Student Edition Sample Page Name 1. Spencer plays video games. He scored 5443 points on Tuesday and 7301 points on Wednesday. He rounds his scores to the nearest thousand. What expression can Spencer use to estimate how many more points he scored on Wednesday than on Tuesday? Answer: 2. The table shows the numbers of people who visited the county fair. County Fair Visitors Day Number of Visitors Thursday 2365 Friday 6738 Saturday 9087 Sunday 4629 Rounding to the nearest thousand, what expression can be used to estimate the number of people that visited the fair on Saturday and Sunday? Answer: 3. Locate each of the following numbers on the number line. 2356 2529 2831 2449 2000 3000 Which numbers round to 2000 when rounded to the nearest thousand? Answer: Which numbers round to 3000 when rounded to the nearest thousand? Answer: 4. Maria lives in a city with a population of 645, 693. What is the population rounded to the nearest ten thousand? Answer: 5. Gina s dad looks at some used cars. The chart shows the number of miles the cars have been driven. Color of Car Number of Miles White 43,659 Black 48,392 Red 36,342 Green 44,975 Blue 34,956 Is the number of miles on the car 40, 000 when rounded to the nearest ten thousand? Check Yes or No for each number of miles. A B C D E 43,659 48,392 36,342 44,975 34,956 Yes No 6. The table shows how much money the Martinez family spent on their trip to New York City. Mr. Martinez rounded the amounts to the nearest hundred. Complete the table to show the rounded amounts. Item New York City Expenses Amount Spent Plane Tickets $1790 Hotel Rooms $1482 Meals Entertainment $1045 $ 985 Introduction Rounded Amount Words for the Wise approximate estimate reasonable round motivationmath LEVEL 4 ILLEGAL TO COPY 49
Student Edition Sample Page Partner Practice 1. Look at the group of numbers. 4379 3793 4499 3542 What do these numbers have in common? A When rounded to the nearest ten, the numbers all round to 4010. B When rounded to the nearest hundred, the numbers all round to 4100. C When rounded to the nearest thousand, the numbers all round to 4000. D The numbers are all greater than 3600. 2. Sidney scored 569 points the first time she played Space Station on her video game system. The next time she played, Sidney scored 810 points. Sidney rounded her scores to the nearest hundred to estimate the total number of points she scored the first two times she played her video game. Which expression shows Sidney s estimate? A 600 + 900 B 500 + 900 C 500 + 800 D 600 + 800 3. Three classes had a reading contest to see which class could read the most minutes. Ms. Busby s class read 12, 580 minutes, Mr. Fulton s class read 13, 245 minutes, and Mrs. Black s class read 12, 284 minutes. Which classes each had a total number of minutes that is 13, 000 when rounded to the nearest thousand? A Mrs. Black s and Mr. Fulton s B Ms. Busby s and Mr. Fulton s C Ms. Busby s and Mrs. Black s D only Mr. Fulton s class Name 4. The table shows how many miles a pilot flew his airplane in four different weeks. The pilot rounded the number of miles to the nearest thousand. Week Number of Miles Rounded Number of Miles 1 16,862 17,000 2 13,137 13,000 3 11,528 12,000 4 18,693 18,000 For which week is the number of miles not correctly rounded to the nearest thousand? A Week 1 C Week 3 B Week 2 D Week 4 5. Use the number line to answer the question. 230,000 240,000 250,000 What is 232, 385 rounded to the nearest ten thousand? A 200, 000 C 240, 000 B 230, 000 D 250, 000 6. Marissa collects coins. She has 1501 U.S. coins and 985 foreign coins. Marissa adds 1500 and 1000 to estimate how many coins she has in her collection. Which statement describes how Marissa rounds the numbers? A Marissa rounds both numbers to the nearest hundred. B Marissa rounds one number to the nearest hundred and one number to the nearest ten. C Marissa rounds both numbers to the nearest ten. D Marissa rounds both numbers to the nearest thousand. 50 ILLEGAL TO COPY motivationmath LEVEL 4
