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STUDY LINK 6 1 177 22 23 Name Date Time Copyright © Wright Group/McGraw-Hill Multiplication/Division Number Stories Fill in each Multiplication/Division Diagram. Then write a number model. Be sure to include a unit with your answer. 1. Trung wants to rearrange his collection of 72 animals on a shelf in his room. How many equal rows of 9 animals can he make? 2. An average porcupine has about 30,000 quills. About how many quills would 4 porcupines have? 3. There are 168 calculators for the students at Madison School. A box holds 8 calculators. How many boxes are needed to hold all of the calculators? Number model: Answer: Number model: Answer: Number model: Answer: porcupines quills per porcupine quills in all boxescalculators per box calculators in all 4. 6.17 8.77 5. 12.13 4.44 Practice rows animals per row animals in allSTUDY LINK 6 2 Equal-Grouping Division Problems Copyright © Wright Group/McGraw-Hill 178 Name Date Time For Problems 1–3, fill in the multiples-of-10 list if it is helpful. If you prefer to solve the division problems in another way, show your work. 1. The community center bought 228 juice boxes for a picnic. How many 6-packs is that? 10 [6s] Number model: 20 [6s] Answer: 6-packs 30 [6s] 40 [6s] 50 [6s] 2. There are 8 girls on each basketball team. There are 184 girls in the league. How many teams are there? 10 [8s] Number model: 20 [8s] Answer: teams 30 [8s] 40 [8s] 50 [8s] 3. How many 3s are in 142? 10 [3s] = Number model: 20 [3s] = Answer: 30 [3s] = 40 [3s] = 50 [3s] = 4. 661 4 5. 13 96 6. 59 82 Practice 17 21–24
LESSON 6 2 Name Date Time Multiples of 10 and 100 179 Copyright © Wright Group/McGraw-Hill Fill in the missing numbers in the problems below. 1. 2. • ?3150 , • 8?320 , • ?40280 , • 30 ?600 , • ?60 2,400 , • 700 ? , 42,000 7. Explain how solving one problem in each set helps you solve the other two problems. 3 150 150 3 How many [3s] are in 150? 8 320 320 8 How many [8s] are in 320? 40 280 280 40 How many [40s] are in 280? 30 600 600 30 How many [30s] in 600? 700 42,000 42,000 700 How many [700s] in 42,000? 3. 4. 5. 6. 17 21 60 2,400 2,400 60 How many [60s] are in 2,400?
STUDY LINK 6 3 Division Copyright © Wright Group/McGraw-Hill 180 Name Date Time 1. Bernardo divided a bag of 83 marbles 2. The carnival committee has 360 small prizes evenly among five friends and himself. to share equally with 5 carnival booths. How many marbles did each get? How many prizes will each booth get? Number model: Number model: Answer: marbles Answer: prizes How many marbles are left over? How many prizes are left over? marbles prizes 3. 4 91 Answer: 4. 427 / 8 Answer: 5. 34.96 1.58 6. 300.2 2.378 7. 43.27 12.67 8. 74.6 31.055 Practice 22 23
181 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill LESSON 6 3 Name Date Time A Pen Riddle Mrs. Swenson bought 2 pens for each of her 3 daughters. ◆ She gave the clerk a $10 bill. ◆ Each pen cost the same amount. ◆ Her change was all in nickels. ◆ No sales tax was charged. ◆ Her change was less than 50 cents. 1. What was the cost of each pen? 2. Show or explain how you got your answer. LESSON 6 3 Name Date Time A Pen Riddle Mrs. Swenson bought 2 pens for each of her 3 daughters. ◆ She gave the clerk a $10 bill. ◆ Each pen cost the same amount. ◆ Her change was all in nickels. ◆ No sales tax was charged. ◆ Her change was less than 50 cents. 1. What was the cost of each pen? 2. Show or explain how you got your answer.
