CPM 1 (Period 1) Assignments

• 6-96. Copy the diagrams of algebra tiles below on your paper.  Then find the perimeter of each shape.  Homework Help ✎
  1. 
  2. 
• 6-97. Jack and Jill are playing a Mystery Game.   They are trying to get four tiles of the same color in a row, column, or diagonal.  Four in a row wins the game.  Homework Help ✎
  1. List the coordinates of the points that they have already played, as shown at right.
  2. Give two more points, one to Jack and one to Jill, so that either one might win.  

• 6-88. Draw a number line from 0 to 2.  Then write the following numbers in its correct place on the number line.  Homework Help ✎
• 0.2              1.5               1.9               1.09            1.19
• 6-89. Find the perimeter and area of each figure below.  Homework Help ✎
  1. 
  2. 
• 6-90. There were 25 words on a recent vocabulary test in English class, and Owen got four words wrong.  What percent did he get correct?  Homework Help ✎

• 6-86. On your paper, sketch the shape made with algebra tiles below.  Then answer parts (a) and (b) below.  6-86 HW eTool (CPM).  Homework Help ✎

  

  1. Find the area of the shape.
  2. If the algebra tiles were rearranged into a different shape, how would the area change?
• 6-87. Your team members forgot to clean up their algebra tiles, and now the tiles are all over your desk.  6-87 HW eTool (CPM).  Homework Help ✎

  

• Sort the tiles so that they are in groups that are all the same.  Write a sentence explaining how many of each type of tile you have. 

• 6-72. Simplify each expression.  Homework Help ✎
  1. 16 − 5(3 − 1)
  2. 31· 4 + 18 · 6
  3. 3.45(2²) − 8.18(1)
  4. 4 · 5 −2² + 3(5 − 4)
• 6-73. Draw a number line and place each of the following numbers in its appropriate place on the line: −5, −2, 4, 6, −1, , −0.5.  Homework Help ✎
• 6-74. Are the following expressions equivalent? Homework Help ✎
  • 3(4x − 2) + 8                          2(6x + 1)
• 6-75. Evaluate the expressions below using r = 3 and h = 5.  Homework Help ✎
  1. 6h − 4
  2. 8r + h
  3. r²

• 6-69. How can you check if the following two expressions are equivalent?  Are they?  Homework Help ✎
• 3(4x − 2)                    12x − 2 
• 6-70. A rectangle has an area of square centimeters and a length of 1.5 centimeters.  What is the width? What is the perimeter?  Homework Help ✎ 
• 6-71. Find the area of each trapezoid below.  Homework Help ✎
  1. 
  2. 

• 6-54. Express each of the following numbers as a product of its prime factors.  Use exponents to represent repeated multiplication, when applicable.  An example is given below.  Homework Help ✎
• 40 = 2 · 20 = 2 · 2 · 10 = 2 · 2 · 2 · 5 = 2³ · 5
  1. 30
  2. 300
  3. 17
  4. 21
• 6-55. Copy the pattern below.  Homework Help ✎

  

  1. Draw the fifth and sixth figures on your paper.
  2. Describe Figure 20.
  3. How many dots will be in Figure 20?
• 6-56. Graph each of the following points and connect them in order. 6-56 HW eTool (Desmos). Homework Help ✎  Click in the lower right corner of the graph to view it in full-screen mode. Desmos Accessibility

• (1, 1), (1, 5), (5, 5), (5, 1), (3, 1), (3, 3), (2, 3), (2, 1), (1, 1)   What is the area of the shape that was formed? What is the perimeter of the shape that was formed?

• 6-57. Ms. Perez is giving her class a pizza party because every student completed the school‑wide book reading challenge.  If an extra-large pizza costs $15 and serves 8 people, how much should Ms. Perez expect to pay for pizzas if her class has 28 students?  Homework Help ✎
• 6-58. Solve each generic rectangle puzzle.  Write your answer in the form:
  (total length)(total width) = sum of individual area parts = total area.  Homework Help ✎
  1. 
  2. 

• 6-51. Name the coordinates of each point shown in the graph below using ordered pairs (x, y).  Homework Help ✎

  

• 6-52. At the school’s fall bake sale, all of the pies were cut into 6 pieces, so each person who bought a piece bought  of a pie. Each slice of pie sold for $1.00. How much money did the school make if all eleven pies were sold? (In other words, find 11 divided by .)  Homework Help ✎
• 6-53. Find the area and perimeter of a rectangle that is 14.5 meters by 5.8 meters.  Homework Help ✎

• 6-36. Multiply the following fractions.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 6-37. Graph and connect the points (1, 1), (1, 5), (4, 5) and (4, 1) in the order listed and then connect the last point you graphed to the first point.  What is the length of each side?  What is the area of the shape that is formed? 6-37 HW eTool (Desmos). Homework Help ✎ Click in the lower right corner of the graph to view it in full-screen mode. Desmos Accessibility
• 6-38. Draw a diagram to help calculate each of the following quotients (the answer to a divison problem).  Homework Help ✎
  1. 4 ÷ 
  2. 6 ÷ 
• 6-39. Jesse has five meters of twine and needs to cut it into lengths that are each  of a meter long.  How many lengths will he have?  Express this problem in a number sentence that uses division. Homework Help ✎

• 6-33. Use a ruler to draw a line exactly 4 inches long and then mark every  inch.  Homework Help ✎
  1. How many  inches are in 4 inches?
  2. Now use the ruler to mark every  inch.  How many  inches are in 1 inch?  
  3. How many  inches are in 2 inches?  in 3 inches?
• 6-34. Draw a diagram that shows how to divide 9 pieces of licorice into packages that hold 5 pieces each.  Then find 9 ÷ 5.  Homework Help ✎
• 6-35. Audrey made the histogram below to show her recent bowling scores.  Homework Help ✎

  

  1. How many games did she play in total?
  2. Between what two values did most of her scores fall?
  3. Challenge: What portion of her scores fell between 130 and 140?

• 6-23. Together, Lucia and Ben have saved $150.  Lucia saved $2 for every $1 that Ben saved.  How much money did each person save?  Homework Help ✎
• 6-24. Find each of the products in parts (a) through (d) below.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 1
• 6-25. Write the points on the graph below as ordered pairs. Homework Help ✎

  

• 6-21. Show how to divide 9 pieces of licorice among 4 people. Homework Help ✎
• 6-22. Ashley painted  of her bathroom ceiling. Alex painted  of the ceiling in the school library.  Homework Help ✎
  1. Who painted the larger fraction of their ceiling?
  2. If the drawings at right accurately represent the relationship between the ceiling sizes, who painted more ceiling area?
  3. Explain why the answers for parts (a) and (b) should be different.

• 6-8. Find the area of each of these trapezoids.  Show all of your steps.  Homework Help ✎
  1. 
  2. 
• 6-9. Consider the generic rectangle shown at right. Homework Help ✎
  1. Copy and complete the generic rectangle. 
  2. Write as many products as you can see in the rectangle.  Find at least four.  For each one, show the factors being multiplied, as well as the product. 
• 6-10. If you had 12 pieces of licorice to share equally among 5 people, how much licorice would each person get?  Be sure to show your thinking clearly.  Homework Help ✎

• 6-5. If you had 2 pieces of licorice to share equally among 3 people, how much licorice would each person get?  Show your thinking clearly. Homework Help ✎
• 6-6. Calculate each of the following parts of parts.  Homework Help ✎
  1.  of
  2.  of
• 6-7. Simplify each numerical expression.  Homework Help ✎
  1. 
  2. 2
  3. 

• CL 5-112. Copy each shape below on your paper, and then find its area and perimeter.  Show all of your work.
  1. 
  2. 
  3. 
• CL 5-113. Draw and label a set of axes on your graph paper.  Plot and label the following points: (1, 3), (4, 2), (0, 5), and (5, 1).

