1 Check Homework Page 82 #s 40-53 (odds in back of book) 40)8n 42)n + 10 44)4a + 8 46)7p + (-28) OR 7p - 28 48) 24t + (-56) OR 24t – 56 50)-4 + 20u 52)

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Check Homework

Page 82 #s 40-53 (odds in back of book)

40) 8n

42) n + 10

44) 4a + 8

46) 7p + (-28) OR 7p - 28

48) 24t + (-56) OR 24t – 56

50) -4 + 20u

52) C (They are not raised to the same power.)

F. Vollman Buckingham Elementary

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*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 patternsAssessment: 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 Equations2.4 L

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How can you translate real world problems into something you can solve using mathematical language?

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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 $252.00 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.

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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.


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x + 6 = 9


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Writing Verbal Sentences as EquationsEXAMPLE 1

Verbal Sentence Equation

The sum of x and 6 is 9. x + 6 = 9


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Writing Verbal Sentences as Equations



The difference of 12 and y is 15. 12 – y = 15

EXAMPLE 1


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The product of –4 and p is 32. –4p = 32

EXAMPLE 1


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The product of –4 and p is 32. –4p = 32

The quotient of n and 2 is 9. = 9n2

EXAMPLE 1


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Checking Possible SolutionsEXAMPLE 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


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Checking Possible SolutionsEXAMPLE 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?

ANSWER9 is not a solution.ANSWER


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Checkpoint

The sum of 3 and z is -10.

The quotient of m and 6 is 4.


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3 + z = (-10)

m = 46

How would you check for possible solutions?


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Solving Equations Using Mental MathEXAMPLE 3

Equation Question Solution Check

x + 3 = 11What number plus 3 equals 11?

8 8 + 3 = 11


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x + 3 = 11 8 8 + 3 = 11

16 – m = 916 minus what number equals 9?

7 16 – 7 = 9

What number plus 3 equals 11?


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x + 3 = 11 8 8 + 3 = 11

16 – m = 9 7 16 – 7 = 9

20 = 5t20 equals 5 times what number?

4 20 = 5(4)

What number plus 3 equals 11?

16 minus what number equals 9?


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x + 3 = 11What number plus 3 equals 11?

8 8 + 3 = 11

16 – m = 916 minus what number equals 9?

7 16 – 7 = 9

20 = 5t20 equals 5 times what number?

4 20 = 5(4)

What number divided by 6 equals –3?

–18 = –3–18

6= –3y6


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Checkpoint

Solve the equations using mental math. You

should be asking yourself questions.

3w = (-15)

2 + n = (-6)


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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?

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Table Team Work

•Pages 87-88

•Numbers 10-22 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.


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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.


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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.

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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 $252.00 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.

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Ticket OutHow 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)


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Writing and Solving an EquationEXAMPLE 4From 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

1500 + 500 = 2000 Use mental math to solve for x.

x + 500 = 2000 Substitute for quantities in verbal model.

ANSWER Because x = 1500, the seed was formed around the year 1500.


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What number plus 500 would equal 2000?

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Writing and Solving an EquationEXAMPLE 4From 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+ =


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Documents

1 Check Homework Page 82 #s 40-53 (odds in back of book) 40)8n 42)n + 10 44)4a + 8 46)7p + (-28) OR 7p - 28 48) 24t + (-56) OR 24t – 56 50)-4 + 20u 52)