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Transcript
7th Grade Unit 1 – The Number System: Packet 1 of 3 Mr. Rothdiener Name: _____________________________________ Packet Outline, Page 1 1.1: Add Integers on the Number Line (7.NS.A.1a-b), Pages 2-4 o I can model integer addition on a number line by using horizontal arrows. o I can understand that the sum of a number and its opposite is zero. 1.2: Add Integers (7.NS.A.1a-b), Pages 5-7 o I can apply the sign rules for integer addition to fluently add integers. 1.3: Subtract Integers (7.NS.A.1c), Pages 8-10 o I can apply the sign rules for integer subtraction, including double negatives, to fluently subtract integers. 1.4: Distance Between Two Rational Numbers (7.NS.A.1c), Pages 11-13 o I can apply the distance formula to calculate the distance between two rational numbers. 1.5: Addition of Rational Numbers (7.NS.A.1b), Pages 14-16 o I can extend the rule for adding integers to rational numbers. 1.6: Subtraction of Rational Numbers (7.NS.A.1c), Pages 17-19 o I can extend the rule for subtracting integers to rational numbers. 1.7: Add and Subtract Rational Numbers (7.NS.A.1b-c), Pages 20-22 o I can add and subtract rational numbers. 1.8: Apply Properties to Add and Subtract Rational Numbers (7.NS.A.1d), Pages 23-25 o I can apply the properties of operations to add and subtract rational numbers. Quiz 1.1 Review, Pages 26-27 o I can apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. 1 1.1: Add Integers on the Number Line (7.NS.A.1a-b) Bell Work: Add using the number line: 4 + 5 Whole-Class: Use the number line to solve each of the following. 1.) 10 + (-4) = 2.) -3 + 2 = Guided Practice: Use the number line to solve each of the following. 3.) 4 + (-7) 4.) -7 + 9 5.) -3 + (-6) 6.) 5 + (-5) 2 Independent Practice: Use the number line to solve each of the following. 7.) 5 + (-6) 8.) -3 + 12 9.) -4 + (-2) 10.) 9 + (-9) 11.) 9 + (-5) 12.) -5 + 4 13.) -1 + (-8) 14.) 3 + (-3) 15.) 6 + (-13) 16.) -4 + 0 3 WORKSHEET 1.1 Use the number line to solve each of the following. 1.) 7 + (-3) 2.) -9 + 15 3.) -8 + (-1) 4.) 4 + (-4) 5.) 1 + (-6) 6.) -7 + 2 7.) -6 + (-1) 8.) -3 + (-3) 9.) 7 + (-11) 10.) -8 + 0 4 1.2: Add Integers (7.NS.A.1a-b) Bell Work: Add using the number line: -4 + (-5) Whole-Class: Add the following integers using the rule. 1.) 5 + 3 = 2.) -5 + (-3) = 3.) 5 + (-3) = 4.) -5 + 3 = 5.) 6 + 2 = 6.) -3 + (-7) = 7.) 90 + (-90) = 8.) -8 + 1 = Guided Practice: Add the following integers using the rule. 9.) 5 + 9 = 10.) -4 + (-2) = 11.) 1 + (-11) = 12.) -20 + 15 = 13.) 12 + 7 = 14.) -6 + (-3) = 15.) 13 + (-13) = 16.) -3 + 8 = 5 Independent Practice: Add the following integers using the rule. 17.) 15 + 7 = 18.) -4 + (-16) = 19.) -18 + (-64) = 20.) -205 + (-123) = 21.) -10 + 7 = 22.) 8 + (-16) = 23.) -234 + 234 = 24.) -12 + 65 = 25.) 105 + (-126) = 26.) -41 + (-7) = 27.) 15 + (-43) = 28.) -67 + 66 = 29.) 21 + (-32) = 30.) -98 + 98 = 31.) -13 + (-13) = 6 WORKSHEET 1.2 Add the following integers using the rule. 1.) 4 + 17 = 2.) -6 + (-12) = 3.) -5 + 8 = 4.) -2 + 6 = 5.) -4 + 7 = 6.) 6 + (-9) = 7.) -5 + (-5) = 8.) -5 + 5 = 9.) 7 + (-7) = 10.) 67 + (-35) = 11.) -31 + (-55) = 12.) -91 + 92 = 13.) -11 + (-22) = 14.) -77 + 77 = 15.) -77 + (-77) = 7 1.3: Subtract Integers (7.NS.A.1c) Bell Work: Add: 4 + (-5) Whole-Class: Subtract the following integers using the rule. 1.) 4 – 5 2.) 8 – 2 3.) -9 – (-2) 4.) -3 – 7 Guided Practice: Subtract the following integers using the rule. 5.) 4 – 9 6.) -2 - (-5) 7.) 11 - (-8) 8.) -5 – 6 9.) 12 – 25 10.) -10 - (-10) 11.) 