• 5-103. This problem is a checkpoint for multiple representations of portions.  It will be referred to as Checkpoint 5.
• For each portion of a whole, write it as a percent, a fraction, and a decimal.  Also show it as a picture or situation.  Use a portions web to organize your answers.  Homework Help ✎
  1. 0.23
  2. seven tenths
  3. 19%
  4. 
• Check your answers by referring to the Checkpoint 5 materials.
• Ideally, at this point you are comfortable working with these types of problems and can solve them correctly.  If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 5 materials and try the practice problems provided.  From this point on, you will be expected to do problems like these correctly and with confidence.
• 5-104. Write an algebraic expression to represent the length of each segment shown below.  Homework Help ✎
  1. 
  2. 
  3. 
• 5-105. Simplify each of the following expressions without using a calculator.  Then use a calculator to check your answers.  Homework Help ✎
  1. 0.045 + 1.2 + 62.003
  2. 56.7 − 0.23
  3. (7.8)(0.03)
  4. 6.3 − 7.5

• 5-101. Choose any strategy to find the area of each shape below.  Use the information in the Math Notes boxes for help.  Assume that the shape in part (a) is a parallelogram and that the shape in part (b) is a  trapezoid.   5-101 HW eTool (Desmos)  Homework Help ✎  Click in the lower right corner of the graph to view it in full-screen mode. 
• 5-102. Find each sum.  Homework Help ✎
  1. −3 + 7
  2. 7 + (−8)
  3. 
• 5-103. This problem is a checkpoint for multiple representations of portions.  It will be referred to as Checkpoint 5.
• For each portion of a whole, write it as a percent, a fraction, and a decimal.  Also show it as a picture or situation.  Use a portions web to organize your answers.  Homework Help ✎
  1. 0.23
  2. seven tenths
  3. 19%
  4. 

• 5-93. Graph the trapezoid A(6, 5), B(8, −2), C(−4, −2), D(−2, 5).  Homework Help ✎
  1. Find the length of the bottom base (segment CB).  Then find the length of the top base (segment AD).  Use grid units.   
  2. Find the distance between the two bases, which is called the height.  Use grid units.
• 5-94. The first four multiples of 7 are 7, 14, 21, and 28.  Use this example to help you as you answer the questions  below.  Homework Help ✎
  1. What are the first six multiples of 9?
  2. What are the first six multiples of 12?
  3. What is the least common multiple of both 9 and 12?
  4. What is the greatest common factor of both 9 and 12?  
• 5-95. Draw a number line.  Then draw and label a dot to show the position of each of the following numbers.  Homework Help ✎
  1. 2.5
  2. 
  3. −2
  4. 0.5
  5. −1
  6. 

• 5-91. Find the area of each parallelogram below.  Show all of your work.  Use the Math Notes box in this lesson if you need help.  Homework Help ✎
  1. 
  2. 
• 5-92. Find the area of the following triangles.  Show all your work.  Homework Help ✎
  1. 
  2. 

• 5-83. Johanna is planting tomatoes in the school garden this year. Tomato plants come in packs of six. She needs 80 plants in the garden and already has 28. How many packs of plants will she need?  Homework Help ✎
• 5-84. Are you ready for a number puzzle?  Homework Help ✎
  1. Use the numbers 7, 5, 6, and 3, only once each, to create an expression that equals 75.  You may use addition, subtraction, multiplication, and/or division, but you must use parentheses.  
  2. Now use the Distributive Property to write an equivalent expression without parentheses.  (You may use the numbers more than once or use different digits for this part only.)

1. 
2. 
3. 3.1 · 2.7

• 5-80. Use any of your new strategies to find the area of the parallelograms below.  The information in the Math Notes box may help.  5-80 HW eTool (Desmos).Homework Help ✎
• 5-81.  Additional Challenge: Jill lives 3 miles from school.  One morning, her friend was giving her a ride.  When they were of the way to school, their car broke down and they had to walk the rest of the way.  Draw a picture to help you figure out how far they walked.  Homework Help ✎
• 5-82. For each of the following products, estimate the answer.  Explain your reasoning.  Then multiply each set of numbers to see how close you were.  Homework Help ✎
  1. 
  2. 
  3. 3.1 · 2.7

• 5-73. Jack and Jill were each placing points on the grid shown below.  Jack’s points are the full circles, and Jill’s are the open  circles.  Homework Help ✎
  • 
• 1. Record Jack and Jill’s points as ordered pairs.
  2. Give the coordinates of one more point that Jill could draw so that she has four of her points in a row. 
• 5-74. Complete each of following statements.  Homework Help ✎
  1. If one cat has 16 whiskers, then seven cats will have        whiskers.
  2. If three slugs have six eye-stalks, then two slugs will have        eye-stalks.
  3. If eight spiders have 64 legs, then 5 spiders will have        legs. 
• 5-75. Draw generic rectangles to calculate each of the following products. Homework Help ✎
  1. 34 · 91
  2. 421 · 36

• 5-72. Zac is making cookies, but he does not have enough brown sugar to make a full recipe.  The full recipe calls for cup of brown sugar.
• If Zac has enough brown sugar for of the full recipe, how much brown sugar does he have?  Homework Help ✎
  1. Represent the  cup of brown sugar the recipe calls for with a diagram. 
  2. Represent the portion of brown sugar that Zac has if he makes only   of the recipe.
  3. What mathematical operation should Zac use to find the amount of brown sugar he has?  Write an expression and then calculate its value. 

• 5-63. Billy and Ken, the school’s cross-country stars, were each running at cross-country practice.  Billy was going to run  of the training course, and Ken was going to run  of the course.  However, during practice it started raining, so they could not finish their runs.  Billy had finished  of his run, while Ken had finished of his run.  Draw a picture to determine which cross-country star ran the farthest.  Homework Help ✎
• 5-64. Add or subtract the following pairs of fractions and mixed numbers.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 5-65. Find the missing side lengths of each rectangle, (a) and (c) or square (b) and (d).  Homework Help ✎
  1. 
  2. 
  3. 
  4. 

• 5-61. Multiply to find the percents below.  Homework Help ✎
  1. 8% of 150
  2. 8.5% of 70
• 5-62. Genevieve is an architect and has just finished the plans for a new library.  She built a scale model to take to a planning meeting.  The City Council members love her design so much that they have asked her for two new models. 
• Help Genevieve decide how she will calculate the measurements of each new model to satisfy each of the given  conditions.  Homework Help ✎
  1. The council wants a model much smaller than Genevieve’s original model to fit in a scale model of the entire city.   
  2. The council wants a model slightly larger than the one Genevieve built to sit on a stand at the entrance of the old library building.   

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• 5-48. Ethan decided to give 10% of his monthly income to charity.  This month, he wrote the calculation at right.  Explain why this calculation is appropriate and finish it for him.  How much money should he give this month?  Homework Help ✎

   $1526

  x 0.1
• 5-49. Melissa wants to re-sod her yard (replace the grass).  Her backyard has a rectangular lawn area that measures 24 feet by 18 feet.  Her front yard has two rectangular areas, one of which measures 18 feet by 14 feet.  The other measures 12 feet by 14 feet.  How many square feet of sod does Melissa need?  Show all of your work clearly. Homework Help ✎

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• 5-34. Complete the diagram below and write the multiplication problem and answer that would go with it.  Homework Help ✎
•                                                           
• 5-35. Draw a rectangle.  Label the lengths of the sides.  Enlarge it so that the ratio of sides of your new rectangle to the original one is .  What are the new dimensions?  Homework Help ✎
• 5-36. When making estimates, it is sometimes useful to approximate unfamiliar fractions by comparing them to numbers that are more familiar to you.  Homework Help ✎
  1. Copy the number line below on your paper, including the dots.  Keep the dots in the same positions.  Label each dot with one of the fractions from the list given  below.
  2. Which of these fractions are greater than or equal to 1?
     
  3. Which of these fractions are close to the number 1?
  4. Which of these fractions are close to ?
  5. Which of these numbers are close to 0?
     

• 5-26. Multiply each pair of numbers below.  Homework Help ✎
  1. 68 · 100
  2. 0.68 · 100
  3. 6.8 · 1000
  4. Describe in words what is happening to the decimal point in each problem, (a) through (c) above.
• 5-27. On your own graph paper, draw a rectangle with a width of 6 cm and a height of 8 cm.
  1. Draw a similar rectangle that is enlarged 300%.  Homework Help ✎
  2. Draw a similar rectangle with lengths that are of the original lengths.
• 5-28. Sophie claims that whenever she increases the perimeter of a rectangle, its area increases. 5-28 HW eTool  Homework Help ✎  Click in the lower right corner of the graph to view it in full-screen mode.
   
  1. She showed the rectangle at right and said, “If I make the base twice as long, then the area increases.”  Is her statement correct for this figure?  Draw a diagram of the rectangle she described and explain whether the area is greater or less than the rectangle at right.  
  2. Is her claim about the relationship of area and perimeter correct for all figures?  For example, is there any way that she could have a rectangle with a greater perimeter than the figure in part (a) but with the same area?  Give examples and explain your reasoning.

