3.5A -‐ Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to round whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations. 3.5B -‐ Number, operation, and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to use strategies including rounding and compatible numbers to estimate solutions to addition and subtraction problems. Suggested Activities/Lessons: • Human Number Line • Approximate Numbers and Rounding • Blank Number Line Math Curriculum Web Site: • Digit Delight (2nd Nine Weeks) • Human Number Line (2nd Nine Weeks) • Estimation Fun (2nd Nine Weeks) Skills Tutor 1. Click on Standards on home page. 2. Click on Select Standards. 3. Scroll down to TEKS 3rd Grade Math. 4. Click Done. 5. Select SkillsTutor Content or TEKS 3rd Grade Math. 6. Search for rounding. 7. Click bolded items to locate activities on rounding. Lesson Plan What do you want your students to know, do and understand as a result of this lesson? Essential Questions, Understandings and TEKS: Essential Questions: What are some patterns you notice in our number system? Understandings: Patterns can be used to compose and decompose numbers. TEKS: 3.5 Number, operation, and quantitative reasoning. The student estimates to determine reasonable results (A) round whole numbers to the nearest ten or hundred to approximate results in problem situations. Lesson Title: Human Number Line Learning objective: The students will create a human number line to round numbers. Evidence: see below Pre-assessment: Give the following problem to the students: Frank and his father were leaving for Houston on a camping trip. They had to travel about 900 miles to the campground. On Sunday they had traveled 282 miles before stopping to rest. By Monday they had traveled another 187 miles. If they travel 214 miles on Tuesday, about how many miles will they need to travel on Wednesday to reach the campground? Use your rubric. Procedure: Play “Digit Delight” if place value review is needed. An additional resource to review place value is a video clip. http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/3_Place_Value/i ndex.html Pass out the red decade number cards to students. Give remaining students black numbers. “I need the person with zero and one hundred to come up and start the two ends of our number line. We are going to place all the red numbers first.” “Everyone with a red number please stand up.” “What would be in the middle between zero and one hundred?” That person come stand half way between the zero and one hundred. Call one person to come place themselves where they THINK they belong on the human number line. (Do not call the numbers up in order) “Let’s say the red numbers that are now on our number line.” 0, 10, 20, 30, 40, 50 , 60, 70, 80, 90, 100 Now ask one black number one at a time to come and place themselves where they belong on the human number line. “Now, we are going to learn how to round these numbers. Rounding numbers is changing a number to the nearest 10 or 100 number that it is closest to. We are going to place the black numbers (round the black numbers) to the closest 10.” In order for all students to have a chance to SEE the black numbers move to the closest red number you will need to take ½ of the human number line to the opposite side of the room. “#50 through 100 please stay in line and follow me as we move to the other side of the room so you can see the first part of the number line.” “Number 19, what two red numbers are you between?” …..10 and 20 “Are you closer to 10 or closer to 20?” …..20 “That’s right 19 is closer to 20 so I want you to sit down in front of #20.” (descriptive feedback) “Number 22, what two red numbers are you between?” ……20 and 30 “Are you closer to 20 or 30?” …..20 “That’s right 22 is closer to 20 so I want you to sit down in front of #20.” Continue on with the remaining black numbers on this side of the room, then work with the numbers 50-100 on the other side of the room. Collect the red numbers. “People who had red numbers give me your number and please return to your seat.” “Black numbers, please give your black number to a person that is sitting down. If there are no more people sitting down without a number then give your black number to someone that is standing.” Pass the red numbers out to people who were previously black numbers and do not have a new number. “Everyone return to your seat.” “Zero and one hundred come up and make the two end of our human number line.” “What number is half way between zero and one hundred?” ….50 “Number 50 come stand in the middle of our human number line.” ……continue like the first time. (This allows the students who had the red numbers first the opportunity to answer the questions, “What decade numbers are you in between? Which number are you closer to?)” ELL Considerations: Preproduction Stage: Where is the number ___? Show me the number it is close to. Early Production Stage: Is 19 close to 10? (no) Is 19 close to 20? (yes) Speech Emergence Stage: Why is 19 closer to 20? Considerations for differentiation: Students play game “Rolling Round Up” in pairs. Teacher circulates around room and views the numbers the students have written in each column to check for understanding. Materials (technology, manipulatives, etc): • Digit Delight gameboard • Number cards for digit delight • Red decade numbers • Black numbers that are 2 digit non-decade • Rolling Round Up Game • 2 dice for each group of 2 students • White boards for Evidence of Learning part. Reflection: CARDS FOR LESSON ON ROUNDING If color printer is not available, you may use die cuts or put numbers on red paper. 