Commutative Property of Addition a + b = b + a Multiplication a b = b a

Transcription

1 1 Properties: Commutative Property of Addition a + b = b + a Multiplication a b = b a 1 Which property is illustrated in each of the equations below? A. Associative Property of Addition (a + b) + c = a + (b + c) Multiplication a (b c) = (a b) c Distributive Property a (b + c) = ab + ac B. m + 0 = m Identity Property Additive Identity: a + 0 = a Multiplicative Identity: a 1 = a Inverse Property Additive Inverse: a + - a = 0 C. D = 4 10 Multiplicative Inverse: E. Describe the properties used in each step. F = 0 G. H. AF 1.3/7.EE.1 AF 1.3/7.EE1 Page 1 of 14 MCC@WCCUSD 10/15/13

2 2 Which of the following expressions result in a negative number? Choose all that apply. A) Which of the following expressions result in a negative number? Choose all that apply. Justify your answer using words or a visual model. Adding a positive. [Move right.] Answer: 3 B) 6 + ( 3) Adding a negative. [Move left.] Answer: 3 Circle zero pairs. Answer: 3 Circle zero pairs. Answer: 3 A) 5 ( 10) B) 5 + ( 10) C) 10 5 D) C) 6 3 Subtracting a positive. [Move left.] Answer: 9 Remove 3 positives. Answer: 9 D) 6 ( 3) Subtracting a negative. [Move right.] Answer: 3 Remove 3 negatives. Answer: 3 E) 6( 3) Multiplying or dividing different signs results in a negative number. Answer: 18 F) 6 ( 3) Multiplying or dividing same signs results in a positive number. Answer: 2 6 groups of ( 3) NS 1.2/7.NS.1, 7.NS.2 NS 1.2/7.NS.1, 7.NS.2 Page 2 of 14 MCC@WCCUSD 10/15/13

3 = = Find the value inside the grouping symbols. Absolute value is the number s distance from zero on a number line. NS 2.5/7.NS.1 NS 2.5/7.NS = 1. Find the prime factors for each number. 4 = = = Write the prime factors of one of the numbers in the LCM bubble. 8 = Compare and cross out factors already in the bubble. 4 = = Place in the bubble factors not already in the bubble Multiply the factors in the bubble = ! $ # & = " 3% ! = $ # " 6 % &+! $! # " 3 &+# 1 % 12 2 " 2 18 = = = = = $ & % NS 2.2/7.NS.1(a-c) NS 2.5/7.NS.1(a c) Page 3 of 14 MCC@WCCUSD 10/15/13

4 5 12 Divide using 3 different methods Divide using 3 different methods NS 1.2/7.NS.2 NS 1.2/7.NS = = NS 1.5/7.NS2d,7.EE.3 NS 1.5/7.NS2d,7.EE.3 Page 4 of 14 MCC@WCCUSD 10/15/13

5 7 Simplify the expression below using three different methods. 7 Simplify the expression below using three different methods. 3( 2x + 5) 2( 3x 4) The negative sign represents the opposite of 3 groups of 2x + 5 AF 1.3/7.EE.1 AF 1.3/7.EE.1 Page 5 of 14 MCC@WCCUSD 10/15/13

6 8 It takes a factory 6 hours to build 20 computers. At this rate, how many hours will it take to build 300 computers? Method: Bar Model 8 Sean can save $10 every 3 days. How long will it take him to save $180? Please use two methods to find the answer. Method: Solving Proportions Multiply by One Cross Multiply Multiply by LCD AF 4.2/7.RP.2 AF 4.2/7.RP.2 Page 6 of 14 MCC@WCCUSD 10/15/13

7 WCCUSD Grade 7 9 The scale drawing of a tree shown below is drawn using a scale of 1 cm = 25 ft. What is the height, in feet, of the tree? 9 The drawing of the California State Capital Building below was made using a scale of 1 cm = 7 ft. What is its actual height in feet? Please use two methods to find the answer. Method: Bar Model Method: Proportions (Cross Multiply) Method: Proportions (Multiply by LCD) MG 1.2/7.G.1 Page 7 of 14 MG 1.2/7.G.1 MCC@WCCUSD 10/15/13

