Lesson Plan -- Adding and Subtracting Integers
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1 Lesson Plan -- Adding and Subtracting Integers Chapter Resources - Lesson 3-7 Add Integers - Lesson 3-7 Add Integers Answers - Lesson 3-8 Subtract Integers - Lesson 3-8 Subtract Integers Answers 1
2 LESSON 3-7 California Standards Gr. 5 NS 2.1: Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. Gr. 6 NS 2.3: Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Also included: Gr. 7 AF 1.3 Words to Remember Inverse property of addition: The sum of a number and its opposite is 0. E Adding Integers Using a Number Line Use a number line to find the sum 1 2. Begin at 0 and draw an arrow left to 4 units to represent starting at. a 1 (2a) 5 0 2a 1 a 5 0 Getting Started In Activity 3-6 you learned how to add integers using 11 and 21 cards. You can also use number lines and absolute values to add integers. 0 Begin at and draw an arrow right 2 units to represent adding 2. Write the sum since the end of the arrow after adding 2 to is at. Adding Opposites When you add a number and its opposite on a number line, you draw an arrow away from zero (for example, 15 units) and then draw another arrow back in the opposite direction the same number of units (for example, 25 units). The result is 0. T Use a number line to find the sum () () () 5 26
3 E Adding Integers Using Absolute Values Use absolute values to find the sum 26 1 (25). Find the absolute value of each term in the expression and Add the absolute values of the integers Write the sum. Since both of the original terms in the expression are negative, the sum must also be negative (25) ANSWER 26 1 (25) 5211 T Use absolute values to find the sum (28) 52( ) 52( 1 ) 52( ) 5 Adding Integers with Same Sign Use the sign of the integers in the original expression when using absolute values to add integers with like signs. Adding Integers with Different Signs It is easiest to add integers with opposite signs using a number line, as shown in Example 1. To use absolute values to add integers that have opposite signs, subtract the least absolute value from the greater absolute value. Use the sign of the integer that has the greatest absolute value. 3 1 (28) 5 ( ) 52(8 2 3) > 3, so the final result will have the same sign as 8. 27
4 Summarize Using a Number Line to Add Integers When an integer is negative, move that many units to the left of 0 or your starting point. When a number is positive, move that many units to the right of zero or your starting point. Using Absolute Values to Add Integers When the integers have the same sign, begin by finding the absolute values of the integers and then finding their sum. Then use the same sign as the sign of the original integers. When the integers have different signs, subtract the least absolute value from the greater absolute value. Use the sign of the integer with the greater absolute value. Match each sum with the number line that represents it A () B C. Find the sum using a number line (26) ( 2) 5 Find the sum using absolute values (28) (211) (29) (210) (26) 1 (212) (260) 1 (8) ( 4) ( )
5 Write a sum expression to represent the situation and state whether you would use a number line or absolute values to find the answer. Then solve the problem. Explain what your answer means. 15. Yoko and Sheila are digging a hole for a fence post. The bottom of their hole is currently 10 inches below the surface of the ground. Yoko digs the hole 5 inches deeper and Sheila digs the hole 8 inches deeper. What is the elevation (in inches) of the bottom of the hole after Sheila is finished? 16. Jasmine and Harley are planting flowers in their flower box. Jasmine fills a watering can with 3 gallons of water. Harley poured 1 gallon of water onto the flowers. How much water is in the watering can after Harley waters the flowers? 17. Fill in the missing words. To add two integers with opposite signs use a(n). When a number in the sum is negative, then the arrow should move. When a number in the sum is positive, then the arrow should move. 18. Explain your reasoning. When is it usually easiest to use absolute values to add integers? 29
6 Answer Key Lesson 3-7, pp Try this: 1. Check students drawings; 1 2. Check students drawings; 3. Check students drawings; 0 4. Check students drawings; ; 8; 15; 215 Practice: 1. B 2. A 3. C 4. Check students drawings; Check students drawings; Check students drawings; (25) 1 (28); absolute values; 3 in.; Sample answer: The hole is currently 23 inches below the surface of the ground (21); number line; 2; Sample answer: There are 2 gallons of water left in the can after Harley waters the flowers. 17. number line; left; right 18. Sample answer: It is easiest to use absolute values when all of the integers in the sum have the same sign.
7 LESSON 3-8 California Standards Gr. 5 NS 2.1: Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. Gr. 6 NS 2.3: Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Words to Remember Opposites : Two numbers that are the same distance from 0 on a number line, but on opposite sides of 0 Subtraction Rule: To subtract an integer, add its opposite (28) (23) (3) and 23 are opposites. 8 and 28 are opposites. Getting Started In Lesson 3-7 you added integers. Now you will subtract integers using a number line or the subtraction rule. Using a Number Line When subtracting a positive integer using a number line, move to the left of the starting point. 0 When you are subtracting a negative integer, move instead to the right. Because you move to the left when you subtract a positive integer, you move in the opposite direction (to the right) when you subtract a negative integer. When subtracting a positive number, move to the left on the number line. E Subtracting a Positive Integer Find the difference using a number line. Move 4 units to the right of 0. Move 6 units to the left of The final position is, so Use the subtraction rule of adding the opposite to check your answer (26) 5 30
8 E Subtracting a Negative Integer Use the rule for subtraction to find the difference 2 2 (23). Rewrite as adding the opposite. 2 2 (23) (13) See Lesson 3-7 for help with adding integers. Add E Subtracting a Negative Integer Use the rule for subtraction to find the difference 2 (). Rewrite as adding the opposite. 2 () 51 (12) Add E Subtracting a Positive Integer Use the rule for subtraction to find the difference Rewrite as adding the opposite (21) Add (21) 527 T Use a number line to find the difference Use the subtraction rule to find the difference ( 5)
9 Summarize Subtracting Integers Using a Number Line To subtract a positive integer, move to the left. To subtract a negative integer, move to the right. Subtracting Integers Using the Subtraction Rule To subtract an integer, add its opposite. Practice Match each difference with the number line that represents it A (25) B C. Find the difference using a number line ( 2) 5 Find the difference using the subtraction rule (28) (211) (29) (211) (0) 5 32
10 Write a difference expression to represent the situation. Then solve the problem and explain what your answer means. 15. At noon the temperature was 848F. Eight hours later the temperature had dropped 148F. What was the temperature at 8:00 P.M.? 16. Brandon is saving money to buy a bike that costs $185. He currently has $120 in his savings account. How much more does Brandon need to save so he can buy the bike? 17. An elevator is stopped at a floor 20 feet below ground. It descends to another floor 65 feet below ground. What is the change in elevation of the elevator? 18. Fill in the missing words. To subtract a positive integer, move to the on a number line. To subtract a negative integer, move to the on a number line. 19. Describe a process. Describe how to use the subtraction rule. 33
11 Answer Key Lesson 3-8, pp Try this: 1. Check students drawings; Check students drawings; Practice: 1. B 2. C 3. A 4. Check students drawings; 5. Check students drawings; Check students drawings; ; 70; Sample answer: The temperature at 8:00 p.m. was 70 F ; 65; Sample answer: Brandon needs to save $65 more for the bike (0); 5; Sample answer: The change in elevation of the elevator was 5 feet. 18. left; right 19. Sample answer: When subtracting integers, add the opposite of the integer being subtracted.
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