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Course 1

2-3 Translating Between Tables and Expressions

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Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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Warm UpName 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

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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

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Learn to write expressions for tables and sequences.

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Write an expression for the missing value in the table.

Additional Example 1: Writing an Expression

2 + 4 = 6

Spike’s Age

2

3

4

6

7

8 4 + 4 = 8

3 + 4 = 7

Rusty’s Age

a a + 4

Rusty’s age is Spike’s age plus 4.

a + 4

When Spike’s age is a, Rusty’s age is a + 4.

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Write an expression for the missing value in the table.

Check It Out: Example 1

1 7 = 7

Ty’s Age

1

2

3

7

14

21 3 7 = 21

2 7 = 14

Rich’s Age

a a 7

Rich’s age is Ty’s age times 7.

a 7

When Ty’s age is a, Rich’s age is a 7 or 7a.

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Write an expression for the sequence in the table.

Additional Example 2: Writing an Expression for a Sequence

Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check.

Position 1 2 3 4 n

Value 7 10 13 16

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.

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Write an expression for the sequence in the table.


Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check.

Position 1 2 3 4 n

Value 7 12 17 22

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

In each row of the table, the area is half the product of the

base and the height. The expression is or 3h.6h2__

3h

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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

In each row of the table, the area is half the product of the

base and the height. The expression is or 2h.4h2__

2h

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1. Write an expression for the missing value in the table.

Lesson Quiz: Part I

Scott’s Age

11

12

13

15

16

17

Ray’s Age

x x + 4

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2. Write an expression for the sequence in the t table.

Lesson Quiz: Part II

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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Course 1

2-4 Equations and Their Solutions

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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29 16

9 16

Warm UpEvaluate each expression for x = 8.

1. 3x + 5 2. x + 8

3. 2x – 7 4. 8x 4

5. 7x – 1 6. x – 3

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.

10

7

4

9 2

8 6

12 5

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Learn to determine whether a number is a solution

of an equation.

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equation

solution

Vocabulary

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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.

3 + 2 5

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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.

12 + 15 27

s + 15 = 27

s = 12 s = 10

10 + 1527

s = 12 is a solution because 12 + 15 = 27.

s = 10 is not a solution because 10 + 15 27.

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Determine whether the given value of the variable is a solution.

Additional Example 1A: Determining Solutions of Equations

b — 447 = 1,203 for b = 1,650

Because 1,203 = 1,203, 1,650 is a solution tob — 447 = 1,203.

b — 447 = 1,203

Substitute 1,650 for b.

1,203 = 1,203?

1,650 — 447 = 1,203 ?

1,203 1,203

Subtract.

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Additional Example 1B: Determining Solutions of Equations

27x = 1,485 for x = 54

Because 1,458 1,485, 54 is not a solution to27x = 1,485.

27x = 1,485

Substitute 54 for x.

1,458 = 1,485?

27 54 = 1,485?

1,4581,485

Multiply.

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u + 56 = 139 for u = 73

Because 129 139, 73 is not a solution tou + 56 = 139.

u + 56 = 139

Substitute 73 for u.

129 = 139?

73 + 56 = 139?

Check It Out: Example 1A

129139

Add.

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45 g = 3 for g = 15

Because 3 = 3,15 is a solution to45 g = 3.

45 g = 3

Substitute 15 for g.

3 = 3?

45 15 = 3?

Check It Out: Example 1B

3 3

Divide.

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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.

Additional Example 2

Because 684 664, 19 yards are not equal to 664 inches.

Substitute.

684 = 664?

Multiply.

36 yd = in.

36 19 = 664 ?

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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.

Because 84 = 84, 7 feet is equal to 84 inches.

Substitute.

84 = 84 ?

12 7 = 84?


12 ft = in.

Multiply.

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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

Lesson Quiz

no

yes

yes

no

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.)

Documents

Course 1