Subtraction of Positive and Negative Numbers

Transcription

1 Subtraction of Positive and Negative Numbers Objective To develop a rule for subtracting positive and negative numbers. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Model differences of positive and negative numbers with manipulatives. [Operations and Computation Goal 1] Write and solve the equivalent addition number model for signed number subtraction problems. [Operations and Computation Goal 1] Use signed number subtraction patterns to describe a rule for subtracting signed numbers. [Patterns, Functions, and Algebra Goal 1] Write number sentences that model signed-number addition and subtraction problems. [Patterns, Functions, and Algebra Goal 2] Key Activities Students use their and counters to explore and describe a rule for subtracting positive and negative numbers. They practice applying the rule. Materials Math Journal 2, pp Study Link 7 8 and counters from Lesson 7 8 slate Playing High-Number Toss: Decimal Version Student Reference Book, p. 321 Math Masters, p. 511 per partnership: 4 each of number cards 0 9 (from the Everything Math Deck, if available) Students compare decimals and practice writing decimals in scientific notation. Ongoing Assessment: Recognizing Student Achievement Use High-Number Toss Record Sheet. [Number and Numeration Goals 1 and 6] Math Boxes 7 9 Math Journal 2, p. 241 Students practice and maintain skills through Math Box problems. Study Link 7 9 Math Masters, p. 209 Students practice and maintain skills through Study Link activities. ENRICHMENT Comparing Elevations Student Reference Book, p. 381 Math Masters, p. 210 Students use addition and subtraction to compare elevations of various places in the world. EXTRA PRACTICE 5-Minute Math 5-Minute Math, pp. 153 and 234 Students find a rule for in/out patterns with negative numbers. Advance Preparation Teacher s Reference Manual, Grades 4 6 pp Unit 7 Exponents and Negative Numbers

2 Getting ed Mental Math and Reflexes Add positive and negative numbers. Students may use and counters. Suggestions: 9 + (-3) (-18) -36 Math Message Use your and cash cards to help you complete page 237 in your journal. Study Link 7 8 Follow-Up Partners compare answers and resolve differences. 1 Teaching the Lesson Math Message Follow-Up (Math Journal 2, p. 237) WHOLE-CLASS DISCUSSION Algebraic Thinking Ask students to show how they used their and counters to obtain their answers. Use Problem 3 to remind students that if the same number of and counters are added to a balance, the balance will remain the same. For Problem 5, 4 and 4 counters must be added to the balance before the required counters can be taken away. Then use change diagrams and number models to summarize Problems 1 5. Problem 1: Problem 2: 5 + 5? 5 + (-5) = ? 5 + (-7) = -2 Date 7 9 Math Message Finding Balances Use your and cash card counters to model the following problems. Draw a picture of the and counters to show how you found each balance. Example: You have 3 counters. Add 6 counters. Balance 3 counters 1. You have 5 counters. Add 5 counters. 2. You have 5 counters. Add 7 counters. Balance 0 2 counters Balance counters 3. Show a balance of 7 using 15 of your and counters. 4. You have 7 counters. Take away 5. You have 7 counters. Take away 4 counters. 4 counters Balance counters Balance counters Math Journal 2, p. 237 Lesson

3 Date 7 9 Adding and Subtracting Numbers You and your partner combine your and counters. Use the counters to help you solve the problems Balance Balance If 4 counters are subtracted If 4 counters are added to from New balance 12 New balance 12 8 (4) Balance Balance If 3 counters are subtracted If 3 counters are added to from New balance 10 New balance Math Journal 2, p (3) 10 Problem 3: Problem 4: Problem 5: ? (-11) + 4 = ? (-7) - (-4) = ? 7 - (-4) = 11 Developing a Rule for Subtracting Positive and Negative Numbers (Math Journal 2, pp. 238 and 239) PARTNER Date Ask partners to pool their counters so they have 20 positive and 20 negative counters to use as they work through problems. Have them complete problems 1 8 on journal pages 238 and 239. When most students have finished, bring the class together to go over the answers. For each problem, ask volunteers to draw a change diagram and write a number model on the board. The number models should be displayed in pairs, as follows: 7 9 Adding and Subtracting Numbers continued Balance Balance If 6 counters are subtracted If 6 counters are added to from New balance 11 New balance Balance Balance If 2 counters are subtracted If 2 counters are added to from New balance 4 New balance 4 6 (2) 4 9. Write a rule for subtracting positive and negative numbers (6) Sample answer: To subtract a positive or negative number b from number a, add the opposite of b to a. Math Journal 2, p. 239 Problems 1 and 2: Problems 3 and 4: 8 - (-4) = = = (-3) = -10 Problems 5 and 6: Problems 7 and 8: 5 - (-6) = (-2) = = = -4 Ask the class to look for similarities and differences between the problems and number models for each of these pairs. Ask students to write about what they notice. As you discuss their written responses, include the following: Similarities Where containers start with the same combination of and counters, the starting balances are the same, and the first numbers in the number models are the same. 586 Unit 7 Exponents and Negative Numbers

