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LESSON 71 • Rectangular Prisms Power Up facts jump start Power Up 71 Count up by 25s from 0 to 250. Count up by 7s from 0 to 77. It is 5:05 in the morning. Draw hands on your clock to show the time in 15 minutes. Write the time in digital form. 5:20 a.m. The temperature in a restaurant kitchen was 28°C. It was 9 degrees cooler in the dining room. Mark your thermometer to show the temperature in the dining room. 19°C mental math a. Number Sense: 35 + 9 44 b. Number Sense: 5 + 4 + 4 + 5 18 c. Time: 45 minutes + 15 minutes 60 min d. Fractions: What fraction of the marbles are white? 36 or 12 problem solving Quinh plans to watch his favorite television show tonight. He told his mother that the show will begin in 14 minutes and will be over in 74 minutes. How long is Quinh’s favorite television show? 60 min or 1 hr New Concept Boxes come in different sizes and can be made of different materials. However, most boxes are alike in many ways. In this lesson we will study the shape of rectangular boxes. The shape of a rectangular box is called a rectangular prism or rectangular solid. Lesson 71 385 Rectangular prisms have flat sides shaped like rectangles. These flat surfaces are called faces. Two faces meet at an edge. Three faces meet at a point. These corner points are called vertices. Each corner point is a vertex. ,iVÌ>}Õ>ÀÊ*ÀÃ `}i >Vi 6iÀÌiÝ Some of the edges of a rectangular prism are parallel and some edges are perpendicular. PARALLELEDGES PERPENDICULAREDGES If we draw a “transparent” rectangular prism, we can see all the faces, edges, and vertices. First, we draw two overlapping rectangles that are congruent. Then we connect the four vertices of one rectangle to the matching vertices of the other rectangle. Represent Practice See student work. drawing a rectangular prism. Example 1 How many faces does a box have? Place a box in front of you. See that it has a front and a back, a top and a bottom, and a left side and a right side. A box has six faces. 386 Saxon Math Intermediate 3 Example 2 Compare these two boxes. Describe how they are alike and how they are different. Both boxes are rectangular prisms. They each have 6 faces, 12 edges, and 8 vertices. Both boxes have rectangular faces. The boxes are different because the faces of the box on the left are longer than they are wide. The faces of the box on the right are all squares. If every face of a rectangular prism is a square, then the figure is a cube. The box on the right in example 2 is a cube. All the edges of a cube are the same length. Lesson Practice a. Draw a picture of a transparent box. ÕLi a. sample: b. How many vertices does a box have? 8 vertices c. How many edges does a box have? 12 edges d. Describe a cube. sample: A cube is a rectangular prism with square faces. Written Practice 1. (20, 28) Distributed and Integrated Molly counted the cars as the train rolled by the intersection. There were 103 cars, counting four engines and the caboose. How many cars were there not counting the engines and caboose? Write a number sentence. Then write your answer in a complete sentence. 103 − 4 = ; sample: There were 98 cars. Formulate 2. Hawkins bought two round-trip train tickets to Grant’s Pass for $9.75 each. What was the cost for both tickets? $19.50 (22) 3. Hawkins paid for the two tickets in problem 2 with a $20 bill. How much money should he get back? 50¢ (26) Lesson 71 387 4. Multiple Choice Which picture below shows the mixed number 145? D B A (46) C D 5. It is morning. The clock shows the time the train arrived in Chicago. Write the time in digital form. 10:23 a.m. (38) ££ £ä £Ó £ Ó 6. Are the rails of train tracks parallel or perpendicular? Î { n Ç (Inv. 4) parallel È x 3 7. The distance from the Upland Station to Burns Crossing is 1710 3 miles. Use words to name 1710 . seventeen and three tenths (46) 8. Find each product. a. 8 × 7 56 b. 4 × 7 28 c. 6 × 7 42 9. Find each product. a. 3 × 8 24 b. 4 × 8 32 c. 6 × 8 48 10. Find each product. (64) a. 9 × 4 36 b. 9 × 6 54 c. 9 × 8 72 (70) (70) 11. (71) Follow the directions in this lesson to draw a rectangular prism. Represent 12. A rectangular prism has how many faces? sample: 6 (71) 13. Use your inch ruler to find the length of the sides of the right triangle. a. side AB 34 in. (35, 69) 388 b. side BC 1 in. c. side CA 114 in. Saxon Math Intermediate 3 14. (68, 69) On your paper draw a triangle congruent to the triangle in problem 13. See student work. Represent 15. Multiple Choice Which polygon shows a line of symmetry? A B C D C (Inv. 7) 16. Martin has three quarters in his pocket. What fraction of a dollar is (29) three quarters? 34 17. If every face of a rectangular prism is a square, then (71) what is the name of the solid? cube 18. $32 + $68 + $124 $224 (24) 19. $206 − $78 $128 (26, 28) 20. Which number on the number line does point M represent? 128 (33) Early Finishers Real-World Connection : Mr. Tuff is making a rectangular table that is 4 feet long and 3 feet wide. Draw the table using the scale 12 inch = 1 foot. See student work. Lesson 71 389 LESSON 72 • Counting Cubes Power Up facts Power Up 72 jump start Count up by 11s from 0 to 110. Count up by 5s from 3 to 53. Write 10,550 as words. ten thousand, five hundred fifty Draw an isosceles triangle. Trace the sides that have equal length with a crayon. See student work. mental math a. Number Sense: Compare these numbers using the symbol <, >, or = 2,560 b. Money: $10.00 − $5.25 < 2,690 $4.75 c. Number Sense: 200 − 80 120 d. Time: It is afternoon. Marta went to the library at the time shown on the clock. She left 1 hour later. What time did she leave the library? 1:15 p.m. problem solving ££ £ä £Ó £ Ó Î { n Ç È x A sheet of paper is folded in half and then cut with scissors as shown. How many pieces of paper will there be after the cut? 3 pieces FOLD FOLD CUT 390 Saxon Math Intermediate 3 New Concept Andre uses a forklift to load boxes into a boxcar. Look at this stack of boxes. Can you count the number of boxes in the stack? We cannot see all the boxes in the stack. One way to find the total is to first find the number of boxes in each layer. Looking at the top of the stack, we see that there are nine boxes in the top layer. Looking at the side, we see that there are three layers of boxes. To find the total number of boxes, we can add: 9 + 9 + 9 = 27. We can also multiply: 3 × 9 = 27. If we add two more layers of boxes to the stack, how many boxes will we have altogether? Write a multiplication fact to show the answer. 5 × 9 = 45 Formulate Activity Counting Cubes Use cubes to build the stacks of cubes shown on Lesson Activity 27. Answer these questions for each stack of cubes. • How many cubes are in one layer? • How many layers are there? • How many cubes are there in all? Example 1 The picture shows a stack of cubes. a. How many cubes are in each layer? b. How many layers are there? c. How many cubes are there in all? a. There are 12 cubes in each layer. b. There are three layers. Lesson 72 391 c. Three layers with 12 cubes in each layer means there are 36 cubes in all. 12 + 12 + 12 = 36 or 3 × 12 = 36 Lesson Practice A box is filled with cubes, as shown at right. a. How many cubes are in each layer? 