Translating Between Tables and Expressions

1
Translating Between Tables and Expressions
2-3
Warm Up
Problem of the Day
Lesson Presentation
Course 1
2
Warm Up Name the next three terms in each
sequence. 1. 7, 10, 13, 16, 2. 105, 88, 71, 54,
3. 64, 128, 256, 512,
19, 22, 25
37, 20, 3
1,024, 2,048, 4,096
3
Problem of the Day Sams house is 3 blocks east
and 5 blocks south of Tyra. If Tyra walks
straight south and then straight east to Sams
house, does she walk more blocks east or more
blocks south? How many more?
south
2 blocks
4
Learn to write expressions for tables and
sequences.
5
Additional Example 1 Writing an Expression
Write an expression for the missing value in the
table.
Rustys age is Spikes age plus 4.
Spikes Age
Rustys Age

2 4 6
2
6
3
7
3 4 7
4 4 8
4
8
a
a 4
a 4
When Spikes age is a, Rustys age is a 4.
6
Check It Out Example 1
Write an expression for the missing value in the
table.
Tys Age
Richs Age
Richs age is Tys age times 7.

1 ? 7 7
1
7
2
14
2 ? 7 14
3 ? 7 21
3
21
a
a ? 7
a ? 7
When Tys age is a, Richs age is a ? 7 or 7a.
7
Additional Example 2 Writing an Expression for a
Sequence
Write an expression for the sequence in the table.
Position 1 2 3 4 n
Value 7 10 13 16

Look for a relationship between the positions and
the values of the terms in the sequence. Use
guess and check.
Guess 7n Guess 3n 4
Check by substituting 2. Check by substituting 2.
7 2 does not equal 10. 3 2 4 10.
The expression 3n 4 works for the entire
sequence.
3 1 4 7, 3 2 4 10, 3 3 4 13, 3
4 4 16
The expression for the sequence is 3n 4.
8
Check It Out Example 2
Write an expression for the sequence in the table.
Position 1 2 3 4 n
Value 7 12 17 22

Look for a relationship between the positions and
the values of the terms in the sequence. Use
guess and check.
Guess 7n Guess 5n 2
Check by substituting 2. Check by substituting 2.
7 2 does not equal 12. 5 2 2 12.
The expression 5n 2 works for the entire
sequence.
5 1 2 7, 5 2 2 12, 5 3 2 17, 5
4 2 22
The expression for the sequence is 5n 2.
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Additional Example 3 Writing Expressions for the
Area of a Figure
A triangle has a base of 6 inches. The table
shows the area of the triangle for different
heights. Write an expression that can be used to
find the area of the triangle when its height is
h inches.
Base (in.) Height (in.) Area (in2)
6 1 3
6 2 6
6 3 9
6 h
6 1 6, 6 2 3
6 2 12, 12 2 6
6 3 18, 18 2 9
3h
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Check It Out Example 3
A triangle has a base of 4 inches. The table
shows the area of the triangle for different
heights. Write an expression that can be used to
find the area of the triangle when its height is
h inches.
Base (in.) Height (in.) Area (in2)
4 3 6
4 4 8
4 5 10
4 h
4 3 12, 12 2 6
4 4 16, 16 2 8
4 5 20, 20 2 10
2h
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Lesson Quiz Part I
1. Write an expression for the missing value in
the table.
Scotts Age
Rays Age
11
15
12
16
13
17
x
x 4
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Lesson Quiz Part II
2. Write an expression for the sequence in the
t table.
Position 1 2 3 n
Value 8 16 24
8n
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Lesson Quiz Part III
3. A rectangle has a width of 7 inches. The
table shows the area of the rectangle for
different lengths. Write an expression that can
be used to find the area of the rectangle when
its length is l inches.
Width (in.) Length (in.) Area (in2)
7 4 28
7 5 35
7 6 42
7 l
7l
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2-4
Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
15
Warm Up Evaluate each expression for x 8. 1.
3x 5 2. x 8 3. 2x 7 4. 8x ? 4 5. 7x
1 6. x 3
29
16
16
9
55
5
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Problem of the Day Complete the magic square so
that every row, column, and diagonal add up to
the same total.
9
2
8
6
12
5
17
Learn to determine whether a number is a solution
of an equation.
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Vocabulary
equation solution
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An equation is a mathematical statement that two
quantities are equal. You can think of a correct
equation as a balanced scale.
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Equations may contain variables. If a value for a
variable makes an equation true, that value is a
solution of the equation.
s 15 27
s 12
s 10
s 12 is a solution because 12 15 27.
s 10 is not a solution because 10 15 ? 27.
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Additional Example 1A Determining Solutions of
Equations
Determine whether the given value of the variable
is a solution.
b 447 1,203 for b 1,650
b 447 1,203
Substitute 1,650 for b.
Subtract.
Because 1,203 1,203, 1,650 is a solution to b
447 1,203.
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Additional Example 1B Determining Solutions of
Equations
Determine whether the given value of the variable
is a solution.
27x 1,485 for x 54
27x 1,485
Substitute 54 for x.
Multiply.
Because 1,458 ? 1,485, 54 is not a solution
to 27x 1,485.
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Check It Out Example 1A
Determine whether the given value of the variable
is a solution.
u 56 139 for u 73
u 56 139
Substitute 73 for u.
Add.
Because 129 ? 139, 73 is not a solution to u
56 139.
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Check It Out Example 1B
Determine whether the given value of the variable
is a solution.
45 ? g 3 for g 15
45 ? g 3
Substitute 15 for g.
Divide.
Because 3 3, 15 is a solution to 45 ? g 3.
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Additional Example 2
Paulo says that his yard is 19 yards long. Jamie
says that Paulos yard is 664 inches long.
Determine if these two measurements are equal.
36 ? yd in.
Substitute.
Multiply.
Because 684 ? 664, 19 yards are not equal to 664
inches.
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Check It Out Example 2
Anna says that the table is 7 feet long. John
says that the table is 84 inches long. Determine
if these two measurements are equal.
12 ? ft in.
Substitute.
Multiply.
Because 84 84, 7 feet is equal to 84 inches.
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Lesson Quiz
Determine whether the given value of each
variable is a solution. 1. 85 13x for x 5 2.
w 38 210 for w 172 3. 8y 88 for y 11 4.
16 w ? 6 for w 98
no
yes
yes
no
5. The local pizza shop charged Kylee 172 for 21
medium pizzas. The price of a medium pizza is 8.
Determine if Kylee paid the correct amount of
money. (Hint 8 pizzas total cost.)
no