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1-1 Using a Problem-Solving Plan Read the introduction to Lesson 1-1 in your textbook. Write your answers a. Find a pattern in the costs. b. How can you determine the cost to mail a 6-ounce letter? c.

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1-1 Using a Problem-Solving Plan Read the introduction to Lesson 1-1 in your textbook. Write your answers a. Find a pattern in the costs. b. How can you determine the cost to mail a 6-ounce letter? c. Suppose you were asked to find the cost of mailing a letter that weighs 8 ounces. What steps would you take to solve the problem? Lesson 1 1 Write a definition and give an example of each new vocabulary word or phrase. 1. conjecture 2. inductive reasoning 3. What is the next term: 3, 6, 12, 24...? Explain. 4. Complete this sentence. In the step of the four-step problem-solving plan, you check the reasonableness of your answer. 5. Explain why each step of the four-step plan is important. Chapter 1 5 Glencoe Pre-Algebra 1-2 Numbers and Expressions Read the introduction to Lesson 1-2 in your textbook. Write your answers a. Study the expressions and their respective values. For each expression, tell the order in which the calculator performed the operations. b. For each expression, does the calculator perform the operations in order from left to right? c. Based on your answer to parts a and b, find the value of each expression Check your answer with a scientific calculator d. Make a conjecture as to the order in which a scientific calculator performs operations. Lesson 1 2 Reading the Lesson Write a definition and give an example of each new vocabulary word or phrase. 1. numerical expression 2. evaluate 3. order of operations 4. In the boxes below, write three different expressions using two operations that each have a value of A mnemonic device helps you remember something. Create your own mnemonic device to remember the order of operations. For example, list the operations in order, use the first letter of each operation and create a phrase with words starting with the same letters. Chapter 1 11 Glencoe Pre-Algebra 1-3 Variables and Expressions Read the introduction to Lesson 1-3 in your textbook. Write your answers a. How much would the baby-sitter earn for working 10 hours? b. What is the relationship between the number of hours and earnings? c. If h represents any number of hours, what expression could you write to represent the amount of money earned? Write a definition and give an example of each new vocabulary word or phrase. 1. variable 2. algebraic expression 3. defining a variable 4. Name three things that make an algebraic expression. 5. Why do you think replacing a variable with a number is called the Substitution Property of Equality? 6. Variable is a word used in everyday English. a. Find the definition of variable in the dictionary. Write the definition. b. Explain how the English definition can help you remember how variable is used in mathematics. Lesson 1 3 Chapter 1 17 Glencoe Pre-Algebra 1-4 Properties Getting Ready for the Lesson Read the introduction to Lesson 1-4 in your textbook. Write your answers a. Suppose you read the Preamble to the U.S. Constitution first and then the Gettysburg Address. Write an expression for the total number of words read. b. Suppose you read the Gettysburg Address first and then the Preamble to the U.S. Constitution. Write an expression for the total number of words read. c. Find the value of each expression. What do you observe? d. Does it matter in which order you add any two numbers? Why or why not? Write a definition and give an example of each new vocabulary word or phrase. 1. properties 2. counterexample 3. simplify 4. deductive reasoning 5. Tell what a counterexample is in your own words. Tell how it is used in mathematics and why it is important. Chapter 1 24 Glencoe Pre-Algebra 1-5 Variables and Equations Read the introduction to Lesson 1-5 in your textbook. Write your answers a. If Rebecca is x years old, what expression represents Emilio s age? b. What two expressions are equal? c. If Emilio is 19, how old is Rebecca? Write a definition and give an example of each new vocabulary word or phrase. 1. equation 2. open sentence 3. solution 4. solving the equation 5. Complete this sentence. When the in an open sentence is replaced with a number, you can determine whether the sentence is true or false. 6. Consider x 4 6. Find a value for x that makes the sentence true and another value that makes it false. 7. Explain how an open sentence is different from an algebraic expression. Chapter 1 30 Glencoe Pre-Algebra 1-6 Ordered Pairs and Relations Read the introduction to Lesson 1-6 in your textbook. Write your answers a. Where should Elisa place an X now? Explain your reasoning. b. Suppose (1, 2) represents 1 over and 2 up. How could you represent 3 over and 2 up? c. How are (5, 1) and (1, 5) different? d. Where is a good place to put the next O? e. Work with a partner to finish the game. Write a definition and give an example of each new vocabulary word or phrase. 