34 - (-7) 12.) -16 – 9 8 Independent Practice: Subtract the following integers using the rule. 13.) 15 - 7 = 14.) -4 - (-16) = 15.) -18 - (-64) = 16.) -205 - (-123) = 17.) -10 - 7 = 18.) 8 - (-16) = 19.) -234 - 234 = 20.) -12 - 65 = 21.) 105 - (-105) = 22.) -41 - (-7) = 23.) -15 - (-15) = 24.) -67 – 66 = 9 WORKSHEET 1.3 Subtract the following integers using the rule. 1.) 4 - 17 = 2.) -6 - (-12) = 3.) -5 - 8 = 4.) -2 - 6 = 5.) -4 - 7 = 6.) 6 - (-9) = 7.) -5 - (-5) = 8.) -5 - 5 = 9.) 7 - (-7) = 10.) 67 - (-35) = 11.) -31 - (-55) = 12.) -91 - 92 = 10 1.4: Distance Between Two Rational Numbers (7.NS.A.1c) Bell Work: Subtract: 4 - (-5) Whole-Class: Use the distance formula p q to find the distance between each pair of numbers. 1.) -5 to 8 2.) -8 to -5 3.) -8 to 5 Guided Practice: Use the distance formula p q to find the distance between each pair of numbers. 4.) -4 to 5 5.) -5 to -3 11 6.) 7 to -1 Independent Practice: Use the distance formula p q to find the distance between each pair of numbers. 7.) -3 to 7 8.) -9 to -2 9.) 10 to -4 10.) -41 to 50 11.) -56 to -30 12.) 70 to -15 13.) -24 to 24 14.) -8 to -13 15.) 93 to -4 16.) Berry is the first person to finish a 5K race and is standing 15 feet beyond the finish line. Another runner, Jeremy, is currently trying to finish the race and has 14 feet before he reaches the finish line. What is the distance between Berry and Jeremy? 12 WORKSHEET 1.4 Use the distance formula p q to find the distance between each pair of numbers. 1.) -19 to -12 2.) 19 to -12 3.) 10 to -43 4.) -10 to -43 5.) -1 to -16 6.) 1 to -16 7.) Melanie finishes the Boilermaker and meets up with her family 120 feet beyond the finish line. Her sister, Michelle, is still running the race and has 230 feet before she reaches the finish line. What is the distance between Melanie and her sister? 13 1.5: Addition of Rational Numbers (7.NS.A.1b) Bell Work: Add using the number line: 3 + (-4) Whole-Class: Use the number line to solve each of the following. 1 2 1.) 10 + (-4 ) = 2.) -3 + 2.25 = Guided Practice: Use the number line to solve each of the following. 1 2 3.) 4 + (-7 ) 4.) -7 + 9.75 1 4 5.) -3 + (-6 ) 6.) 5.5 + (-5.5) 14 Independent Practice: Use the number line to solve each of the following. 1 2 7.) 5 + (-6 ) 8.) -3 + 12.5 9.) -4 + (-2.75) 10.) 9 1 4 11.) 9 + (-5 ) 1 1 + (-9 ) 2 2 12.) -5 + 4.25 13.) Samantha owes her father $7.00. She just got paid $5.50 for babysitting. If she gives that money to her dad, how much will she still owe him? 15 WORKSHEET 1.5 Use the number line to solve each of the following. 1 2 1.) 7 + (-3 ) 2.) -9 + 15.5 1 4 3.) -8 + (-1 ) 4.) 4.75 + (-4.75) 1 2 5.) 1 + (-6 ) 6.) -7 + 2.25 16 1.6: Subtraction of Rational Numbers (7.NS.A.1c) Bell Work: Subtract: 3 - (-7) Whole-Class: Subtract the following rational numbers using the rule. 1.) 4 – 5 1 2 2.) 8 – 2 1 4 3.) -9 – (-2.5) Guided Practice: Subtract the following rational numbers using the rule. 4.) 4 1 –9 2 1 4 5.) 11 - (-8 ) 17 6.) -5 – 6.25 Independent Practice: Subtract the following rational numbers using the rule. 7.) 2 – 7 10.) 8 1 2 1 – 15 2 8.) 12 – 5 3 4 9.) -5 – (-4.5) 1 4 11.) 23 - (-4 ) 12.) -17 – 2.75 13.) At the start of a trip, a car’s tank contained 9 gallons of gasoline. During the trip, the car consumed 6 gasoline is left in the tank? 18 1 gallons of gas. How much 8 WORKSHEET 1.6 Subtract the following rational numbers using the rule. 1.) 7 – 9 4.) 11 1 2 1 – 14 2 2.) 10 – 7 1 4 3.) -4 – (-9.5) 1 4 5.) 16 - (-4 ) 6.) -8 – 17.25 7.) Suppose a 5th grader turned 10 years old today. How old was she 3 1 2 years ago? Write an equation and use a number line to model your answer. 