10 cubes b. How many layers are there? 3 layers c. How many cubes are there? Written Practice 30 cubes Distributed and Integrated 1. Sidney was on a 480-mile trip. When the train stopped in Omaha, Sidney had traveled 256 miles. How much farther did Sidney have to travel? 224 miles (20) 2. (18) It is 185 miles from Elam to Junction City. How far is it from Elam to Junction City and back? Write a number sentence. Formulate 185 + 185 = 370 miles 3. Livestock were hauled east from Denver, Colorado, to Chicago, Illinois. Use the scale and your ruler to find the approximate distance from Denver to Chicago. 1,000 mi (Inv. 4) $ENVER #HICAGO INCHäMILES 4. It is morning in Chicago. Write the time shown at right in digital form. 8:44 a.m. (38) ££ £ä £Ó £ Ó 5. Find each product. You may use the multiplication table. (59, 64) a. 7 × 2 14 b. 7 × 5 35 c. 7 × 9 63 6. Find each product. a. 8 × 4 32 b. 8 × 6 48 c. 8 × 7 56 7. Find each product. a. 6 × 3 18 b. 6 × 4 24 c. 6 × 7 42 (70) (70) 8. Find each product. (64) 392 Saxon Math Intermediate 3 Î { n Ç È x a. 9 × 3 9. (71) b. 9 × 7 27 c. 9 × 9 63 81 In Lesson 71 we learned how to draw a rectangular prism. Use the same process to draw a cube. (Hint: Begin by drawing two overlapping squares.) Represent 10. What is the shape of every face of a cube? square 11. A rectangular prism has how many edges? 12 9. sample: (71) (71) 12. Multiple Choice Which polygon does not show a line of symmetry? D B C D A (Inv. 7) 13. Harold put some small cubes together to make this larger cube. (72) How many small cubes make the larger cube? 8 cubes Use polygon ABCD and a ruler to answer problems 14–16. 14. a. How long is each side of the polygon? 1 in. (35, 58) b. What is the perimeter of the polygon? 15. What is the shape of the polygon? $ ! 4 in. parallelogram (66) 16. a. Which two angles are obtuse? # angles B and D " (65, 66) b. Which two angles are acute? 17. (55, 61) The numbers below make a pattern on a multiplication table. What are the next three numbers in this pattern? 36, 49, 64 Conclude 0, 1, 4, 9, 16, 25, 18. 36¢ + 74¢ + $2 (22, 24) angles A and C $3.10 , , , ... 19. $2.00 − $1.26 $0.74 (26, 28) 20. A driveway is 10 yd long and 7 yd wide. What is the area of the driveway? 70 sq. yd YD (62, 63) YD Lesson 72 393 LESSON 73 • Volume Power Up facts Power Up 73 jump start Count up by halves from 5 to 10. Count up by fourths from 2 to 4. Write two multiplication facts using the numbers 9, 7, and 63. 9 × 7 = 63; 7 × 9 = 63 Write these money amounts in order from least to greatest. $10.05, $10.50, $10.95, $11.50 $10.50 mental math $10.95 a. Number Sense: 38 + 8 $10.05 $11.50 46 b. Number Sense: 3000 + 100 + 50 + 8 3,158 c. Measurement: What is the perimeter of the triangle? 12 in. 4 in. d. Geometry: What type of triangle is shown in problem c? equilateral problem solving 4 in. 4 in. 2 Denair wrote an addition problem and then erased +1 some of the digits. Find the missing digits in the 27 problem. 12 + 15 27 New Concept Visit www. SaxonMath.com/ Int3Activities for a calculator activity. 394 One way to describe the size of a box is to say how much space there is inside the box. If we fill up the box with cubes we can describe the space inside the box in cubic units. Instead of saying how many raisins or apples or oranges a box can hold, we might say how many cubic inches it can hold. We might describe the size of a boxcar by saying how many cubic feet or cubic yards it can hold. Saxon Math Intermediate 3 The amount of space an object occupies is called its volume. A cube with edges one inch long has a volume of one cubic inch. 1 ft 1 ft 1 ft The activity below will help us 1 cubic foot understand volume. We will find the number of one-inch cubes needed to fill a box. Activity Volume Materials: Lesson Activity 28, empty boxes such as shoe boxes or tissue boxes, rulers, one-inch cubes For this activity, you will work together in small groups. Use your ruler to measure the length, width, and height of your box. width length height Record the length, width, and height in the table on Lesson Activity 28. Write the number of inches without a fraction. For example, if the length is 1134 inches, just write 11 inches. Dimensions of Box length in. width in. height in. Next, figure out how many cubes are needed to make one layer on the bottom of the box. If you do not have enough cubes to cover the bottom of the box, you might need to multiply to find the number. Lesson 73 395 Record the number of cubes that will fit on the bottom of the box. This is the bottom layer. Then figure out how many layers the box could hold without going over the top. Finally, figure out the total number of cubes the box will hold. This is the approximate volume of the box in cubic inches. Number of Cubes in Box number of cubes in bottom layer number of layers total number of cubes in box Write the approximate volume of the box as a number of cubic inches. Example Millie filled a small gift box with 1-inch cubes. The picture shows the top layer. There are two layers of cubes. How many cubes are in the box? What is the volume of the box in cubic inches? We see the top layer. There are 4 rows of cubes and 5 cubes in each row. 4 × 5 = 20 There are 20 cubes in the top layer. Since there are 2 layers, there are 40 cubes in the box. 20 + 20 = 40 The volume of the box is 40 cubic inches. Could you find the volume of Millie’s box in cubic feet? Why or why not? sample: no; 1 cubic foot is 1 foot wide and that Discuss would not fit in Millie’s box. Lesson Practice Jorge stores work supplies in 1-foot cubic boxes in his garage. a. What is the volume of each box? 1 cubic foot FT b. What is the volume of this stack of boxes? 24 cubic feet FT 396 Saxon Math Intermediate 3 FT Written Practice Distributed and Integrated 1. A round-trip ticket to Topeka cost $149. Cory has $98. How much more money does he need to buy a ticket? $51 (36) 2. (40) In a common year, June 30 is the 181st day of the year. How many days are there in the last six months of the year? 184 days Analyze 3. The railroad tie cutters worked 9 hours a day, 6 days a week. How many hours did the tie cutters work in a week? 54 hours (60, 64) 4. The ride to Pawtucket lasts an hour and a half. The train left the station at 8:45 a.m. The clock showed the time it arrived in Pawtucket. Write the time in digital form. 10:15 a.m. (39) 5. A pallet is loaded with boxes, as shown. a. How many boxes are in each layer? (72) 6 boxes b. How many layers are there? 4 layers c. How many boxes are there? 24 boxes 6. If each box in problem 5 is one cubic foot, then what is the volume of the stack of boxes? (73) 24 cubic feet 7. Find each product: a. 3 × 6 18 b. 3 × 8 24 c. 3 × 7 21 8. Find each product: a. 5 × 9 45 b. 9 × 2 18 c. 9 × 9 81 (70) (64) 9. Change this addition into multiplication and find the total: (54) 6 × $5 = $30 $5 + $5 + $5 + $5 + $5 + $5 10. (71) Represent Draw a cube. See student work. 11. A cube has how many vertices? 