Student Edition Sample Page Name 1. Ana rounded the number of points she made playing a video game to 30, 000. She rounded to the nearest ten thousand. Select all the numbers that could have been Ana s score. A 37, 843 B 26, 403 C 34, 569 D 25, 126 E 35, 000 F 32, 987 2. For the school fund raiser, Mrs. Bax s class collected 4864 pennies, and Miss Finley s class collected 2234 pennies. To estimate the difference between the number of pennies collected by the two classes, Mrs. Bax rounded both numbers to the nearest thousand. Which expression shows the numbers rounded to the nearest thousand? A 4000 2000 B 5000 3000 C 5000 2000 D 4000 3000 3. Mr. Reynolds and Mr. Montoya work for the same trucking company. Last week Mr. Reynolds drove his truck 4379 miles. Mr. Montoya drove 6512 miles. To estimate the total number of miles both men drove, they rounded the numbers to the nearest hundred. Which expression shows the numbers rounded to the nearest hundred? A 4300 + 6500 B 4400 + 6500 C 4400 + 6600 D 4300 + 6600 Independent Practice 4. Xavier went shopping for camping equipment. The table shows the prices of the items Xavier bought. Camping Equipment Rounded Item Price Amount Sleeping Bag $63 $60 Lantern $59 $50 Ice Chest $35 $40 Mess Kit $12 $10 Xavier rounded the amounts to the nearest ten dollars to estimate the total amount he spent. Which amount is not rounded correctly? A $63 C $35 B $59 D $12 5. In a recent election, two candidates received 24, 591 and 41, 264 votes. Marco added 25, 000 and 40, 000 to find the total number of votes. Which statement describes how Marco rounded the numbers? A Marco rounded both numbers to the nearest thousand. B Marco rounded both numbers to the nearest ten thousand. C Marco rounded the first number to the nearest ten thousand and the second number to the nearest thousand. D Marco rounded the first number to the nearest thousand and the second number to the nearest ten thousand. 6. Mazy estimated an answer to a problem to be 6000. Which number is 6000 when rounded to the nearest thousand? A 5498 C 6512 B 5595 D 6526 motivationmath LEVEL 4 ILLEGAL TO COPY 51
Student Edition Sample Page Assessment 1. The postal carrier delivered 3683 pieces of mail on Monday and 2856 pieces on Tuesday. Which expression can be used to estimate the total number of pieces of mail the postal carrier delivered? A 3000 + 3000 B 3000 + 2000 C 4000 + 3000 D 4000 + 4000 Name 3. Bud recycled 1086 old tires in May and 3764 tires in June at his tire shop. Bud subtracted 1000 from 3800 to estimate how many more tires he recycled in June than in May. Which statement describes how Bud rounded the numbers? A Bud rounded both numbers to the nearest hundred. B Bud rounded both numbers to the nearest thousand. C Bud rounded the first number to the nearest thousand and the second number to the nearest hundred. D Bud rounded the first number to the nearest hundred and the second number to the nearest thousand. 2. Greg read that about 42, 000 people attended a football game. The actual attendance number was rounded to the nearest thousand. Select all the numbers that are 42, 000 when rounded to the nearest thousand. A 41, 832 B 42, 715 C 42, 975 D 41, 941 E 42, 511 F 42, 099 4. The National Weather Service launches two weather balloons. One balloon reaches an altitude of 76, 452 feet. The other balloon reaches an altitude of 92, 795 feet. Which expression to find the approximate difference in the altitudes of the two weather balloons shows the numbers rounded to the nearest thousand? A 92, 000 77, 000 B 93, 000 76, 000 C 93, 000 77, 000 D 92, 000 76, 000 5. Global Airways reported the number of passengers for the first 6 months of the year. The information is displayed on the table. During which months was the number of passengers 10, 000 when rounded to the nearest thousand? Answer: Passengers Month Number of Passengers January 16,588 February 10,051 March 9,649 April 15,704 May 10,428 June 24,407 52 ILLEGAL TO COPY motivationmath LEVEL 4
