Name: Packet Due: Tuesday, November 20, 2018 Module 3 - Expressions & Equations Unit 5 Packet 2 - Solving Equations & Inequalities Standard 7.EE.A.1 7.EE.A.2 7.EE.B.3 7.EE.B.4 Description Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Use variables to represent quantities in a real-world or mathematical problems, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Lesson I can 5.5 Part 1 & 2 Solve and graph one-step inequalities 5.6 Solve two-step equations 5.7 Solve two-step equations 5.8 Solve two-step inequalities SCHEDULE Thursday 11/8 Friday 11/9 Tuesday 11/13 Thursday 11/15 5.5 Part 1 HW: Page 6-7 5.5 Part 2 and Mid-Unit Quiz HW: Page 10 5.6 HW: Page 13 5.7 HW: Page 16 Friday 11/16 Monday 11/19 Tuesday 11/20 5.8 HW: Page 21 Unit 5 Review Unit 5 Quiz Packet Completion Rubric 4 3 2 1 0 Nothing in packet is missing. Responses consistently meet ALL of the criteria for high quality work. Exemplary effort is evident throughout entire packet. Packet is 75-100% complete/accurate. Work/effort misses the criterion for high quality consistently. Packet is 50-75% complete/accurate. Work/effort has evidence of quality but not consistently. More than 50% of the packet is incomplete or incorrect. Work does not meet the expected level of quality. Packet is entirely incomplete or not turned in. Grading Breakdown: 0-1.9 = F 2-2.4 = D 2.5-2.9 = C 3-3.4 = B 3.5-4 = A
Module 5 Solving Equations & Inequalities Lesson 5.5 Part 1 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. What is an inequality? Remember: An equation shows that two expressions are equal. For example: 3 + n = 7 3 + 4 = 7 7 = 7 Whereas, an shows that two quantities are not always equal. For example: n+2 < 7 n < 5 This statement is read as n is less than 5. Reading Inequalities 1) n < 5 2) 5 > n This is read as: n is to 5 5 is to n This is read as: 5 is to n n is to 5 Inequality symbols 1
You Try! Write the following inequalities in words: Solving Inequalities Our goal is to have the variable ( x ) on its own side of the inequality sign. Example: x + 2 > 12 1. Subtract 2 from both sides: 2. Simplify: Solving Inequalities with Addition and Subtraction You can or the same number from both sides of the inequality and the inequality will remain true. 2
Solving Inequalities with multiplication and division You can or both sides of an inequality by a positive number and the inequality will remain true. Inequality Sign Rule! When multiplying or dividing by a number, you must the inequality symbol. For Example: 1) -7x > 21 Divide by -7 2) Flip the sign 3) Well done! Direction of the Inequality 3
You Try! x + 5 < 14 5x > -15 x - 7 > 11 x 3 11-3x < 18 x + 5 6 Guided Practice 1. 2. 3. 4. 5. 6. 7. 8. 9. 4
10. 11. 12. 13. 14. 15. 16. 17. 18. 5
Independent Practice 6
7
Module 5 Solving Equations & Inequalities Lesson 5.5 Part 2 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Graphing After solving the inequality, graph the possible solutions on the number line. When plotting the initial point: n > 15 (circle filled in) n < -13 (blank circle) You Try! 8
Solve-Graph-Check Summary After you have solved and graphed possible solutions, you can check the inequality by plugging in one of the solutions. For example : Original : n -3 < 2 1. Solve: n < 5 2. Graph: 3. Check: Plug in any solution, let s say 3: 3 < 5 3 is less than 5 You Try! Solve-Graph-Check! 1) y - 5-7 2) 21 > 12 + x 3) -10y < 60 4) 7 -t/6 It s time for our Mid Unit Quiz! Any lingering questions to ask before we start? 9
Independent Practice Use Solve-Graph-Check to complete the following problems: 10
Module 5 Solving Equations & Inequalities Lesson 5.6 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Direct Instruction Video 1 Notes: What does it mean to solve a two step equation? 1. 2. 3. Video 2: Example - Solving a two step equation SOLVING TWO-STEP EQUATIONS STEP 1: Get the entire variable term by itself STEP 2: Get the variable by itself STEPS STEP 1: Get the entire variable term by itself PROBLEM 5x + 10 = 20 STEP 2: Get the variable by itself STEP 1: Get the entire variable term by itself z 4 = 10 STEP 2: Get the variable by itself 11
8y + 10 = 98 STEP 1: Get the entire variable term by itself STEP 2: Get the variable by itself Guided Practice Task Card: Task Card: _ Task Card: _ Task Card: Task Card: _ Task Card: Task Card: _ Task Card: 12
Independent Practice 1. 6x + 8 = 50 2. 2n - 5 = 11 3. 13 = -4k + 9 4. 7-37 = 34 5. 6. 7. 8. 9. 10. 13
Module 5 Solving Equations & Inequalities Lesson 5.7 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Direct Instruction Video notes: Direct Instruction - Let s try this one together! 17t + 22(4-t) = 70 14
Guided Practice Card: Card: Card: Card: Card: Card: Card: Card: Card: 15
Independent Practice 16
Module 5 Solving Equations & Inequalities Lesson 5.8 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Review of Solving Two-Step Equations The method of solving two-step inequalities is similar to solving. Consider the equation: 2x +2 = 8 As mentioned in yesterday s video, the x in this equation is involved in TWO different operations: addition and multiplication. To get x alone, you need to use TWO inverse operations (subtraction and division): Solving Two-Step Inequalities Consider if this equation was turned into an inequality: 2x +2 < 8 Just like with two-step equations, you would use inverse operations (in this case, subtraction and division) to get the x alone: We used to solve this inequality. You Try! Remember: Solve-Graph-Check 17
Solving Two Step Inequalities Video Notes 2 1 Solve the following problem: 3 > -4y - 8 3 18
Scavenger Hunt! 19
20
Independent Practice Directions : Solve and graph the following inequalities. Show your work. 1) 2n + 7 49 2) -2t + 13-21 3) 59 > -7v + 6 1 3 2 a 3 8 4) 14 > 6m- 2 5) + 24 > 23 6) - 28 < 48 f 2 t 2 a 9 7) -29 + 52 8) 4 + > 12 9) 111.2-3.5y + 1.2 21
Module 5 Solving Equations & Inequalities Module 5 Review DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Review Activity 22
Date Do-Now Lesson 5.5 Part 1 Date: Lesson 5.5 Part 2 Date: Lesson 5.6 Date: 23
Lesson 5.7 Date: Lesson 5.8 Date: End of Unit Reflection 1. What do you feel were your strengths during the lessons from this unit? 2. What areas do you feel like you need more support? Are there any lessons that you feel like you need to develop the skills further? 3. What can you do to improve your understanding? 4. How can I (your teacher) support your learning better and improve your understanding? 24