Student Activity 1 Work with your partner to answer the following problems. Problem 1: Solve 3x 6 18. Model the equation: Use a square for x and a circle for 1. To solve the equation, you will need to 6 circles from sides of the equation. Show your model with the action you described above. To have the value of 1x, we need to rearrange both sides into equal groups of. Show your model with the action you described above. The solution of the equation is x = Does your solution make the original equation true? Does + 6 = 18? Yes, x = is the solution for the equation. Problem 2: Solve 5x 4 26 algebraically. Show all your steps. Check your solution to make sure it will satisfy the original equation. Show your work. TEKSING TOWARD STAAR 2014 Page 1
Problem 3: Solve 3x 6 42.3 algebraically. Show all your steps. Check your solution to make sure it will satisfy the original equation. Show your work. Problem 4: Solve 1 5 3 2 x algebraically. Model: Show your steps involved in solving the equation using your model. Check your solution set for its truth value. Show your work. Problem 5: Solve 2x 3 7 by modeling. Use a square for x and a circle for 1. Show your model. What actions did you do to both sides of the equation First action: Second action: TEKSING TOWARD STAAR 2014 Page 2
The solution set is x =. Show that it satisfies the equation. Problem 6: The length of a rectangle is 19 units. The length is 5 units more than twice the width, w. What is the width of the rectangle? Translate the verbal description into mathematical symbols. The length, which is 19 units, is 5 units more than twice the width, w. This situation can be modeled by the equation. Solve your equation either by a model or algebraically. Show your work. Check your solution into the words of the problem. Show that it satisfies the equation. Problem 7: A coin collection contains nickels and dimes. The number of dimes is 8. Three times the number of nickels decreased by 7 is equal to the number of dimes. How many nickels are in the collection? Translate the verbal description into mathematical symbols. (Create a statement like in the first part of Problem 6) This situation can be modeled by the equation. Solve your equation either by a model or algebraically. Show your work. TEKSING TOWARD STAAR 2014 Page 3
Show that it makes sense in the problem situation. TEKSING TOWARD STAAR 2014 Page 4
Student Activity 2 Work with your partner to answer the following problems. Problem 1: Solve 3x 3 12. Model the equation: Use a square for x and a circle for 1. What is the first action you will do to both sides of the inequality? Show your model after the action. To solve the inequality, you will need to regroup the symbols on both sides of the inequality sign into groups. Show your model with the action you described above. The solution of the inequality is x. Choose a number in the solution set to test for its truth value. Problem 2: Solve 6x 12 30 algebraically. Show all your steps. TEKSING TOWARD STAAR 2014 Page 5
Choose a number in your solution set to test for its truth value. Show your work. The solution set is Problem 3: Solve 2x 15.9 x algebraically. Show all your steps. How will you eliminate the +x for the right side? Choose a number in your solution set to test for its truth value. Show your work. Problem 4: Solve 3x 8 x by modeling. Use a square to represent x and a circle to represent 1. Model: Show your steps involved in solving the inequality. What is the first action you did to both sides? What is the second action you did to both sides? TEKSING TOWARD STAAR 2014 Page 6
Choose a number that is NOT in the solution set and test its truth value. Show your work. Problem 5: Solve 2x 4 12.4 algebraically. Show your steps involved in solving the inequality. Choose a number in your solution set and test it for its truth value. Show your work. Choose a number that is NOT in the solution set and test its truth value. Show your work. Problem 6: The length of a rectangle is 22 units. The length is greater than 9 times the width, w, increased by 4. What inequality describes the width of the rectangle? Translate the verbal description into mathematical symbols. The length, which is 22 units, is greater than 9 times the width, w increased by 4 This situation can be modeled by the inequality Solve your inequality either by a model or algebraically. Show your work. TEKSING TOWARD STAAR 2014 Page 7
Choose a number in your solution set to check in the words of the problem. Does it satisfy the conditions of the problem? Problem 7: A bag contains red and blue tiles. The number of blue tiles is 22. Twice the number of red tiles increased by 8 is more than the number of blue tiles. How can you describe the number of red tiles in the bag? Translate the verbal description into mathematical symbols. (Create a statement like in the first part of Problem 6) This situation can be modeled by the inequality. Solve your inequality either by a model or algebraically. Show your work. Does your solution make sense in the original problem? Problem 8: The inverse operation of addition is. 8 will undo adding 8. The inverse operation of division is. Multiplying by will undo dividing by 2. TEKSING TOWARD STAAR 2014 Page 8
Problem 9: In solving an equation using division, you discover you need to divide 1 into 4 equal groups. Can 1 be divided into 4 equal parts? Explain what you would do if represents 1. What would be the solution for the inequality modeled below? x x > + Problem 10: Create an equation that would have a solution of x = 7. Create an inequality that would have a solution of x > 3. Problem 11: A rectangle has an area of 24 square feet. The length of the rectangle is 6 feet. What is the width of the rectangle? Write an equation to represent this situation. Solve the equation. Does your solution make sense? TEKSING TOWARD STAAR 2014 Page 9
