Number, Operation, and Quantitative Reasoning


 Job Arnold
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1 Number, Operation, and Quantitative Reasoning Activity: TEKS: Just Make It Easy! 3.5 Number, operation and quantitative reasoning. The student estimates to determine reasonable results. The student is expected to: (A) round whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations; and (B) use strategies including rounding and compatible numbers to estimate solutions to addition and subtraction problems Geometry and spatial reasoning. The student recognizes that a line can be used to represent numbers and fractions and their properties and relationships. The student is expected to locate and name points on a number line using whole numbers and fractions including halves and fourths Underlying processes and mathematical tools. The student applies Grade 3 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (A) identify the mathematics in everyday situations; (B) solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (C) select or develop an appropriate problemsolving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) use tools such as real objects, manipulatives, and technology to solve problems Underlying processes and mathematical tools. The student communicates about Grade 3 mathematics using informal language. The student is expected to: (A) explain and record observations using objects, words, pictures, numbers, and technology; and (B) relate informal language to mathematical language and symbols Underlying processes and mathematical tools. The student uses logical reasoning. The student is expected to: (B) justify why an answer is reasonable and explain the solution Just Make It Easy! Page 1
2 process. Overview: Materials: Grouping: Time: Students will use number lines to round numbers to solve problems. They will practice this strategy when playing the game Easy. Coyotes All Around by Stuart J. Murphy Number line Transparencies/Handouts 1 and 2 Let s Practice Rounding Transparency/Handout 3 Easy game board Transparency/Handout 4, one per student Number cards Transparency/Handout 5, one set for class Make it Easy Problems Transparency/Handout 6 Introductory activity whole group 2 class periods Lesson: Procedures 1. Ask students to think of things that are round. Ask students which numbers on the number line they would consider to be round numbers. Have students highlight or color the same color all of the numbers that end with a zero on their number lines (Transparencies/Handouts 1 and 2). 2. Share the book, Coyotes All Around by Stuart J. Murphy. Discuss how Clever Coyote uses the number line to round each of the numbers. For example, on page 12, when counting roadrunners, Clever Coyote says, 21 is very close to 20, 12 is close to 10, 17 is closer to 20 than to 10, and 8 is almost 10. Ask students: Why is it easier to add numbers after the numbers have been rounded to the nearest ten? How close to the exact sum was Clever Coyote s answer? How close did Clever Coyote get to the exact Notes Examples may include wheels, donuts, tires, cookies, etc. Students usually think of numbers that end with zero as being round numbers. Rounding numbers is one way to estimate the sum or difference of numbers. The knowledge of place value is important to a student s understanding of rounding and estimating whole numbers. Students can find each number on their own number lines. Be sure to point out to students what Clever Coyote did when she needed to round the number 25. When a number is exactly in the middle between the round numbers on the number line, mathematicians always round up to the next 10. So, Clever Coyote rounded 25 to 30. Just Make It Easy! Page 2
3 number of lizards and grasshoppers? 3. Review the 4step problemsolving process with students. 4. Show Transparency/Handout 3, Let s Practice Rounding. Use the 4step plan to work the problem. Mr. Russell works in a toy store. Today, a customer wants to buy a birthday gift for about $ Should Mr. Russell show her a board game for $18.00, a stuffed animal for $23.00, or a skateboard for $27.00? You can help Mr. Russell by rounding each amount to the nearest ten. Encourage students to use their number lines to help them round the numbers. Have students work the other problems. 5. Use Transparency/Handout 4 for a game board for each student. Have the students decide where on their game boards they want to write the numbers that are listed at the top of the transparency. In TEKS 3.14 (B), the student is expected to understand the problem, make a plan, carry out the plan, and evaluate the solution for reasonableness. A method that can be used to help students comprehend the problem situation is: a. Have students read the problem chorally. You will set the pace and then fade out so that you can key in on the students oral reading behaviors. Make note of any difficulties (slowing down, voices dropping out, vocabulary, mispronunciations, etc ). b. Remove the problem, and ask students to tell you what they remember about the problem. Restate each student s contribution. It is likely that students will have only partial or incorrect recall of the details in the problem. Emphasize the need for rereading any problem. c. Show the problem again, and repeat step a. d. Remove the problem again, and elicit details from the students, restating each student s contribution. e. Finally, present the problem again and clarify anything that might have caused difficulty during the reading of the problem. This strategy will allow for each game board to have numerals written in different squares. Just Make It Easy! Page 3