8 (71) Lesson 73 397 12. Which letter does not show a line of symmetry? (Inv. 7) 13. F # $ % & Connect (2) Find the next three numbers in this sequence: 14, 21, 28, 35, 14. Find each product: a. 6 × 7 42 (61, 70) , b. 7 × 7 , 42, 49, 56 , ... c. 8 × 7 49 56 Add or subtract, as shown: 15. $800 − $724 16. $6.49 + $5.52 $76 (28) $12.01 (22) 17. 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 81 (10, 54) 18. Use words to write each fraction or mixed number. a. 3 b. 31 c. 9 d. 23 4 2 7 10 (41, 46) a. three sevenths; b. three and one half; c. nine tenths; d. two and three fourths 19. A drawing of a box is shown at right. (71) a. What is the length of the box? 10 inches IN b. What is the width of the box? c. What is the height of the box? 6 inches IN 4 inches 20. What is the area of the top of the box in problem 19? 60 sq. in. (62) Early Finishers Real-World Connection : Mr. Crosby’s mini van weighs 2,746 pounds. When he drives his daughter and four of her friends to softball practice the car weighs 3,273 pounds with the weight of the passengers. How much do the passengers of the car weigh altogether? Write 2,746 and 3,273 using words. 527 pounds; two thousand seven hundred forty-six, three thousand two hundred seventy-three 398 Saxon Math Intermediate 3 IN LESSON 74 • Weight: Ounces, Pounds, and Tons Power Up facts jump start Power Up 74 Count down by 4s from 40 to 0. Count down by 8s from 80 to 0. Draw an array to show the multiplication fact 4 × 2. See student work. Label the number line by 25s from 0 to 250. 0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250 mental math a. Number Sense: 900 + 400 + 300 1600 b. Measurement: How many inches are in 5 feet? c. Money: $5.75 + $1.00 60 in. $6.75 d. Patterns: What number is missing in the pattern below? 16 1 problem solving 4 9 25 36 Jim, Ron, and George were standing in line. There were 38 people in front of them and 3 people behind them. Altogether, how many people were standing in line? 44 people New Concept The weight of an object is a measure of how heavy it is. Weight can be measured in ounces. A metal spoon weighs about one ounce. Weight can also be measured in pounds. A playground ball might weigh about a pound. A pound is equal to 16 ounces. Very heavy objects can be measured in tons. A small car weighs a ton. A ton is equal to 2,000 pounds. Lesson 74 399 -ETALSPOON 0LAYGROUNDBALL 3MALLAUTOMOBILE OUNCE POUND TON Units of Weight 1 pound = 16 ounces 1 ton = 2,000 pounds A 1-pound box of cereal costs the same as three 4-ounce boxes. Which is the better buy? Three 4-ounce boxes Verify is less than one pound. So the one pound box of cereal is the better buy. Example 1 Which of these objects would weigh about a pound? &ORK 3HOE A B C 6AN Choice B, a shoe, weighs about a pound. A fork weighs about an ounce. A small van might weigh two tons. Example 2 If a large car weighs about two tons, then it weighs about how many pounds? A ton is 2,000 pounds. We can add to find the number of pounds in two tons. 2,000 pounds + 2,000 pounds = 4,000 pounds A car that weighs about two tons weighs about 4,000 pounds. 400 Saxon Math Intermediate 3 Activity Weighing Objects Use a scale to weigh various objects in the classroom. Make a table like the one below to record the name of each object and its weight. Can you find an object that weighs one ounce? Can you find an object that weighs one pound? Weights of Objects Name of Object Lesson Practice Weight a. Would you describe the weight of a large dog in ounces, pounds, or tons? pounds b. Multiple Choice Which object weighs about an ounce? A A ÀÌ `>ÞÊV>À` B ÝÊvÊViÀi> C ÀVÊÜ> 3AXON/3SAXON/S3AXON/S c. The kitten weighed about two pounds. About how many ounces did the kitten weigh? 32 ounces d. Multiple Choice The horse weighed about one half of a ton. About how many pounds did the horse weigh? B A 500 pounds B 1,000 pounds C 1,500 pounds D 2,000 pounds Lesson 74 401 Written Practice Distributed and Integrated 1. Jefferson sat by the window and watched the train go by. He counted thirty-eight coal cars and twenty-seven boxcars. Altogether, how many coal cars and boxcars did he count? 65 cars (18) 2. (36) The miners loaded 16 tons of ore in the morning. Their goal was 28 tons by nightfall. How many more tons of coal did they need to load to reach their goal? Write a number sentence 16 + = 28; 12 tons Formulate 3. Automobiles were shipped west from Jonestown to Seagraves. Use the scale to find the approximate distance from Jonestown to Seagraves. 200 mi (Inv. 4) *ONESTOWN 3EAGRAVES INCHMILES 4. It is noon in Detroit. Write the time in digital form. 12:00 p.m. (3) 5. Are the stripes on a United States flag parallel or perpendicular? (Inv. 4) parallel 6. The work crew was paid $16,000 for laying a mile of track on flat land. Use words to name $16,000. sixteen thousand dollars (32) 7. How many ounces are equal to one pound? 16 ounces (74) 8. The tunnel was four tenths of a mile long. Write four tenths as a fraction. 104 (41) 9. The first rail line connecting the east coast of the United States to the west coast was completed in 1869. How many years ago was that? Answer will vary depending on current year. (39) 10. Find each product. (59) a. 6 × 2 12 402 Saxon Math Intermediate 3 b. 8 × 5 40 c. 5 × 6 30 11. Change this addition to multiplication and find the total. (54) 3 ft + 3 ft + 3 ft + 3ft 12. How many pounds are equal to (74) a. one ton? 2,000 pounds 13. Find each product. (70) a. 6 × 7 42 b. 7 × 8 4 × 3 ft = 12 ft b. two tons? 4,000 pounds c. 6 × 8 56 48 Add or subtract, as shown: 14. $6.75 − $4.48 15. $1 − 1¢ $2.27 (26) 99¢ (26, 28) 16. Find the missing addend: 10 + 20 + m = 100 70 (9) 17. Dora made this rectangular prism using 1-inch cubes. a. How many cubes did she use? 30 (72, 73) b. What is the volume of the rectangular prism? 30 cubic inches 18. (Inv. 4) Each quarter inch on this map represents 10 miles. How many miles is it from a. Calmer to Seaton? 60 mi Model b. Calmer to Bayview? 90 mi c. Bayview to Seaton? 150 mi 3EATON #ALMER "AYVIEW 19. Multiple Choice Which of these polygons does not have at least one right angle? How can you tell? B; sample: The shape does not have any square corners. A B C D (65, 67) 20. a. The polygon in problem 19, choice D has how many sides? 5 (67) b. What is the name for a polygon with this number of sides? pentagon Lesson 74 403 • Geometric Solids LESSON 75 Power Up facts Power Up 75 jump start Count up by 6s from 0 to 60. Count up by 12s from 0 to 120. Write “five and two fifths” using digits. 5 25 Use the clues below to find the secret number. Write the secret number on your worksheet. 25 • • • • mental math two-digit number perfect square sum of the digits is 7 odd number a. Estimation: Round 466 to the nearest hundred. b. Number Sense: 44 + 11 c. Money: $1.60 − $0.80 500 55 $0.80 d. Fractions: What fraction of the rectangle is not shaded? 