Problem 12: William has $8 to spend at the pretzel shop. A large pretzel costs $1.25 and a soft drink costs $0.75. He buys one drink and p pretzels. Write an inequality that can be used to find the number of pretzels William can buy. Solve the inequality to determine the possible number of pretzels William can buy. Does your solution make sense? TEKSING TOWARD STAAR 2014 Page 10
Student Activity 3 MATERIALS: Per Group of 4: 1 set of equations/inequalities; 2 sets of solution sets. Per Student: 1-2 sheets of white paper. PROBLEMS: How can you model an equation or inequality using squares and circles? How can you solve an equation or inequality algebraically? PROCEDURE: You will work in groups of 4 for Student Activity 3. Your teacher will number you 1,2, 3, or 4. 1 and 2 will work together and 3 and 4 will work together. The set of equations/inequalities are to be placed face down on the desk top. Each pair of students takes a set of solution sets. Part 1: Round 1: Students 1 and 2 randomly select an equation/inequality card. They turn the card over. They will solve the equation/inequality by modeling. While they are solving by modeling, students 3 and 4 will solve the equation/inequality algebraically. They will select the solution set card that matches their solution set, but they do NOT show the card to students 1 and 2. When students 1 and 2 have solved their problem, they will select from their solution set of cards, the card that matches the solution set they got. Then the two partner pairs show each other the solution set card they have selected. If they agree, they check the solution to make sure it will satisfy the equation, or if it is an inequality, they all 4 decide on a number to test. When they have agreed, record on the Equation/Inequality Solution Chart. Set the equation/inequality card to the side so it will not be drawn again. Round 2: Students 3 and 4 randomly select an equation/inequality card. They turn the card over. They will solve the equation/inequality by modeling. While they are solving by modeling, students 1 and 2 will solve the equation/inequality algebraically. They will select the solution set card that matches their solution set, but they do NOT show the card to students 3 and 4. When students 3 and 4 have solved their problem, they will select from their solution set of cards, the card that matches the solution set they got. Then the two partner pairs show each other the solution set card they have selected. If they agree, they check the solution to make sure it will satisfy the equation, or if it is an inequality, they all 4 decide on a number to test. When they have agreed, record on the Equation/Inequality Solution Chart. Set the equation/inequality card to the side so it will not be drawn again. Round 3: Repeat the steps in Round 1. Round 4: Repeat the steps in Round 2. Round 5: Repeat the steps in Round 1. Round 6: Repeat the steps in Round 2. TEKSING TOWARD STAAR 2014 Page 11
Equation/Inequality Card Equations and Inequalities Solution Chart Solution Set Was there agreement when solution sets were revealed? Part 2: How many inequality cards were drawn during the 6 rounds? Do you and your partner feel confident about your solution set for the inequalities even if you can t test every number? Explain your answer. Did you and your partner draw any situation cards? If so, did you translate them correctly? Choose one of the equations or inequalities you did NOT draw. Write a situation to fit the equation or inequality. Choose one of the solution set cards you did not use. inequality that would have that solution set. Write an equation or TEKSING TOWARD STAAR 2014 Page 12
NAME DATE SCORE /5 7.10A/7.11A/7.11B Skills and Concepts Homework 1 1. What is a solution set for an equation or inequality? 2. What are equivalent equations or inequalities? 3. Solve by creating a model. 2x 8 2 4. Jonas has a bag of red and white marbles. The bag contains 18 red marbles. The number of red marbles is 4 more than twice the number of white marbles, x. How many white marbles are in the bag? Write an equation to represent the situation. Solve the equation. Show your work. Check your solution. 5. Betty has hair ribbons that are either blue or red. She has 19 blue ribbons. The number of blue ribbons she has is 8 less than three times the number of red ribbons, x. How many red ribbons does she have? Write an equation to represent the situation. Solve the equation algebraically or by modeling. Show your work. Check your solution. TEKSING TOWARD STAAR 2014 Page 13
NAME DATE SCORE /5 7.10A/7.11A/7.11B Skills and Concepts Homework 2 1. Determine if the given value makes the given equation or inequality true. Show work to support your decision. 2x 5 9; x 7 3x 6 9; x 3 2. Model the inequality: 3x 1 5 Solve the inequality. 3. Solve algebraically: 2 3 7 3 x (Hint: What is the reciprocal of 2 3?) 4. Lennon has a bag of red and white marbles. The bag contains 18 red marbles. The number of red marbles is greater than 3 times the number of white marbles, x, decreased by 6. How many white marbles are in the bag? Write an inequality that represents the situation. Solve the inequality algebraically or by modeling. Show your work. Choose a number in your solution set and test it for its truth value. TEKSING TOWARD STAAR 2014 Page 14
5. Margie has tomato and pepper plants in her garden. She has 4 tomato plants. The number of tomato plants is one-half the number of pepper plants, x, decreased by 2. How many pepper plants does she have in her garden? Write an equation that represents the situation. Solve the equation. Show your work. Check your solution. TEKSING TOWARD STAAR 2014 Page 15