Student Edition Sample Page Name Analysis Analyze 1. What is the least number that is 1000 when rounded to the nearest thousand and 800 when rounded to the nearest hundred and 770 when rounded to the nearest ten? Critical Thinking Answer: Explain your answer. Analysis Analyze 2. Use the clues to answer the rounding riddles. When rounded to the nearest 10, I am the least number that rounds to 500. What number am I? Answer: When rounded to the nearest thousand, I am the greatest whole number that rounds to 4000. What number am I? Answer: I am the sum of the following three numbers: 1273 rounded to the nearest 10 1273 rounded to the nearest 100 1273 rounded to the nearest 1000 Answer: Journal Synthesis Describe a situation when it would be best to round a number to the nearest 100. Create Describe a situation when it would be best to round a number to the nearest 1000. motivationmath LEVEL 4 ILLEGAL TO COPY 53
Student Edition Sample Page Motivation Station Roll and Round Name Play Roll and Round with a partner or in a small group. Each group needs four dice, a pencil, and a paper clip to use with the spinner. Each player needs a game sheet. In turn, each player rolls four dice and records the numbers in the Digits Rolled column of the table. The player decides what number to create using the four digits and records this number in the My Number column. The player then spins the spinner to determine whether to round the number to the nearest 10, 100, or 1, 000 and records the rounded number in the Rounded Number column. On each play, the player adds the new rounded number to the previous rounded number and keeps a running total. The object of the game is to be the first player to reach the target number of 10, 000 without going over. A player may choose to stop rolling at any point in the game if he/she believes that continuing play would exceed the target number of 10, 000. Spinner Digits Rolled My Number Rounded Number Target Number 10,000 Parent Activities 1. Record the mileage on your car and have your child round the number to the nearest ten thousand, thousand, and hundred. Discuss how the rounded numbers differ. 2. Find the populations of three cities that have fewer than 1, 000, 000 people. Have your child round one of the populations to the nearest ten thousand, one to the nearest thousand, and one to the nearest hundred. 54 ILLEGAL TO COPY motivationmath LEVEL 4
Standards (Student pages 49 54) California Common Core State Standards for Mathematical Content: 4.NBT.A.3 Domain Cluster Standard Number and Operations in Base Ten* Generalize place value understanding for multi-digit whole numbers. (Major Cluster) 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. * Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. Other Standards Addressed in this Unit 4.NBT.A.1, 4.NBT.A.2, 3.NBT.A.1 Common Core State Standards for Mathematical Practice Addressed in this Unit MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. Unpacking the Standards In grade 3, students used place value understanding to round whole numbers to the nearest 10 or 100. In grade 4, students extend this concept to rounding multi-digit whole numbers less than 1,000,000 to any place. motivationmath LEVEL 4 ILLEGAL TO COPY 99
Getting Started Introduction Activity The teacher reads and discusses the book A Million Fish More or Less by Patricia C. McKissack. (DOK 1, Bloom s Level: Comprehension/Understand) Suggested Formative Assessment The teacher asks probing questions such as the following. What clue was given in the story that the number of fish Hugh Thomas claims to have caught was not an exact number? Do you think the number of fish Hugh Thomas claims to have caught was an approximation or an exaggeration? What is the fewest number of fish Hugh Thomas could have caught if he rounded the actual number caught to 1,000,000? What is a real-life situation in which rounded numbers are used? What is a real-life situation that requires exact numbers? (DOK 3, Bloom s Level: Analysis/Analyze) Children s Literature Connections Hottest, Coldest, Highest, Deepest Steve Jenkins Highest, Longest, Deepest John Malam A Million Fish More or Less Patricia C. McKissack 100 ILLEGAL TO COPY motivationmath LEVEL 4 mentoringmindsonline.com
