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Course 1

Course 1. 2-1. Variables and Expressions. Warm Up. Problem of the Day. Lesson Presentation. Course 1. Warm Up Simplify. 1. 4 + 7  3  1 2. 87  15  5 3. 6(9 + 2) + 7 4. 35  7  5. 24. 84. 73. 25. 4 3 1. 5 2. Problem of the Day How can the digits 1 through 5 be arranged

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Course 1

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  1. Course 1 2-1 Variables and Expressions Warm Up Problem of the Day Lesson Presentation Course 1

  2. Warm Up Simplify. 1. 4 + 7  3  1 2. 87  15  5 3. 6(9 + 2) + 7 4. 35  7  5 24 84 73 25

  3. 4 31 52 Problem of the Day How can the digits 1 through 5 be arranged in the boxes to make the greatest product? 

  4. Learn to identify and evaluate expressions.

  5. Vocabulary variable constant algebraic expression

  6. A variable is a letter or symbol that represents a quantity that can change. A constant is a quantity that does not change.

  7. Algebraic Expressions NOT Algebraic Expressions An algebraic expression contains one or more variables and may contain operation symbols. So p 7 is an algebraic expression. 150 + y 85 ÷ 5 35 w + z 10 + 3 5 To evaluate an algebraic expression, substitute a number for the variable and then find the value.

  8. y 5  y 16 80 27 y = 27; 5  = y = 35; 5  = 35 Additional Example 1A: Evaluating Algebraic Expressions Evaluate the expression to find the missing values in the table. Substitute for y in 5  y. y = 16; 5  16 = 80 27 135 135 175 35 175 The missing values are 135 and 175.

  9. z z  5 + 42 Substitute for z in z  5 + 42. 20 20 45 60 Additional Example 1B: Evaluating Algebraic Expressions Evaluate the expression to find the missing values in the table. z = 20; 20  5 + 16 = 20 25 z = 45; __  5 + 16 = __ 45 25 60 28 z = 60; __  5 + 16 = __ 28 The missing values are 25 and 28.

  10. x x  9 18 2 x = 36;  9 = 36 x = 54;  9 = 54 Check It Out: Example 1A Evaluate the expression to find the missing values in the table. Substitute for x inx  9. x = 18; 18  9 = 2 4 36 4 6 54 6 The missing values are 4 and 6.

  11. z 8 z + 23 Substitute for z in 8  z + 23. 7 64 9 11 Check It Out: Example 1B Evaluate the expression to find the missing values in the table. z = 7; 8  7 + 8 = 64 9 80 z = 9; 8  __+ 8 = __ 80 11 96 z = 11; 8  __ + 8 = __ 96 The missing values are 80 and 96.

  12. Instead of . . . You can write . . . 35 y Writing Math When you are multiplying a number times a variable, the number is written first. Write “3x” not “x3.” Read 3x as “three x.” You can write multiplication and division expressions without using the symbols  and . x 3 x 3 x(3) 3x 35 ÷ y

  13. Additional Example 2: Evaluating Expressions with Two Variables A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long? Make a table to help you find the number of square units for each length. 3 x 4 = square units 12 16 4 x 4 = square units 16 20 5 x 4 = square units 20 24 6 x 4 = square units 24 The rectangle will cover 12, 16, 20, or 24 square units.

  14. Check It Out: Example 2 A rectangle is 3 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long? Make a table to help you find the number of square units for each length. 2 x 3 = square units 6 9 3 x 3 = square units 9 12 4 x 3 = square units 12 15 5 x 3 = square units 15 The rectangle will cover 6, 9, 12, or 15 square units.