• 5-24. Write each of the mixed numbers below as a fraction greater than one, and write each of the fractions greater than one as a mixed number.  Include a diagram to explain each answer.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 5-25. Calculate each of the following parts of parts.  Homework Help ✎
  1. of  
  2.  of  

• 5-16. Kelani wants to cut a piece of rope into several equally-sized pieces and then have a 10-foot piece remaining.  Write an algebraic expression to represent the length of each rope shown in the diagrams below.  Then use the equation you create to help Kelani figure out how long to make each of the equally-sized pieces.  Homework Help ✎
   
  1. A 25-foot piece of rope (find  n).    
  2. A 310-foot piece of rope (find  x).  
  3. A 13-foot piece of rope (find  j).    
• 5-17. Convert each mixed number to a fraction greater than one, or each fraction greater than one to a mixed number.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 

• 5-13. Use a portions web to rewrite each decimal as a percent, as a fraction, and with words.  Homework Help ✎
  1. 0.2
  2. 0.05
  3. 1.75
  4. 0.002
• 5-14. Find each of the parts of parts described below.  For each one, create a diagram that demonstrates your thinking.  Homework Help ✎
  1.  of
  2. 
  3.  of
  4. 
• 5-15. Simplify each expression.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
  5. 
  6. 

• 5-6. Recall the definition of absolute value from the Math Notes box in Lesson 3.2.4.  For each pair of points below, find the distance between the given points.  Show your work using absolute value symbols.  Homework Help ✎
  1. (13, 14) and (−3, 14)
  2. (−9, 1) and (−9, 11)
• 5-7. Change each fraction greater than one to a mixed number, and change each mixed number to a fraction greater than one.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 5-8. Simplify each of the following expressions.  Be sure to simplify each of your answers as much as possible.  Write any answers greater than one as mixed numbers.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 

• 5-4. The diagrams below show the portion of another class mural that Josephine was supposed to paint and how much she actually did paint.  Use the pictures to answer the questions that follow.  Homework Help ✎

  The portion Josephine was supposed to paint:	The portion Josephine actually painted:

  1. Approximately what portion of the painting was Josephine supposed to paint? 
  2. Approximately what fraction of her assigned portion did Josephine actually complete? 
  3. Write a product to show what portion of the mural Josephine actually painted. 
• 5-5. Draw a rectangle with a width of 8 units and a length of 6 units.  Homework Help ✎
  1. What is the enlargement ratio if you enlarge the figure to have a width of 16 units and a length of 12 units? 
  2. If you wanted to reduce the 8 by 6 rectangle by a ratio of , what would the dimensions of the new rectangle be?

• CL 4-89. Copy the dot pattern below and draw Figures 0, 4, and 7. Write an expression to describe how the pattern is growing.
                     
• CL 4-90. Draw a right triangle on graph paper that has a base of 4 units and a height of 2 units.  Enlarge it so that each side is 2.5 times as long as the original.

• 4-82. Use an algebraic expression to represent each sequence of lengths shown below.  Homework Help ✎
  1. 
  2. 
  3. 
• 4-83. In parts (a) through (c) below, refer to the previous problem.  You will find the length of the line segments in problem 4-82 by substituting given values for the variables.  For example, if  x  is 3 units in part (a) of problem 4-82, the line segment would be  3 + 1 + 3 = 7 units long.  Homework Help ✎
  1. Find the length of the line segment in part (a) of problem 4-82 using x = 4
  2. Find the length of the line segment in part (b) of problem 4-82 m = 4
  3. Find the length of the line segment in part (c) of problem 4-82 using y = 5.5
• 4-84. Write each fraction greater than one as a mixed number and each mixed number as a fraction greater than one.  Homework Help ✎
  1. 5
  2. 
  3. 7
  4. 

• 4-72. Simplify the following expressions.  Homework Help ✎
  1. 
  2. 
  3. 
• 4-73. A new shipment of nails is due any day at Hannah’s Hardware Haven, and you have been asked to help label the shelves so that the nails are organized in length from least to greatest.  She is expecting nails of the following sizes: 1 inch, 1 inch, 2 inch,  inch, and 1 inch.  Use the ruler below to help Hannah order the labels on the shelves from least to greatest.  Homework Help ✎

  

• 4-74. Cecelia wants to measure the area of her bedroom floor.  Should she use square inches or square feet?  Complete parts (a) through (c) below as you explore this question.  Homework Help ✎
  1. Write a sentence to explain which units you think Cecelia should use. 
  2. If Cecelia’s bedroom is 12 feet by 15.5 feet, what is the area of the bedroom floor?  Show how you got your answer.   
  3. Find the perimeter of Cecelia’s bedroom floor.  Show how you got your answer.  

• 4-70. On graph paper, draw any quadrilateral.  Then enlarge (or reduce) it by each of the following ratios.  Homework Help ✎
  1. 
  2. 
• 4-71. George drew the diagram at right to represent the number 2. “Look,” said Helena, “This is the same thing as .” What do you think?  Explore this idea in parts (a) through (c) below.  Homework Help ✎
• 1. Is Helena correct? If so, explain how she can tell that the diagram represents . If she is not correct, explain why not.
  2. Draw a diagram to represent the mixed number 3 . How can you write this as a single fraction greater than one?
  3. How can you write as a mixed number? Be sure to include a diagram in your answer.

• 4-61. Compute each sum or difference.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 4-62. Find each quotient without using a calculator.  Homework Help ✎
  1. 42.5 ÷ 1.5
  2. 589.2 ÷ 16
  3. 5 ÷ 9

• 4-58. Draw two different simple geometric shapes (such as rectangles or right triangles) on graph paper.  Homework Help ✎
  1. Choose one shape and enlarge it so that each side is twice as long as the original.
  2. Choose the other shape and reduce it so that each side is half the length of the original.
• 4-59. Study the pattern below.  Sketch and label the fourth and fifth figures.  Then predict how many dots will be in the 100^th figure.  Write an expression you can use to determine the number of dots in any figure.  Homework Help ✎
• 
• 4-60. Simplify each of the following absolute value expressions.  Homework Help ✎
  1. 
  2. 
  3. 

• 4-49. Four friends worked together to wash all of the cars that the Kumar family owns.  They received $43.00 for doing the work and agreed to divide the earnings evenly.  How much money will each friend earn?  Show how you know.  Homework Help ✎
• 4-50. Copy and complete the generic rectangle below.  What multiplication problem does it represent and what is the product? Homework Help ✎

  

• 4-51. Use the portions representation web to rewrite each percent as a fraction, as a decimal and with words or a picture.  Homework Help ✎
  1. 13%
  2. 20%
  3. 130%
  4. 32%

• 4-47. Use graph paper to complete the steps below.  Then answer the question that follows.  Homework Help ✎
  • Draw a square that measures 5 units on each side.
  • Draw a design inside your 5 × 5 square. 
  • Then draw a square that measures 15 units on each side.
  • Enlarge your picture as accurately as possible so that it fits inside of the 15 × 15 square. 
• How much wider and how much longer is your new picture?  
• 4-48. Tina is going to put 1‑inch square tiles on the picture frame shown below.  Homework Help ✎

                                

  1. If the frame is one tile wide, how many 1-inch-square tiles will she need?
  2. Would more 1-inch square tiles fit inside the frame or on the frame?  Show how you know.

• • 4-36. Find the prime factorization for each number below. Homework Help ✎
    1. 36
    2. 45
    3. Find the greatest common factor for 36 and 45. 
    4. Find the least common multiple for 36 and 45. 
  • 4-37. Simplify each of the following absolute value expressions.   Homework Help ✎
    1. 
    2. 
    3. 
  • 4-38. Copy the following problems, then use the number line to help you fill in < (less than) or > (greater than) on the blank line between each pair of numbers.  Homework Help ✎

    

    1. −4.84 ___ −8.48
    2. 7 ___ −7
    3. −6.5 ___ −5
    4. −1 ___0
  
  

• 4-34. Julian was studying a pattern made with toothpicks, and he started the table shown below.  Homework Help ✎

• Figure Number	Number of Toothpicks
  1	7
  2	10
  3	13
  4
  5

  1. Copy and complete the table.
  2. Draw axes and plot Julian’s points.
  3. How can you describe what all of these points have in common?
• 4-35. Estimate each sum or difference below by stating which whole numbers the answer should be between.  Then check your conclusion by calculating the actual sum or difference.  Homework Help ✎
  1. 5.2 − 2.09
  2. 25 − 17
  3. 3 + 2
  4. 103.57 + 29.6

• 4-18. Melissa collected the dates of all her friends’ birthdays.  The histogram at right shows what she found out.  Make a list of the months when her friends’ birthdays occur and how many birthdays there are in each month.  Homework Help ✎
• 4-19. Review the Math Notes box in this lesson. Then convert each mixed number to a fraction greater than one, or each fraction greater than one to a mixed number.  Homework Help ✎
  1. 4
  2. 
  3. 100
  4. 
• 4-20. Each expression below begins with –5 and then adds something to it.  As you look at each expression, state which direction you should move on a number line if you start at –5.  Then simplify each expression.  

