Formative Assessment Opportunity: Performing operations with integers is an essential skill in algebraic mathematics. This lesson is an excellent

Transcription

1 Formative Assessment Opportunity: Performing operations with integers is an essential skill in algebraic mathematics. This lesson is an excellent opportunity to assess your students understanding of the fundamental rules for solving operations with positive and negative integers. First, use Practice questions 1-22 on pg. 3 to engage students in a self-assessment of their skills with integers. Second, using pgs. 1-2 conduct mini-lessons on adding, subtracting, multiplying, dividing, and raising an integer to a whole power let students tune into the mini-lessons as needed. Finally, use Practice questions 1-9 on pg. 4 to assess where students are at the end of the lesson.

2 Ready Reference integer the set consisting of the positive and negative whole numbers and zero whole number any of the numbers 0, 1, 2, 3, 4, Rules for Multiplying Integers positive positive positive positive negative negative negative positive negative negative negative positive Rules for Dividing Integers positive positive positive positive negative negative negative positive negative negative negative positive Sometimes it is necessary to add, subtract, multiply, and divide integers. There are also times when you may need to raise a whole number to a whole number power. One way to add or subtract integers is to use a number line. When multiplying and dividing integers, it is helpful to remember the rules listed above. Use repeated multiplication when you raise a whole number to a whole number power. Example 1 Add. 3 ( 5) Draw a number line. Start at 0. Move 3 units to the right. Then move to the left 5 units ( 5) Example 2 Subtract. 6 ( 1) To subtract an integer, add its opposite. 6 ( 1) ( 1) Example 3 Subtract. 3 6 Step 1 To subtract, add the opposite. 3 ( 6) Step 2 If needed, draw a number line. Start at 0. Move 3 units to the right. Then move to the left 6 units Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com 1

3 Example 4 Tara is keeping track of her score while playing a game. Red markers indicate negative points and yellow markers indicate positive points. What is Tara s score if she has 7 red markers and 2 yellow markers? Find the sum. 7 2 Step 1 Find the absolute values Step 2 Subtract the absolute values. 7 2 Step 3 Determine the sign of the sum. The signs of 2 and 7 are different. The sum is negative because 7 has the greater absolute value. Solution What is Tara s score if she has 7 red markers and 2 yellow markers? Example 5 Multiply. 5( 4) Use the rules for multiplying integers. positive negative negative 5 4 Example 6 Divide. ( 12) 4 Use the rules for dividing integers. negative positive negative 12 4 Example 7 Evaluate. 4 3 Rewrite the power using repeated multiplication Then multiply Example 8 Evaluate. ( 2) 4 Rewrite the power using repeated multiplication. Then multiply. ( 2) 4 ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) ( 2) 2 Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com

4 Practice Add ( 9) ( 6) ( 3) ( 75) Subtract ( 6) ( 1) Multiply or Divide ( 4)( 8) 11. ( 25)( 3)( 2) 12. ( 1)(0)(12) ( 3) ( 3) Solve each problem. 17. Simplify the expression Does the expression ( 6) ( 10) result in a positive or negative integer? 19. Does the expression ( 4) ( 16) result in a positive or negative integer? 20. Simplify the expression. ( 2) A repairman got on an elevator 3 floors below ground level. The elevator went down 2 floors, went up 16 floors, and then went down 1 floor. Then the repairman got off the elevator. On which floor of the building was the repairman? _ 22. Is ( 8)( 5) greater than, less than, or equal to (5)( 8)? Explain. Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com 3

5 Practice Operating with Integers DIRECTIONS Read each question. Then circle the letter for the correct answer. 1. Which of the following expressions results in a positive number? A B C D 6 ( 2) 2 ( 6) ( 2) ( 6) 6 ( 2) 5. The temperature rose from 8 to 6. What was the increase in temperature? A 14 B 2 C 2 D Which of the following expressions results in a negative number? A 6 2 B ( 6) ( 2) C 2 ( 6) D ( 6) 2 ( 4) 3. Which of the following expressions results in a positive number? A 5 3 B 3 5 C 3( 5)( 1) D ( 5)( 3) 4. Which of the following expressions results in a negative number? A B C D 15 ( 3) 15 ( 3) 3 ( 15) Which of the following is true? A 17 ( 2) ( 1) 20 B 17 ( 2) ( 1) 14 C 17 ( 2) ( 1) 14 D ( 10) 3 A 1,000 B 300 C 300 D 1, A 7.5 B 17 C 30 D The weather forecaster said to expect a high temperature of 5ºC during the day and a low temperature at night of 4ºC. What is the predicted high temperature minus the predicted low temperature? A 29ºC B 21ºC C 1ºC D 9ºC 4 Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com