  15. Lesson Quiz 1. Evaluate the expression to find the missing values in the table. 95 44 20 2. A rectangle is 6 units wide. How many square units does the rectangle cover if it is 2, 3, 4, or 5 units long? 12 18 24 30

  16. Course 1 Translate Between Words and Math 2-2 Warm Up Problem of the Day Lesson Presentation Course 1

  17. Warm Up Evaluate each expression for x = 9. 1. 7 + x 2. 4x 3. 2x + 1 4. 36 16 36 19 4 x

  18. Problem of the Day Draw a square around the numbers of four adjacent days on the calendar for this month. Add all the numbers in the square and subtract four times the first number. What number do you get? 16

  19. Learn to translate between words and math.

  20. In word problems, you may need to translate words to math. Put together or combine Add Find how much more or less Subtract Put together groups of equal parts Multiply Separate into equal groups Divide

  21. Additional Example 1A: Social Studies Application Lake Superior is the largest lake in North America. Let a stand for the area in square miles of Lake Superior. Lake Erie has an area of 9,910 square miles. Write an expression to show how much larger Lake Superior is than Lake Erie. To find how much larger, subtract the area of Lake Erie from the area of Lake Superior. a – 9,910 Lake Superior is a – 9,910 square miles larger than Lake Erie.

  22. Additional Example 1B Let p represent the number of colored pencils in a box. If there are 26 boxes on the shelf, write an algebraic expression to represent the total number of pencils on the shelf. To put together 26 equal groups of p, multiply 26 times p. 26p, or26• p There are 26p pencils on the shelf.

  23. Check It Out: Example 1A The Nile River is the world’s longest river. Let n stand for the length in miles of the Nile. The Paraná River is 3,030 miles long. Write an expression to show how much longer the Nile is than the Paraná. To find how much longer, subtract the length of the Paraná from the length of the Nile. n – 3,030 The Nile is n – 3,030 miles longer than the Paraná.

  24. Check It Out: Example 1B Let p represent the number of paper clips in a box. If there are 125 boxes in a case, write an algebraic expression to represent the total number of paper clips in a case. To put together 125 equal groups of p, multiply 125 times p. 125p or125• p There are 125p paper clips in a case.

  25. + Operation Numerical Expression Words Algebraic Expression Words 37 + 28 • 28 added to 37 • 37 plus 28 • the sum of 37 and 28 • 28 more than 37 There are several different ways to write math expressions with words. x+ 28 • 28 added to x • x plus 28 • the sum of x and 28 • 28 more thanx

  26. Operation Numerical Expression 90 — 12 • 12 subtracted from 90 • 90 minus 12 • the difference of 90 and 12 • 12 less than 90 • take away 12 from 90 Words Algebraic Expression k— 12 • 12 subtracted from k • 12minusk • the difference of k and 12 • take away 12 from k Words

  27. Operation Numerical Expression 8  48 or 8  48 or (8)(48) or 8(48)or(8)48 • 8 times 48 • 48 multiplied by 8 • the product of 8 and 48 Words Algebraic Expression 8 wor(8)(w)or8w • 8 timesw • w multiplied by 8 • the product of 8 and w • 8 groups of of w Words

  28. 327 3 n 3  Operation 327 3 or Numerical Expression • 327 divided by 3 • the quotientof 327 and 3 Words n  3 or Algebraic Expression Words • ndivided by 3 • thequotient of n and 3

  29. Additional Example 2: Translating Words into Math Write each phrase as a numerical or algebraic expression. A. 987 minus 12 987  12 B. x times 45 45 • x or 45x

  30. y y 22 or 22 Check It Out: Example 2 Write each phrase as a numerical or algebraic expression. A. 42 less than 79 79  42 B. y divided by 22

  31. Additional Example 3: Translating Math into Words Write two phrases for each expression. A. 16 __ b • 16 divided by b • the quotient of 16 and b B. (75)(32) • 75 times 32 • the product of 75 and 32

  32. B. 12 c Check It Out: Example 3 Write two phrases for each expression. A. 17 – 14 • 14 subtracted from 17 • 17 minus 14 • 12 divided byc • the quotient of 12 and c

  33. Lesson Quiz 1. Let x represent the number of minutes Kristen works out in one week. Write an expression for the number of minutes she works out in 4 weeks. 4x Write each phrase as a numerical or algebraic expression. 2. 7 less than x 3. The product of 12 and w x 7 12w Write a phrase for each expression. 4. 17 + x 5.n  12 x more than 17 or x added to 17 n divided by 12 or the quotient of n and 12

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