• For example, if the expression reads –5 + (–9), you would write “left, –14,” since from –5 you would move left on a number line 9 units and would end up at –14.  Homework Help ✎

  1. −5 + (−4.5)
  2. −5 + (−8)
  3. −5 + 6

• 4-16. Look at the figure formed by square tiles below.  How can you find out how many small squares there are in this diagram without counting each one?  Think about this as you answer the questions below.  Homework Help ✎
• 
  1. Write and simplify an expression involving addition to count the number of small squares. 
  2. Write and simplify an expression involving subtraction to count the number of small squares. 
• 4-17. A team of students worked on problem 4-12.  The team’s work is shown below.  Unfortunately, the expressions, descriptions, and diagrams got mixed up!  Match the counting method, word description, and diagram that describe the same strategy.  Homework Help ✎

• • Counting Methods	Word Descriptions	Diagrams
    a. 4 · 10 − 4	1. Start in one corner and count 9 four times around the picture frame.	A.
    b. 10 + 9 + 9 + 8	2. Take a side length of 10 four times and take away the four corners.	B.
    c. 9 · 4	3. Take the entire 100's grid and subtract the inside part of the picture frame.	C.
    d. (10 · 10) − (8 − 8)	4. Take the top length, then add the two vertical sides and add the bottom.	D.

• 4-10. Read the Math Notes box in this lesson. Then complete the following division problems.  Homework Help ✎
  1. 683 ÷ 4
  2. 212 ÷ 9
• 4-11. Rewrite each decimal as a fraction or fraction as a decimal.  Homework Help ✎
  1. 0.007
  2. 0.103
  3. 1.21
  4. 
  5. 
  6. 

• 4-8. Now Croakie can do a super high jump!  Homework Help ✎
• The first time he performed his new super-high-jump routine, he did three super-high jumps and then hopped five feet.  The second time, he did only two super-high jumps and then hopped six feet.  Both times, he covered the same distance.  His attempts are shown in the diagram below.

  

  1. How far does Croakie travel in one super-high jump?  Explain or show how you know. 
  2. How long is his whole super-high-jump routine?  How can you tell? 
• 4-9. Simplify each expression below.  For each expression, draw a picture or show how you know your answer makes sense.  Homework Help ✎
  1. 5 +(−4) + 12.65
  2. 6.5 + (−2) + 10.5
  3. 4(−5 + 100)
  4. −212 + (−102)
  5. 4 + 6(3) + 2(5 − 1)
  6. 5 + 3(5) + (−4)(5)

1. In his new routine, Croakie makes seven super jumps, all the same length, and then hops 3 feet.  How long is each super jump? 
2. If  x  represents the length of one super jump and  2x  represents the length of two super jumps, write an expression that represents Croakie’s routine.  

• CL 3-140. Compute each sum.
  1. 
  2. 1.4 + (−2.3)
  3. −5.2 + (−8.39)
  4.  + 4.29
• CL 3-141. Marcus used the Venn diagram at right that shows the prime factors of 21 and 35.
  1. How can Marcus use the diagram to find the least common multiple of 21 and 35?  Explain.
  2. How can Marcus use the diagram to find the greatest common factor of 21 and 35?  Explain.

• CL 3-138. Copy the number line below on your paper.  Then label the following numbers on the line in the appropriate locations.
   
  
  1. 
  2. 120%
  3. 0.07
  4. 1
  5. 83%
  6. 
• CL 3-139. Label the dimensions and the area for each generic rectangle shown below.  Then write a mathematical sentence showing the multiplication of factors and the product.
  1. 
  2. 

• 3-130. Find the greatest common factor and the least common multiple of each of the following sets of numbers.  Homework Help ✎
  1. 12 and 7
  2. 3, 15 and 9
  3. 20 and 30
• 3-131. The following representations have been drawn to represent portions of a 100% block.  Write each of the portions in at least two different forms.  Homework Help ✎
  1. 
  2. 
• 3-132. This problem is a checkpoint for addition and subtraction of fractions.  It will be referred to as Checkpoint 3.
• Compute each sum or difference.  Simplify if possible.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 

• 3-128. Evaluate each absolute value expression below.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 3-129. Name the endpoints of the segment shown on the graph below.  What is the length of the segment?  Write an absolute value expression to show how to calculate the length of the segment.  Homework Help ✎

  

• 3-121. A triangular flower bed (space for planting flowers) needs a thin metal border all the way around it.  The sides are 7 feet, 6 feet, and 9 feet long.  Homework Help ✎
  1. How many feet of border should be purchased?  Make a sketch and show your work. 
  2. If borders cost $8.75 per yard (and only whole numbers of yards can be purchased), how much would the border cost? 
• Name__________________________________
• 3-122. One of the topics you will review in this course is reading graphs. Look at the graph below. This graph shows positive and negative values on both axes. It divides the plane into four parts, or quadrants. It is called a four-quadrant graph. The quadrants are numbered I, II, III, and IV in a counter-clockwise manner as shown.  Homework Help ✎
  1. The coordinates (the x- and y- values) for point A are (–4, 3). Explain how these numbers tell you the position of point A using the graph.
  2. Name the coordinates (x, y) for points B and C.
  3. If Deepak moved from point A 8 units to the right and 10 units down, at what point on the graph would he end up?  Which quadrant is the new point in?|

• 3-118. Simplify the following expressions.  Show your work.  Homework Help ✎
  1. 8.23 + 10.9
  2. −6 − 9
  3. 8 − 3 − 4
  4. 0−3
  5. 15−20
  6. −9 + 14
  7. 
  8. 5 −9
• 3-119. Solve the number puzzles below. 3-119 HW eTool Homework Help ✎
  1. If I add 9 to my number, I get 6.  What is my number? 
  2. If I start at –5 on a number line and end up at –8, what direction did I move?  How many units did I move? 
  3. If I moved up 8 and then moved down 8, what can you tell me about my ending position?

• 3-109. The yearbook staff at Jefferson Middle School has been busy taking pictures.  Of the 574 pictures the staff members have taken, only 246 of the pictures will make it into the yearbook.  Approximately what portion of the pictures that were taken will make it into the yearbook?  Use a complete portions web to show your answer.  Show your work.  Homework Help ✎
• 3-110.  Carefully copy the graph and point A on a piece of graph paper. 3-110 HW eTool (Desmos). Homework Help ✎
  1. Plot the points listed below.  Then connect them in the order given and connect point Dto point A.
     A (2, 3), B (3, 7), C (7, 7) , D (8, 3) 
  2. What is the name of the shape that you drew?

• Name______________________
• 3-106. Find the missing value in each number sentence.  Homework Help ✎
  1. 4 −3.5 + 3.5 − 1 = _____
  2. −2 + 4 + 4 = _____
  3. 
• 3-107. Find common denominators and calculate each of the following sums.  Homework Help ✎
  1. 
  2. 
  3. 3-108. In parts (a) and (b) below, copy the vertical number lines and use them to show the solution to the problems.  Homework Help ✎
     1. 5 − 2
     2. 2 + 1
     3. Show how to find the answer to  −3 + 4 − 1 on a number line.
     4. Rachel said that −4 −3 ends up being positive because two negatives always give a positive.  Draw the problem on a number line, and then explain whether you agree or disagree with Rachel.   