19 1.7: Add and Subtract Rational Numbers (7.NS.A.1b-c) Bell Work: Subtract: 4 - 5 1 2 Whole-Class: Add or subtract the following rational numbers. 1.) 10 – 16 1 2 2.) -7 + 8 3.) -7.5 – (-2.5) 4.) -4 – 11 Guided Practice: Add or subtract the following rational numbers. 5.) 1 – 11 2 9.) -12 + 4 3 - (-3) 4 6.) -0.75 - (-8) 7.) 11 10.) -0.25 - (-0.25) 11.) 0.25 + (-9) 20 8.) -2 – 31 12.) -1 + 1 2 1 4 Independent Practice: Add or subtract the following rational numbers. 13.) 4 – 7 16.) 11 1 4 1 – 19 2 14.) 27 – 14 3 4 17.) 35 - (-7.75) 15.) -5.25 + (-4.5) 18.) -5.75 – 2.25 1 2 19.) A fish was swimming 3 feet below the water’s surface at 7:00 1 4 AM. Four hours later, the fish was at a depth that is 5 feet below where it was at 7:00 AM. What rational number represents the position of the fish with respect to the water’s surface at 11:00 AM? 21 WORKSHEET 1.7 Add or subtract the following rational numbers. 1.) 7 – 8 4.) 45 1 2 3 – 54 4 2.) 31 – 20 1 4 5.) 21 - (-6.25) 3.) -7.5 + (-1.25) 6.) -3.5 – 14.5 1 2 7.) A bird that was perched atop a 15 foot tree dives down six feet to a branch below. How far above the ground is the bird’s new location? 22 1.8: Apply Properties to Add and Subtract Rational Numbers (7.NS.A.1d) Bell Work: Simplify: 4 – 15 – 4 Whole-Class: Use the properties of operations to make simplifying the expressions easier. 1.) -5 – 12 + 5 {commutative property of addition, associative property of addition, and additive inverse} 2.) –(3 + 4) – 21 + 7 {distributive property, commutative property of addition, associative property of addition, and additive inverse} Guided Practice: Use the properties of operations to make simplifying the expressions easier. 3.) 4 2 2 - 7.3 + (-4 ) 9 9 {commutative property of addition, associative property of addition, and additive inverse} 23 1 6 5 6 4.) 2 + 19.7 – (-9 ) {double negative property, commutative property of addition, associative property of addition} Independent Practice: Use the properties of operations to make simplifying the expressions easier. 5.) 7 1 1 - (7 - 13) 2 2 {distributive property, associative property of addition, and additive inverse} 2 9 6.) -7 + 6.5(0) + 8 + 7 2 9 {multiplication property of zero, commutative property of addition, associative property of addition, and additive inverse} 24 WORKSHEET 1.8 Use the properties of operations to make simplifying the expressions easier. 1.) 4 4 4 - (4 - 10) 7 7 {distributive property, associative property of addition, and additive inverse} 2.) -5.2 – (-3.1) + 5.2 {double negative property, commutative property of addition, associative property of addition, and additive inverse} 3.) 2 3 + 20.3 + 5 5 5 {commutative property of addition and associative property of addition} 25 Quiz 1.1 Review (7.NS.A.1) Use your knowledge of math to complete each of the following questions. Show your work! 1-6: Add or subtract the following rational numbers. 1.) 16 – 23 4.) 35 1 2 1 – 83 4 2.) 54 – 13 3 4 5.) 81 - (-21.75) 3.) -64.5 + (-5.25) 6.) -245.5 + 245.5 7-8: Use the distance formula p q to find the distance between each pair of numbers. 7.) -7 to 15 8.) -9 to -2 26 9-11: Use the properties of operations to make simplifying the expressions easier. 9.) 12 6 6 - (12 - 784) 13 13 {distributive property, associative property of addition, and additive inverse} 10.) -9.8 – (-7.6) + 9.8 {double negative property, commutative property of addition, associative property of addition, and additive inverse} 11.) 1 8 + 31.4 + 14 9 9 {commutative property of addition and associative property of addition} 27