4 Where the same number of counters is added to or taken out of the containers, the second numbers in the number models are the same. Where the new balances after the transactions are the same, the results of the number model operations are the same. Differences Where the transactions for a pair of counters are opposites of each other, the operations in the number models are opposites of each other. One is subtraction, and the other is addition. Where the counters that are subtracted or added have opposite signs, the second numbers in the number models are opposites. Refer students to Problem 1. Subtracting -4 from 8 has the same effect as adding 4 to 8. In Problem 3, subtracting 3 has the same effect as adding -3. Help students describe a rule for subtracting positive and negative numbers. Ask them to record the rule in their own words in Problem 9 on journal page 239. Have students use slates to practice subtracting positive and negative numbers. Ask students to write the equivalent addition number model. Suggestions: 6 minus (-9) = -3 6 minus = 15-6 minus (-9) = minus = 3 Adjusting the Activity Have students use larger numbers. Remind students of their rule for subtracting positive and negative numbers. Suggestions: 52 minus (-25) minus minus (-24) -12 Date A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Subtracting Positive and Negative Numbers (Math Journal 2, p. 240) PARTNER Ask students to complete journal page 240 independently, then compare answers with a partner and resolve differences. Circulate and assist. 7 9 Subtraction Problems Rewrite each subtraction problem as an addition problem. Then solve it (80) 4. 9 (2) (30) (7) 8. 0 (6.1) (Ç45) (45) (10) The Healthy Delights Candy Company specializes in candy that is wholesome. Unfortunately, they have been losing money for several years. During the year 2006, they lost $12 million, ending the year with a total debt of $23 million. a. What was Healthy Delights total debt at the beginning of 2006? b. Write a number model that fits this problem. 10. In 2007, Healthy Delights is expecting to lose $8 million. a. What will Healthy Delights total debt be at the end of 2007? b. Write a number model that fits this problem $11 million , or 11 (12) 23 $31 million , or 23 (8) 31 Math Journal 2, p. 240 Lesson

5 Date Make the following changes to the numeral 29,078. the digit in the ones place to 4, in the ten-thousands place to 6, in the hundreds place to 2, in the tens place to 9, in the thousands place to 7. Write the new numeral. 6 7, When Antoinette woke up on New Year s Day, it was 4 F outside. By the time the parade started, it was 18 F. How many degrees had the temperature risen by the time the parade began? Solve. 302 m = 198 m = 104 Explain how you got your answer. I used the fact family to find the missing number. I wrote to get m. 3. Complete the table. 4. Insert parentheses to make each sentence true. Standard Scientific Notation Notation a. ( 48 6 ) + ( 2 4 ) = b. ( 48 ( )) 4 = 24 3, , ,000 Math Boxes Math Journal 2, p c. 45 = d. 0 = e. 30 = Write < or >. a. 1_ 4 < 3_ 8 b. 2_ 7 < 2_ 5 c. 8_ 9 > 7_ 8 d. e. ( ( )) ( ) ) ( )( ) 7_ 12 > 3_ 6 5_ 12 < 5_ Ongoing Learning & Practice Playing High-Number Toss: Decimal Version (Student Reference Book, p. 321; Math Masters, p. 511) PARTNER High-Number Toss was introduced in Lesson 2-5. Have students play the decimal version of the game as indicated on Student Reference Book, page 321 and record their rounds on the Record Sheet (Math Masters, page 511). Ongoing Assessment: Recognizing Student Achievement High Number Toss Record Sheet Use the Record Sheet (Math Masters, page 511) for High Number Toss: Decimal Version to assess students ability to write and compare decimals. Students are making adequate progress if they have written and compared the decimals correctly through thousandths. Some students may be able to find the difference between the two decimals. [Number and Numeration Goals 1 and 6] Math Boxes 7 9 (Math Journal 2, p. 241) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skill in Problem 6 previews Unit 8 content. Study Link Master Name Date Study Link 7 9 (Math Masters, p. 209) INDEPENDENT STUDY LINK 7 9 Addition and Subtraction Problems Solve each problem. Be careful. Some problems involve addition, and some involve subtraction. Reminder: To subtract a number, you can add the opposite of that number (-16) = (-43) = (-4) = = (-11) = (-11) = = = _ 2 + (-2 1_ 2 (-10) 2 ) = = For each temperature change in the table, two number models are shown in the Temperature after column. Only one of the number models is correct. Cross out the incorrect number model. Then complete the correct number model Home Connection Students solve problems involving addition and subtraction of positive and negative numbers. 3 Differentiation Options Temperature before Temperature Practice Find the number that each variable represents. Temperature after 40 up = (-7) = 10 down (-8) = 10-8 = 2-15 (15 below zero) -20 (20 below zero) up = = down = (-10) = u = 65,664 e = 3 w = m = = u e = = w m = 3.99 ENRICHMENT Comparing Elevations (Student Reference Book, p. 381; Math Masters, p. 210) INDEPENDENT Min To apply students understanding of adding and subtracting signed numbers, have them compare the elevations of U.S. locations that are above and below sea level. When they have Math Masters, p. 209 EM3MM_G5_U07_ indd 209 1/19/11 11:42 AM 588 Unit 7 Exponents and Negative Numbers