STUDY LINK 64 Copyright © Wright Group/McGraw-Hill 182 Name Date Time Interpreting Remainders 1. Mrs. Patel brought a box of 124 strawberries to the party. She wants to divide the strawberries evenly among 8 people. How many strawberries will each person get? Picture: Number model: Answer: strawberries What did you do about the remainder? Circle the answer. A. Ignored it B. Reported it as a fraction or decimal C. Rounded the answer up Why? 2. Mr. Chew has a box of 348 pens. He asks Maurice to divide the pens into groups of 16. How many groups can Maurice make? Picture: Number model: Answer: groups What did you do about the remainder? Circle the answer. A. Ignored it B. Reported it as a fraction or decimal C. Rounded the answer up Why? Practice 3. 68 7 4. 74 4 5. 46 98 6. 3 95 179
LESSON 64 Name Date Time A Remainder of One 183 Copyright © Wright Group/McGraw-Hill Use 25 centimeter cubes to represent the 25 ants in the story A Remainder of One. 1. Divide the cubes into 2 equal rows. Draw what you did. How many cubes are in each row? cubes How many cubes are left over? cube(s) 3. Divide the cubes into 4 equal rows. Draw what you did. How many cubes are in each row? cubes How many cubes are left over? cube(s) 2. Divide the cubes into 3 equal rows. Draw what you did. How many cubes are in each row? cubes How many cubes are left over? cube(s) 4. Divide the cubes into 5 equal rows. Draw what you did. How many cubes are in each row? cubes How many cubes are left over? cube(s)
184 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill LESSON 64 Name Date Time Multiples Number Story Paolo has fewer than 40 marbles in a bag. If he splits up the marbles among his 4 friends, he’ll have 3 left over. If he divides them among his 7 friends, he’ll have 2 left over. 1. How many marbles are in the bag? marbles 2. Show or explain how you got your answer. MARBLES LESSON 64 Name Date Time Multiples Number Story Paolo has fewer than 40 marbles in a bag. If he splits up the marbles among his 4 friends, he’ll have 3 left over. If he divides them among his 7 friends, he’ll have 2 left over. 1. How many marbles are in the bag? marbles 2. Show or explain how you got your answer. MARBLES
STUDY LINK 65 Treasure Hunt 185 Name Date Time Copyright © Wright Group/McGraw-Hill Marge and her friends are playing Treasure Hunt. Help them find the treasure. Follow the directions. Draw the path from the oak tree to the treasure. Mark the spot where the treasure is buried. 1. Start at the dot under the oak tree; face north. Walk 4 steps. 2. Make a quarter turn, clockwise. Walk 5 steps. 3. Face south. Walk 2 steps. 4. Face east. Walk 2 1 2steps. 5. Make a 3 4turn, clockwise. Walk 5 steps. 6. Make a 3 4turn, clockwise. Walk 6 1 2steps. 7. Make an X to mark the spot where you end. 1 step Oak Tree N WE S 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 0 0 Practice 8. 88 3 9. 71 6 10. 603 / 7 11. 934 / 5 107
LESSON 65 Name Date Time Time (Analog) 186 Copyright © Wright Group/McGraw-Hill 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011 12 1 2 3 4 5 6 7 8 91011
LESSON 65 Name Date Time Time (Digital) 187 Copyright © Wright Group/McGraw-Hill
LESSON 65 Name Date Time Time (Words) 188 Copyright © Wright Group/McGraw-Hill 8 o’clockHalf-past 2 o’clockQuarter-to 7 o’clockQuarter- past 5 o’clock Half-past 8 o’clock3 o’clockQuarter-to 11 o’clockQuarter- after 4 o’clock Half-past 6 o’clockHalf-past 12 o’clockQuarter-to 3 o’clockHalf-past 10 o’clock Quarter-to 9 o’clockQuarter- after 9 o’clockQuarter- after 1 o’clockHalf-past 11 o’clock
LESSON 65 Name Date Time Clock Angle Challenge 189 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Use the full-circle protractor and the clock from journal pages 152 and 153 to help you solve the problems below. 1. How long does it take the hour handto move 1°? Explain. 2. How long does it take the minute handto move 1°? Explain. LESSON 65 Name Date Time Clock Angle Challenge Use the full-circle protractor and the clock from journal pages 152 and 153 to help you solve the problems below. 1. How long does it take the hour handto move 1°? Explain. 2. How long does it take the minute handto move 1°? Explain. 141 142 141 142
