1 Check Homework Page 82 #s (odds in back of book) 40)8n 42)n )4a )7p + (-28) OR 7p ) 24t + (-56) OR 24t – 56 50) u 52) C (They are not raised to the same power.) F. Vollman Buckingham Elementary

2 *Simplified real world problems using mathematical language CB Standards We are Working Towards: 2.1 understand and apply concepts related to #s, # systems, and # relationships; 2.2 Understand and apply concepts related to computation; 2.3 Understand and apply concepts related to measurement and estimation; 2.4 apply mathematical reasoning to make mathematical connections with other disciplines; 2.5 select and communicate appropriate problem solving strategies; 2.8 Use algebraic methods to describe patterns Assessment: Teacher Observation; Checkpoints Goal: You will be able to use mathematical language to solve real world problems through verbal models and variable equations. Variables and Equations 2.4 LESSON How can you translate real world problems into something you can solve using mathematical language?

3 Variables and Equations 2.4 LESSON Doylestown is doing something new! Go-cart rides will be available at the Arts Festival for children. The cost is $6.00. Suppose the go-cart operator takes in a total of $ the first day. How many times did the go-carts get used that day? Table Talk: How might you solve this problem? 1. Write a verbal model. 2.Write an expression. 3.Evaluate.

4 An equation is a mathematical sentence formed by placing an equal sign, =, between two expressions. A solution of an equation with a variable is a # that produces a true statement when it is substituted for the variable. Variables and Equations 2.4 LESSON x + 6 = 9 F. Vollman Buckingham Elementary

5 Writing Verbal Sentences as Equations EXAMPLE 1 Verbal SentenceEquation The sum of x and 6 is 9. x + 6 = 9 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

6 Writing Verbal Sentences as Equations Verbal SentenceEquation The sum of x and 6 is 9. x + 6 = 9 The difference of 12 and y is – y = 15 EXAMPLE 1 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

7 Writing Verbal Sentences as Equations Verbal SentenceEquation The sum of x and 6 is 9. x + 6 = 9 The difference of 12 and y is – y = 15 The product of –4 and p is 32. –4p = 32 EXAMPLE 1 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

8 Writing Verbal Sentences as Equations Verbal SentenceEquation The sum of x and 6 is 9. x + 6 = 9 The difference of 12 and y is – y = 15 The product of –4 and p is 32. –4p = 32 The quotient of n and 2 is 9. = 9 n2n2 EXAMPLE 1 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

9 Checking Possible Solutions EXAMPLE 2 Tell whether 9 or 7 is a solution of x – 5 = 2. Substitute 9 for x. x – 5 = 2 4 ≠ 2 9 is not a solution. 9 – 5 = 2 ? ANSWER Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

10 Checking Possible Solutions EXAMPLE 2 Tell whether 9 or 7 is a solution of x – 5 = 2. Substitute 9 for x. x – 5 = 2 4 ≠ 2 9 – 5 = 2 ? Substitute 7 for x. x – 5 = 2 2 = 2 7 is a solution. 7 – 5 = 2 ? ANSWER 9 is not a solution. ANSWER Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

11 Checkpoint The sum of 3 and z is -10. The quotient of m and 6 is 4. Variables and Equations 2.4 LESSON 3 + z = (-10) m = 4 6 How would you check for possible solutions? F. Vollman Buckingham Elementary

12 Solving Equations Using Mental Math EXAMPLE 3 EquationQuestionSolutionCheck x + 3 = 11 What number plus 3 equals 11 ? = 11 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

13 Solving Equations Using Mental Math EXAMPLE 3 EquationQuestionSolutionCheck x + 3 = = – m = 9 16 minus what number equals 9 ? 716 – 7 = 9 What number plus 3 equals 11 ? Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

14 Solving Equations Using Mental Math EXAMPLE 3 EquationQuestionSolutionCheck x + 3 = = – m = 9716 – 7 = 9 20 = 5t 20 equals 5 times what number? 420 = 5(4) What number plus 3 equals 11 ? 16 minus what number equals 9 ? Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

15 Solving Equations Using Mental Math EXAMPLE 3 EquationQuestionSolutionCheck x + 3 = 11 What number plus 3 equals 11 ? = – m = 9 16 minus what number equals 9 ? 716 – 7 = 9 20 = 5t 20 equals 5 times what number? 420 = 5(4) What number divided by 6 equals –3? –18 = –3 –18 6 = –3 y6y6 Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

16 Checkpoint Solve the equations using mental math. You should be asking yourself questions. 3w = (-15) 2 + n = (-6) F. Vollman Buckingham Elementary

17 Kim is having a party and decides to serve quesadillas as appetizers. There will be 12 people at the party. Each quesadilla will be cut into 4 wedges, and she expects each person to eat 3 wedges. How many quesadillas does she need to make? 4. How many wedges are needed to feed 12 people? 3. Write an expression for the number of wedges in x quesadillas. 4 x 5. Use answers to #s 3 and 4 to write an equation you can use to solve for the total # of quesadillas Kim needs to make. 2. Let x equal the number of quesadillas she needs. 12 * 3 = 36 4 x = 36 What number times 4 is 36?

18 Table Team Work Pages Numbers evens and numbers 32, 34, 35 (follow all directions; check odds in back of the book) When finished: Revisit with Mrs. Vollman at back table OR Extend by completing problems 2.4A #s 19 and 20 (wksh hanging on front board) If finished everything before your classmates, play 24. Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary

19 10) p / 7 = 16 12) No 14) Yes 16)C; 9 18) D; -9 20) 7 22)-79 32)Approximately 8 seconds 34) 24 oz Answer Key--Circle numbers you’d like to review at the front board. 2.4A 19) a. 6x b. 30 pieces c. 6x = 30 d. Five dishes of lasagna 20) a. 20+x=28 b. x=8 in. F. Vollman Buckingham Elementary

20 Create Your Own Table Team Work Review number 7 on page 87 Review numbers 32 and 34 on page 88 You may use these as starting points for creating your own real world problem that could be solved best by using your new mathematical language.

21 Variables and Equations 2.4 LESSON Doylestown is doing something new! Go-cart rides will be available at the Arts Festival for children. The cost is $6.00. Suppose the go-cart operator takes in a total of $ the first day. How many times did the go-carts get used that day? 1.Write a verbal model. Cost * number of children riding = total amount made that day 2.Write an equation. Let x be the number of children. 3. Evaluate.

22 Ticket Out How did you use your mathematical language and knowledge to translate that real world problem into something you could actually solve? Ticket Out Hmwk: 2.4A (hmwk #s4-18 even) F. Vollman Buckingham Elementary

23 Writing and Solving an Equation EXAMPLE 4 From 1998 to 2002, biologist Jane Shen-Miller grew several lotus plants from ancient seeds she found in China. The oldest seed was about 500 years old. Estimate the year when this seed was formed. Let x represent the year when the seed was formed. Estimate x, so use 2000 for the year when the seed sprouted = 2000 Use mental math to solve for x. x = 2000 Substitute for quantities in verbal model. ANSWER Because x = 1500, the seed was formed around the year Variables and Equations 2.4 LESSON What number plus 500 would equal 2000?

24 Writing and Solving an Equation EXAMPLE 4 From 1998 to 2002, biologist Jane Shen-Miller grew several lotus plants from ancient seeds she found in China. The oldest seed was about 500 years old. Estimate the year when this seed was formed. First write a verbal model for this situation. Year seed was formed Age of seed when it sprouted Year seed sprouted += Variables and Equations 2.4 LESSON F. Vollman Buckingham Elementary