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The Properties of Mathematics 1 Warm Up OBJECTIVE: Students will be able to identify the properties of operations. Language Objective: Students will be able to recite the properties of operations. Fill in the blanks with any operation: 6 = 11 ,,, 1. 9 8 2. 15 4 3 = 3 3. (2 5) 3 = 21 Careful… the last one is tricky! 2 Launch Evaluate the following expressions in two different ways. . 9. 5 2. 218 1. 92+7+13 99 +13 112 2nd method 92+(7+13 (20) ) 92+ 112 3 .5 90 2nd method 2 .9 .5 . . 10 .9 90 Explore: Marvin the Magician’s Cards Marvin the Magician needs your help! He uses a deck of math cards for one of his tricks. However, only some cards are TRUE. Help Marvin find the TRUE cards. Examples 4 3 3 4 12 0 0 TRUE! FALSE! 4 Explore: Marvin the Magician’s Cards In your groups: 1st : Determine which cards are true and false. Be sure to support your reasoning. 2nd: For the true cards only, complete the worksheet provided. 5 Summary: Definitions Click on a card. 13 8 8 13 12 5 5 12 4 0 4 (4 2) 8 4 (2 8) 15 0 0 6 9 1 9 2(5 3) (2 5)3 Summary: Definitions Let’s discuss the card: 13 8 8 13 Algebraically a b b a Changing the order of the numbers does not change the SUM. Commutative Property of Addition Click to Return 7 Summary: Definitions Let’s discuss the card: 12 5 5 12 Algebraically a b b a Changing the order of the numbers does not change the PRODUCT. Commutative Property of Multiplication Click to Return 8 Summary: Definitions Let’s discuss the card: 9 1 9 Algebraically a 1 a a number by 1 Multiplying leaves it unchanged. Identity Property of Multiplication Click to Return 9 Summary: Definitions Let’s discuss the card: 4 0 4 Algebraically a0 a Adding a number by 0 leaves it unchanged. Identity Property of Addition Click to Return 10 Summary: Definitions Let’s discuss the card: 2(5 3) (2 5)3 Algebraically a(bc) (ab)c When MULTIPLYING more than 2 numbers, the way we group them does not change the PRODUCT. Associative Property of Multiplication Click to Return 11 Summary: Definitions Let’s discuss the card: (4 2) 8 4 (2 8) Algebraically (a b) c a (b c) When ADDING more than 2 numbers, the way we group them does not change the SUM. Associative Property of Addition Click to Return 12 Summary: Definitions Let’s discuss the card: 15 0 0 Algebraically a 0 0 Multiplying a number by 0 is always 0. Zero Property of Multiplication Click to Return 13 Summary: Definitions Let’s discuss the card: (4 2) 8 4 (2 8) Algebraically (a b) c a (b c) When ADDING more than 2 numbers, the way we group them does not change the SUM. Associative Property of Addition Click to Return 14 Summary: Definitions Let’s discuss the card: 4 0 4 Algebraically a0 a Adding a number by 0 leaves it unchanged. Identity Property of Addition Click to Return 15 Summary: Definitions Let’s discuss the card: 12 5 5 12 Algebraically a b b a Changing the order of the numbers does not change the PRODUCT. Commutative Property of Multiplication Click to Return 16 Summary: Definitions Let’s discuss the card: 2(5 3) (2 5)3 Algebraically a(bc) (ab)c When MULTIPLYING more than 2 numbers, the way we group them does not change the PRODUCT. Associative Property of Multiplication Click to Return 17 Summary: Definitions Let’s discuss the card: 13 8 8 13 Algebraically a b b a Changing the order of the numbers does not change the SUM. Commutative Property of Addition Click to Return 18 Summary: Definitions Let’s discuss the card: 9 1 9 Algebraically a 1 a a number by 1 Multiplying leaves it unchanged. Identity Property of Multiplication Click to Return 19 Practice PART I Using the Properties of Mathematics, match Column A to Column B. Write the expression from Column B that matches the expression in Column A in the blank provided. State the property that proves the equation true. You can choose from Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication. You may use a property more than once. Column A Column B Commutative of Multiplication 5 14 5(14x) 5 (14 x) 5x 14 5 (x 14) 20 Associative of Multiplication Associative of Addition Commutative of Addition Commutative of Multiplication Practice PART II Evaluate the following expressions quickly. State the property you used to help make the computation faster. 1. 15 + 15 + 7 + 8 2. 5 9 4 5 4 9 Commutative 15 + 15 +15 of 20 9 45 Multiplication 180 Associative of Addition 3. 11 + 3 + 9 + 17 4. 13 2 5 13 10 11 + 9 + 3 + 17 130 20 + 20 Associative of Multiplication Commutative of Addition 5. Tharzan’s grades for his last four quizzes are stated below. He wants to find the average of his grades. Show Tharzan how he can add his scores quickly using the properties you learned in class before he divides. Explain. Quiz Grades: 81 + 0 + 88 + 82 Possible answer: add the 88 and 82 to get 172 using the Associative of Addition. Then add 81 and 172 to get 253, using the Commutative of Addition, and adding 0 will not change the sum because of the Identity of Addition. 21 Practice Click here for PART IV PART III 1. Is the following equation 12 – 9 = 9 – 12 true? Explain. No, because 12 – 9 is 3 and 9 – 12 is less than 0. 2. Do you think the Commutative Property works for subtraction? Why or why not? No. Changing the order in subtraction does not give you the same answer. 3. Is the following equation (15 – 9) – 6 = 15 – (9 – 6) true? Explain. No. The left side of the equation equals 6 – 6, which equals 0. The left side of the equation equals 15 – 3, which equals 12. 4. Do you think the Associative Property works for subtraction? Why or why not? No. Regrouping the numbers in subtraction does not give you the same answer. 22 Practice PART IV Make 24! Using the numbers provided, and the four basic operations, +, - , , ÷ , make the number 24. 1. 1, 5, 4, 3 2. 5 4 3 1 3, 12, 4, 1 3 4 12 1 3. 10, 9, 7, 2 (9 7) (2 10) Agenda 23