Vocabulary Focus The following are essential vocabulary terms for this unit. approximate estimate reasonable round Vocabulary Activity Acrostic Poem Students create acrostic poems that express the meaning or critical attributes of the word round. The letters in the word may be the first letter of each line of the poem or be placed in any position. Here are some examples with the word cup. C ustomary unit A quart Contains 4 U sed for liquid measure Equal to 8 ounces P ints contain two of them Measures liquid that Pours Students work with partners and read the original acrostic poems. (DOK 3, Bloom s Level: Synthesis/Create) Suggested Formative Vocabulary Assessment The teacher or a student reads one of the poems written in the previous activity. Another student explains how the poem helps define the vocabulary word. The student may also offer suggestions to improve the poem to give a better description. The teacher may need to provide more support for some students before beginning instruction in this unit. (DOK 2, Bloom s Level: Analysis/Analyze) motivationmath LEVEL 4 ILLEGAL TO COPY 101
Suggested Instructional Activities 1. The teacher shows students how to use a roller coaster model to round numbers to the nearest ten, hundred, or thousand. The teacher guides students to discuss the boundary numbers that are used to label the bottom of each hill. Then, they discuss the halfway point numbers that label the top of each hill. The example shows with rounding to the nearest hundred. The number 181 is located between the boundary numbers 100 and 200. Since 181 is greater than 150, it is located past 150 on the downhill slope. Students discuss which way the roller coaster will coast to reach the nearest hundred. The number 181 will coast down to 200, so 181 rounds to 200. Finally, students discuss what happens at a halfway point such as 50 or 150. Repeat this process with a roller coaster number line labeled for thousands. 50 150 250 181 0 100 200 300 (DOK 1, Bloom s Level: Comprehension/Understand) 2. The teacher creates BINGO cards with rounded numbers in the spaces (e.g., 300, 4,000, 50,000, 600,000). After the cards are distributed to the students, the teacher calls a number. Students round the called number to the greatest place value (e.g., 47,345 rounds to 50,000.). Students locate the rounded value on their cards and cover the appropriate spaces. Play proceeds like a traditional BINGO game. (DOK 1, Bloom s Level: Application/Apply) 3. Students play the Roll and Round game on page 54 in the student edition. Students discuss strategies for playing the game. (DOK 2, Bloom s Level: Analysis/Analyze) 4. Students work in groups of four. Students discuss a step-by-step process for rounding numbers to a given place and create graphic organizers to outline the steps in the procedure. Each group explains their graphic organizer to the class and posts the graphic organizer on the bulletin board. (DOK 2, Bloom s Level: Synthesis/Create) 102 ILLEGAL TO COPY motivationmath LEVEL 4 mentoringmindsonline.com
Suggested Formative Assessment The teacher displays five 6-digit numbers on a place value chart. Students round each number to the nearest hundred thousand, ten thousand, thousand, hundred, and ten. An example is shown. Number Nearest Hundred Thousand Nearest Ten Thousand Nearest Thousand Nearest Hundred Nearest Ten 782,307 800,000 780,000 782,000 782,300 782,310 349,562 448,923 934,518 604,185 The teacher asks students to explain how they rounded the numbers. Based on student responses, the teacher adjusts instruction or plans interventions to meet their needs. (DOK 1, Bloom s Level: Application/Apply) Suggested Reflection/Closure Activity In groups of three, students complete Critical Thinking activity 1 on page 53 in the student edition. What is the least number that is: 1000 when rounded to the nearest thousand, 800 when rounded to the nearest hundred, and 770 when rounded to the nearest ten? Students share and justify their responses. (DOK 3, Bloom s Level: Analysis/Analyze) Suggested Formative Assessment Given a group of six numbers, students select all the numbers that round to a given number. They justify why they did not select each of the other numbers. The teacher notes misconceptions and provides additional support as needed. (DOK 2, Bloom s Level: Analysis/Analyze) motivationmath LEVEL 4 ILLEGAL TO COPY 103