6 0 0 Coast 500 Miles 500 Kilometers Miles 0 Kilometers Miles 600 Kilometers finished the page, consider having them identify these locations on the landform map of the United States on Student Reference Book, page 381 and compare this information with the chart of elevation along the 39th parallel on the Student Reference Book page. EXTRA PRACTICE 5-Minute Math SMALL-GROUP 5 15 Min Algebraic Thinking To offer students more experience solving What s My Rule? problems involving negative numbers, see 5-Minute Math, pages 153 and 234. Name Date 4, ,300 Denver, CO 2,400 Tucson, AZ 1,000 Atlanta, GA 600 Chicago, IL 0 Sea Level Comparing Elevations 280 Death Valley, CA 1,300 Dead Sea (Israel/Jordan) Teaching Master This number line shows the elevation of several places. Elevation measures how far above or below sea level a location is. For example, an elevation of 5,300 for Denver means that Denver is 5,300 feet above sea level. An elevation of 280 for Death Valley means that some point in Death Valley is 280 feet below sea level. Fill in the table below. Use the example as a guide. Example: If you start at Denver and travel to Atlanta, what is your change in elevation? Solution: Draw an arrow next to the number line. it at the elevation for Denver (5,300 feet). it at the elevation for Atlanta (1,000 feet). Use the number line to find the length of the arrow (4,300 feet). Your final elevation is lower, so report the change in elevation as 4,300 feet down. Write a number model for the problem: 5,300 1,000 4,300. at Travel to in Elevation Number Model Denver Atlanta 4,300 feet down 5,300 1,000 4,300 Chicago Tucson feet Death Valley Dead Sea 1, ,800 2,400 1,020 down feet Dead Sea Death Valley feet Tucson Death Valley feet up 280 (1,020) 1,300 1,020 up 1,300 1, ,680 down 2,400 (2,680) 280 Dead Sea Atlanta 2,300 feet up 1,300 2,300 1,000 Math Masters, p. 210 American Tour Games Geography Landform Map of the United States Ranges Central Valley Cascade Range 39 Great Basin 39 Sierra Nevada Pacific Ocean Atlantic Ocean Alaska Range Rocky Brooks Range Elevation along the 39th Parallel Feet above Sea Level Great Plains Coastal Central Plain Gulf of Mexico Appalachian Alaska Widely spaced mountains Hawaii Plateaus Hills Plain Plains Coastal Plain Rocky 14,000 ft 12,000 ft Sierra Nevada 10,000 ft 8,000 ft 6,000 ft Appalachian Coast 4,000 ft Ranges Mississippi River Washington, 2,000 ft D.C. 0 ft Longitude (degrees W) Student Reference Book, p. 381 High-Number Toss: Decimal Version Materials number cards 0 9 (4 of each) scorecard for each player Players 2 Skill Decimal place value, subtraction, and addition Object of the game To make the largest decimal numbers possible. Directions 1. Each player makes a scorecard like the one at the right. Players fill out their own scorecards at each turn. 2. Shuffle the cards and place them number-side down on the table. 3. In each round: Player 1 draws the top card from the deck and 0. writes the number on any of the 3 blanks on the scorecard. It need not be the first blank it can be any of them. Player 2 draws the next card from the deck and writes the number on one of his or her blanks. Players take turns doing this 2 more times. The player with the larger number wins the round. 4. The winner s score for a round is the difference between the two players numbers. (Subtract the smaller number from the larger number.) The loser scores 0 points for the round. Player 1: Player 2: Game 1 Round 1 0. Round 2 0. Round 3 0. Round 4 Player 2 has the larger number and wins the round. Since , Player 2 scores point for the round. Player 1 scores 0 points. 5. Players take turns starting a round. At the end of 4 rounds, they find their total scores. The player with the larger total score wins the game. Student Reference Book, p. 321 Scorecard T o tal: Score Lesson

7 Name Date High-Number Toss: Decimal Version Record Sheet Circle the winning number for each round. Fill in the Score column each time you have the winning number. 321 Player 1 Player 2 (Name) (Name) Round Player 1 <, >, = Player 2 Score Sample < Copyright Wright Group/McGraw-Hill Total Score 511