4 6. The teacher or a student draws number cards, (Transparency/Handout 5), and calls out that number. Students should use their number lines if they need help deciding to which ten their number is nearest. Each student must round the number called to the nearest ten. If that rounded number appears on the student s card, he or she may cover it with a chip. The first person to cover four in a row, column, or diagonal is the EASY winner. 7. Now the students should use rounding to estimate the sums and differences on Transparency/Handout 6, Make It Easy Problems. Remember that according to the refined TEKS, there are no rules for rounding. Using a number line is one strategy used to round numbers. Homework: Have students create their own problems to estimate sums and differences. Just Make It Easy! Page 4
5 Number Line To make the centimeter Number Line: Cut on the dotted lines. Overlap the ends, putting the 20 from the first strip on top of the 20 on the second strip. Continue overlapping in the same way, putting the 40 on the 40, the 60 on the 60, and the 80 on the 80. Make sure the centimeters are accurate at the overlapped edges. Tape the strips together. Transparency/Handout 1 Just Make It Easy! Page 5
6 Transparency/Handout 2 Just Make It Easy! Page 6
7 Let s Practice Rounding Transparency/Handout 3 You can round numbers to the nearest ten to tell about how many or how much. When you round a number to the nearest ten, you find the ten it is nearest to on the number line. Remember that if the number is exactly halfway between the two tens, mathematicians always round to the greater ten. 1. Mr. Russell works in a toy store. Today, a customer wants to buy a birthday gift for about $ Should Mr. Russell show her a DVD for $18.00, a stuffed animal for $23.00, or rollerblades for $27.00? You can help Mr. Russell by rounding each amount to the nearest ten. First, think about which two tens on the number line the number comes between. Decide which ten the number is nearer. Is 18 nearer to 10 or 20? Round $18 to $ Is 23 nearer to 20 or 30? Round $23 to $ Is 27 nearer to 20 or 30? Round $27 to $ The DVD costs about $. The stuffed animal costs about $. The rollerblades cost about $. Which gifts should Mr. Russell show the customer? Why? Which gifts should Mr. Russell not show the customer? Why? Just Make It Easy! Page 7
8 2. Use the number line to round each number to the nearest ten Use the following numbers to answer these questions: Which of the above numbers round to 40? Which of the above numbers round to 70? Which of the above numbers round to 60? Which of the above numbers round to 50? 4. Lauren has a total of $ Katherine has a total of $ Jeff has $ Is his total closer to Lauren s total or to Katherine s total? 5. If Susan rounds the number of dollars she has to the nearest ten, she would say she has $ What is the least number of dollars she could have? Explain your answer. Just Make It Easy! Page 8
9 EASY Game Board This is the EASY game board. Write one numeral in each square of the game board. You do not have to use all of the numerals. You may use numerals more than once. Here are the EASY numerals: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200. E A S Y Just Make It Easy! Page 9
10 Transparency/Handout 4 Number Cards Just Make It Easy! Page 10
11 Transparency/Handout 5 Number Cards (continued) Just Make It Easy! Page 11
12 Transparency/Handout 5 Make It Easy! When numbers are rounded to the nearest ten, it is easy to estimate sums and differences. On these problems, round the numbers first and then estimate their sums or differences. 1. Mr. Russell works in a toy store. Today, a customer wants to buy gifts for each of his four children. He selected a stuffed animal for $12.00, a doll for $18.00, an art set for $21.00, and a set of building blocks for $ About how much did he spend before taxes? 2. Three children have been saving their money all year so they could buy a present for their mother on Mother s Day. Lauren has a total of $ Katherine has a total of $ Jeff has $ About how much money do they have altogether? 3. Susan has 58 trading cards and Chuck has 36 trading cards. About how many trading cards do they have together? About how many more does Chuck need to have as many as Susan? 4. Chris saved $ The bike she wants costs about $ About how much more does Chris need to save to buy the bike? 5. Estimate which sum is about 500. Circle the correct number sentence =? =? =? =? Transparency/Handout 6 Just Make It Easy! Page 12
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