Transcript 2.4A - fvollman

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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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
Goal: You will be able to use mathematical language to solve real
world problems through verbal models and variable equations.
*Simplified real
world problems using
mathematical
language
How can you translate
real world problems into
something you can solve
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
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LESSON
2.4 Variables and Equations
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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LESSON
2.4 Variables and Equations
x+6=9
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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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
1
Writing Verbal Sentences as Equations
Verbal Sentence
Equation
The sum of x and 6 is 9.
x+6=9
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
1
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
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
1
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
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
1
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.
n
=9
2
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
2
Checking Possible Solutions
Tell whether 9 or 7 is a solution of x – 5 = 2.
Substitute 9 for x.
x–5=2
?
9–5 =2
4≠2
ANSWER
9 is not a solution.
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
2
Checking Possible Solutions
Tell whether 9 or 7 is a solution of x – 5 = 2.
Substitute 9 for x.
x–5=2
Substitute 7 for x.
x–5=2
9–5 =2
7–5 =2
4≠2
2=2
?
ANSWER
9 is not a solution.
?
ANSWER
7 is a solution.
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
Checkpoint
The sum of 3 and z is -10. 3 + z = (-10)
The quotient of m and 6 is 4.
m=4
6
How would you check for possible solutions?
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
3
Solving Equations Using Mental Math
Equation
Question
x + 3 = 11
What number
plus 3 equals 11?
Solution
8
Check
8 + 3 = 11
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
3
Solving Equations Using Mental Math
Equation
Question
Solution
Check
x + 3 = 11
What number
plus 3 equals 11?
8
8 + 3 = 11
16 – m = 9
16 minus what
number equals 9?
7
16 – 7 = 9
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
3
Solving Equations Using Mental Math
Equation
Question
Solution
Check
x + 3 = 11
What number
plus 3 equals 11?
8
8 + 3 = 11
16 – m = 9
16 minus what
number equals 9?
7
16 – 7 = 9
20 = 5t
20 equals 5 times
what number?
4
20 = 5(4)
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
3
Solving Equations Using Mental Math
Equation
Question
Solution
Check
x + 3 = 11
What number
plus 3 equals 11?
8
8 + 3 = 11
16 – m = 9
16 minus what
number equals 9?
7
16 – 7 = 9
20 = 5t
20 equals 5 times
what number?
4
20 = 5(4)
y
= –3
6
What number divided
by 6 equals –3?
–18
–18
= –3
6
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F. Vollman Buckingham Elementary
Checkpoint
Solve the equations using mental math. You
should be asking yourself questions.
3w = (-15)
2 + n = (-6)
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F. Vollman Buckingham Elementary
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?
2. Let x equal the number of quesadillas she needs.
3. Write an expression for the number of wedges in x quesadillas. 4 x
4. How many wedges are needed to feed 12 people? 12 * 3 = 36
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.
4 x = 36
What number times 4 is 36?
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LESSON
2.4 Variables and Equations
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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F. Vollman Buckingham Elementary
Answer Key--Circle numbers you’d like to review at the front board.
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
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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F. Vollman Buckingham Elementary
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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LESSON
2.4 Variables and Equations
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 Out
How did you use your mathematical language and knowledge
to translate that real world problem into something you could
actually solve?
Hmwk: 2.4A (hmwk #s4-18 even)
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F. Vollman Buckingham Elementary
LESSON
2.4 Variables and Equations
EXAMPLE
4
Writing and Solving an Equation
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
x + 500 = 2000
Substitute for quantities in verbal model.
What number plus 500 would equal 2000?
1500 + 500 = 2000
ANSWER
Use mental math to solve for x.
Because x = 1500, the seed was formed around the year 1500.
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LESSON
2.4 Variables and Equations
EXAMPLE
4
Writing and Solving an Equation
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
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F. Vollman Buckingham Elementary