Direct students to Lesson 2 CONNECT Writing About Math and respond to the prompt.
2. After a few minutes of independent writing, ask students to share their answers and explain their thinking. Students should mention using place value to compare the numerals (or numbers) to determine the value of the digits.

WRAP-UP (3 min)
One Million Ants!

1. Ask students to reflect on the statement shared during ACCESS and then consider 
the question: If there are 1,000,000 ants for every 1 person, how many people do you 
think it would take to have one milliard ants? 

2. Direct students to Turn and Talk to share their thinking with a friend.

3. Allow a few students to share and explain their thinking. 
It would take 1,000 people to have 1,000,000,000 ants. It is not required that students 
get the correct answer to this problem. It is more important that students engage in 
conversation about how to solve the problem. Listen for students who mention the use 
of place value or place value relationships.
PRACTICE

Direct students to Lesson 2 PRACTICE and have them complete the problems. 
Address student errors and misconceptions around very large numbers. 

Check Your Understanding

1. Use the digits 3, 5, 7, 8, 8, 1, 6, 2 to make the greatest number you can. Then use the same digits to make the smallest number you can. 

Greatest: 88,765,321
Smallest: 12,356,788 

2. How did the value of the 2 change from your greatest number to your smallest 
number? Why did it change? Use words and numbers to explain your thinking.

If students answered Question 1 correctly, they should recognize that the 2 has a value 
of 20 in the largest number, but a value of 2,000,000 in the smallest number. The value 
changed because the location of the digit changed.

3. How are 23,450 and 230,450 similar? How are they different? Use words and numbers 
to explain your thinking.
Students may recognize that the two numbers have similar digits except the second numeral has a 0 in the Thousands place, making the number much larger.

4. List three possible values for the digit 5.
Answers should include three of the following: 5, 50, 500, 5,000, 50,000, 500,000, 5,000,000, 50,000,000, 500,000,000, and 5,000,000,000

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