38 problem solving Predict how many students can sit at four tables that are joined into one big square. To check your prediction, draw a diagram of the tables and place numbers where students can sit along the edges. 8 students 404 Four students can sit at a square table (one student on each side). If two tables are joined together, six students can sit. (Notice that nobody can sit at the edges where the tables touch.) Saxon Math Intermediate 3 New Concept Geometric shapes that take up space are sometimes called solids. Cubes and other rectangular prisms are examples of geometric solids. The chart below shows some more geometric solids. Geometric Solids Shape Name Cube Rectangular prism Triangular prism Pyramid Cylinder Cone Sphere Are rectangles, triangles, and circles solids? Why or why not? sample: No, they are not solids. They are flat shapes that Classify do not take up space. Example 1 Which of these figures does not represent a solid? A B C D Figure C, the pentagon, is a flat shape. It is not a solid. Lesson 75 405 The world around us is filled with objects that are shaped like solids and combinations of solids. In example 2 we show some common objects that are shaped like solids. Example 2 3AXONobject /S Which 3best AXON/Srepresents a cylinder? A B 3AXON/S 3AXON/S C D The object shaped most like a cylinder is choice B. Activity Solids Find pictures in magazines or draw pictures of objects that are the shapes of the solids described in this lesson. Display the pictures on a classroom poster along with the names of the solid shapes. Lesson Practice Write the geometric name for the shape of each figure below. a. b. triangular prism d. Saxon Math Intermediate 3 sphere e. rectangular prism 406 c. cylinder f. cone pyramid Written Practice 1. (33, 36) Distributed and Integrated Bill wants to load a crate so it weighs 100 pounds. He placed the crate on a scale as shown at right. How many more pounds can he put into the crate? 25 pounds Analyze 2. Hector bought two matinee tickets to a movie. Each (22) ticket cost $7.75. What was the total cost of both tickets? $15.50 3. (60, 70) The train has seven boxcars. Each boxcar has eight wheels. How many wheels are there on all seven boxcars? Write a number sentence. Then write your answer in a complete sentence. 7 × 8 = 56; Formulate sample: There are 56 wheels on all seven boxcars. 4. Vegetables were sent north from San Francisco, California, to Seattle, Washington. Find the approximate distance from San Francisco to Seattle. (Inv. 4) 3AN&RANCISCO 800 mi INMI 3EATTLE 5. The clock shows the time the train arrived in Seattle Friday afternoon. Write the time in digital form. 12:03 p.m. (38) 6. (46, 49) 114 3 18. Draw pictures to show and Then compare the two mixed numbers using a comparison symbol. See student work; 1 14 < 1 38 or 1 38 > 1 14 Model 7. Find each product. a. 9 × 5 45 b. 7 × 9 63 c. 2 × 9 8. Find each product. a. 5 × 0 0 b. 9 × 1 9 c. 10 × 8 (64) (56) 18 80 Lesson 75 407 9. (35) The drawing shows the top part of an old train rail. Use your ruler to find the distance across the top of the rail. 1 34 in. Model ? 10. Teresa bought a pencil for 22¢ and paid for it with a dollar bill. What coins should she get back in change? sample: 3 quarters and 3 pennies (26, 28) 11. How many pounds is (74) a. two tons? 4,000 pounds 12. Find each product. (70) a. 6 × 3 18 13. $472 − $396 b. 7 × 6 b. four tons? 8,000 pounds c. 8 × 7 42 56 14. $354 + $263 + $50 $76 (23) $667 (24) 15. 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 50 (10, 54) 16. Find the missing addend: 36 = 12 + a + 16 8 (9) 17. Wilson put 1-cubic-foot boxes into stacks like the one shown at right. a. How many boxes are in a stack? 27 (73, 74) b. What is the volume of a stack? FT FT 27 cubic feet 18. For a–c, describe the weight of each animal as about an ounce, (74) a pound, or a ton. CROW BISON a. b. c. MOUSE pound 408 Saxon Math Intermediate 3 ton ounce FT 19. Name each solid in a–c. (75) a. b. cylinder c. pyramid sphere 20. Multiple Choice Which figure below does not show a line of symmetry? C A B C D (Inv. 7) Early Finishers Real-World Connection : Jerry and Phil took a math test on Wednesday. They scored 178 points altogether. Jerry scored ten points higher than Phil. What is each student’s score? Jerry, 94; Phil, 84 Lesson 75 409 LESSON 76 • Multiplication Facts: 11s and 12s Power Up facts Power Up 76 jump start Count up by 11s from 0 to 110. Count up by square numbers from 1 to 144. Write these numbers in order from least to greatest. 1,025, 1,250, 12,050, 12,500 1,025 mental math 12,050 12,500 1,250 Draw a square. Divide the square into 4 parts. Shade 3 of the square. How much of the square is not 4 shaded? See student work; 14 a. Number Sense: 18 × 10 180 b. Number Sense: 10 + 19 + 6 35 c. Time: It is afternoon. Stella’s birthday party began at the time shown on the clock. It ended 2 hours later. What time did the party end? 4:30 p.m. 42 days Saxon Math Intermediate 3 .UMBEROF-INUTES This graph shows the amount of time Layne spent on his homework last week. Altogether, how many hours did Layne spend on his reading and math homework last week? 3 hr 410 d. Calendar: How many days are in 6 weeks? problem solving 4IME3PENTON(OMEWORK 2EADING 3CIENCE -ATH New Concept Since Lesson 56 we have been learning and practicing multiplication facts. In this lesson we will practice the remaining facts through 12 × 12. sample: From 1 × 11 through 9 × 11, the factor multiplying 11 appears in the tens place and ones place. sample: 11 × 11 = 121 and 11 × 12 = 132; samples: The ones digit is a sequence of even numbers that repeats. For 1 × 12 through 4 × 12, the ones digit is double the tens digit. On the multiplication table, look down the 11s column and notice a pattern. Analyze Describe the pattern you see. Which 11s facts do you need to practice so that you can remember them? Conclude Look down the 12s column. What patterns can you find? Activity Modeling 11s and 12s We can model multiplying by 11 using 812 -by-11-inch sheets of paper. On the floor or any other large surface, extend a tape measure to 66 inches. Starting at the 0 mark, place a sheet of paper lengthwise along the tape measure. Make sure that the paper is lined up with the 0 tick mark and the 11 tick mark on the tape measure. Lesson 76 411 Continue placing sheets of paper end to end along the tape measure until you reach 66 inches. Name the total length in inches as you put each sheet of paper in place. 11 in., 22 in., 33 in., 44 in., 55 in., 66 in. How many sheets of paper did you use? Number of pages 1 2 3 4 5 6 Make a table showing the numbers of pages and inches for each page you placed. 6 Number 11 22 33 44 55 66 of inches Recall from Lesson 60 that multiplying the number of groups times the number in each group gives us the total. number of groups × number in each group = total So 6 sheets × 11 inches for each sheet = 66 inches. We can model multiplying by 12 using 1-foot rulers. Extend a tape measure to 72 inches. Arrange the rulers end to end along the tape measure. Name the total length in inches as you put each ruler in place. 