# Lesson 12. Lesson 12. Suggested Lesson Structure. Round to Different Place Values (6 minutes) Fluency Practice (12 minutes)

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1 Objective: Solve multi-step word problems using the standard addition reasonableness of answers using rounding. Suggested Lesson Structure Fluency Practice Application Problems Concept Development Student Debrief Total Time (12 minutes) (5 minutes) (34 minutes) (9 minutes) (60 minutes) Fluency Practice (12 minutes) Round to Different Place Values 4.NBT.3 Find the Sum 4.NBT.4 (6 minutes) (6 minutes) Round to Different Place Values (6 minutes) Materials: (S) Personal white boards Note: This fluency reviews rounding skills that are building towards mastery. T: (Project 726,354.) Say the number. S: Seven hundred twenty-six thousand, three hundred fifty-four. T: What digit is in the hundred thousands place? S: 7. T: What s the value of the digit 7? S: 700,000. T: On your personal white boards, round the number to the nearest hundred thousand. S: (Students write 726, ,000.) Repeat process, rounding 726,354 to the nearest ten thousand, thousand, hundred, and ten. Follow the same process and sequence for 496, D.14

2 Find the Sum (6 minutes) Materials: (S) Personal white boards Note: Reviewing this mental math fluency will prepare students for understanding the importance of the algorithm. T: (Write =.) Solve mentally or by writing horizontally or vertically. S: (Students write = 649.) Repeat process and sequence for ; 13, ,412; 3, ; ; and 23, , ,368. Application Problem (5 minutes) The basketball team raised a total of \$154,694 in September and \$29,987 more in October than in September. How much money did they raise in October? Draw a tape diagram and write your answer in a complete sentence. NOTES ON MULTIPLE MEANS OF REPRESENTATION: Students below grade level may have difficulty conceptualizing the larger numbers. Use smaller numbers to create a problem. Relate it in terms of something with which they are familiar. Have students make sense of the problem and direct them through the process of creating a tape diagram. The pizza shop sold five pepperoni pizzas on Friday. They sold ten more sausage pizzas than pepperoni pizzas. How many pizzas did they sell? Have a discussion about the two unknowns in the problem and about which unknown needs to be solved first. Students may draw a picture to help them solve. Then, relate the problem to that with bigger numbers and numbers that involve regrouping. Relay the message that it s the same process. The difference is that the numbers are bigger. Note: This Application Problem reviews the addition algorithm practiced in yesterday s lesson by solving a comparative word problem. Concept Development (34 minutes) Problem 1 Solve a multi-step word problem using a tape diagram. The city flower shop sold 14,594 pink roses on Valentine s Day. They sold 7,857 more red roses than pink roses. How many pink and red roses did the city flower shop sell altogether on Valentine s Day? Use a tape diagram to show your work. 1.D.15

3 T: Read the problem with me. What information do we know? S: We know there are 14,594 pink roses sold. T: To model this, let s draw one bar to represent the pink roses. Do we know how many red roses were sold? S: No, but we know that there were 7,857 more red roses sold than pink roses. T: A second bar can represent the number of red roses sold. (Model on tape diagram.) T: What is the problem asking us to find? S: The total number of roses. T: We can draw a bracket to the side of both bars. Let s label it R for pink and red roses. T: First, solve to find how many red roses were sold. S: (Students solve 14, ,857 = 22,451.) MP.2 T: What does the bottom bar represent? S: The bottom bar represents the number of red roses, 22,451. (Bracket 22,451 to show the total number of red roses.) T: Now we need to find the total number of roses sold. T: How do we solve for R? S: Add the totals for both bars together. 14, ,451 = R. T: Solve with me. What does R equal? S: R equals 37,045. (Write R = 37,045.) T: Let s write a statement of the answer. S: The city flower shop sold 37,045 pink and red roses on Valentine s Day. Problem 2 Solve a two-step word problem using a tape diagram and assess the reasonableness of the answer. On Saturday, 32,736 more bus tickets were sold than on Sunday. On Sunday, only 17,295 tickets were sold. How many people bought bus tickets over the weekend? Use a tape diagram to show your work. 1.D.16

8 Problem Set 2. Raffle tickets were sold for a school fundraiser to parents, teachers, and students. 563 tickets were sold to teachers. 888 more tickets were sold to students than to teachers. 904 tickets were sold to parents. How many tickets were sold to parents, teachers, and students? a. About how many tickets were sold to parents, teachers, and students? Round each number to the nearest hundred to find your estimate. b. Exactly how many tickets were sold to parents, teachers, and students? c. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain. 3. From 2010 to 2011, the population of Queens increased by 16,075. Brooklyn s population increased by 11,870 more than the population increase of Queens. a. Estimate the total combined population increase of Queens and Brooklyn from 2010 to (Round the addends to estimate.) 1.D.21

9 Problem Set b. Find the actual total combined population increase of Queens and Brooklyn from 2010 to c. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain. 4. During National Recycling Month, Mr. Yardley s class spent 4 weeks collecting empty cans to recycle. Week Number of Cans Collected 1 10, , ,011 a. During Week 2, the class collected 1,256 more cans than they did during Week 1. Determine the final count of cans collected by Mr. Yardley s class at the end of the 4 weeks. b. Assess the reasonableness of your answer in part a by estimating the total number of cans collected. 1.D.22

10 Exit Ticket Name Date Directions: Model the problem with a tape diagram. Solve and write your answer as a statement. 1. In January, Scott earned \$8,999. In February, he earned \$2,387 more than he did in January. In March, Scott earned the same amount as he did in February. How much did Scott earn altogether during those three months? Is your answer reasonable? Explain. 1.D.23

12 Homework 3. Last year on Ted s farm, his four cows produced the following liters of milk: Cow Liters of Milk Produced Daisy 5,098 Betsy Mary 9,980 Buttercup 7,087 a. Betsy produced 986 more liters of milk than Buttercup. How many liters of milk did all 4 cows produce? b. Is your answer reasonable? Explain. 1.D.25

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