Creating Equations and Inequalities from Word P roblems

1. Creating Equations and Inequalities from Word Problems Unit 1, Day 4

2. Warm-up • Compare and contrast your slip of paper with other class mates. • Your slips of paper can be separated into three distinct groups. • Find all other classmates that you believe should go into your group. • Once everyone in the class belongs to a group, decide as a group if you agree that everyone’s slip belongs in that group. • Once you agree, decide on a label that best describes all slips of paper in your group. (Keep it quite!)

3. Review: Translating basic problems • How do I translate “8x=24” into a written statement? • Eight times a number is 24 • This is an equation • How do I translate “fourteen times a number added to three” into a numerical statement? • 14p + 3 • This is an expression • How do I translate “2/y > 4w” into a written statement? • Two divided by a number is greater than four times another number • This is an inequality

4. Translating Word Problems • Word problems offer you a context. • Word problems often give you more information than necessary • Word problems can usually be simplified into basic problems (something you already know how to work with!)

6. Steps to Translating: Look for your goal • Read through the entire problem and get a goal in mind • Your goal should be what the problem is asking you to do

7. Steps to Translating: Define your variables • Look for something we are trying to find (goal) or do not know • Decide what you are going to call your variables

8. Steps to Translating: Cross out unimportant information • Ignore or cross out any added filler in problems • Specifically, look for numbers that will not help you in reaching your goal Highlight important information • Look for numbers already given • Look for math phrases

9. Steps to Translating: Write out your equation or inequality • Use all the information you decided was important and all of your variables

10. Steps to Translating: Check that your answer matches your goal • Go through the word problem one more time, phrase by phrase, and make sure everything in it matches up to how you would read your numerical problem. • Then, make sure you have answered what the problem actually asked.

11. Example #1 • Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement.

12. Solving: Follow through your steps Goal • Model an equation of Suzanne’s old balance to her new balance Variables • d=number of dollars Suzanne withdrew

13. Solving: Follow through your steps Highlight important information Cross out unimportant information • Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement. • Suzanne made a withdrawal of d dollars from her savings account. Her old balance was $350, and her new balance is $280. Model the mathematical statement.

14. Solving: Follow through your steps Write your equation or inequality • 350 – d = 280 Check that your answer matches your goal

15. Example #2 • Eleni is x years old. In thirteen years she will be twenty-four years old. Model her age as a mathematical statement.

16. Example #3 • A large pizza pie with 15 slices is shared among p students so that each student's share is 3 slices. Model each student’s share.

17. Using Inverse Operations to Solve Equations and Inequalities Unit 1, Day 5

18. Inverse Operations • Inverse: the direct opposite • The inverse operation “cancels out” an original operation in the equation or inequality • Mathematical operations performed on one side of the equation/inequality must be performed on the other side to keep the statement true

19. Inverse Operations • The inverse operation of Addition is… • The inverse operation of Subtraction is… • The inverse operation of Multiplication is… • The inverse operation of Division is… • The inverse operation of squaring is… • The inverse operation of taking the square root is… Subtraction Addition Division Multiplication Taking a square root Squaring

20. Inverse Operation Examples

21. Solving Algebraic Equations in One VariableTo solve equations we must follow these rules: (1) Take care of anyDistributive Property or any other Multiplication/Divisionfound in the equation. (2) Combine Like Terms on the left and right of the equal sign individually. (3) Move the variables to one side of the equation and the constants to the other side (isolate the variable) using inverse operations. (4) Get the variable alone (coefficient of 1) by dividing each side of the equation by the variable’s coefficient. You may have to use the reciprocal of the coefficient if there is a fraction attached to the variable in the last step.

22. Practice Problems - Equations x = 3 w b = -63 y = 4 CHECK YOUR SOLUTIONS!

23. Practice Problems - Inequalities 1. 2. 3. 4. 5. 3 CHECK YOUR SOLUTIONS!

24. Solving Algebraic Inequalities • Follow the same rules as solving equations EXCEPT • When multiplying or dividing by a negative, be sure to flip your inequality sign.

25. Creating and Solving Equations • A number is divided by 3. Then 14 is added to the quotient. The result is 33.What is the original number? • Landon has 37 baseball cards. If 4 cards can fit on one page, how many pages does Landon need to buy?

26. You Try! • The square root of a number is subtracted from the sum of the number and 12. The result is 42. What is the original number? • Kata has a savings account that contains $230. She decides to deposit $5 each month from her monthly earnings for baby-sitting after school. Write an expression to find how much money Kata will have in her savings account after X months. Let X represent the number of months. Then find out how much she will have in her account after 1 year.