12 in., 24 in., 36 in., 48 in., 60 in., 72 in. How many rulers did you use? 6 6 rulers × 12 inches for each ruler = 72 inches Write a multiplication fact to represent each ruler you placed. 1 × 12 = 12; 2 × 12 = 24; 3 × 12 = 36; 4 × 12 = Formulate 48; 5 × 12 = 60; 6 × 12 = 72 Example 1 Milton measured the total length of sheets of copy paper placed end to end. Each sheet of paper was 11 inches long. He recorded the results in a table. Make a table to show the total length of one through 12 sheets of paper. 412 Saxon Math Intermediate 3 We set up the table to show the number of sheets and the length in inches. We start with one sheet of paper with a length of 11 inches. We add 11 inches for each sheet of paper added to the row. Number of Sheets Length in Inches 1 2 3 4 5 6 7 8 9 10 11 12 11 22 33 44 55 66 77 88 99 110 121 132 Example 2 Use a multiplication table to find each product. a. 3 × 12 b. 6 × 12 c. 12 × 12 a. 3 × 12 = 36 b. 6 × 12 = 72 c. 12 × 12 = 144 Lesson Practice Find each product. a. 11 × 11 121 b. 11 × 12 d. 12 × 6 72 e. 7 × 12 g. 9 × 12 108 h. 12 × 10 132 c. 12 × 5 60 f. 8 × 12 96 84 i. 12 × 12 120 144 j. The word “dozen” means 12. John raises chickens and puts the eggs in cartons. Each carton contains a dozen eggs. Make a table to show the number of eggs in one through 12 cartons. How many eggs are in 9 cartons? How many eggs are in 12 cartons? 108; 144 Written Practice Number of boxes 1 2 3 4 5 6 7 8 9 10 11 12 Length in eggs 12 24 36 48 60 72 84 96 108 120 132 144 Distributed and Integrated 1. Jeff walked along the length of a rail. He took nine big steps. Each big step was about 3 feet long. The rail was about how many feet long? 27 feet (34, 60) 2. The California Gold Rush was in 1849. The first railroad across the country was complete in 1869. How many years were there from 1849 to 1869? 20 years (39) Lesson 76 413 3. Fruit was shipped from Plains to Westcott . Find the approximate distance from Plains to Wescott. 300 miles (Inv. 4) 0LAINS 7ESTCOTT INCHMILES 4. Name each shape below. a. cone b. (75) 5. Find each product: a. 9 × 6 54 (64) b. 4 × 9 cylinder c. sphere c. 9 × 9 36 81 6. This picture is an old Santa Fe Railroad logo. Are the two dark stripes inside the circle parallel or perpendicular? (Inv. 4) perpendicular 7. The work crew was paid $48,000 for laying a mile of track in the mountains. Use words to name $48,000. forty-eight thousand dollars (32) 8. Change this addition to multiplication and find the total. (54, 76) 6 × 12 = 72 12 + 12 + 12 + 12 + 12 + 12 9. How many pounds are equal to a. three tons? 6,000 pounds (74) b. four tons? 8,000 pounds 10. The bridge is three tenths of a mile wide. Write three tenths as a (41) 3 fraction. 10 11. Find each product: (70) a. 8 × 7 56 12. 85¢ + 76¢ + $10 b. 4 × 6 c. 6 × 7 24 $11.61 (22, 24) 13. $5.00 − $3.29 42 $1.71 (26, 28) 14. The hallway was 12 feet wide. How many inches are equal to 12 feet? 144 in. (60, 76) 15. Find each product: a. 11 × 11 121 (61, 76) 414 Saxon Math Intermediate 3 b. 11 × 12 132 c. 9 × 12 108 16. Boxes are stacked on the shelf as shown at right. a. How many boxes are in the stack? 16 (72, 73) b. What is the volume of the stack? 17. (57) FT FT 16 cubic feet FT The rows of desks in the classroom formed an array. Write a multiplication fact for this array, which is shown at right. 5 × 5 = 25 Formulate 18. Write the two fractions represented by the shaded squares. Then compare the two fractions. 34; 68; 34 ⫽ 68 (41, 47) 19. (35) On this map, how many inches is it from a. Granville to Lexington? 134 in. Model b. Lexington to Hampshire? 2 14 in. c. Granville to Hampshire through Lexington? 4 in. 'RANVILLE (AMPSHIRE ,EXINGTON 20. If each 14 inch on the map in problem 19 represents 10 miles, how many miles is it from Lexington to Hampshire? 90 miles (Inv. 4) Early Finishers Real-World Connection : Mrs. Lee is sorting items by their shapes. She made a pile for items that are shaped like cylinders. She made a second pile for items that are shaped like rectangular solids. She made a third pile for items that are shaped like spheres. Make a list of items Mrs. Lee can put in each pile. See student work. Lesson 76 415 LESSON 77 • Multiplying Three Numbers Power Up facts Power Up 77 jump start Count up by 7s from 0 to 77. Count up by 12s from 0 to 120. There are 5,280 feet in one mile. Write this number using words. five thousand, two hundred eighty feet Write two multiplication facts using the numbers 6, 8, and 48. 6 × 8 = 48; 8 × 6 = 48 mental math a. Money: $10.00 − $6.75 $3.25 b. Number Sense: 170 + 20 c. Number Sense: 20 × 10 190 200 d. Time: It is 7:35 a.m. How many minutes is it until 8:00 a.m.? 25 min problem solving Here we show examples of figures with a special made-up name, Snips. We also show nonexamples (figures that are not examples) of Snips. Study the examples and nonexamples. 3NIPS .OT 3NIPS Which of these figures is a Snip? Explain your answer. A B C Sample: Figure C is a Snip because it is divided into two halves and has one dot in each half. 416 Saxon Math Intermediate 3 New Concept In Lesson 10 we learned how to add three numbers. In this lesson we will learn how to multiply three numbers. To find the product of 2 × 3 × 4, we begin by multiplying two factors. We multiply 2 × 3. The product is 6. 2×3×4 6×4 Next we multiply 6 by the remaining factor, 4. 6 × 4 = 24 The product is 24. Example Multiply: 4 × 2 × 7 First we multiply 4 × 2 to get 8. Then we multiply 8 × 7 to find the product of all three factors: 8 × 7 = 56. Activity Multiplying to Find Volume Materials: 1-inch cubes In the activity in Lesson 73, we found the volume of a box by counting the total number of cubes the box would hold. In this activity, we will use multiplication to find volume. First, we will use cubes to build a rectangular prism. A rectangular prism has length, width, and height. HEIGHT WIDTH LENGTH Lesson 77 417 Build a rectangular prism that is 3 units long, 2 units wide, and 2 units high, as shown below. Count the number of cubes you used to build the rectangular prism. How many cubes are there in all? What is the volume of the rectangular prism? 12 12 cubic units What is the length, width, and height of the rectangular prism? 3; 2; 2 What is the product when you multiply 3 × 2 × 2? 12 What is the relationship between the length, width, and height of a rectangular prism and its volume? Discuss sample: Volume = length × width × height Lesson Practice Find each product in a–d. a. 2 × 2 × 2 8 c. 1 × 2 × 11 22 b. 3 × 3 × 4 36 d. 6 × 2 × 5 60 e. What is the length, width, and height of this figure? 3; 2; 3 f. Find the volume of the figure by multiplying its length, width, and height. Written Practice 1. (36) 18 cubic units Distributed and Integrated The boxcar could carry 36 tons of cargo. Fifteen tons of cargo were already in the car. How many tons of additional cargo could the boxcar carry? Write a number sentence. Then write your answer in a complete sentence. 15 + d = 36; The boxcar could carry 21 tons. Formulate 2. Four round tables were in the room. There were eight chairs around each table. Altogether, how many chairs were there? 