1. Engage NY Module 2 LESSON 2
Objective: Estimate multi-digit by rounding factors to a basic fact and using place value patterns.

2. SPRINT – Multiply by 10, 100, and 1,000
This Sprint will help students build automaticity in multiplying by 10, 100, and 1,000.
Problem
Answer
9 x 10
73 x 1,000
80 x 1,000
8 x 10
65 x 100
951 x 100
32 x 10
629 x 10
867 x 10
84 x 100
294 x 1,000
951 x 10
50 x 10
860 x 100
129 x 1,000
174 x 100
492 x 1,000
7 x 100
4 x 10
4 x 100
11 x 100
800 x 10
300 x 100
10 x 1,000
238 x 100
69 x 10
25 x 10 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

3. 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, ,625 ~ 49,000
48,625 ~ 48, ,625 ~ 48,630
50,000
40,000
45,000
48,625
49,000
48,000
48,500
48,625
48,700
48,600
48,650
48,625
48,630
48,620
48,625

4. 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 = _____
310
620
6200
230
920
9200
320
960
9600

5. APPLICATION PROBLEM

6. 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 = x 6 = 87, 600
730 hours per day
Bradley practices the guitar 87,600 minutes more than Jonas in 2 years.

7. 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

8. 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.

9. 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.

10. 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.

11. Concept Development - Problem 5-7
Estimate the product for the following numbers and explain your thinking.
Problem
Rounded #s
Estimate
1,320 x 88
13,205 x 880
3,120 x 880
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.

12. 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 _______.

13. Lesson 2 – Problem Set
Complete the table using your understanding of place value and knowledge of rounding to estimate the product.
Factors
Rounded Factors
Estimate
2,809 x 42
28,090 x 420
8,932 x 59
89 tens x 63 tens
398 hundreds x 52 tens

14. Lesson 2 – Problem Set
For which of the following expressions would 200,000 be a reasonable estimate? Explain how you know.
Problems
2,146 x 12
21,467 x 100
2,146 x 121
21,477 x 1,217

15. Lesson 2 – Problem Set
Fill in the missing factors to find the given estimated product.
Problems
Rounded Factors
Estimated Product
571 x 43
24,000
726 x 674
490,000
8,379 x 541
4,000,000

16. 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?

17. Lesson 2 – Exit Ticket Round the factors and estimate the products.
Rounded Factors
Estimate
656 x 106
3,108 x 7,942
425 x 9,311
8,633 x 57,008

18. 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.