Translating Between Tables and Expressions 2-3 Warm Up Problem of the Day Lesson Presentation Course 1 Course 1

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

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

Learn to write expressions for tables and sequences.

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 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.

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.

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.

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. 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.

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 __

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 __

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

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

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

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

Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2. x + 8 29 16 9 16 55 5

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

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

Vocabulary equation solution

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

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 10 + 15 27 12 + 15 27 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

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.

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.

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

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.

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.

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.

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