Engage NY Module 2 LESSON 2 Objective Estimate

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. Problem Answer 9 x 10 90 73 x 1, 000 73, 000 80 x 1, 000 80, 000 8 x 10 80 65 x 100 6, 500 951 x 100 95, 100 32 x 10 320 629 x 10 6, 290 867 x 10 8, 670 84 x 100 8, 400 294 x 1, 000 294, 000 951 x 10 9, 510 50 x 10 500 860 x 100 86, 000 129 x 1, 000 129, 000 174 x 100 17, 400 492 x 1, 000 492, 000 7 x 100 700 4 x 10 40 4 x 100 400 11 x 100 1, 100 800 x 10 8, 000 300 x 100 30, 000 10 x 1, 000 10, 000 238 x 100 23, 800 69 x 10 690 25 x 10 250

Round to Different Place Value � Using a vertical number line round 48, 625 to the nearest ten thousands, hundreds, and tens. › 48, 625 ~ 50, 000 › 48, 625 ~ 48, 600 50, 000 48, 625 ~ 49, 000 48, 625 ~ 48, 630 49, 000 48, 700 48, 630 48, 625 45, 000 48, 500 48, 650 48, 625 40, 000 48, 600 48, 620

Multiply by Multiples of 10 � 31 310 x 10 = ______ � 31 x 10 x 2 = 6200 _____ 230 � 23 x 10 = ____ 9200 ____ 320 � 230 x 10 x 4= ______ 9600 � 32 x 10 = _______ � 320 x 10 x 3 = ______ 620 310 x 2 = ______ 310 x 2 = 6200 920 230 x 49200 = 960 230 x 40 = _____ 9600 320 x 3 = _______ 320 x 30 = _____

APPLICATION PROBLEM

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) › � Do all of the classes have exactly 29? › � 20 classes How would I estimate the total number of students? › � 30 students What could I round 18 to? › � 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? › � 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? › � 29 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 x 5 = 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 x 5 = 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 (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. 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 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 1 st and 2 nd 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 2 nd 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 _______.

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

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

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

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. Factors 656 x 106 3, 108 x 7, 942 425 x 9, 311 8, 633 x 57, 008 Rounded Factors Estimate

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.