8 10 Apples cost $4 for every 2 lbs. Make a line graph that demonstrates this relationship. How much will it cost for 21 lbs of apples? Graph: 10 Two pizzas cost $10. Make a line graph that shows the relationship between the number of pizzas purchased and the total cost. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? Graph: The graph shows that the cost of apples will rise $4 for every 2 lbs of apples. How much would it cost for 21 lbs of apples? Method 1: Table The table shows that the cost of apples per pound is twice the weight of the apples. the cost of 21 lbs of apples is $42. Method 2: Bar Model if 1 pound of apples costs $2, then 21 pounds of apples costs $42. AF 3.4/7.RP.2 AF 3.4/7.RP.2 Page 8 of 14 MCC@WCCUSD 10/15/13

9 11 Mark drove on the highway at 70mph for 3 hours before taking a short break. He then got on a country road and drove 45mph for 2 more hours. How far did he travel in all? 11 An airplane flew at 550mph for 4 hours. It then slowed down to 420mph for 2 ½ hours as it approached its destination. How far did the airplane travel in all? Method: Bar Model Please use two methods to find the answer. Method: Distance Equation distance = rate time 1 st leg 2 nd leg 210 miles + 90 miles = 300 miles AF 4.2/7.RP.2 End of Study Guide AF 4.2/7.RP.2 Page 9 of 14 MCC@WCCUSD 10/15/13

10 1 You Try Solutions: Which property is illustrated in each of the equations below? A. 2 Which of the following expressions result in a negative number? A) 5 ( 10) = = 5 Think of subtraction as adding the opposite value. inverse property of multiplication Number Line B. m + 0 = m Tile Spacers additive identity C. associative property of addition B) 5 + ( 10) = 15 D = 4 10 Number Line commutative property of multiplication Tile Spacers E. distributive property F = 0 inverse property of addition C) 10 5 = 15 Number Line G. Tile Spacers inverse property of multiplication H. identity property of multiplication D) 10 5 = 2 Multiplying or dividing different signs results in a negative number. Answer: 2 AF 1.3/7.EE.1 NS 1.2/7.NS.1, 7.NS.2 Page 10 of 14 MCC@WCCUSD 10/15/13

11 = 5 16 Divide using 3 different methods NS 2.5/7.NS.1 4 NS 1.2/7.NS NS 2.5/7.NS.1(a c) NS 1.5/7.NS2d,7.EE.3 Page 11 of 14 MCC@WCCUSD 10/15/13

12 7 Simplify the expression below using three different methods. 8 Sean can save $10 every 3 days. How long will it take him to save $180? 2( 3x 4) Please use two methods to find the answer. Method: Bar Model The negative sign represents the opposite of 2 groups of 3x 4 Method: Proportions Multiply by One Cross Multiply AF 1.3/7.EE.1 Multiply by LCD AF 4.2/7.RP.2 Page 12 of 14 MCC@WCCUSD 10/15/13

13 WCCUSD Grade 7 9 The drawing of the California State Capital Building below was made using a scale of 1 cm = 7 ft. What is its actual height in feet? 10 Two pizzas cost $10. Make a line graph that shows the relationship between the number of pizzas purchased and the total cost. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? Method: Bar Model The graph shows that for every 2 pizzas, the cost will rise $10. How much will it cost for 7 pizzas? How much will it cost for 17 pizzas? Method 1: Bar Model Method: Proportions (Cross Multiply) if 1 pizza costs $5, then 7 pizzas will cost $35 and 17 pizzas will cost $85. Method: Proportions (Multiply by LCD) Method 2: Table The table shows that the cost of any number of pizzas is calculated by the number of pizzas times five. the cost of 7 pizzas is $35 and the cost of 17 pizzas is $85. AF 3.4/7.RP.2 MG 1.2/7.G.1 Page 13 of 14 MCC@WCCUSD 10/15/13

14 11 An airplane flew at 550mph for 4 hours. It then slowed down to 420mph for 2 ½ hours as it approached its destination. How far did the airplane travel in all? Method: Bar Model Method: Distance Equation distance = rate time 1 st leg 2 nd leg 2200 miles miles = 3,250 miles AF 4.2/7.RP.2 Page 14 of 14 MCC@WCCUSD 10/15/13