6 Ready Reference integer the set consisting of the positive and negative whole numbers and zero whole number any of the numbers 0, 1, 2, 3, 4, Rules for Multiplying Integers positive positive positive positive negative negative negative positive negative negative negative positive Rules for Dividing Integers positive positive positive positive negative negative negative positive negative negative negative positive Sometimes it is necessary to add, subtract, multiply, and divide integers. There are also times when you may need to raise a whole number to a whole number power. One way to add or subtract integers is to use a number line. When multiplying and dividing integers, it is helpful to remember the rules listed above. Use repeated multiplication when you raise a whole number to a whole number power. Example 1 Add. 3 ( 5) Draw a number line. Start at 0. Move 3 units to the right. Then move to the left 5 units ( 5) Example 2 Subtract. 6 ( 1) To subtract an integer, add its opposite. 7 6 ( 1) ( 1) Example 3 Subtract. 3 6 Step 1 To subtract, add the opposite. 3 ( 6) Step 2 If needed, draw a number line. Start at 0. Move 3 units to the right. Then move to the left 6 units Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com 1

7 Example 4 Tara is keeping track of her score while playing a game. Red markers indicate negative points and yellow markers indicate positive points. What is Tara s score if she has 7 red markers and 2 yellow markers? Find the sum. 7 2 Step 1 Find the absolute values Step 2 Subtract the absolute values Step 3 Solution Determine the sign of the sum. The signs of 2 and 7 are different. The sum is negative because 7 has the greater absolute value. 5 What is Tara s score if she has 7 red markers and 2 yellow markers? Example 5 Multiply. 5( 4) Use the rules for multiplying integers. positive negative negative Example 6 Divide. ( 12) 4 Use the rules for dividing integers. negative positive negative Example 7 Evaluate. 4 3 Rewrite the power using repeated multiplication Then multiply Example 8 Evaluate. ( 2) 4 Rewrite the power using repeated multiplication. Then multiply. ( 2) 4 ( 2) ( 2) ( 2) ( 2) 16 ( 2) ( 2) ( 2) ( 2) 2 Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com

8 Practice Add ( 9) ( 6) ( 3) ( 75) Subtract ( 6) ( 1) Multiply or Divide ( 4)( 8) 11. ( 25)( 3)( 2) 12. ( 1)(0)(12) ( 3) ( 3) Solve each problem Simplify the expression. 5 2 negative 18. Does the expression ( 6) ( 10) result in a positive or negative integer? positive 19. Does the expression ( 4) ( 16) result in a positive or negative integer? Simplify the expression. ( 2) A repairman got on an elevator 3 floors below ground level. The elevator went down 2 floors, went up 16 floors, and then went down 1 floor. Then the repairman got off the elevator. tenth floor On which floor of the building was the repairman? _ 22. Is ( 8)( 5) greater than, less than, or equal to (5)( 8)? Explain. Greater than; ( 8)( 5) 40 and (5)( 8) Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com 3

9 Practice Operating with Integers DIRECTIONS Read each question. Then circle the letter for the correct answer. 1. Which of the following expressions results in a positive number? A B C D 6 ( 2) 2 ( 6) ( 2) ( 6) 6 ( 2) 5. The temperature rose from 8 to 6. What was the increase in temperature? A 14 B 2 C 2 D Which of the following expressions results in a negative number? A 6 2 B ( 6) ( 2) C 2 ( 6) D ( 6) 2 ( 4) 3. Which of the following expressions results in a positive number? A 5 3 B 3 5 C 3( 5)( 1) D ( 5)( 3) 4. Which of the following expressions results in a negative number? A B C D 15 ( 3) 15 ( 3) 3 ( 15) Which of the following is true? A 17 ( 2) ( 1) 20 B 17 ( 2) ( 1) 14 C 17 ( 2) ( 1) 14 D ( 10) 3 A 1,000 B 300 C 300 D 1, A 7.5 B 17 C 30 D The weather forecaster said to expect a high temperature of 5ºC during the day and a low temperature at night of 4ºC. What is the predicted high temperature minus the predicted low temperature? A 29ºC B 21ºC C 1ºC D 9ºC 4 Peoples Education Measuring Up MyQuest TM Lesson and Practice measuringuplive.com