1. Translating Between Tables and Expressions 2-3
Warm Up
Problem of the Day
Lesson Presentation
Course 1
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
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?
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.
Spike’s Age
Rusty’s age is Spike’s age plus 4.
Rusty’s Age 2 6
= 6 3 7
= 7 4 8
= 8 a
a + 4
a + 4
When Spike’s age is a, Rusty’s age is a + 4.

6. 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.

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.
The expression 3n + 4 works for the entire sequence.
3 • = 7, 3 • = 10, 3 • = 13, 3 • = 16
The expression for the sequence is 3n + 4.

8. Write an expression for the sequence in the table. Position 1 2 3 4 n
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.
The expression 5n + 2 works for the entire sequence.
5 • = 7, 5 • = 12, 5 • = 17, 5 • = 22
The expression for the sequence is 5n + 2.

9. 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 2 9 h
6 • 1 = 6, 6 ÷ 2 = 3
6 • 2 = 12, 12 ÷ 2 = 6
6 • 3 = 18, 18 ÷ 2 = 9 3h
In each row of the table, the area is half the product of the
base and the height. The expression is or 3h. 6h 2 __

10. 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 8 5 10 h
4 • 3 = 12, 12 ÷ 2 = 6
4 • 4 = 16, 16 ÷ 2 = 8
4 • 5 = 20, 20 ÷ 2 = 10 2h
In each row of the table, the area is half the product of the
base and the height. The expression is or 2h. 4h 2 __

11. Lesson Quiz: Part I
1. Write an expression for the missing value in the table.
Scott’s Age
Ray’s Age 11 15 12 16 13 17 x
x + 4

12. 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

13. 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 5 35 6 42 l 7l

14. Equations and Their Solutions
2-4
Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
Course 1

15. Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2. x + 829 16 9 16 55 5

16. Problem of the Day
Complete the magic square so that every row, column, and diagonal add up to the same total. 10 7 4 9 2 8 6 12 5

17. Learn to determine whether a number is a solution of an equation.

18. Vocabulary
equation
solution

19. An equation is a mathematical statement that two quantities are equal
An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale.
3 + 2 5

20. Equations may contain variables
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 27 27
s = 12 is a solution because = 27.
s = 10 is not a solution because  27.

21. Because 1,203 = 1,203, 1,650 is a solution to b — 447 = 1,203.
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
1,650 — 447 = 1,203 ?
Substitute 1,650 for b.
1,203 = 1,203 ?
Subtract.
1,203
Because 1,203 = 1,203, 1,650 is a solution to
b — 447 = 1,203.

22. Because 1,458  1,485, 54 is not a solution to 27x = 1,485.
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
27  54 = 1,485 ?
Substitute 54 for x.
1,458 = 1,485 ?
Multiply.
1,458
1,485
Because 1,458  1,485, 54 is not a solution to
27x = 1,485.

23. 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
= 139 ?
Substitute 73 for u.
129 = 139 ?
Add.
129
139
Because 129  139,
73 is not a solution to
u + 56 = 139.

24. 45  g = 3 for g = 15 45  g = 3 ? 45  15 = 3 Substitute 15 for g.
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
45  15 = 3 ?
Substitute 15 for g.
3 = 3 ?
Divide. 3
Because 3 = 3,
15 is a solution to
45  g = 3.

25. Because 684  664, 19 yards are not equal to 664 inches.
Additional Example 2
Paulo says that his yard is 19 yards long. Jamie says that Paulo’s yard is 664 inches long. Determine if these two measurements are equal.
36  yd = in.
36  19 = 664 ?
Substitute.
684 = 664 ?
Multiply.
Because 684  664, 19 yards are not equal to 664 inches.

26. Because 84 = 84, 7 feet is equal to 84 inches.
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.
12  7 = 84 ?
Substitute.
84 = 84 ?
Multiply.
Because 84 = 84, 7 feet is equal to 84 inches.

27. 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