1. coordinate system 2. y-axis 3. coordinate plane 4. origin 5. x-axis 6. ordered pair 7. x-coordinate 8. y-coordinate 9. graph 10. relation 11. domain 12. range Chapter 1 36 Glencoe Pre-Algebra 1-7 Scatter Plots Read the introduction to Lesson 1-7 in your textbook. Write your answers a. What appears to be the trend in sales of movies on videocassette? b. Estimate the number of movies on videocassette sold for Write a definition and give an example of the new vocabulary term. 1. scatter plot 2. Scatter plots are used to show relationships. a. For a positive relationship, as x increases, y. b. For a negative relationship, as x increases, y. 3. The scatter plot compares the weights and heights of the players on a high school football team. Heights of Football Players Height 6'1 6'0 5'11 5'10 5'9 5'8 5'7 5'6 Weight (in pounds) a. What type of relationship exists, if any? b. Based on the scatter plot, predict the weight of a 5 5 player who decided to join the team. Chapter 1 42 Glencoe Pre-Algebra 2-1 Integers and Absolute Value Read the introduction to Lesson 2-1 in your textbook. Write your answers a. What does a value of 3 represent? b. Which city was farthest from its normal rainfall? c. How could you represent 5 inches above normal rainfall? Write a definition and give an example of each new vocabulary word or phrase. Lesson negative number 2. integers 3. coordinate 4. inequality 5. absolute value 6. Absolute is a word that is used frequently in the English language. a. Find the definition of absolute in a dictionary. Write the definition that most closely relates to mathematics. b. Explain how the English definition can help you remember the meaning of absolute value in mathematics. Chapter 2 5 Glencoe Pre-Algebra 2-2 Adding Integers Read the introduction to Lesson 2-2 in your textbook. Write your answers a. What integer represents the total yardage on the two plays? b. Write an addition sentence that describes this situation. Write a definition and give an example of each new vocabulary word or phrase. 1. opposites 2. additive inverse Lesson Draw a number line model that shows how to find the sum 4 ( 2). Explain your model. 4. The sum of any number and its is zero. 5. Suppose that one of your classmates was absent the day you learned how to add integers. a. Explain to your classmate how to add two integers with the same sign. b. Explain to your classmate how to add two integers with different signs. Chapter 2 11 Glencoe Pre-Algebra 2-3 Subtracting Integers Read the introduction to Lesson 2-3 in your textbook. Write your answers a. What is 6 8? b. What direction do you move to indicate subtracting a positive integer? c. What addition sentence is also modeled by the number line on page XX? 1. To subtract an integer, add its. 2. Draw a number line model that shows how to find the difference 4 2. Explain your model. 3. Can 9 ( 3) be rewritten as 9 3? Explain. 4. You have learned how to use addition to subtract both positive and negative integers. Write one example of each difference described Then show how to use addition to find the difference. a. subtracting a positive integer from a positive integer b. subtracting a positive integer from a negative integer c. subtracting a negative integer from a positive integer Lesson 2 3 d. subtracting a negative integer from a negative integer Chapter 2 17 Glencoe Pre-Algebra 2-4 Multiplying Integers Read the introduction to Lesson 2-4 in your textbook. Write your answers a. Suppose the altitude is 4 kilometers. Write an expression to find the temperature change. b. Use the pattern in the table on page 100 to find 4( 7). 1. The product of two integers with sign(s) is negative. 2. The product of two integers with sign(s) is positive. 3. Draw a number line model that shows how to find the product 4( 2). Explain your model.. 4. Show how to use a pattern to find ( 5)( 1). 5. You can use the when you multiply more than two integers. 6. In your own words, describe how to tell the sign of the product of two integers. Lesson 2-4 Chapter 2 23 Glencoe Pre-Algebra 2-5 Dividing Integers Read the introduction to Lesson 2-5 in your textbook. Write your answers a. How many groups are there? b. What is the quotient of 12 ( 4)? c. What multiplication sentence is also shown on the number line? d. Draw a number line and find the quotient 10 ( 2). Write a definition and give an example of the new vocabulary word. 1. average (mean) 2. The quotient of two integers with sign(s) is negative. 3. The quotient of two integers with sign(s) is positive. 4. Draw a number line model that shows how to find the quotient 9 ( 3). Explain your model. 5. You have learned how to divide positive and negative integers. Write one example of each quotient described Then find the quotient. a. dividing a positive integer by a negative integer b. dividing a negative integer by a negative integer Lesson 2 5 c. dividing a negative integer by a positive integer Chapter 2 29 Glencoe Pre-Algebra 2-6 The Coordinate System Read the introduction to Lesson 2-6 in your textbook. Write your answers a. Latitude is measured north and south of the equator. What is the latitude of Dallas? b. Longitude is measured east and west of the prime meridian. What is the longitude of Dallas? c. What does the location 32 N, 96 W mean? Write a definition and give an example of the new vocabulary word. 1. quadrants 2. A point graphed on the coordinate system has a(n) and a(n). 