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Course 1

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

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Course 1

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  1. Translating Between Tables and Expressions Course 1 2-3 Warm Up Problem of the Day Lesson Presentation 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. Rusty’s age is Spike’s age plus 4. Spike’s Age Rusty’s Age 2 + 4 = 6 2 6 3 7 3 + 4 = 7 4 + 4 = 8 4 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 = 7 1 7 2 14 2  7 = 14 3  7 = 21 3 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. Look for a relationship between the positions and the values of the terms in the sequence. Use guess and check. Guess 7nGuess 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.

  8. Check It Out: Example 2 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. Guess 7nGuess 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.

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

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

  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. 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 linches. 7l

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

  15. Warm Up Evaluate each expression for x = 8. 1. 3x + 5 2.x + 8 3. 2x – 74. 8x  4 5. 7x– 1 6.x– 3 29 16 16 9 55 5

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

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

  18. Vocabulary equation solution

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

  20. 10 + 15 27 12 + 15 27 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 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

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

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

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

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

  25. ? 36  19 = 664 ? 684 = 664 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. Substitute. Multiply. Because 684  664, 19 yards are not equal to 664 inches.

  26. ? ? 84 = 84 12 7= 84 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. Substitute. 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

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