32 chairs (60, 70) 3. a. (71) Represent Draw a picture of a cube. b. A cube has how many faces? 6 faces c. A cube has how many vertices? 418 Saxon Math Intermediate 3 sample: 8 vertices 4. Represent (34, 52) Draw a rectangle that is 4 inches long and 1 inch wide. See student work. 5. a. What is the perimeter of the rectangle you drew in problem 4? 10 (58, 62) in. b. What is the area of the rectangle? 4 sq. in. 6. How many pounds are equal to a. one ton? b. two tons? (74) 2,000 pounds c. three tons? 4,000 pounds 7. Draw a picture to show the fraction 37. 6,000 pounds See student work. (42) 8. A large horse weighs about half of a ton. A half ton is equal to how many pounds? 1,000 pounds (74) 9. The train was eight tenths of a mile long. Write eight tenths as a fraction. 108 (41) 10. Boxes were stacked on a pallet. Each box was one cubic foot. a. How many layers of boxes were there in the stack? 4 (72, 73) b. How many boxes were in each layer? 9 c. How many boxes were there in the stack? 36 d. What is the volume of the stack of boxes? 36 cubic feet 11. Draw an obtuse angle. See student work. (65) Lesson 77 419 Judy saw these numbers on a boxcar. Refer to this illustration to answer problems 12 and 13. RA IL EX PR ES S LD LMT 107,400 lb NEW 7-57 12. The “load limit” of this boxcar is 107,400 pounds. Use words to (32) name this number. one hundred seven thousand, four hundred pounds 13. On the boxcar, Judy saw NEW 7-57. This shows the month and (1) year the boxcar was built. Name the month and full year this boxcar was built. July, 1957 14. $648 + $286 $934 (16) 15. $7.50 − $7.29 16. 2 × 3 × 4 $0.21 (26) 24 (77) 17. a. Name the shape shown. triangular prism (75) b. How many triangular faces does it have? c. How many rectangular faces does it have? d. How many faces does it have in all? 18. Find each product: (76) a. 8 × 12 96 b. 9 × 12 108 2 3 5 c. 11 × 12 19. Multiple Choice Which pair of triangles are congruent? A B C D (68, 69) 20. a. What fraction of the face of the spinner is blue? (41, 45) 3 4 b. If the spinner is spun once, is the arrow more likely to stop on blue or white? blue 420 Saxon Math Intermediate 3 132 A LESSON 78 • Multiplying Multiples of Ten Power Up facts jump start Power Up 78 Count down by 3s from 45 to 0. Count down by 6s from 60 to 0. It is 2:20 in the afternoon. Draw hands on your clock to show the time in 2 hours. Write the time in digital form. 4:20 p.m. The high temperature on the first of the month was 48°F. The high temperature on the last day of the month was 7 degrees warmer. Mark your thermometer to show the high temperature at the end of the month. 55°F mental math a. Time: How many years are in 8 decades? b. Number Sense: 10 + 18 + 5 80 years 33 c. Money: Compare these money amounts using the symbol < > or =. 5 quarters > 12 dimes d. Measurement: What is the perimeter of the parallelogram? IN 14 in. IN problem solving Megan inserted 4 coins into the vending machine to purchase a snack bar that cost 65¢. The machine returned 1 nickel in change. What coins did Megan use in the vending machine? 2 quarters, 2 dimes Lesson 78 421 New Concept The multiples of ten are the numbers that we say when we count by tens. 10, 20, 30, 40, 50, . . . Each multiple of ten can be written as a number times 10. 20 = 2 × 10 30 = 3 × 10 40 = 4 × 10 One way to multiply multiples of ten is to multiply three factors. Below we multiply 4 × 30 by writing 30 as 3 × 10. 4 × 30 ⋀ 4 × 3 × 10 Next we multiply 4 × 3, which is 12. Then we multiply 12 × 10. 4 × 3 × 10 ⋁ 12 × 10 = 120 A shortcut is to multiply the digit in the tens place and then attach a zero to the product. For 4 × 30, we multiply 4 × 3 = 12. Then we add a zero to the 12 to make 120. 4 × 3 0 = 120 Example 1 Diana has seven $20 bills. How much money is that? Instead of adding seven 20s, we can multiply $20 by 7. We know that 7 × 2 is 14, so 7 × $20 is $140. Example 2 There are 40 cubes in each layer of this figure. How many cubes are there in all 4 layers? Instead of adding four 40s, we multiply 40 by 4. Since 4 × 4 is 16, we know that 4 × 40 is 160. The figure contains 160 cubes. 422 Saxon Math Intermediate 3 Lesson Practice a. How much money is eight $20 bills? $160 b. If 5 classrooms each have 30 students, then how many students are in all 5 classrooms? 150 Find each product for problems c–f. c. 4 × 60 240 d. 7 × 30 210 e. 8 × 40 320 f. 3 × 80 240 Written Practice 1. (60, 70) Distributed and Integrated Clovis bought eight new railroad cars for his model train. Each car cost seven dollars. How much did Clovis pay for all eight cars? Write a number sentence. 8 × 7 = $56 Formulate 2. One hundred ninety people crowded into the model train show. The room could hold 240 people. How many more people could be in the room? 50 (36) 3. Lilly bought a ticket for $14.75. She paid for the ticket with two $10 bills. How much money should Lilly get back? $5.25 (26, 28) 4. What solid is the shape of a can of soup? cylinder (75) 5. a. (71) Represent Draw a picture of a rectangular prism. b. A rectangular prism has how many vertices? 5. a. sample: c. A rectangular prism has how many edges? 8 vertices 12 edges 6. Judith made the rectangle at right with square tiles. The sides of each tile are one inch long. a. How long is the rectangle? 6 inches (52, 62) b. How wide is the rectangle? c. How many tiles did she use? 4 inches 24 tiles d. What is the area of the rectangle? 24 sq. in. 7. What is the perimeter of the rectangle in problem 6? 20 in. (58) Lesson 78 423 8. Find each product: a. 7 × 0 0 (59, 64) b. 7 × 5 c. 7 × 9 35 63 9. Ten miles is 52,800 feet. Use words to write 52,800. (32) fifty-two thousand, eight hundred 10. Find each product: (76) a. 5 × 12 60 b. 6 × 12 11. Find each product: a. 6 × 7 42 b. 6 × 8 12. Find each product: (78) a. 3 × 20 60 b. 6 × 30 (64, 70) 13. $676 + $234 c. 6 × 9 48 c. 4 × 40 180 14. $1.00 − 73¢ $910 (16) 15. 3 × 3 × 3 c. 7 × 12 72 84 54 160 27¢ (26, 28) 16. 7 × 50 27 (77) 350 (78) 17. Multiple Choice A full-grown cat could weigh B (74) A 8 ounces. B 8 pounds. C 8 tons. 18. a. Connect (41, 74) How many ounces equal a pound? b. An ounce is what fraction of a pound? 16 ounces 1 16 This map shows where Leslie and Monica live. Use this map to answer problems 19 and 20. #OLLINS %ATON 3PUR !RROW , . - 7ILDROSE 19. Name two roads perpendicular to Wildrose. 7 % 3 Arrow and Spur (Inv. 4) 20. Write directions that describe how to get to Monica’s home from (31) Leslie’s home. sample: Go east on Eaton to Arrow, south on Arrow to Wildrose, east on Wildrose to Spur, north on Spur to Collins, and east on Collins to Monica’s home. 424 Saxon Math Intermediate 3 LESSON 79 • Length: Centimeters, Meters, and Kilometers Power Up facts jump start Power Up 79 Count down by 4s from 40 to 0. Count down by 8s from 80 to 0. Write the largest 4-digit number that uses each of the digits 3, 2, 6, and 4. What is the value of the digit in the hundreds place? 