Transcript PowerPoint

Translating
Between
Tables
Translating
Between
2-3
2-3 and
Expressions
Tables
and Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course
1
Course 11
Course
2-3
Translating Between Tables
and Expressions
Warm Up
Name the next three terms in each
sequence.
1. 7, 10, 13, 16, 19, 22, 25
2. 105, 88, 71, 54, 37, 20, 3
3. 64, 128, 256, 512, 1,024, 2,048, 4,096
Course 1
2-3
Translating Between Tables
and Expressions
Problem of the Day
Sam’s house is 3 blocks east and 5 blocks
south of Tyra. If Tyra walks straight south
and then straight east to Sam’s house,
does she walk more blocks east or more
blocks south?
south
How many more?
2 blocks
Course 1
2-3
Translating Between Tables
and Expressions
Learn to write expressions for tables and
sequences.
Course 1
2-3
Translating Between Tables
and Expressions
Additional Example 1: Writing an Expression
Write an expression for the missing value in
the table.
Spike’s Age Rusty’s Age Rusty’s age is Spike’s age plus 4.
2
6
2+4 =6
3
7
3+4 =7
4
8
4+4 =8
a
a+4
a +4
When Spike’s age is a, Rusty’s age is a + 4.
Course 1
Translating Between Tables
and Expressions
2-3
Check It Out: Example 1
Write an expression for the missing value in
the table.
Ty’s Age
Rich’s Age Rich’s age is Ty’s age times 7.
1
7
17 =7
2
14
2  7 = 14
3
21
3  7 = 21
a
a7
a7
When Ty’s age is a, Rich’s age is a  7 or 7a.
Course 1
2-3
Translating Between Tables
and Expressions
Additional Example 2: Writing an Expression for
a Sequence
Write an expression for the sequence in the table.
Position
Value
1
7
2
10
3
13
4
16
n
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.
Course 1
2-3
Translating Between Tables
and Expressions
Check It Out: Example 2
Write an expression for the sequence in the table.
Position
Value
1
7
2
12
3
17
4
22
n
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.
Course 1
2-3
Translating Between Tables
and Expressions
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 • 1 = 6, 6 ÷ 2 = 3
6
2
6
6 • 2 = 12, 12 ÷ 2 = 6
6
3
9
6 • 3 = 18, 18 ÷ 2 = 9
6
h
3h
In each row of the table, the area is half the product of the
6h
base and the height. The expression is __ or 3h.
2
Course 1
2-3
Translating Between Tables
and Expressions
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 • 3 = 12, 12 ÷ 2 = 6
4
4
8
4 • 4 = 16, 16 ÷ 2 = 8
4
5
10
4
h
4 • 5 = 20, 20 ÷ 2 = 10
2h
In each row of the table, the area is half the product of the
4h
base and the height. The expression is __ or 2h.
2
Course 1
2-3
Translating Between Tables
and Expressions
Lesson Quiz: Part I
1. Write an expression for the missing value in
the table.
Course 1
Scott’s Age
Ray’s Age
11
15
12
16
13
17
x
x+4
2-3
Translating Between Tables
and Expressions
Lesson Quiz: Part II
2. Write an expression for the sequence in the
t table.
Position
Value
Course 1
1
8
2
16
3
24
n
8n
2-3
Translating Between Tables
and Expressions
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.
Course 1
Width (in.)
Length (in.)
Area (in2)
7
4
28
7
5
35
7
6
42
7
l
7l