10 20 30 40 50 60 70 80 90 100 0 19 22 28 33 44 47 55 51 63 68 73 77 82 88 94 98 89 72 41 13 11 53 Digit Delight Materials: Directions: Gameboard Two game markers of different colors Cards (two sets numbered 0-‐9 and two “wild” cards) Two players To start, players place markers anywhere on the board. Cards are shuffled and placed in a face-‐down stack. In turns, each player picks a card. Players may move one space in any direction but must move to a number that has the digit shown on the card. Players receive as many points as the value of the digit in his/her Number. (Example: 7 received 7 points in 457…..7 received 70 points in 379 or 700 points in 708) If a player cannot move to a number with digit on card drawn, then turn is lost. If players draw a “wild card” move, can be to ANY number. (But can only move one space) and any digit in the number may be used for the player’s Score. Play continues until all cards are used. Player with the highest score wins. 130 713 542 985 425 249 476 316 308 867 960 547 609 176 713 542 958 542 590 476 248 790 613 591 329 839 671 258 824 179 645 825 325 801 718 956 417 832 470 879 102 910 130 238 832 630 407 315 340 CARDS FOR DIGIT DELIGHT 0 1 2 3 4 5 6 7 8 9 WILD CARD Rolling Round Up *Review rounding *Materials: 2 dice, 2 game boards, pencil *Played in pairs lst player rolls the dice and arrange the digits to form a number. Then the player rounds the number to the nearest ten and record on his/her game board in appropriate column. (Write the number that was rolled in the rounded column. Play continues until one player reaches the goal line for any column. Goal line 0 10 20 30 40 50 60 70 Assessment Objective 1 – TEKS 3.5A Name _______________ Date _____________ 1. Put the numbers in the box in the correct place on the number line. 42 40 44 48 54 50 56 52 60 2. Beside each number, write the number it would round to. 42 ____ 48 ____ 54 ____ 56 ____ Approximate Nambers and Rounding In our number system, some numbers are "nice" or easy to think about and work with. What makes a nice number is sort of fuzzy. However, numbers such as 100, 500, and 750 are easier to use than 94, 517, and 762. Multiples of 100 are very nice, and multiples of 10 are not bad either. Multiples of 25 (50, 75, 425, 675, etc.) are nice because they combine into 100s and 50s rather easily, and we can mentally place those between multiples of 100s. Multiples of 5 are a little easier to work with than other numbers. Flexible thought w i t h numbers and many estimation skills are related to the ability to substitute a nice number for one that is not so nice. The substitution may be to make a mental computation easier, to compare i t to a familiar reference, or simply to store the number i n memory more easily. In the past, students were taught rules for rounding numbers to the nearest 10 or nearest 100. Unfortunately, the emphasis was placed on applying the rule correctly. (If the next digit is 5 or more, round up; otherwise, leave the number alone.) A context to suggest why they may want to round numbers was usually a lesser consideration. To round a number simply means to substitute a nice number that is close so that some computation can be done more easily. The close number can be any nice number and need not be a multiple of 10 or 100, as has been traditional. It should be whatever makes the computation or estimation easier or simplifies numbers sufficiently i n a story, chart, or conversation. You might say, "Last night it took me 57 minutes to do my homework" or "Last night it took me about one hour to do my homework." The first expression is more precise;, the second substitutes a rounded number for better communication. A number line with nice numbers highlighted can be useful i n helping children select near nice numbers. A n unlabeled number Une like the one shown i n Figure 2.6 can be made using three strips of poster board taped end to end. Labels are written above the line on the chalkboard. The ends can be labeled 0 and 100, 100 and 200, . . . , 900 40(5 'I and 1000. The other markings then show multiples of 25, I 463 I I I FIGURE 2 . 6 I I I I I I I I 1 I I 500 I I I • • • s . <?» » • « • • • • » , » , » , • « , « o e < A blank number line can be labeled in different ways to help students with near and nice numbers. 10, and 5. Indicate a number above the line that you want to round. Discuss the marks (nice numbers) that are close. • Numbers Beyond 1000 • • Extending students' conceptual understanding of numbers beyond 1000 is sometimes difficult to do because physical models for thousands are not commonly available. Encouraging students to extend the patterns i n the place-value system and to create familiar real-world referents helps students develop a fuller sense of these larger numbers. Extending ttie Place- Value System Two important ideas typically developed for three-digit numbers should be carefully extended to larger numbers. First, the grouping of ten idea should be generalized. & <s # c-> £> 0 # ^ a Q ?^ © a 0 c< e a ©# 3 # © ® ?3 s I 1 N U M B E R S BE/OKD 1000 Blank Number Lines www.Math-Drills.Com