STUDY LINK 66 Measuring Angles Copyright © Wright Group/McGraw-Hill 190 141 142 Name Date Time 1. This angle is (, ) 90. G: ° 3. This angle is (, ) 90. I: ° 2. This angle is (, ) 90. H: ° 4. This angle is (, ) 90. J: ° First estimate and then use your full-circle protractor to measure each angle. 5. On the back of this page, draw and label angles with the following degree measures: ABC78DEF145GHI213JKL331 Try This 6. 96 4 7. 66 8 8. 314 2 9. 928 5 Practice G H I J
LESSON 66 Name Date Time A Waxed-Paper Protractor 191 Copyright © Wright Group/McGraw-Hill 1. Follow the steps below to make a waxed-paper protractor. Step 1:Take a sheet of waxed paper. Step 3:Fold it in half again. Step 5:Cut off the top.Step 2:Fold the paper in half. Be sure to crease it tightly. Step 4:Bring the folded edges together and fold it in half. Repeat this step again. Step 6:Unfold. fold fold fold 2. Use your waxed-paper protractor to measure the angles below. a. b. Angle Mmeasures about wedges. Angle Rmeasures about wedges. 3. Use a straightedge to draw more angles on the back of this sheet. Measure the angles and record the numbers of wedges. M R fold
STUDY LINK 6 7 Measuring Angles with a Protractor Copyright © Wright Group/McGraw-Hill 192 Name Date Time First estimate whether the angles measure more or less than 90°. Then use a half-circle protractor to measure them. B C S R Q PN O M L K A 1. A: ° 2. B: ° 3. C: ° 4. QRS: ° 5. NOP: ° 6. KLM: ° Practice 7. 93 6 8. 547 7 9. 48 39 10. 51 64 Try This 143
LESSON 6 7 Name Date Time Exploring Triangle Measures 193 Copyright © Wright Group/McGraw-Hill You need 2 sheets of paper, a straightedge, and a protractor. 1. Draw a large triangle on each sheet of paper. The 2 triangles should not look the same. 2. Label the vertices of one triangle A, B,and C. Label the vertices of the other triangle D, E,and F. Be sure to write the labels inside the triangles. 3. Using your protractor, measure each angle as accurately as you can. Record the degree measures in the tables below. 4. Find the sum of the degree measures in triangle ABCand in triangle DEF. 5. Write a true statement about the sum of the measures of the 3 angles of a triangle. Angle Degree Measure AAbout ° BAbout ° CAbout ° Sum About ° 143 Angle Degree Measure DAbout ° EAbout ° FAbout ° Sum About °
STUDY LINK 6 8 Coordinate Grids Copyright © Wright Group/McGraw-Hill 194 144 Name Date Time 1. Plot and label each point on the coordinate grid. A(1,7) B(6,6) C(10,1) D(4,3) E(8,6) F(2,9) G(9,1) H(10,4) 1 2 4 3 5 6 7 8 9 10 0 12345678 9 10 0 A 2. Write the ordered number pair for each point plotted on the coordinate grid. I(,) J(,) K(,) L(,) M(,) N(,) O(,) P(,) Q(,) R(,) 2 7 3 5 1 2 4 3 5 6 7 8 9 10 0 12345678 9 10 0 I J K L M N O P Q R 3. 28 7 4. 304 5 5. 52 89 6. 43 36 Practice
STUDY LINK 6 9 Latitude and Longitude 195 272 273 Name Date Time Copyright © Wright Group/McGraw-Hill Use your Student Reference Book to help you complete this Study Link. Read the examples and study the figures on pages 272 and 273. 1. Do the following on the picture of the world globe. a. Label the North and South Poles. b. Draw and label the equator. c. Label the prime meridian. d. Draw and label a line of latitude that is north of the equator. e. Draw and label a line of longitude that is west of the prime meridian. f. Mark a point that is in the Southern Hemisphere and also in the Eastern Hemisphere. Label the pointA. g. Mark a point that is in the Northern Hemisphere and also in the Western Hemisphere. Label the point B. 2. The entire continent of Africa is shown in the figure above. Is Africa mostly in the Western Hemisphere or in the Eastern Hemisphere? 3. Do the equator and prime meridian meet over water or over land? Practice 4. 47 / 3 5. 7 98 6. 217 5 7. 804 / 6
Longitude 140 E or W Longitude 90 E or W Longitude 40 E or W Latitude 90 N or S LESSON 6 9 Name Date Time Latitude and Longitude Cards 196 Copyright © Wright Group/McGraw-Hill Latitude 0 EquatorLatitude 10 N or SLatitude 20 N or SLatitude 30 N or SLatitude 40 N or S Latitude 50 N or SLatitude 60 N or SLatitude 70 N or SLatitude 80 N or S Longitude 0 Prime MeridianLongitude 10 E or WLongitude 20 E or WLongitude 30 E or W Longitude 50 E or WLongitude 60 E or WLongitude 70 E or WLongitude 80 E or W Longitude 100 E or WLongitude 110 E or WLongitude 120 E or WLongitude 130 E or W Longitude 150 E or WLongitude 160 E or WLongitude 170 E or WLongitude 180 International Date LineLongitude PLAYER’S CHOICE