3. In which quadrant does the point A(4, 2) lie? 4. Draw a coordinate grid with points to represent your classroom and where your classmates sit. Explain how to name the locations of your classmates. Chapter 2 36 Glencoe Pre-Algebra 3-1 The Distributive Property Read the introduction to Lesson 3-1 in your textbook. Write your answers a. Draw a 2-by-5 and a 2-by-4 rectangle. Find the total area in two ways. b. Draw a 4-by-4 and a 4-by-1 rectangle. Find the total area in two ways. Lesson 3 1 c. Draw any two rectangles that have the same width. Find the total area in two ways. d. What did you notice about the total area in each case? Write a definition and give an example of the new vocabulary term. 1. term expressions 2. In rewriting 3(x 2), which term is distributed to the other terms in the expression? 3. Distribute is a word that is used frequently in the English language. a. Find the definition of distribute in a dictionary. Write the definition. b. Explain how the English definition can help you remember how the word distributive relates to mathematics. Chapter 3 5 Glencoe Pre-Algebra 3-2 Simplifying Algebraic Expressions Read the introduction to Lesson 3-2 in your textbook. Write your answers a. 3x 2 4x 3 b. 2x 5 x c. 4x 5 3 d. x 2x 4x Write a definition and give an example of each new vocabulary word or phrase. 1. term 2. coefficient Lesson like terms 4. constant 5. simplest form 6. simplifying an expression 7. Is 2(r 1) in simplest form? Explain. 8. Constant is a word used in everyday English as well as in mathematics. a. Find the definition of constant in a dictionary. Write the definition. b. Explain how the English definition can help you remember how constant is used in mathematics. Chapter 3 11 Gelncoe Pre-Algebra 3-3 Solving Equations by Adding or Subtracting Read the introduction to Lesson 3-3 in your textbook. Write your answers a. Without looking in the bag, how can you determine the number of blocks in the bag? b. Explain why your method works. Write a definition and give an example of each new vocabulary phrase. 1. inverse operations 2. equivalent equations 3. Are x 2 8 and x 6 equivalent equations? Explain. 4. How is adding 2 blocks to each side of a balanced scale like the Addition Property of Equality? Lesson 3 3 Chapter 3 17 Glencoe Pre-Algebra 3-4 Solving Equations by Multiplying or Dividing Read the introduction to Lesson 3-4 in your textbook. Write your answers a. Suppose lunch in Mexico costs 77 pesos. Write an equation to find the cost in U.S. dollars. b. How can you find the cost in U.S. dollars? 1. How do you undo multiplication in an expression? x 2. What does the expression mean? 2 x 3. Explain how to find the value of x in the equation 3. How do you check your answer? 4 You have learned about four properties of equalities: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, and Division Property of Equality. In each circle, write three equations that can be solved by using the given property. Include at least one negative integer in each circle. These equations can be solved by using the given property. Addition Property Subtraction Property Multiplication Property 2 2 Division Property Lesson Chapter 3 23 Glencoe Pre-Algebra 3-5 Solving Two-Step Equations Read the introduction to Lesson 3-5 in your textbook. Write your answers a. What property is shown by removing a tile from each side? b. What property is shown by separating the tile into two groups? c. What is the solution of 2x 1 9? Write a definition and give an example of the new vocabulary phrase. 1. two-step equation 2. To solve two-step equations, use to undo each operation in reverse order. Suppose you start with a number x, multiply it by 2, add three, and the result is 17. The top row of boxes at the right represents the equation 2x To solve the equation, you undo the operations in reverse order. This is shown in the bottom row of boxes. Start Start 3 x? 2 x? Start Start Start 2 x? So, x 7. Complete the bottom row of boxes in each figure. Then find the value of x x? 4 x? Lesson 3 5 Chapter 3 29 Glencoe Pre-Algebra 3-6 Writing Two-Step Equations Read the introduction to Lesson 3-6 in your textbook. Write your answers a. Let m represent the number of miles walked. Write an expression that represents the amount Logan can raise when he walks m miles. b. Suppose Logan raised $308. Write and solve an equation to find the number of miles Logan walked. c. Why is your equation considered to be a two-step equation? Refer to Example 3. Read the Explore and Plan steps. Then complete the following. 