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• Name____________________
• 3-94. Lucas’ frog is sitting at −2 on the number line. 3-94 HW eTool (CPM). Homework Help ✎
  1. His frog hops 4 units to the right, 6 units to the left, and then 8 more units to the right.  Write an expression (sum) to represent his frog’s movement. 
  2. Where does the frog land?
  3. What number is the opposite of where Lucas’ frog landed? 
• 3-95. Draw and label a set of axes on your graph paper. Plot and label the following points: (1, 3), (4, 2), (0, 5), and (5, 1).  Homework Help ✎

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• 3-84. Walter is mixing cement for his new patio.  He knows he needs to use a water-to-cement ratio of 20 to 30.  What percent of his total mixture is water?  Homework Help ✎
• 3-85. David wants to find  and is wondering if using decimals can help him make sense of adding fractions.  Homework Help ✎
  1. How could  be written using decimals?  What is the sum as a decimal?
  2. How could your answer from part (a) be written as a fraction?
  3. Rewrite  as a fraction that could be added easily to .

• 3-76. Preston picked five playing cards and got a 2, 3, 6, 5, and 1.  Homework Help ✎
  1. What two-digit and three-digit numbers could he create that would have the greatest sum?  Is there more than one possibility?  What is that sum? 
  2. What two-digit and three-digit numbers could he create that would have the smallest sum?  Is there more than one possibility?  What is that sum? 
• 3-77. Use the Distributive Property to rewrite each product below. Simplify your answer.  Homework Help ✎
  1. 28 · 63
  2. 17(59)
  3. 458(15)

• 3-73. In this lesson, you looked for ways to convert between equivalent forms of fractions, decimals, and percents.  Using the portions web, write the other forms of the number for each of the given portions below.  Show your work so that a team member could understand your process.  Homework Help ✎
  1. Write  as a decimal, as a percent, and with words/picture. 
  2. Write 0.30 as a fraction, as a percent, and with words/picture.   
  3. Write 85% as a fraction, as a decimal, and with words/picture. 
  4. Write one and twenty-three hundredths as a percent, as a decimal, and as a fraction. 
• 3-74. Maya and Logan each made up a “Guess my Decimal”game just for you. 
  Use their clues to determine the number.  Homework Help ✎
  1. Maya gives you this clue: “The decimal I am thinking of is 3 tenths greater than 80%.  What is my decimal?”  Show your work. 
  2. Logan continues the game with this clue: “My decimal is 3 hundredths less than 3 tenths.”  Use pictures and/or words to show your thinking. 
• 3-75. Amanda and Jimmy have jobs as dog walkers.  Examine the graph at right and answer the following questions.  Homework Help ✎
• 1. Who has more hours of dog walking?  How do you know?
  2. Who has earned the least amount of money?  How do you know?
  3. Are both students earning the same amount of money per hour?  Show your work to justify your answer.

• 3-65. Estimate the amount of gas left in this car’s gas tank with a fraction.  Homework Help ✎

   

• 3-66. Randall and Stephano work in a restaurant.  Randall earned $27.50 one day, $25.00 the next day, and $32.50 on the third day.  Stephano works fewer hours, but more days.  He earned $17.50 one day, $22.50 the next day, $12.50 the third day, $15.00 the fourth day, and $17.00 the fifth day.  Who earned the most money?  How much more?  Homework Help ✎
   
   

• 3-62. Add or subtract the following fractions.  Homework Help ✎
  1. 
  2. 
• 3-63. Copy the incomplete axes and fill in the missing numbers to make the scaling consistent.  Homework Help ✎
  1. 
  2. 
• 3-64. For each of the representations below, write the portion in each of the forms listed.  Remember that a hundred block now represents 100%.  Homework Help ✎
  • Percent
  • Decimal
  • Fraction
  • Description in words
  1. 
  2. 
  3. 
  4. 

• 3-48. Which of the following fractions could you add together easily?  Explain.  Homework Help ✎

  , ,  ,  ,  ,  ,  ,  ,  ,  ,  

• 3-49. Alex earns $7.75 a day by walking dogs for his neighbors. If he walks dogs for 12 days, how much money will he make? Show how you got your answer.  Homework Help ✎

• 3-50. Use the Lesson 3.1.3B Resource Page to shade in the amounts represented by the following descriptions, and then write them in the stated form. 3-50 HW eTool (CPM). Homework Help ✎
  1. Shade 7 hundredths, and write the portion as a percent.
  2. Shade 7 tenths, and write the portion as a fraction.
  3. Shade 28%, and write the portion as a fraction.
  4. Shade 31.5%, and write the portion as a decimal

• 3-45. An article in the local paper states that 30% of the students at Oak Grove Middle School earned a place on the Silver Honor Roll. If there are 920 students at Oak Grove, how many are on the Silver Honor Roll?  Use a percent ruler to help you decide.  Show all of your work.  Homework Help ✎
• 3-46. Given the following descriptions of portions, write each portion as a percent.  Use a 100% block to help you visualize the portions. 3-46 HW eTool (CPM). Homework Help ✎
  1. 3 tenths and 6 hundredths
  2. 8 hundredths
  3. 17 hundredths
  4. 11 tenths
• 3-47. Maurice's gas tank can hold 60 liters of gas. On your paper, copy and label the percent ruler below.  Then use it to find how many liters are in the tank when it is:  Homework Help ✎

  

  1. 50% full
  2.  full
  3.  full

• 3-33. Maribel is taking advantage of the sale at Cassie’s Cashew Shoppe.  She wants to figure out how much she will save on a purchase of $34.  Maribel’s percent ruler is shown below.  Copy the ruler on your paper and help her figure out what 20% of $34 is.  Homework Help ✎
• 
• 3-34. As you have discovered, any fraction can be rewritten in many equivalent ways.  When choosing a denominator that will work to add two fractions, there is no single correct choice.  Often, people find it convenient to use the smallest whole number that all denominators divide into evenly.  This number is called the lowest common denominator. 
• For example, when adding the fractions , you could choose to rewrite each fraction with 48 or 96 in the denominator.  However, the numbers will stay smaller if you choose to rewrite each fraction with a denominator of 24, since 24 is the lowest number that 3, 6, and 8 divide into evenly.  (Dividing into a number evenly means that there is no remainder.)
• For each of the following sums, first rewrite each fraction using the lowest common denominator.  Then add.  Read the Math Notes box in this lesson for additional help.  Homework Help ✎
  1. 
  2. 
• 3-35. Find the following sums or differences.  Homework Help ✎
  1. 12.35 + 1.08
  2. 8.02 − 0. 64
  3. 568.38 − 134.21
  4. 0.29 + 0.92

• 3-31. For each of the following portions, draw a diagram of the mixture in the jar.  Then shade a layer that would correspond to this portion of raisins.  Finally, order these portions from least to greatest.  Homework Help ✎
  1. 40%
  2. 
  3. 25%
  4. 
• 3-32. At Cassie’s Cashew Shoppe, a sign says, “Today only: 20% off anything.”  Maribel realizes that she has a coupon for  off the price of anything in the shop.  Which discount should she use, the 20%-off deal or the  -off coupon?  Does it matter?  Explain.  Homework Help ✎

• 3-15. Find the measure indicated in each question below.  Homework Help ✎

• a.	Find the perimeter of the triangle.	b.	Find the area of the large rectangle.
  c.	Find the area and perimeter of the rectangle at right.

• 3-16. Write down at least three different pairs of numbers that add together to get 1.  Homework Help ✎
•  
• 3-17. Use the Distributive Property to rewrite each of the expressions below.  Then simplify.  Homework Help ✎
  1. 12(309)
  2. 8(100 + 10 + 8)
• 3-18. If five notebooks cost $5.25, how much would three notebooks cost?  Homework Help ✎

• 3-12. Copy and complete each of the following Giant One problems. Homework Help ✎
  1. 
  2. 
  3. 
• 3-13. Rachel says that when she ran 115 yards, she went farther than Beth, who only ran 327 feet.  Is Rachel correct?  Explain how you know.  Remember that 1 yard = 3 feet.  Homework Help ✎
• 3-14. Look at the two histograms below.  They give you information about the heights of players on two basketball teams, the Tigers and the Panthers.  Use the histograms to answer the following questions.  Homework Help ✎
• 
  1. Which team has taller players?  Which has shorter players?  Explain your thinking. 
  2. Which team has heights that vary more?  Explain your thinking. 
  3. Which team has more players that are about the same height?

• CL 2-96. Place the digits 4, 7, 5, 6, and 8 in the boxes below to make the largest and smallest sums possible.
• 
• CL 2-97. Draw a Venn diagram to represent the following situation.  Then use your diagram to answer the questions below.
•  
• Out of 50 students, 15 are taking English and 30 are taking chemistry.  Of those students taking English and chemistry, 6 are in both classes.
  1. How many students are taking chemistry and not English?
  2. How many students are taking English and not chemistry?
  3. How many students are taking neither of the classes?