Interventions 1. The teacher creates a large number line on the floor with painter s tape or on the sidewalk with chalk. The teacher labels two boundary numbers (e.g., 2000 and 3000). Students identify the midpoint on the number line, and one student stands at that point. The teacher calls a number to be rounded within these boundaries such as 2337. Students discuss where this number would be located, and another student stands at that approximate location on the number line. Students determine which way to round based on the location of the midpoint. The activity may be repeated with other numbers and boundary points. (DOK 1, Bloom s Level: Application/Apply) 2. Students round a number to a given place. Then students write step-by-step directions or explanations for the methods they used to round. (DOK 1, Bloom s Level: Comprehension/Understand) 3. The teacher reads books such as Hottest, Coldest, Highest, Deepest by Steve Jenkins or Highest, Longest, Deepest by John Malam. Students discuss the numbers and round each number to several different places, recording the results in a chart. (DOK 1, Bloom s Level: Application/Apply) Suggested Formative Assessment Each student writes a summary of how to round numbers, including three examples. The teacher uses this information to plan additional interventions as needed. (DOK 3, Bloom s Level: Analysis/Analyze) Extending Student Thinking The word round has several meanings. In fourth-grade math, it means to approximate a number to a given place value. Round can also refer to figures that are shaped like circles. Each student generates a list of math words that have more than one meaning. The student then creates an electronic slideshow to present the word and show its meanings with words, numbers, or pictures. Multiple-meaning words might include acute, angle, area, base, center, meter, convert, factor, foot, formula, gram, line, mass, meter, obtuse, plot, pound, prime, product, ray, right, second, square, volume, or yard. (DOK 3, Bloom s Level: Analysis/Analyze and Synthesis/Create) 104 ILLEGAL TO COPY motivationmath LEVEL 4 mentoringmindsonline.com
Answer Key and Codings Page Question Answer DOK Level Bloom s Original/Revised 1 7000 5000 1 Comprehension/Understand 2 9000 + 5000 1 Application/Apply 2356 2529 49 2449 2831 3 2000 3000 2356 and 2449 2529 and 2831 1 Application/Apply 4 650,000 1 Comprehension/Understand 5 6 A Yes B No C Yes D Yes E No Item New York City Expenses Amount Spent Rounded Amount Plane Tickets $1790 $1800 Hotel Rooms $1482 $1500 Meals $1045 $1000 Entertainment $ 985 $1000 1 Analysis/Analyze 1 Comprehension/Understand 1 C 2 Analysis/Analyze 2 D 1 Application/Apply 50 3 B 1 Application/Apply 4 D 1 Analysis/Analyze 5 B 1 Comprehension/Understand 6 A 2 Analysis/Analyze motivationmath LEVEL 4 ILLEGAL TO COPY 105
Answer Key and Codings Page Question Answer DOK Level Bloom s Original/Revised 1 B, C, D, F 1 Analysis/Analyze 2 C 1 Analysis/Analyze 51 3 B 1 Analysis/Analyze 4 B 1 Analysis/Analyze 5 D 2 Analysis/Analyze 6 B 1 Application/Apply 1 C 1 Application/Apply 2 A, D, F 1 Analysis/Analyze 52 3 C 1 Analysis/Analyze 4 B 1 Application/Apply 5 February, March, and May 1 Analysis/Analyze 53 1 2 765 Explanations will vary. 495 4499 3570 2 Analysis/Analyze 2 Analysis/Analyze Journal Answers will vary. 2 Synthesis/Create 54 Motivation Station Results will vary. 1 Application/Apply 106 ILLEGAL TO COPY motivationmath LEVEL 4 mentoringmindsonline.com