1. It takes 14 oranges to make a small pitcher of juice. Annette has 112 oranges. How many pitchers of juice can she make? Number model: Answer: pitchers of juice How many oranges are left over? oranges 2. Each bouquet needs 17 flowers. The florist has 382 flowers in his store. How many bouquets can the florist make? Number model: Answer: bouquets How many flowers are left over? flowers 3. 726 16 4. 4 276 STUDY LINK 6 10 Division 197 Name Date Time Copyright © Wright Group/McGraw-Hill 5. 45 4 6. 319 7 7. 29 63 8. 89 183 Practice 22 23
LESSON 6 10 Name Date Time Division “Magic” 198 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill 1. Write a 3-digit number. _______ Enter it into your calculator twice to make a 6-digit number. For example, if you picked 259, then you would enter 259259 in your calculator. 2. Divide the 6-digit number by 7. Then divide the result by 11. Finally, divide that result by 13. 3. What is the final quotient? 4. Repeat Steps 1 and 2. New number: _______ Final quotient: _______ 5. Do you think this trick works with anythree-digit number? Explain. LESSON 6 10 Name Date Time Division “Magic” 1. Write a 3-digit number. _______ Enter it into your calculator twice to make a 6-digit number. For example, if you picked 259, then you would enter 259259 in your calculator. 2. Divide the 6-digit number by 7. Then divide the result by 11. Finally, divide that result by 13. 3. What is the final quotient? 4. Repeat Steps 1 and 2. New number: _______ Final quotient: _______ 5. Do you think this trick works with anythree-digit number? Explain.
Unit 7: Family Letter 199 Name Date Time Copyright © Wright Group/McGraw-Hill Fractions and Their Uses; Chance and Probability One of the most important ideas in mathematics is the concept that a number can be named in many different ways. For example, a store might advertise an item at 1 2off its original price or at a 50% discount— both mean the same thing. Much of the mathematics your child will learn involves finding equivalent names for numbers. A few weeks ago, the class studied decimals as a way of naming numbers between whole numbers. Fractions serve the same purpose. After reviewing the meaning and uses of fractions, students will explore equivalent fractions—fractions that have the same value, such as 1 2,2 4,3 6, and so on. As in past work with fractions, students will handle concrete objects and look at pictures, because they first need to “see” fractions in order to understand what fractions mean. Fractions are also used to express the chance that an event will occur. For example, if we flip a coin, we say that it will land heads-up about 1 2of the time. The branch of mathematics that deals with chance events is called probability.Your child will begin to study probability by performing simple experiments. Please keep this Family Letter for reference as your child works through Unit 7. 1 c c 3 4 c c 1 2 1 4 50 mL 100 mL 150 mL 200 mL 250 mL A measuring cup showing fractional increments STUDY LINK 6 11
denominator The number below the line in a fraction. In a fraction where the whole is divided into equal parts, the denominator represents the number of equal parts into which the whole (or ONE or unit whole) is divided. In the fraction ba,bis the denominator. equal chance outcomes orequally likely outcomes If each of the possible outcomes for a chance experiment or situation has the same chance of occurring, the outcomes are said to have an equal chance or to be equally likely. For example, there is an equal chance of getting heads or tails when flipping a coin, so heads and tails are equally likely outcomes. equivalent fractions Fractions with different denominators that name the same number. For example, 1 2and 4 8are equivalent fractions. fair (coin, die, or spinner) A device that is free from bias. Each side of a fair die or coin will come up about equally often. Each section of a fair spinner will come up in proportion to its area. fair game A game in which every player has the same chance of winning. mixed number A number that is written using both a whole number and a fraction. For example, 2 1 4is a mixed number equal to 2 1 4. numerator The number above the line in a fraction. In a fraction where the whole (or ONE or unit whole) is divided into a number of equal parts, the numerator represents the number of equal parts being considered. In the fraction ba,ais the numerator. probability A number from 0 through 1 that tells the chance that an event will happen. The closer a probability is to 1, the more likely the event is to happen. whole (or ONE or unit whole) The entire object, collection of objects, or quantity being considered; the ONE; the unit whole; 100%. “whole” box InEveryday Mathematics,a box in which students write the name of the whole (or ONE or unit whole). 