• 2-88. The following number lines are missing some numbers.  Sketch each one on your paper and use the information provided to complete the number lines.  Homework Help ✎
  1. 
  2. 
  3. 
  4. 
• 2-89. For each of the following problems, complete the fraction on the right so that the fractions are equal. Be sure to show your work clearly. Homework Help ✎
  1. 
  2. 
  3. 
• 2-90. This problem is a checkpoint for addition and subtraction of decimals.  It will be referred to as Checkpoint 2.
• Add or subtract the following decimals.  Homework Help ✎
• 1. 2.95 + 18.3 + 11
  2. 9.2 − 0.375
  3. 0.275 + 27.5
  4. 90 − 0.903

• 2-86. Look at the generic rectangle at right.  Homework Help ✎
  1. What two numbers are being multiplied using this rectangle?  How can you tell? 
  2. Write the product as a sum of the areas and find the answer.  
  3. Use the Distributive Property to write an equation showing that the product is equal to an expression with parentheses, multiplication, and addition. 
• 2-87. In Section 2.1, you learned how to create dot plots, bar graphs, histograms, and stem-and-leaf plots.  Which of these representations would best display the data given below?  Use that representation to display the data.  Homework Help ✎

• Boot sizes of the Math Marching Team:

• 10, 8, 12, 10, 10, 9, 10, 11, 12, 8, 8, 9, 10, 11,
• 10, 9, 11, 11, 12, 11, 10, 11, 8, 10, 12, 8

• 2-77. Figure out whether each of the following pairs of fractions is a pair of equivalent fractions.  Be sure to show all of your work or explain your thinking clearly.  Homework Help ✎
  1. and
  2. and
  3. and
• 2-78. Misty and Yesenia have a group of Base Ten Blocks.  Misty has six more blocks than Yesenia.  Yesenia’s blocks represent 17.  Together they have 22 blocks, and the total numbers of blocks represent 85.  What blocks could each girl have?  What is the value?  Homework Help ✎
• 2-79. COMPARING WAYS TO REPRESENT DATA.
• Use the golf-tournament data below to complete parts (a) through (e). Homework Help ✎
• Ages of golfers participating in a golf tournament:
• 44, 48, 40, 25, 28, 37, 29, 34, 45, 51, 43, 35, 38, 57, 50, 35, 47, 30, 63, 43, 44, 60, 46, 43, 33, 45, 42, 34, 32
  1. Use the data to create a dot plot. 
  2. Why is a dot plot not the best choice for graphing this data?   
  3. Create a stem-and-leaf plot for the data.   
  4. Use the stem-and-leaf plot to create a histogram for the data. 
  5. What range of ages do most golfers fall between?  Do you see any ages that are much larger or smaller than other ages?   

• 2-75. Solve each generic-rectangle puzzle.  For each part, write a multiplication sentence, as you did in problem 2-72. Homework Help ✎
  1. 
  2. 
• 2-76. James is painting his 10-by-8-foot bedroom wall that contains a 2-by-3-foot window.  Homework Help ✎
  1. Draw a diagram of his wall and the window. 
  2. How many square feet of wall does he need to paint?  

• 2-67. Jenny has been saving her babysitting money for a class field trip to Washington, D.C.  She wants to save $200.00 over three months.  She saved $53.00 the first month and $67.00 the second month.  Homework Help ✎
  1. Estimate (without calculating) the amount that Jenny needs to earn during the third month to meet her goal.  
  2. Now show how Jenny could calculate the amount of money she needs to earn. 
• 2-68. Find three fractions that are equivalent to three eighths.  Explain your method.  Homework Help ✎
• 2-69. Janelle and three of her friends bought four smoothies for a total of $3.  If she purchases smoothies on another day for herself and nine of her friends, how much money will she spend?  Homework Help ✎

• Please get parent conference slip signed, as well
• 2-55. Draw a generic rectangle to multiply 37 · 42. Homework Help ✎
  1. Write an equation using addition that shows the total area of the generic rectangle. 
  2. Multiply 37 · 42 by using the standard algorithm for multiplication.  That is, place one of the numbers under the other and use the procedure for multiplication that you were taught in previous courses.  Show your work.  Compare your result with your answer from part (a). 
  3. Which method of multiplication do you prefer?  Why? 
• 2-56. Riley is looking at the diagram at right in his math book.  Identify the factors and product represented by the rectangle.  Homework Help ✎

• 2-58. Ruth’s brother, Ethan, planted a garden for her as a surprise while she was away.  He planted seeds for vegetables in 50% of the garden.  He also planted flowers and herbs.  Homework Help ✎
•  
• The entire circle in the graph at right represents the area of Ruth’s garden.  If the lightly shaded portion represents flowers, estimate what percentage of the garden could be herbs.  Explain your estimate.
•  
• 2-59. Add or subtract.  Homework Help ✎
  1. 34.62 + 74.8
  2. 213.09 − 37.2
  3. 3.15 + 36.8 + 7

• 2-49. Given the data in the table below, copy and complete the histogram below to represent families of various sizes.  Remember that data falling on a tick mark (3, 6, 9, …) goes in the bin to the right of that mark.  What range do most families fall between?    Do you see any families that are much larger or much smaller than other families?  Homework Help ✎
• 
• 2-50. Consider the units in this list: inches, centimeters, feet, yards, meters, kilometers, and miles.  For each situation given below, list the units that would be most commonly used to measure the length or distance described.  Homework Help ✎
  1. Distance from Bellingham, WA, to Washington, DC. 
  2. Length of a small stuffed animal. 
  3. How far you walk during lunchtime at school.  
  4. Height of your classroom.  
  5. Length of your shortest fingernail.   

• 2-46. Find the area and perimeter of the figure at right.  All angles are right angles.  Show all of your work.  Homework Help ✎
• 
• 2-47. Draw and label two different rectangles, each with perimeters of 20 units.  Do the rectangles have the same area?  Explain your thinking. 2-47 HW eTool (CPM). Homework Help ✎
• 2-48. Think about the Base Ten blocks you used during the lesson.  Using 1 hundred block, 3 ten blocks, and 6 one blocks, create a shape with the largest possible perimeter.  Remember that the blocks need to be touching along a side, not connected at a corner.  Sketch your solution and show all of your work. 2-48 HW eTool (CPM). Homework Help ✎

• 2-36. Use the numbers 2, 3, and 4 and the operations (mathematical processes) of addition, subtraction, multiplication, or division to create three different numerical expressions with three different values.  One of the expressions should have a value of 14. Homework Help ✎
• 2-37. What is the best way to display the data below?  Why?  Display the data using the method you chose.  Homework Help ✎

                    Daily high temperature for Honolulu, Hawaii in December of 2009: 

  83, 83, 81, 82, 80, 83, 81, 82, 79, 83, 84, 82, 81, 81,
  80, 81, 84, 80, 80, 81, 81, 82, 80, 79, 78, 80, 84, 82, 82, 81, 83

• 2-38. Find the missing number that makes each of the following number sentences true.  Homework Help ✎
  1. 15 · ? = 90
  2.  = 18
  3. 6 · ? = 96
  4.  = 18

• -34. Assume that the shaded tiles in the large square at right each have an area of one square foot.  Use this information to answer the following questions. Homework Help ✎
  1. What is the total area of the shaded squares?
  2. What is the total area of the un-shaded squares?
  3. Find the total number of square feet of area in the figure in two different ways.
• 2-35. Hector measured the area of his desktop by covering it with quarters (25¢ coins).  Can he find the area using these circular units of measure exactly, or will he have to estimate?  Explain your answer.  Homework Help ✎

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• 2-24. Lakisha made a giant triangle using two pattern blocks: one green triangle and one red trapezoid. Homework Help ✎
  1. What is the area of the entire shape if the green triangle has an area of 1 square cm?
  2. What is the area of the entire shape if the red trapezoid has an area of 1 square inch?
• 2-25. Find the area of the shape below that was cut from graph paper.  Use square centimeters as your units.  The problem has been started for you.  Homework Help ✎
• 

• 2-17. Maria was putting together party favors (small bags of treats for each person) for her niece’s birthday party.  In each bag, she put three small chocolate candies, and four hard candies.  If Maria had 12 bags, how many candies did she use in all?  How could you represent this with a number expression?  Homework Help ✎
• 2-18. How many different rectangles can you draw with an area (number of “tiles”) of 28?  What is the perimeter (number of “toothpicks”) of each one?  Show your work. 2-18 HW eTool(CPM). Homework Help ✎
• 2-19. Ms. Katz paid $50 for a used bicycle and then sold it to her neighbor for $60.  She decided to buy it back, but she had to pay $70 for it.  If she then sold it again for $80, how much money did she make or lose overall?  Show your solution in enough detail so a teammate could easily understand how you found your answer. Homework Help ✎

• 2-15. Copy the sequences and fill in the missing numbers. Explain the pattern in words.  Homework Help ✎
  1. 5, 14, 23, 32, 41, ____, ____, ____
  2. 3, 6, 12, 24, 48, ____, ____, ____
• 2-16. Lyn asked some of her classmates how many people are normally at home for dinner. 