6,432; 400 Draw an isosceles triangle in the workspace on your worksheet. Then draw a line to show the triangle’s line of symmetry. See student work. mental math a. Measurement: Which of these units would you use to measure a sheet of paper? inches feet pounds miles b. Number Sense: 26 × 10 c. Number Sense: 12 × 100 inches 260 1,200 d. Algebra: The table below shows costs for a longdistance phone call. Find the missing money amount in the table. 32¢ problem solving Minutes 1 2 3 Cost 8¢ 16¢ 24¢ 4 5 40¢ Alex is half as old as Beyonce. Beyonce is 2 years older than Chandra. Chandra is 10 years old. How old is Alex? 6 years old Lesson 79 425 New Concept We have measured lengths in inches, feet, yards, and miles. These units are called customary units and are used mostly in the United States. Nearly every other country uses the metric system. Metric units of length include centimeters, meters, and kilometers. A ruler that is 12 inches long is about 30 centimeters long. A meter is 100 centimeters and is a little longer than a yard. A kilometer is 1000 meters and is a little more than half of a mile. Metric Units of Length Unit Abbreviation Reference centimeter cm width of a finger meter m one BIG step kilometer km 6 10 mile 1 meter = 100 centimeters 1 kilometer = 1000 meters Activity Metric Units of Length Most rulers have an inch scale on one side and a centimeter scale on the other side. Find the centimeter scale on your ruler. Use it to measure some objects at your desk in centimeters. 1. How wide is your paper? about 22 cm 2. How long is your paper? about 28 cm 3. How long is your pencil? See student work. 4. How long is this segment? 10 cm Work in small groups to measure with a meterstick. 5. About how many meters wide is the classroom door? about 1 m 6. About how many meters high is the classroom door? about 2 m 426 Saxon Math Intermediate 3 7. About how many meters long is the chalkboard or bulletin board in your classroom? See student work. 8. About how many meters long (or wide) is your classroom? See student work. Example 1 Multiple Choice Which length could be the length of a pencil? A 15 centimeters B 15 meters C 15 kilometers D 15 feet A 15 centimeters Example 2 The train engine pulled a line of 50 boxcars that was about a kilometer long. How many meters is a kilometer? A kilometer is 1000 meters. Example 3 A 12-inch ruler is about 30 centimeters. If 3 rulers are laid end to end, about how many centimeters long would the 3 rulers be? Since each ruler is about 30 cm long, 3 rulers would be 3 × 30 cm, which is about 90 cm long. 3 × 30 cm = 90 cm Analyze Is the less than a meter length of 3 rulers more or less than a meter? Example 4 Find the length and width of this rectangle in centimeters. Then find the perimeter of this rectangle in centimeters and find its area in square centimeters. Lesson 79 427 Using a centimeter ruler, we find the length and width. Length 4 cm Width 3 cm We use these measures to find the perimeter and area. Perimeter Area Lesson Practice 4 cm + 3 cm + 4 cm + 3 cm = 14 cm 4 cm × 3 cm = 12 square cm a. Draw a segment 2 inches long. Then measure the segment in centimeters. Two inches equals about how many centimeters? 5 cm b. How many centimeters long is the cover of your math book? 28 cm c. A meter is how many centimeters? 100 cm d. It takes about 10 minutes to walk a kilometer. How many meters is a kilometer? 1000 m Refer to the rectangle to answer problems e–h. e. How long is the rectangle in centimeters? 4 cm f. How wide is the rectangle in centimeters? 2 cm g. How many centimeters is the perimeter of the rectangle? 12 cm h. How many square centimeters is the area of the rectangle? 8 square cm Written Practice Distributed and Integrated 1. The passenger car had nine rows of seats. Four passengers could sit in each row. How many passengers could sit in the passenger car? 36 passengers (60) 2. (1, 36) 428 In a common year, March 31 is the ninetieth day of the year. How many days are in the last nine months of the year? (Hint: Think of how many days are in a whole year.) 275 days Analyze Saxon Math Intermediate 3 3. The westbound crew laid four miles of track each day for six days. How many miles of track did the crew lay in six days? 24 miles of track (60) 4. a. Represent (71) Draw a picture of a cube. b. A cube has how many faces? a. sample: 6 faces c. A cube has how many edges? 12 edges d. A cube has how many vertices? 8 vertices 5. Natalie arranged some wooden cubes to make the shape at right. a. How many cubes did she use? 12 cubes (72, 73) b. If each cube is one cubic inch, what is the volume of the shape? 12 cubic inches 6. (52, 79) Use a centimeter ruler to draw a rectangle that is 5 cm long and 2 cm wide. See student work. Represent 7. a. What is the perimeter of the rectangle you drew in problem 6? 14 cm (58, 62) b. What is the area of the rectangle? 8. a. (69, 79) 10 sq cm How long, in centimeters, is each side of this triangle? 2 cm Model b. What is the name for a triangle with three equal sides? equilateral 9. a. (69, 79) Represent problem 8. Draw a triangle congruent to the triangle in See student work; All three sides of the triangle should measure 2 cm. b. What is the perimeter of the triangle you drew? 10. Find each product. (64) a. 9 × 7 63 b. 6 × 9 11. Find each product. (78) a. 2 × 40 80 b. 3 × 70 54 210 6 cm c. 4 × 9 36 c. 4 × 50 200 12. Change this addition into multiplication and find the total. (54) 5 × 7 days = 35 days 7 days + 7 days + 7 days + 7 days + 7 days Lesson 79 429 13. A giraffe can weigh 4,000 pounds. How many tons is (74) 4,000 pounds? 2 tons 14. Find each product. (70) a. 8 × 4 32 b. 8 × 6 15. $7.60 + $8.70 + $3.70 c. 8 × 7 48 16. $7.50 − $3.75 $20.00 (22, 24) 1 1 $3.75 (26) 17. Find the next four numbers in this sequence: (2, 46) 56 3 1, 14, 12, 14, 2, , , , 3 2 14, 2 12, 2 4, 3 , ... 18. The thermometers show the boiling points of water (4) on the Celsius and Fahrenheit scales. Write the temperatures. 100°C and 212°F. 19. A drawing of a rectangular prism is shown below. (71) IN IN IN b. What is its width? c. What is its height? & a. What is its length? # 8 in. 3 in. 4 in. 20. What is the area of the top of the rectangular prism in problem 19? (62) 24 sq in. Early Finishers Real-World Connection 430 : Shantell is making bead necklaces for the craft fair. She can make 10 necklaces a day. She has to make 80 total for the craft fair. How many weeks will it take her to make all 80 necklaces if she only works 3 days a week? 3 weeks Saxon Math Intermediate 3 LESSON 80 • Mass: Grams and Kilograms Power Up facts jump start Power Up 80 Count up by 11s from 0 to 110. Count up by square numbers from 1 to 144. Use these clues to find the secret number. Write the secret number on your worksheet. 27 • two-digit number • between 20 and 40 • product of the digits is 14 Draw a 10-centimeter segment on your worksheet. See student work. mental math a. Calendar: How many months are in 3 years? b. Number Sense: 23 + 40 36 months 63 c. Time: 50 minutes − 15 minutes 35 min d. Number Line: What year is shown by point G? & problem solving 1935 ' ( Scott’s basketball team will use two-digit numbers on their uniforms. Each player can choose a 1 or a 2 for the first digit. The second digit must be a 0, 1, or 2. What are the possible uniform numbers? 