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### Engage NY Module 2

LESSON 2

Objective: Estimate multi-digit by rounding factors to a basic fact and using place value patterns.

SPRINT – Multiply by 10, 100, and 1,000

- This Sprint will help students build automaticity in multiplying by 10, 100, and 1,000.

90

80

320

8,400

500

17,400

40

8,000

23,800

73,000

6,500

6,290

294,000

86,000

492,000

400

30,000

690

80,000

95,100

8,670

9,510

129,000

700

1,100

10,000

250

Round to Different Place Value

- Using a vertical number line round 48,625 to the nearest ten thousands, thousands, hundreds, and tens.
- 48,625 ~ 50,000 48,625 ~ 49,000
- 48,625 ~ 48,600 48,625 ~ 48,630

50,000

49,000

48,700

48,630

48,625

48,625

45,000

48,500

48,625

48,625

48,650

48,625

40,000

48,000

48,620

48,600

Multiply by Multiples of 10

- 31 x 10 = ______ 310 x 2 = ______
- 31 x 10 x 2 = _____ 310 x 10 x 2 = _____
- 23 x 10 = ________ 230 x 4 = ________
- 230 x 10 x 4= ______ 230 x 40 = _____
- 32 x 10 = _______ 320 x 3 = _______
- 320 x 10 x 3 = ______ 320 x 30 = _____

620

310

6200

6200

230

920

9200

9200

320

960

9600

9600

APPLICATION PROBLEM

Jonas practices guitar 1 hour a day for 2 years. Bradley practices the guitar 2 hours a day more than Jonas. How many more minutes does Bradley practice the guitar than Jonas over the course of 2 years?

365 x 2 = 730 hours per day

Jonas

365 x 4= 1460 x 60 = 1460 x 10 x 6 = 14600 x 6 = 87, 600

730 hours per day

Bradley practices the guitar 87,600 minutes more than Jonas in 2 years.

Concept Development - Problem 1

- How many students do we have in class? (class, building, or grade level)
- 29

- Do all of the classes have exactly 29?
- No

- There are 18 classes, but we are not sure exactly how many students are in each class. What could I do to find a number that is close to the actual number of students in our school?
- We could use the number in our class.

- True, but 29 is a little more difficult to multiply in my head. I’d like to use a number that I can multiply mentally. What could I round 29 to so it is easier to multiply?
- 30 students

- What could I round 18 to?
- 20 classes

- How would I estimate the total number of students?
- Multiply 30 x 20

- What would my estimate be? Explain your thinking.
- 600: (3 x 2) = 6 and all I need to do is add 2 zeroes to the 6.
- 600: (3 x 2) x (10 x 10) = 600

Concept Development - Problem 2

- 456 x 42
- Suppose I don’t need to know the exact product, just an estimate. How could I round the factors to estimate the product?
- Hundreds and tens
- Tens and tens

- What can we round 456 to? What can we round 42 to?
- 450 and 40 or 500 and 40

- Well 450 x 40 could still be difficult for some people to do mentally, but 500 x 40 should be easy to do mentally for everyone.
- What is 500 x 40? Explain your thinking.
- 20,000 (4 x 5) x (100 x 10) or 4 x5 = 20 plus 3 zeroes because that is what I have in the original problem.

Concept Development - Problem 3

- 4,560 x 42
- Suppose I don’t need to know the exact product, just an estimate. How could I round the factors to estimate the product?
- Hundreds and tens
- Tens and tens
- Thousands and tens

- What can we round 4,560 to? What can we round 42 to?
- 4,600 and 40, 4,560 and 40, or 5,000 and 40

- What option would be the easiest to multiply mentally?
- 5,000 and 40

- What is 5000 x 40? Explain your thinking.
- 200,000 (4 x 5) x (1000 x 10) or 4 x5 = 20 plus 4 zeroes because that is what I have in the original problem.

Concept Development - Problem 4

- 4,560 x 420
- Suppose I don’t need to know the exact product, just an estimate. How could I round the factors to estimate the product?
- Thousands and tens
- Thousands and hundreds
- Hundreds and hundreds

- What can we round 4,560 to? What can we round 420 to?
- 4,600 and 400, 4,560 and 40, or 5,000 and 400

- What option would be the easiest to multiply mentally?
- 5,000 and 400

- What is 5000 x 400? Explain your thinking.
- 2,000,000 (4 x 5) x (1000 x 100) or 4 x 5 = 20 plus 5 zeroes because that is what I have in the original problem.

Concept Development - Problem 5-7

- Estimate the product for the following numbers and explain your thinking.

- What is the answer to each problem? Explain your answer.
- 1000 x 90 = 90,000 or 1,300 x 90 = 117,000
- 10,000 x 900 = 9,000,000 or 13,000 x 900 = 11,700,000
- 3,000 x 900 = 2,700,000 or 3,100 x 900 = 2,790,000

- What do you notice about the 1st and 2nd problems?
- You are dealing with the basically the same numbers, but different place values and the estimates are the same numbers, but the second one is 100 times greater because each factor is 10 times greater in the 2nd problem.

Lesson 2 – Problem Set

- Round the factors to estimate the products.
- 597 x 52 = _____ x _____ = ______
- A reasonable estimate for 597 x 52 is _______.

- 1,103 x 59= _____ x _____ = ______
- A reasonable estimate for 1,103 x 59 is _______.

- 5,840 x 25 = _____ x _____ = ______
- A reasonable estimate for 5,8420 x 25 is _______.

- 597 x 52 = _____ x _____ = ______

Lesson 2 – Problem Set

- Complete the table using your understanding of place value and knowledge of rounding to estimate the product.

Lesson 2 – Problem Set

- For which of the following expressions would 200,000 be a reasonable estimate? Explain how you know.

Lesson 2 – Problem Set

- Fill in the missing factors to find the given estimated product.

Lesson 2 – Problem Set

- There are 19,763 tickets available for a New York Knicks home game. If there are 41 home games in a season, about how many tickets are available for all the Knicks’ home games?
- Michael saves $423 dollars a month for college.
- About how much money will have saved after 4 years?
- Will your estimate be lower or higher than the actual amount Michael will save? How do you know?

Lesson 2 – Exit Ticket

- Round the factors and estimate the products.

Problem Set, Debriefing, Exit Ticket, and Homework

- Complete Problem Set in small groups.
- Check answers and discuss difficulties.
- Handout Exit Ticket and independently.
- Handout Homework.

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