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...
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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.)
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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.
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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
Verbal Sentence Equation
The sum of x and 6 is 9. x + 6 = 9
The difference of 12 and y is 15. 12 – y = 15
EXAMPLE 1
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Writing Verbal Sentences as Equations
Verbal Sentence Equation
The sum of x and 6 is 9. x + 6 = 9
The difference of 12 and y is 15. 12 – y = 15
The product of –4 and p is 32. –4p = 32
EXAMPLE 1
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Writing Verbal Sentences as Equations
Verbal Sentence Equation
The sum of x and 6 is 9. x + 6 = 9
The difference of 12 and y is 15. 12 – y = 15
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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Solving Equations Using Mental MathEXAMPLE 3
Equation Question Solution Check
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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Solving Equations Using Mental MathEXAMPLE 3
Equation Question Solution Check
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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Solving Equations Using Mental MathEXAMPLE 3
Equation Question Solution Check
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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