10, 11, 12, 20, 21, 22 New Concept In the U.S. Customary System, ounces, pounds, and tons are units of weight. In the metric system, grams and kilograms are units of mass. Lesson 80 431 The mass of a dollar bill is about one gram. The mass of a large paper clip is also about one gram. A kilogram is 1,000 grams. The mass of your math textbook is about one kilogram. On Earth a kilogram weighs a little more than 2 pounds. Metric Units of Mass Unit Abbreviation Reference gram g dollar bill or large paper clip kilogram kg basketball 1 kilogram = 1,000 grams Activity Metric Units of Mass Copy the table below, and list two or three objects in each column of the table. Compare with a large paper clip to decide if an object is close to a gram or more than a gram. Compare with a basketball to decide if an object is more or less than a kilogram. Mass of Objects Close to a gram More than a gram, less than a kilogram More than a kilogram Example 1 Which is the best estimate for the mass of a pencil? 12 grams 12 kilograms The mass of a pencil is greater than a paper clip but much less than a basketball. So the mass is several grams but much less than a kilogram. The best estimate is 12 grams. Example 2 The mass of a pair of adult’s shoes is about one kilogram. How many grams is a kilogram? 432 Saxon Math Intermediate 3 A kilogram is 1,000 grams. Analyze About how many grams is one shoe? Since 500 + 500 = 1,000, the mass of one shoe is about 500 grams. Lesson Practice a. The mass of a dollar bill is about a gram. A kilogram of dollar bills would be about how many dollar bills? 1,000 b. Which is the best estimate for the mass of a monthold baby? 5 kilograms 5 grams 5 kilograms c. Arrange these objects in order from least mass to greatest mass: eyelash, paper clip, pencil, math book, desk your math book your desk a pencil an eyelash a paper clip Written Practice Distributed and Integrated 1. Rick and Antonia played a game with dot cubes. If they rolled a 2 or 4, Rick got a point. If they rolled a 1, 3, 5, or 6, Antonia got a point. Was their game fair? Why or why not? no; sample: There are (Inv. 5) four ways for Antonia to get a point but only two ways for Rick to get a point. 2. (78) The train traveled across the prairie at a steady speed of 40 miles each hour. Copy and complete the table below to find how far the train traveled in 5 hours. 200 mi Conclude Hours 1 2 Miles 40 80 3 4 5 3. The elevator had a weight limit of 4,000 pounds. How many tons is 4,000 pounds? 2 tons (74) 4. What is the name for a parallelogram that has four right angles? (65, 66) rectangle Lesson 80 433 5. Write the fraction of each rectangle that is shaded. Then compare the shaded rectangles. 23; 56; 23 < 56 (61, 70) 6. Multiple Choice Which of these multiplications does not equal 12? D A 1 × 12 B 2×6 C 3×4 D 6×6 (61, 70) 7. What is the total value of four quarters, eight nickels, two dimes, and a penny? $1.61 (25) 8. An odometer shows the following display: (32) a. Write the miles shown. 57,630 b. Use words to state the number of miles the car has been driven. fifty-seven thousand, six hundred thirty miles 9. Name each figure below. a. rectangle (67, 75) c. 10. (71) triangle Represent edges? b. rectangular prism d. triangular prism Draw a picture of a cube. A cube has how many sample: ; 12 edges 11. Alberto made this rectangular shape with 1-centimeter square tiles. a. How long is the rectangle? 6 cm (52, 62) b. How wide is the rectangle? c. How many tiles did he use? 3 cm 18 cm d. What is the area of the shape? 434 Saxon Math Intermediate 3 18 sq. cm 12. Change this addition to multiplication and find the total: (54, 76) 6 × 12 in. = 72 in. 12 in. + 12 in. + 12 in. + 12 in. + 12 in. + 12 in. 13. Find each product: (70) a. 8 × 7 56 b. 7 × 6 14. Find each product: (78) a. 4 × 30 120 b. 6 × 30 c. 3 × 7 42 21 c. 8 × 30 180 240 15. A meter is 100 cm. A door that is 2 meters tall is how many (79) centimeters tall? 200 cm 16. $587 − $295 17. $5.45 + $3.57 $292 (23) $9.02 (22) 18. What is the best estimate of the mass of a full-grown cat? (80) 4 kilograms 4 kilograms 4 grams 19. Which letter does not show a line of symmetry? Z (Inv. 7) 7 8 20. a. (72, 77) 9 : Show how multiplying three numbers helps you find the number of cubes in this stack. 4 × 3 × 2 = 24 Formulate b. What is the volume of the stack of cubes? 24 cubic centimeters CM CM CM Lesson 80 435 I NVE S TIGATION 8 Focus on • More About Geometric Solids In Lesson 75 we learned the geometric names of several different solids. In this investigation we will practice identifying, classifying, and describing geometric solids. Recall from Lesson 71 that rectangular prisms have faces, edges, and vertices. %DGE &ACE 6ERTEX Other geometric solids made of flat surfaces also have faces, edges, and vertices. Give the geometric name for each of the solids in problems 1–4. Describe the solid by its number and shape of faces. Then count the numbers of edges and vertices. Use the Relational GeoSolids to help you answer the questions. 1. cube; 6 square faces; 12 edges; 8 vertices 2. 3. rectangular prism; 6 rectangular faces; 12 edges; 8 vertices 4. triangular prism; 2 triangular faces and 3 rectangular faces; 9 edges; 6 vertices pyramid; 1 square face and 4 triangular faces; 8 edges; 5 vertices Some solids have surfaces that are not flat. Name each solid shown and described in problems 5–7. 5. 6. CURVEDSURFACE FLATSURFACES SHAPEDLIKECIRCLES cylinder 436 Saxon Math Intermediate 3 CURVEDSURFACE FLATSURFACE SHAPEDLIKEACIRCLE cone 7. sphere CURVEDSURFACE Activity Classifying Solids Your teacher will show the class several objects labeled with letters from A–J. For each object, write its geometric name in the correct place on Lesson Activity 29. Then explain in your own words how you know that name is correct. Use what you know about geometric solids and their attributes to answer problems 8–12 . Use your Relational GeoSolids to help answer the questions. 8. Multiple Choice Which geometric solid shown below does not belong? How do you know? A; sample: It is made of all flat surfaces. The other three solids have curved surfaces. A B C D Investigation 8 437 #RACKERS #RACKERS 9. Multiple Choice Which object best represents a triangular prism? C A #RACKERS C B D 10. Multiple Choice Which geometric solid shown below has two flat surfaces and one curved surface? B A B C D 11. Multiple Choice Which geometric solid shown below has eight vertices? D 438 A B C D Saxon Math Intermediate 3 12. Multiple Choice What is the geometric name for this solid? A A pyramid B rectangular prism C triangular prism D cube Investigate Further Look around the classroom or around your house to find objects in the shape of each geometric solid we discussed in this investigation. Share the objects with the class, and choose an example of each to display. Investigation 8 439