PowerPoint
Translating Between
Tables and Expressions
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
2
Rusty’s Age
Rusty’s age is Spike’s age plus 4.
6 2 + 4 = 6
3
4
7
8
3 + 4 = 7
4 + 4 = 8 a a + 4 a + 4
When Spike’s age is a , Rusty’s age is a + 4.
Course 1
2-3
Translating Between Tables and Expressions
Check It Out: Example 1
Write an expression for the missing value in the table.
Ty’s Age
1
2
3 a
Rich’s Age
7
14
21 a
7
Rich’s age is Ty’s age times 7.
1
7 = 7
2
7 = 14
3
7 = 21 a
7
When Ty’s age is a , Rich’s age is a
7 or 7 a .
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.
7 • 2 does not equal 10.
Check by substituting 2.
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 2 3 4 n
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.
7 • 2 does not equal 12.
Check by substituting 2.
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 (in 2 )
6
6
6
6
1
2
3 h
3
6
9
3h
6 • 1 = 6, 6 ÷ 2 = 3
6 • 2 = 12, 12 ÷ 2 = 6
6 • 3 = 18, 18 ÷ 2 = 9
In each row of the table, the area is half the product of the base and the height. The expression is or 3h .
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 (in 2 )
4
4
4
4
3
4
5 h
6
8
10
2h
4 • 3 = 12, 12
4 • 4 = 16, 16
4 • 5 = 20, 20
÷
÷
÷
2 = 6
2 = 8
2 = 10
In each row of the table, the area is half the product of the base and the height. The expression is or 2h .
Course 1
2-3
Translating Between Tables and Expressions
Lesson Quiz: Part I
1. Write an expression for the missing value in the table.
Scott’s Age Ray’s Age
11
12
15
16
13 17 x x + 4
Course 1
2-3
Translating Between Tables and Expressions
Lesson Quiz: Part II
2. Write an expression for the sequence in the t table.
Position
Value
1
8
2
16
3
24 n
8n
Course 1
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.
Width (in.) Length (in.) Area (in 2 )
7
7
7
7
4
5
6 l
28
35
42
7 l
Course 1