  She recorded her results in the histogram shown at right.

    Homework Help ✎
  1. How many classmates were surveyed?
  2. How many classmates have eight or nine people at home for dinner?
  3. Can you tell which is the most common number of people at home for dinner? Why or why not?

• 2-8. On a hot summer day, Leo and Stefano decided to buy some refreshments at the Fruit and Smoothies store.  Fruit kabobs cost $1.75 each and smoothies cost $2.50 each. Homework Help ✎
  1. Leo ordered two fruit kabobs and one smoothie.  How much did he spend?
  2. Stefano ordered three fruit kabobs and four smoothies.  How much did he spend?
  3. Arturo could not decide, but he had $9.00 he could spend on fruit kabobs and smoothies.  He knows he wants at least one of each.  What are some combinations he can afford?  (Show at least three possibilities.)
• 2-9. Lulu is playing “Toothpicks and Tiles” from Lesson 1.1.2.  She has arranged 10 tiles as shown below.  She wants to rearrange them so that the number of toothpicks remains the same.  Draw one possible arrangement of the tiles. 2-9 HW eTool (CPM) Homework Help ✎

• 
• 2-10. Add or subtract.  Remember to line up the decimal point. Homework Help ✎
  1. 53.199 − 27.61
  2. 155.96 + 56.232
  3. 83.617 − 36.518

• 2-6. For the problem below, display the data using a dot plot, bar graph, or Venn diagram.  Decide which type of data display is best and explain why.  Homework Help ✎

  Appliances sold at Housemart during the month of September:

  Washers: 35              Dryers: 21                 Ovens: 19

  Refrigerators: 27                              Dishwashers: 23

• 2-7. Elizabeth wants to challenge you to a “Toothpicks and Tiles” game.  Using exactly 6 tiles, solve her challenges below.  Justify your answers with pictures and labels. 2-7 HW eTool (CPM) Homework Help ✎
  1. Find a pattern where the number of toothpicks is more than double the number of tiles.
  2. Find a pattern where the number of toothpicks is 4 more than the number of tiles.

• 1-29. Use the histogram below to answer the following questions.  The histogram contains the amount of snowfall in Urbana, IL during winter from 1990 – 2009.  Homework Help ✎

  

  1. Which range of snowfall measurements occurred most often?  
  2. Were there any years with unusually high or low snowfall amounts?
  3. Half of the years had snowfall amounts above how many inches? 
• 1-30. Copy the number patterns below and write the next four numbers in the pattern.  Assume the pattern continues as shown.  Describe the pattern in words.  Homework Help ✎
  1. 2, 7, 12, 17, 22, ___, ___, ___, ___
  2. 1, 4, 9, 16, 25, ___, ___, ___, ___
  3. 1, 1, 2, 3, 5, 8, ___, ___, ___, ___

• L 1-99. Find the perimeter and area of each figure below.
  1. 
  2. 
  3. 
  4. Sketch at least one way to rearrange the tiles in part (a) so that the shape has a larger perimeter.
• CL 1-100. Write the missing number that makes each of the following number sentences true.
  1. 12 · ? = 180
  2. = 12
  3. 7 · ? = 98
  4.  = 11

• 1-91. Study the dot pattern below. 1-91 HW eTool (CPM) Homework Help ✎

  

  1. Sketch the 4th and 5th figures.
  2. How many dots will the 50th figure have?
• 1-92. Write the prime factorization of each of the numbers below. Homework Help ✎
  1. 24
  2. 52
  3. 105
• 1-93. Throughout this book, key problems have been selected as “checkpoints.”  Each checkpoint problem is marked with an icon like the one at left.  These checkpoint problems are provided so that you can check to be sure you are building skills at the expected level.  When you have trouble with checkpoint problems, refer to the review materials and practice problems that are available in the “Checkpoint Materials”. 
• This problem is a checkpoint for using place value to round and compare decimal numbers.  It will be referred to as Checkpoint 1.
• Use your knowledge of place value to round the decimals to the specified place in parts (a) through (c).  Place the correct inequality sign (<  or  >) in parts (d) through (f).  Homework Help ✎
  1. 17.1936  (hundredths)
  2. 0.2302  (thousandths)
  3. 8.256  (tenths)
  4. 47.2__47.197
  5. 1.0032__1.00032
  6. 0.0089__0.03
• Check your answers by referring to the Checkpoint 1 materials.
• Ideally, at this point you are comfortable working with these types of problems and can solve them correctly.  If you feel that you need more confidence when solving these types of problems, then review the Checkpoint 1 materials and try the practice problems provided.  From this point on, you will be expected to do problems like these correctly and with confidence.

• 1-88. Copy and complete the table of multiples below (count by 2’s and count by 3’s).  Homework Help ✎
• 
  1. Write down all the numbers that appear in both rows.  Describe any pattern(s) that you notice.
  2. What is the smallest number that appears in both rows?  This number is said to be the least common multiple of 2 and 3.
  3. Find three more common multiples of 2 and 3.
  4. Can you find the largest number that is a common multiople of both 2 and 3? If so, what is it? If not, explain why not.
• 1-89. How many “hands” long is your bed?   Homework Help ✎
  1. Using your hands as units of measure, first estimate (without actually counting) the number of “hands” that you think will fit across the length of your bed.
  2. Now measure and record the length of your bed using your hands.
• 1-90. Write a whole number in the box in the fraction  that makes it:  Homework Help ✎
  1. Equal to 1.
  2. Greater than 1.
  3. Less than 1.
  4. Equal to 0.
  5. Greater than 100.

• 1-85. Use your multiplication table to figure out the missing number in each of the following number sentences.  Each missing number is represented by n. 1-85 HW eTool (CPM) Homework Help ✎
  1. 15n = 225
  2. 
  3. 11n = 143
  4. 
• 1-86. Jack has four tiles and wants to find out how many different shapes he can make with them. 1-86 HW eTool (CPM) Homework Help ✎
  1. Sketch all of the arrangements that Jack could make with his tiles so that all of the tiles touch at least one other tile completely along a side.  Assume that no tiles can overlap.  How many arrangements are there?
  2. For each diagram that you drew in part (a), find the area (the “tiles”) and the perimeter (the “toothpicks”).  What do you notice?
• 1-87. Write four different fractions that are equal to 1.  Use your calculator to check that you are correct.  Homework Help ✎

• 1-70. How many pennies are represented by each expression below?  Homework Help ✎
  1. 3 + (4 · 5)
  2. (4 · 3) + 7
  3. (2 · 3) + 5 + (4 · 2)
• 1-71. Using whole numbers, fractions, and decimals, write at least eight addition equations that have a sum of 10.  Write more if you can.  Homework Help ✎
• 1-72. Use your knowledge of place value to place the correct inequality sign (<, > ) between each pair of numbers.  Homework Help ✎
  1. 5.207 ___ 5.27
  2. 3.006 ___ 3.06
  3. 2.408 ___ 2.40
  4. Round each number in part (b) to the nearest tenth.