1. Suppose you have already saved $75 and plan to save $5 a week. a. Complete the table Week Amount Saved ($) n 5(0) 5(1) 5(2) 5(3) 5(n) b. Write an equation that represents how many weeks it will take you to save $ Suppose you have already saved $25 and plan to save $10 each week. a. Complete the table Week Amount Saved ($) n b. Write an equation that represents how many weeks it will take you to save $175. Chapter 3 36 Glencoe Pre-Algebra 3-7 Sequences and Equations Read the introduction to Lesson 3-7 in your textbook. Write your answers a. What is the braking distance for a car going 70 mph? b. What is the difference in reaction distances for every 10-mph increase in speed? c. Describe the braking distance as speed increases. Write a definition and give an example of each new vocabulary word or phrase. 1. sequence 2. arithmetic sequence 3. term 4. common difference 5. What is the common difference in the sequence 8, 17, 26, 35,...? 6. Sequence is a word that is used in everyday English. a. Find the definition of sequence in a dictionary. Write the definition. b. Explain how the English definition can help you remember how sequence is used in mathematics. Chapter 3 42 Glencoe Pre-Algebra 3-8 Using Formulas Read the introduction to Lesson 3-8 in your textbook. Write your answers a. Write an expression for the distance traveled by a duck in t hours. b. What disadvantage is there in showing the data in a table? c. Describe an easier way to summarize the relationship between the speed, time, and distance. Write a definition and give an example of each new vocabulary word. 1. formula 2. perimeter 3. area 4. The word perimeter is composed of the prefix peri- and the suffix -meter. a. Find the definitions of peri- and -meter in a dictionary. Write their definitions. b. Find two other words in a dictionary that begin with the prefix peri-. Write their definitions. c. Explain how your definitions can help you remember how perimeter is used in mathematics. Chapter 3 48 Glencoe Pre-Algebra 4-1 Powers and Exponents Read the introduction to Lesson 4-1 in your textbook. Write your answers a. Write 16 as a product of factors of 2. How many factors are there? b. How many factors of 2 form the product 128? c. One megabyte is 1024 kilobytes. How many factors of 2 form the product 1024? Write a definition and give an example of each new vocabulary word or phrase. Lesson base 2. exponent 3. power 4. standard form 5. expanded form 6. Write each expression using exponents. a b. x x x y y c. ( 2)( 2)( 2) d. 5 r r m m m 7. The number ( ) ( ) ( ) ( ) is written in form, while 3502 is written in form. 8. Explain how the terms base, power, and exponent are related. Provide an example. Chapter 4 5 Glencoe Pre-Algebra 4-2 Prime Factorization Read the introduction to Lesson 4-2 in your textbook. Write your answers a. Use grid paper to draw as many different rectangular arrangements of 2, 3, 4, 5, 6, 7, 8, and 9 squares as possible. b. Which numbers of squares can be arranged in more than one way? c. Which numbers of squares can only be arranged one way? d. What do all rectangles that you listed in part c have in common? Explain. Write a definition and give an example of each new vocabulary word or phrase. 1. composite number 2. factor 3. factor tree 4. prime factorization 5. prime number 6. Composite is a word used in everyday English. a. Find the definition of composite in the dictionary. Write the definition. b. Explain how the English definition can help you remember how composite is used in mathematics. Chapter 4 12 Glencoe Pre-Algebra 4-3 Greatest Common Factor (GCF) Read the introduction to Lesson 4-3 in your textbook. Write your answers a. Which numbers are in both circles? b. Find the product of the numbers that are in both circles. c. Is the product also a factor of 12 and 20? d. Make a Venn diagram showing the prime factors of 16 and 28. Then use it to find the common factors of the numbers. Write a definition and give an example of each new vocabulary word or phrase. 1. Venn diagram 2. greatest common factor 3. Summarize in your own words how to find the greatest common factor of two numbers using each method. a. prime factorization b. lists of factors c. a Venn diagram Chapter 4 18 Glencoe Pre-Algebra 4-4 Simplifying Algebraic Fractions Read the introduction to Lesson 4-4 in your textbook. Write your answers a. Are the three fractions equivalent? Explain your reasoning. b. Which figure is divided into the least number of parts? c. Which fraction would you say is written in simplest form? Why? Write a definition and give an example of each new vocabulary phrase. 1. simplest form 2. algebraic fraction 3. Use a Venn diagram to explain how to simplify Explain the similarities and differences between simplifying a numerical fraction and simplifying an algebraic fraction. Chapter 4 24 Glencoe Pre-Algebra 4-5 Multiplying and Dividing Monomials Read the introduction to Lesson 4-5 in your textbook. Write your answers a. Examine the exponents of the factors and the exponents of the products in the last column. What do you observe? b. Make a conjecture about a ru

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