5 9numerator 5 / 9 5 95 / 9 denominator Copyright © Wright Group/McGraw-Hill 200 Unit 7: Family Letter cont. STUDY LINK 611 Vocabulary Important terms in Unit 7: A die has six faces. If the die is fair, each face has the same chance of coming up. Whole 24 pennies
201 Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on concepts taught in this unit, try these interesting and rewarding activities: 1.Have your child look for everyday uses of fractions in grocery items, clothing sizes, cookbooks, measuring cups and spoons, and statistics in newspapers and on television. 2.Encourage your child to express numbers, quantities, and measures, such as a quarter of an hour, a quart of orange juice, a dozen eggs, and a pint of milk. 3.While grocery shopping, help your child compare prices by looking at shelf labels or calculating unit prices. Help your child make decisions about the “better buy.” If a calculator is available, have your child take it to the store. 4.Have your child look for everyday uses of probabilities in games, sports, and weather reports. Ask your child to make a list of events that could never happen, might happen, and are sure to happen. In this unit, your child will work on his or her understanding of fractions and probability by playing the following games. For detailed instructions, see the Student Reference Book. Chances AreSeeStudent Reference Book, pages 236 and 237. This game is for 2 players and requires one deck of Chances Are Event Cards and one deck of Chances Are Probability Cards. The game develops skill in using probability terms to describe the likelihood of events. Fraction MatchSeeStudent Reference Book, page 243. This game is for 2 to 4 players and requires one deck of Fraction Match cards. The game develops skill in naming equivalent fractions. Fraction OfSeeStudent Reference Book, pages 244 and 245. This game is for 2 players and requires one deck of Fraction Of Fraction Cards and one deck of Fraction Of Set Cards. The game develops skill in finding the fraction of a number. Fraction Top-ItSeeStudent Reference Book, page 247. This is a game for 2 to 4 players and requires one set of 32 Fraction Cards. The game develops skill in comparing fractions. Getting to OneSeeStudent Reference Book,page 248. This is a game for 2 players and requires one calculator. The game develops skill in estimation. Grab BagSeeStudent Reference Book, page 249. This game is for 2 players or two teams of 2 and requires one deck of Grab Bag cards. The game develops skill in calculating the probability of an event. Building Skills through Games Unit 7: Family Letter cont. STUDY LINK 611
Copyright © Wright Group/McGraw-Hill 202 Study Link 7 2 1. b.4c.12d.82.6 3.124.75.28 6.107.308.10 9.1210.1211.2 1 2 12.2313.19 2 3 14.13 15.41 7 9 Study Link 7 3 1.50-50 chance2.very unlikely 4.55.5926.3,948 7.1,6908.16,170 Study Link 7 4 3.84.0.8815.9.845 6.1.597.0.028 Study Link 7 5 1.Less than $1.00; 0.75 0.100.85 2.3 3 4 3. 1 6 4.2 3 8 5.Sample answers: 6.87.458.499.22 Study Link 7 6 1.C, F, I2.B, D3.E, H4.A, G 5. 2 3 7. 5 6 9. 1 2 10. 1 6 Study Link 7 7 5.23 3 4 6.197.42 Study Link 7 8 Sample answers for 1–10: 1. 12 0;1 5;12 00 0 2. 16 0;3 5;16 00 0 3. 15 0;1 2;15 00 0 4. 3 4;3 40 0;17 05 0 5.0.36.0.637.0.78.0.4 9.0.70; 17 00 0 10.0.2; 12 0 11.70212.3,227 13.975 Study Link 7 9 1.2.3. 4.5.6. 7.Answers vary.8.Answers vary. 9. 1 4;14 0;3 7;2 54 0 10. 11 2;13 2;17 2;18 2;1 11 2 11. 51 0;21 0;1 5;1 3;1 2 12. 14 00;14 2;4 8;4 5;4 4 13.514.10015.36 Study Link 7 10 3.284.275.306.36 Study Link 7 11 3.294.16 1 2 5.1056.141 1 5 Study Link 7 12 1.Answers vary. 2.Answers vary. 3.Answers vary. 4. a. 1 4 b. 1 4 c. 1 2 5.Sample answer: I think it will be about the same fraction for 1000 times as it was for 20. 6.3367.7,8668.3,8709.4,828 As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through some of the Study Links in this unit. Unit 7: Family Letter cont. STUDY LINK 611 1 4 1 4 1 4 1 41 1 4 13 2 3 61 2 4 3 61