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Coach Lesson 20 M7A2.a

Coach Lesson 20 M7A2.a. When given a problem, students will Define a variable Write an equation Solve the equation Interpret the solution. Words to Know. Equation: a mathematical sentence that contains an equal sign Example: 9 + 3 = 12 Example: 3x = 12

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Coach Lesson 20 M7A2.a

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  1. Coach Lesson 20M7A2.a When given a problem, students will Define a variable Write an equation Solve the equation Interpret the solution

  2. Words to Know • Equation: a mathematical sentence that contains an equal sign • Example: 9 + 3 = 12 • Example: 3x = 12 • Inverse Operations: the opposite of the operation shown. • Inverse of addition is subtraction. • Inverse of multiplication is division.

  3. Example 1 • Solve the equation below for x. x + 9 = 16 When some number and 9 are added, it will equal 16. Use the inverse operation to solve. Inverse of addition is subtraction. 16 – 9 = 7… therefore x must equal 7. Check your work: 7 + 9 = 16

  4. Example 2 • Solve the equation below for z. 3z = 27 What number times 3 will equal 27? Use the inverse operation to solve. (Inverse of multiply is divide.) 27/3 = 9… therefore z must equal 9. Check your work: 3(9) = 27

  5. Example 3 • Mario is 32 years older than his daughter, Frida. If Frida is 19, how old is Mario? Step 1: Define a variable. The unknown is Mario’s age, so we will call that m. m = Mario’s age. Step 2: Write an equation. Mario’s age minus 32 is 19, which is Frida’s age. m – 32 = 19 Step 3: Solve the equation. Remember to use inverse operation to solve. 19 + 32 = 51… therefore m must equal 51. Step 4: Interpret the solution. Since m equals 51, we know that Mario’s age must be 51.

  6. Example 4 • Hyun brought a bag of crayons to class and divided them equally among the 5 students in her group. Each student received 16 crayons. How many crayons did Hyun bring to class? • Step 1: Define a variable. The unknown is how many crayons Hyun brought. We can choose c as our variable to stand for # of crayons. • Step 2: Write an equation. The number of crayons divided into 5 equal groups was 16. c /5 = 16 • Step 3: Solve the equation. Use the inverse operation of division to solve. 16 • 5 = 80… therefore c must equal 80. • Step 4: Interpret the solution. Since c represents the number of crayons, we know that there were a total of 80 crayons that Hyun brought to her class.

  7. Coached Example If 4 pairs of socks cost $9, can you find the cost of one pair? Thinking it through… You need to find the cost of __________. Start by letting s = this cost. Then you can write the equation. You could use the multiplication equation _____________ or the division equation ________________. Either way, you divide ________ by _________. So one pair of socks costs _______________.

  8. Answers to coached example. Find the cost of one pair of socks. 4s = 9 (multiplication equation) 9/4 = s (division equation) Divide 9 by 4. One pair of socks costs $2.25.

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