• 1-68. Harry had a pile of 48 pennies.  He organized them into a rectangular array with exactly four rows with 12 pennies in each row.  Homework Help ✎
• Draw diagrams to represent at least two other rectangular arrays he could use.  Do you think there are more?  Explain your thinking.
• 1-69. For each number of pennies below, arrange them first into a complete rectangular array and then into a different rectangular array that has a remainder of one (so there is one extra penny).  Write an expression for each arrangement. Homework Help ✎
  1. 10 pennies
  2. 15 pennies
  3. 25 pennies

• 1-59. Connie is helping her mother gather together the loose change (coins) in their house.  They have collected a large jar full of quarters and dimes.  Connie wants to arrange the coins on the table to make it easy to know how much money they have. Homework Help ✎
  1. On your paper, draw a diagram to show Connie how she can arrange her quarters and dimes to make her money easy to count.
  2. Draw another arrangement that would also be easy to count.
  3. Which of your arrangements do you think is easiest to count?  Explain why.
• 1-60. Use your knowledge of place value to place the correct inequality sign (<  or  >) between each pair of numbers.   Homework Help ✎
  1. 16.5 ___ 16.52
  2. 4.110 ___ 4.10
  3. 5.963 ___ 5.9
  4. Write the numbers given in part (b) in words.  
• 1-61. Aria and 19 of her friends plan to go to a baseball game.  They all want to sit together.  Aria wants to order the seats in the shape of a rectangle, but she cannot decide on the best arrangement.  She starts by considering one row of 20 seats.   
• Draw a diagram showing Aria’s idea for a seat arrangement.  Then draw all of the other possible rectangular arrangements for 20 seats.  Label each arrangement with its number of rows and the number of seats in each row.  Are all arrangements practical?  Explain.  Homework Help ✎

• 1-57. Which is greater: three sets of (5 − 2) or two sets of (2 + 3)?  Draw diagrams to support your conclusion.  Homework Help ✎
• 1-58. The diagrams at right represent piles of pennies.  Homework Help ✎
  1. Which pile has more pennies?  Explain your reasoning.
  2. Write two different number expressions to represent the number of pennies in each pile.
  3. Write a number comparison (using  > ,  < , or  = ) to show if the number of pennies in one pile is greater than the other or if they are the same.

• 1-48. Matthew’s mother asked him to go to the store for her.  To get to the store, he walked seven city blocks.  He caught the bus and rode 13 blocks.  He got off and walked one and a half blocks to the store.  He purchased the items his mother wanted and returned home the same way.  How many total blocks did he travel?  Homework Help ✎
• 1-49. Which numbers make these division problems correct?  Replace each box and triangle with a single-digit number.  Homework Help ✎
  1. 
  2. 
• 1-50. A line segment is a piece of a straight line.  On your paper, draw two line segments that are the same length and each about as long as a pen.  Homework Help ✎
  1. Draw marks on the first line segment to show how you can divide it into eight equal lengths.
  2. Draw marks on the second line segment to show how you can divide it into five equal lengths.
  3. Was one of these tasks easier than the other?  Which one?  Why?

• 1-46. Match each of the following descriptions of pennies with its possible numeric expression.  Then calculate the value of each expression.  Homework Help ✎

  1.	8(12) + 7	2.   6(20) + 5	3.   11(10) + 7	4.   9(12) + 5
  a.	11 piles of 10 pennies with 7 leftover pennies
  b.	A rectangular array of pennies that is 9 pennies long and 12 pennies wide with 5 leftover pennies
  c.	8 stacks of 12 pennies with 7 leftover pennies
  d.	A rectangular array of pennies that is 6 pennies wide and 20 pennies long with 5 leftover pennies

• 1-47. Write one whole number or one fraction in each blank to make each statement true.  Homework Help ✎
  1. One hundred pennies equals ____ dollar(s).
  2. Two hundred pennies equals ____ dollar(s).
  3. Fifty pennies equals ____ dollar(s).
  4. Ten pennies equals ____ dollar(s).
  5. One penny equals ____ dollar(s).

• 1-39. Find a pattern in each number sequence below.  Then use your pattern to generate the next five numbers in the sequence.  Explain the pattern.  Homework Help ✎
  1. 2, 5, 3, 6, 4, ____,  ____,  ____,  ____,  ____
  2. 100, 99, 97, 94, 90, ____,  ____,  ____,  ____,  ____
• 1-40. Round each number to the specified place. Homework Help ✎
  1. 33.54296  (ten thousandth)
  2. 307,407  (thousand)
  3. 285.39154  (hundredth)
  4. 6811.09  (ten)

• 1-36.  Bob and Mark decided to try the peanut and raisin investigation at home.  Bob started with 10 peanuts on his tray, and Mark started with 10 raisins on his tray, as shown in the diagram at right. Homework Help ✎
• 1. Mark gave 3 raisins to Bob, as shown in the diagram below.  How does the number of peanuts and raisins on Bob’s tray compare to the number of peanuts and raisins on Mark’s tray? 
  2. Copy the diagram below.  Circle a group of any 3 peanuts and raisins on Bob’s tray.  Besure to circle some of each for a total of 3.  Then give them to Mark.  Does Bob now have more of Mark’s raisins, or does Mark have more of Bob’s peanuts? 
  3. Now start from the beginning and repeat parts (a) and (b) assuming that 8 (instead of 3) snack items are handed from one student to the other.  Explain your results.
• 1-37. Eli walked 12 feet down the hall of his house to get to the door.  He continued in a straight line out the door and across the yard to the mailbox, a distance of 32 feet.  He came straight back across the yard 14 feet and stopped to pet his dog.  Homework Help ✎
  1. Draw a diagram of Eli’s walking pattern.
  2. How far has he walked?
  3. How far from the house is he now?

• 1-30. Copy the number patterns below and write the next four numbers in the pattern.  Assume the pattern continues as shown.  Describe the pattern in words.  Homework Help ✎
  1. 2, 7, 12, 17, 22, ___, ___, ___, ___
  2. 1, 4, 9, 16, 25, ___, ___, ___, ___
  3. 1, 1, 2, 3, 5, 8, ___, ___, ___, ___
• 1-31. Round each number to the specified place.  Read the Math Notes box in this lesson for a reminder of rounding to a given place value.   Homework Help ✎
  1. 5,294.6
     (hundred)
  2. 45,469.23
     (thousand)
  3. 7526.442
     (hundredth)
  4. 492.3069
     (thousandth)
• 1-32. The graph below shows how far Ben is from home during a typical school day.  Use the graph to answer the questions.  Write your answers in complete sentences.  Homework Help ✎

  

  1. What was Ben doing between 7:00 a.m. and 8:00 a.m.?
  2. What do you think Ben was doing between 9 a.m. and 2:30 p.m.?
  3. What time did Ben leave to return to his starting point?

1. Create a question that could be answered by using all of the data.
2. Create a question that could be answered using just some of the data.
3. How could you organize the data to answer your questions?  Write your answer using complete sentences.

• 1-21.  Find the perimeter of each figure below.  The markings on part (b) mean that the lines are parallel.  The markings on part (e) show that all sides are the same length.  As you find each perimeter, be sure to show your work.  Homework Help ✎

  a.		b.
  c.		d.
  e.		f.

• 1-22. For each shape drawn in problem 1-21, choose one of the labels below that best describes that shape.  Be as specific as you can.  Look in the glossary of this book for more information if you do not remember what one of the words describes.  Homework Help ✎

• right triangle	scalene triangle	obtuse triangle
  isosceles triangle	rhombus	rectangle
  square	trapezoid	hexagon

• 1-23. Use the bar graph below to answer the following questions.  Homework Help ✎

  

  1. How many people attended the fair on Tuesday?
  2. Which day had the largest attendance?
  3. What was the total attendance for the week?

• 3. For each pattern, explain how you made your prediction for the 100th figure.
• 1-20. The value of a decimal becomes clearer when the place value is spoken or written as the number it names.  For example, 0.1 makes more sense if it is read as “one tenth” rather than “zero point one.”  Homework Help ✎
  1. Write the following numbers in words so that the place value can be identified.  

     0.4               1.3               0.56               2.008

  2. Now reverse your thinking.  Write the decimals that go with the following words.  

     thirty-five hundredths                three and two tenths                six hundredths

• 1-10. Janelle wants to challenge you to a “Toothpick and Tiles” game (described in problem 1-8).  Using exactly four tiles, solve her challenges below.  Justify your answers with pictures and labels. 1-10 HW eTool (CPM) Homework Help ✎
  1. Create a tile pattern where the number of toothpicks is exactly double the number of tiles.
  2. Create a tile pattern where the number of toothpicks is more than double the number of tiles.
• 1-11. In this lesson, you looked at the number of tiles and number of toothpicks used to form shapes made of square tiles as you played the “Toothpick and Tiles” game.  The math words that also describe the number of tiles and toothpicks are areaand perimeter.  Read the Math Notes box for this lesson to review how area and perimeter are related to tiles and toothpicks, then answer the questions below. 1-11c HW eTool (CPM) Homework Help ✎
  1. Find the area and perimeter of the figure at right.
  2. Find the area and perimeter of the rectangle at right.
  3. Now design your own shape with 5 square tiles.
     Record the perimeter and the area.